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- The measurement of productivity change and sources of growth
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THE MEASUREMENT OF PRODUCTIVITY CHANGE AND SOURCES OF GROWTH: THE CASE OF KOREA
By CHIANG KIM A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULLFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1991 ACKNOWLEDGEMENTS This thesis could not have been completed without an unusual amount of excellent advice by the committee. I am particularly grateful to the surpervisor G.S. Maddala, who provided valuable and detailed comments. I also acknowledge the helpful comments of Dr. Leonard Cheng, Dr. Lawrence Kenny, and Dr. John Shonkwiler. I am thankful too to Dr. Yasushi Toda and Dr. Mark Rush. Finally, I thank my wife Misook for her patience and encouragement. TABLE OF CONTENTS ACKNOWLEDGEMENTS ...................................... ii ABSTRACT .............................................. v CHAPTERS 1 INTRODUCTION .................................. 1 Research Background ........................... 1 Purposes of the Study ......................... 3 2 THE MEASUREMENT OF PRODUCTIVITY CHANGE ........ 6 The Model: the Producer's Behavior ............ 6 Value Shares and Rate of Productivity Growth .................................... 6 Share Elasticities and Substitution ......... 8 Biases of Productivity Growth and Pattern of Production .............. .............. 11 Acceleration of Productivity Growth ......... 13 Restrictions Based on Producer Theory ....... 14 Hicks neutrality .......................... 14 Constant return to scale .................. 15 Concavity of production function .......... 15 Existence of value-added function ......... 19 Econometric Models: Translog Production Function ....... 23 Estimation and Hypothesis Testing: Full Information Maximum Likelihood (FIML) and Seemingly Unrelated Regression (SUR) ........ 27 Data Sources .................................. 29 Empirical Results ............................. 30 3 THE MEASUREMENT OF SOURCES OF GROWTH .......... 55 The Model: Input-output Analysis .............. 55 Decomposition of Output Growth Based on Absolute Growth ........................... 57 Decomposition of Output Growth Based on Proportional Growth ....................... 60 Difference Between Two Methods: A Graphic Representation .............................. 61 iii Input-output Data Base............................ 63 Estimation of Sources of Growth: SAS/IML..........64 Interpretation of the Results.................... 66 4 SUMMARY AND CONCLUSION............................ 77 APPENDIX.................................................... 80 REFERENCES................................................. 137 Abstract of Dissertation Presented to Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THE MEASUREMENT OF PRODUCTIVITY CHANGE AND SOURCES OF GROWTH: THE CASE OF KOREA By Chiang Nam Kim December 1991 Chairperson: Professor G.S. Maddala Major Department: Economics In this dissertation I measure and analyze the productivity change on the supply-side and the sources of growth on the demand-side in the economy of South Korea. On the supply-side I measure total factor productivity(TFP) of industrial sectors by estimating their translog production functions and value shares simultaneously. In addition to measuring TFP, useful indexes for share elasticities, biases of productivity growth and acceleration of productivity growth are obtained. Share elasticities are used for checking the concavity of the production function, and biases of productivity growth for determining the pattern of production. On the demand-side, using growth accounting through material balance equations, the increase of output is decomposed into the effect of deviations in domestic demand, exports, changes in the import structure of intermediate and final goods, and the effect of changes in the matrix of inputoutput coefficients. The demand-side analysis will yield estimates of the contribution of import substitution and export promotion to the economic growth. The results indicate that domestic demand and export expansion were the two major factors contributing to growth and structural change. However, import substitution and technological change were quite substantial and much more important than export expansion in the recession period (19791981). In contrast, our results on total factor productivity imply that technical progress played a relatively small role in the industrialization process. CHAPTER 1 INTRODUCTION Research Background Different countries have followed different growth paths, determined partly by initial conditions and resource endowments, and partly by government policies. Some have emphasized import-substitution strategies, others exportpromotion strategies. The strategy of encouraging domestic industry by limiting imports of manufactured goods is known as the strategy of import substitution. Another way to promote manufacturing is called an export promotion strategy.'1 It is known that Korea accomplished rapid growth by export promotion policies during 1962-1978.2 After having achieved success through export promotion strategies for nearly two decades, Korea encountered severe economic difficulties in 1979-1982, as indicated in Table I-1. What were the cause of this sudden economic recession? It may be I Krugman, P. R., and M. Obsfeld (1988), pp 229-238. 2 Corbo, V., A. 0. Krueger, and F. Ossa (1985), Ch. 4. Kim, K. S., and M. Roemer (1979), Ch. 5. Frank, C. R., K. S. Kim, and L. E. Westphal (1975), Ch. 6. Westphal, L. E., (1978), pp 347-382. Krueger, A. 0., H. B. Lary, T. Monson, and N. Akrasanee (1981), pp 341-392. 2 argued that the second oil shock and the subsequent recession in the advanced countries were the major causes. In view of the uninterrupted rapid growth observed in the other Asian Countries of Table I-1, however, domestic factors were also responsible. Table I-1. GDP Growth Rate at Constant Prices. Period Korea Japan Thail- Sing- Industrial Developing land apore countries countries 1975 7.5 2.7 7.1 4.1 -0.8 4.7 1976 12.7 4.8 8.7 7.5 5.2 5.5 1977 10.8 5.3 7.2 7.9 3.9 6.1 1978 10.1 5.2 10.1 8.6 4.0 4.3 1979 7.3 5.3 6.1 9.4 3.0 4.7 1980 -3.0 4.3 5.8 10.3 0.6 4.4 1981 6.9 3.7 6.3 9.9 1.5 2.7 1982 5.5 3.1 4.1 6.3 -0.2 1.8 1983 9.5 3.2 5.8 7.9 3.0 0.2 1984 7.9 5.1 6.2 8.1 5.0 2.8 1985 8.2 4.5 4.0 --- 3.0 --Source: IMF, International Financial Statistics, 1986. But Korea was able to recover from the recession. This phenomenon leads us to some questions: Did Korea continue to pursue the export promotion policies in view of unfavorable external conditions? Which factor on the demand-side was the most important contribution to the growth of output after that recession? How important have export expansion and import substitution been in the process of industrialization? Can we measure total factor productivity (TFP) by using generalized production function instead of the restrictive ones like the Cobb-Douglas or the CES productions function? How can we 3 characterize the pattern of production on the supply-side? What has been the role of changes in the input-output coefficients? This thesis will attempt to answer these questions through input-output analysis. Purposes of the Study In this study I measure and analyze productivity change and the sources of growth in South Korea's manufacturing sector. Specifically I follow two complementary approaches. One is to measure total factor productivity in manufacturing and test restrictions usually imposed on production functions. The other is to measure the contributions of the various components of intermediate and final demand to growth and structural change. In order to retain flexibility in production functions for the manufacturing sectors in Korea, I adopt the transcendental logarithmic(translog) production functions for the first time rather than more restrictive ones such as CobbDouglas or CES production function so that I can test assumptions such as constant return to scale, Hicks neutrality, the concavity of production function, and the existence of value-added. Total factor productivity for the same manufacturing sectors in Korea has been measured by growth accounting which 4 is based on the assumption of Hicks neutrality.3 Later on we will compare our measurement of TFP to what others have measured for the same sectors in Korean manufacturing. The estimation of total factor productivity(TFP) will be based on gross output, capital, labor, intermediate input and time. In addition to measuring TFP and testing the restrictions which are imposed by the theory of production, we can get some useful indexes for share elasticities, biases of productivity growth and acceleration of productivity growth in estimating the translog production function. On the demandside, the contributions of the various components of intermediate and final demand to the growth and structural change can be estimated. Changes in the composition of demand are useful in providing an understanding of sectoral growth and structural change. Besides, an analysis of demand is needed to answer the question of the relative role of import substition and export promotion in economic growth. Manufacturing in South Korea is disaggregated according to the classification in the country's input-output table. We first constructed the input and output data for production function by aggregating detailed industrial data into broadly defined industries in accordance with the input-output table. The productivity analysis can be done at both the aggregate and disaggregate levels. The supply-side analysis indicates that our measurement 3 Kim, K. S., and S. Y. Park (1989). 5 of total factor productivity is different from what others have measured. In the demand-side analysis, the relative contribution of export expansion to growth and structural change has changed according to different method of measurement. CHAPTER 2 THE MEASUREMENT OF PRODUCTIVITY CHANGE The Model: the Producer's Behavior The starting point for our model is a production function for each industrial sector in the manufacturing. Let the production functions for each of the n industrial sectors be given by Xi=F' (Mi,K,Li, T) (ii,2,...,n). () where X, is the output, Mi, Ki, Li, and T are the intermediate, capital, and labor inputs and time. Firms are assumed to maximize profits under perfect competition. Value Shares and Rate of Productivity Growth The value shares of intermediate, capital, and labor inputs, say VM1, VKi, VLi, in the value of output can be defined by = (2) i X Vk- qiX (3) PL VL- (i= ,2,...,n). (4) qiX1 where qi, PMi, Pki, and PLi denote the prices of outputs and intermediate, capital, and labor inputs, respectively. Profit maximization in the market of perfect competition implies the equality between the share of each input in the value of output and the elasticity of output with respect to that input: '31nX. VM-i (Mi,Ki,Li, T) (5) i 81nXi V 1_ K (M Ki, Li, T) (6) 81nX V l]nL (Mi, Ki Li, T) (i=1,2,...,n). (7) These conditions can be obtained from the following procedure. Profits, H', are defined in value terms as i i i'=qiX -PMM -PKKi-pLLi (i=1,2,...,n). (8) Assuming that producers wish to maximize profits, H"', will be defined as: Ii*=max [I -A{Xi-Fi (Mi, Ki, Li, T))] (i=1, 2, ... ,n) (9) We can differentiate equation (9) with respect to ), Xi, pm', pK, pi and T to derive the conditions for profit maximization in perfect competition: 8 i(a) Xi+Fi(Mi,Ki,Li,T)=O dri* (b) X =qi-X=0 80 8F i (C) +i P -_ =0 8Hi" i .8Fi (d) =-pK+A- -0 8K. 8K. aHfl' i aFi (e) --PK + -0 (f) L PL -0 Conditions (b) to (f) imply that the value shares of each input equal to the elasticity of output with respect to that input as denoted in equations (5), (6), and (7). The rate of productivity growth, say VT'I, for each sector is defined as the rate of growth of output with respect to time, holding intermediate input, capital input, and labor input constant:' i alnX VT=- aT (Mi K L T) (i=,2,...,n). (10) Share Elasticities and Substitution Effects on value shares from a change in input are given 1 Jorgenson, Gollop, and Fraumeni (1987). 9 by share elasticities.2 Share elasticities are defined as the derivatives of the value shares with respect to the logarithms of intermediate, capital, and labor inputs: U (Mi, Ki, Li, T), (11) UM- (M Ki, Li T) (12) 81 alnK 8V2 UML- =8 (Mi, Ki, Li, T), (13) U _= _K (M, K., L, T) (14) 8lnK1 avk UK K (M Ki, L T) ,(15) 81lnLUL =- (Mi Ki ,Li T), (i=l,2, . ,n). (16) 8lnL If we set the elasticity of output with respect to each input equal to the corresponding value share, then we can get the share elasticities with respect to each input by differentiating the production function {F'} logarithmically twice with respect to the logarithms of intermediate, capital, and labor inputs: 2 The concept of share elasticities was introduced first by Christenson, Jorgenson, and Lau (1971;1973) and P.A.Samuelson(1973). i 21 nX U= 2nx (Mi, Ki, L1, T) 8-l InX u = o (Mi, K, Li, T) 1nM8i1nK' U( lnii (M., Ki, Li, T) UL8lnMfilnL i821InXi UKXK= alnK2 (MI, K1, Li, T) 81 nK~ a,- In X UA= nK..alnL (MI, K1, L1, T) 81dnK 81nLi 8 InXi U= lnL' (M, K, L, T) 81nL y (17) (18) (19) (20) (21) (22) Interchanging the order of differentiation, we can observe that the share elasticities with respect to each input are symmetric. i 8 inX 8 InXi i UMK- 81nMi81nK 81lnKialnMi Uf' a" I nX 81 nXi U =1 1 1 =1 U UL-81nMK1nL1 81nLy81nM 8 ("i nX 8I1nxi . U2I = U KL 81nKid1nLi 81nLialnKi (23) (24) (25) These relationships hold for all values of intermediate, capital, and labor inputs, and time. (i=1,2,...,n) . 11 We can analyze the share elasticities to derive implications of patterns of substitution for the relative distribution of the value of output among the three inputs. If a share elasticity is positive, the value share increases with an increase in the quantity of the corresponding input. If a share elasticity is negative, the value share decreases with the increase of the corresponding input. Finally, if a share elasticity is zero, the value share is independent of the quantity. Biases of productivity growth and Pattern of Production The concept of Hicks neutrality leads to a definition of biases in terms of factor shares. Hicks' definition is as follows: Technical change is said to be neutral, labor-saving, or labor-using depending on whether, at a constant capitallabor ratio, the marginal rate of substitution stays constant, increases, or decreases. If the marginal rate of substitution is rising, then the labor share is declining. This leads immediately to the following definition of biases. The biases of productivity growth can be defined as derivatives of the value shares with respect to time: U = Alvj jT (26) 3Binswanger (1974). a vi U =-- (M Ki, Li, T) (27) U = K(Mi, K Li, LIT) (i=l,2,...,n). (28) Alternatively, the biases of productivity growth can be defined as derivatives of the rate of productivity growth with respect to the logarithms of intermediate, capital, and labor inputs: av4 U& al= (M, Ki, Li, T) (29) 8v i ____UTK j, KI, Li, T) (30) avi UTL lC (M K L T) (31) If we set the elasticity of output with respect to each input equal to the corresponding value share and interchange the order of differentiation, we find that the two definitions are equivalent: &' Inx 8 Inx. U 2 nX 81 UnXi (32) 81nMaT ST8nM Ua = a.: ini' lnX U 1T- dnKdT 8 T =1nKU (33) o2 1inxi. a2inX. ULT= 8lnLT aTUlnL( The implications for the relative distribution of the value of output among the three inputs can be provided by the biases of productivity growth. If a bias is positive, the corresponding value share increases with time. If a bias is negative, the value share decreases with time. Lastly, the value share is independent of time if a bias is zero. Acceleration of Productivity Growth Finally, the acceleration of productivity growth can be defined as the derivative of the rate of productivity growth with respect to time, since the logarithmic derivative of the production function is equal to the rate of productivity growth:4 a d21nX, av2 UT T T (Mi ,Ki L iT) (i= ,2,...,n). (35) The biases and the acceleration of productivity growth are independent of the changes of the inputs and time because they are the second-order logarithmic derivatives of the production function with respect to the logarithms of the inputs and time. ' Jorgenson, Gollop, and Fraumeni (1987). Restrictions based on Producer Theory We can derive restrictions on share elasticities and biases of productivity growth implied by the producer's theory. Hicks neutrality First we derive restrictions which are implied by Hicks neutrality of productivity growth. The production function is Hicks neutral if and only if T is separable from intermediate, capital, and labor inputs, that is, Xi=F'(G MV,K,,Li),T) (i l,2,...,n). (36) From this equation we can derive the restrictions on the biases of productivity growth which are imposed by Hicks neutrality: U,4=LjT=:LI1I':0 (i=1,2,...,n). (37) Under Hicks neutrality the rate of productivity growth depends only on the time term. VT=A +BIT (i=l,2,...,n). (38) I will test to ascertain whether production functions in Korean manufacturing can be characterized as having Hicks neutral technological change. Constant returns to scale Next we express the assumption for constant return to scale in terms of share elasticities and biases of productivity growth. First, the sum of the share elasticities for a given value share, defined by the corresponding second-order logarithmic derivatives, is equal to zero under constant return to scale since all the value shares of the production function add up to unity under constant returns to scale. Ui U K -t111 =0 (39) U&+ L Tj" _A 1-i" 0 (40) Ub++L[=r 0 (i=l,2, . ,n). (41) In addition, the sum of the biases of productivity growth is equal to zero: UMT+UKT--'LT =O (i=1,2,...,n). (42) Concavity of production function We can derive the restrictions for the concavity of the production function in terms of share elasticities. The share elasticities can be expressed in terms of the second-order partial derivatives of the production (Fi) with respect to the inputs:5 i a2nF' M2 a2Fi U1= -----VM(V,- 1) 8lnMj F'aM$ i 8a1 nFi UMK81nM8lnK MiKi 82Fi F' aMi.Ki i a2lnFi MiL 8i 2F i Uge- --V V 81nMilnL Fi 8Mi8L M i a21nFi Ki a2Fi UKK lnK F V(VK 1) 81n K' F aK2 i = iK] :-IF UKL= 81nK SlnLi a~i oFi V V FK 8KiLi 2 i 8 I21nFi L i2F i U = -V (V-1) 81nLj Fi Ll where S81nF Mi Fi S81 riFv a M, via81nF KI 3Fi K lnK Fa K VI_ 1nF Li aF' 1nLi Fi aLi To derive the restrictions for the concavity of production functions, we construct the matrix of share elasticities U 5 The relationship between share elasticities and the condition of concavity is represented in Jorgenson (1986). The conditions for concavity in terms of the Cholesky factorization is represented in Lau (1978;1979). (43) (44) (45) (46) (47) (48) (i=1,2,...n). UA UK UML U= U4 UIK U L U& U ULL, (49) And we can express the matrix of share elasticities U' by the Hessian matrix of second-order partial derivatives of the production functions H, in the form (50) u=1 Niiivv/+ U'- NH N' v'v+VI F1 where F, FmK FmL H' = F& FKK FKL FL F- FA M, 0 0 N= 0 K; 0 0 L i~ v 0 0 vj Vi= 0 vK 0 vi= v 0 0 v, vjj (i=1,2,...,n). (i=1,2, ...,n) . The Hessian matrix H can be denoted in the form 1 1 1 NiHIN'=Uiviv1 iV (i=1,2,...,n). (51) F2 The Hessian matrix H should be negative semidefinite under the concavity of the production function. Therefore if the production function is concave, then the matrix { U' + vivi V' ) is negative semidefinite. Sufficient conditions for the matrix ( U' + v'v' V1 ) to be negative semidefinite are that the matrices of share elasticities U are negative semidefinite since the matrices { v'v' V' } are negative semidefinite for all nonnegative value shares which are greater than zero and less than one. To check the concavity of the production functions in terms of the matrices { U' ), we can transform the matrix ( U ) in terms of its Cholesky factorization U2 QiD'Qz (52) where 1 0 0] d1 0 0 Qi q 1 0 DI= 0 dj 0 (i=1,2,...,n). q j1 q3 1 0 0 d If and only if the diagonal elements (dl, d2, d3) of the 19 matrix D are nonpositive the matrix U is negative semidefinite. These conditions must holds if production functions are concave. Existence of value-added function:6 Value-added refers to the addition to the value of product at a particular stage of production. All intermediate inputs are netted out of the calculation. Some researchers have used value-added indices to measure total factor productivity across countries.7 In order to measure TFP in terms of value-added, a value-added function relating net output to the inputs of capital and labor must exist. For this to be true, capital, labor, and time must be separable from intermediate inputs. If this separability assumption is testable and rejected, we would rather abandon the calculation of value-added TFP. A value-added function, where three inputs, capital, labor, and time, produce value-added, exists if and only if the production function is separable in capital, labor inputs, and time from intermediate input. There are two alternative sets of restrictions that are jointly necessary and sufficient for the existence of a value6 Jorgenson and Lau (1975), Blackorby, Primont, and Russel (1977), and Denny and Fuss (1977). 7 Jorgenson and Nishimuzu (1978), and Christensen, Cummings, and Jorgenson (1980). 20 added function. The first set of jointly necessary and sufficient conditions for the existence of a value-added function can be derived by the following procedure.8 The production function for each sector can be written in the following form, if the production function is separable in Ki, Li, and T from Mi: Xi=F' (G(K,L, T),Mi) (i=l,2,...,n). (53) Under this restriction the value shares of capital and labor inputs and the rate of productivity growth are given by i alnZ_ 8lnFj ainGi 81nK OlnGi 1nK, (54) i 8lnZ 81nF 81nGI L= 8lnL 8lnG' 81nL (55) S81nZi 81lnF lnGi (i=,2 ..,n) (56) 81nT 81nGi 81nTi Next if we differentiate logarithmically the above production function twice, first with respect to the logarithm of intermediate input and then with respect to the logarithms of capital, labor, and time, we obtain the second-order logarithmic derivatives as functions of these inputs and time. We express these second-order logarithmic derivatives as 8 The methodology for testing separability was originated by Jorgenson and Lau (1975). See also Jorgenson, Gollop and Fraumeni (1987). follows. SainXi aI21nXi aG rV UIc nK rk' (57) UMK= alnMllnK alnMiaG lnK( S a- I nX a InX BG i =ri (58) M anMi1lnLi a1nMaG 8lnLi ___lnX t'lnX1 BG.i (9 U 21nXi 1 a V (59) anMiT a1nMBiaG aT where 2lnF' 8inMi1nGi r = (i=1,2,...,n) . 8inF' alnGi The necessary condition for the existence of a valueadded function is that there is a common factor of proportionality between the two share elasticities and the bias of productivity growth and the corresponding value shares and the rate of productivity growth. The sufficient condition requires that the common factor r' is equal to zero. The second set of necessary and sufficient conditions for the existence of value-added functions comes from weak separability, since weak separability and the existence of a consistence aggregate index are equivalent restrictions.9 The production function { F' ) is said to be weakly separable if and only if the marginal rate of substitution (MRS) between any two inputs from the input subset ( Ki, Li, T I is independent of the quantities of the intermediate input ( Mi ). 8Fi a2Fi 8Ki 8K 8M -, BKam (60) aFi -J F aLi afLdM aFi azFi aK 8K SM -, (61) aF 8 F aTi 3TiMi 8Fi 82Fi L (i=1,2, ...,n) (62) 8F' a j a2 F'1 aFaM 8T.8M. These conditions for weak separability can be written in terms of value share and share elasticities. VK UAl VK LJ4JK vT (63) (64) 9 Berndt and Christensen (1973). S(i= ,2,... ,n). (65) Econometric Models: Translog Production function We can specify the production function as the exponential function of second-order Taylor series.10 + i ' x;=exp[A +A IriM+AflnKi+AflnL+A T +Bi(InM ) 2+BKinMn lnKi+BLnM lnLi+B1 lnM T + B K (InKi) 2 BKlnK inLi yBJT1nKiT (i=1, 2, . n) (66) + 1 B/ (InLi ) +BinLi T 2 +K~KI)_+BnKlnL+B 1nK_,T 2 LiL,,..n (66 + 1 B Tn l 2 The value shares of intermediate, capital, and labor inputs are given by the derivatives of the logarithm of the production function with respect to the logarithms of intermediate, capital, and labor inputs. VA =Af +B4inMI +BJKlnKj +BlnL, +BjT (67) i i i i i +MLni +BMTT (7 VALK M+BKlnK +B lnLi +BKTT (68) VL=A+B, ilnMi +BLK nKi +BlnL +BAT (i=l,2, .., n) (69) The rates of productivity growth are given by the derivatives of logarithm of production function with respect 10 Christenson, Jorgenson, and Lau (1971;1973). to time: VT =A +B-I1nM +B,1nK +B/j1nL +B T (70) From this specific form of the production function we can derive the restrictions on the parameters imposed by production theory. First, if we set the inputs equal to unity and time equal to zero, we obtain necessary conditions for the production functions to be increasing: Ai0 AM>O From the translog production functions we can derive the restrictions for Hicks neutrality, that is, each input has no bias in technological change: BMT=BT= Br= 0 (71) Under Hicks neutrality the rate of productivity growth depends only on the time term. VT =A +BTV (72) The translog production function for an industrial sector is constant return to scale if and only if the parameters satisfy the conditions: (i=1,2,...,n). Af0 (i=1,2,...,n). (i=1,2,...,n) . (i=1,2,...,n). AM+AK+Af=i (73) BMK+ BKK+ B-L= 0 (74) B0+Bm'+ o (75) BML +BKL '-B=0 (76) B T+BKT BLT=O ( l,2 ...,n).(77) We obtain the first set of necessary conditions for the existence of value-added functions from equation (57), (58), and (59) Evaluating these equations where the three inputs are equal to unity and time is equal to zero, we obtain the following restrictions: Bm'K=p 'A (78) 1 i BML=P AL (79) B(80) These equations imply that the value shares of capital and labor inputs and the rate of productivity growth are proportional to the corresponding elasticities of the share of capital and labor with respect to intermediate input and the bias of productivity growth with respect to intermediate input. The sufficient conditions require pi=0 26 The second set of restrictions for the existence of value-added functions result from the fact that output is a linear logarithmic function of intermediate input and valueadded: Xi=exp[A+AlrinM+AlnVi] (i=l,2,...,n). (81) where Aln V =AK inKi +A inL +A T + 1 BK ( lnK ) +B lnKlnL+B InK T The value shares of capital, and labor and the rate of productivity growth can be expressed as . 1 n l-V, V =A V(82) 81 nKi 81ny1 V=A1nV 1 (83) a1nL 1+ l n V,. V : = VT (il=1,2,...,n). (84) VTTA If these equations are substituted into equations which are the conditions for weak separability, a second set of restriction are obtained: K (85) iA B. AL L... -1 (86) AT B$ Li l, ,. ) (87) Estimation and Hypothesis testing: Full Information Maximum Likelihood (FIML) and Seemingly Unrelated Regression Since our model of production is a system of equations with cross equation parameter restrictions, it is likely that the disturbances of the individual equations are correlated. If so, the technique of joint estimation gives more efficient estimates than separate regression of each equation. Jorgenson, Gollop, and Fraumeni estimated the unknown parameters of the translog production function for the industrial sectors in American economy". They formulated the econometric model by combining the first two equations for the value shares with the equations for the rate of productivity growth. They estimated the parameters of the equations for the remaining value shares from estimates of the parameters of the first two value shares, using the restrictions on these parameters given by the assumption of constant returns to scale. 11 Jorgenson, Gollop, and Fraumeni (1987). 28 With their method we cannot estimate the parameters (AT1,BTTI) in the translog production. In addition to this weakness, we have to assume constant returns to scale in production. Based on these facts, I estimate the system of equations, logX, VM, Vk, with the method of full information maximum likelihood (FIML) and seemingly unrelated regression (SUR). The FIML and SUR estimators have identical efficiencies asymptotically for large sample properties. The SUR takes account of the fact that the structural equations may be correlated in cross equation disturbance term and makes use of the covariance matrix of the disturbances among the equations. The asymptotic covariance matrix of the SUR estimator is identical with that of the FIML estimator. In terms of computational ease, the SUR method is simpler than the FIML method, because the latter results in nonlinear equations in unknown parameters that must be solved. With FIML, however, we can use the likelihood ratio test for testing hypotheses. Regardless of the large sample properties of two estimators, we obtain smaller standard errors with the SUR method than the FIML method for the data of Korean manufacturing. But the TSP software package does not print some test statistics for the SUR method. Therefore we used both methods to estimate the system of equations model and compare the empirical results. First we started our estimation from the generalized 29 model and move to increasingly more restricted ones to test the restrictions which are imposed by the production theory. In our model the rates of productivity growth, VTcan not be observable. Therefore, we computed the rates of productivity growth(TFP) by using the estimated coefficients. One of value shares in estimation is ommitted in order to avoid perfect multicollinearity. Data Sources The data for the Korean manufacturing sector were compiled by KIET (Korea Institute for Economics & Technology). They estimate the annual time series data of output as well as the intermediate, capital, and labor inputs for 39 industries of the manufacturing sector from 1963 to 1983. These data are based on the Report on Mining and Manufacturing Survey and Input-output tables. We use the data from 1963 to 1983 because these are the only years for which data are available. First we aggregated data for 39 industries to 9 more broadly defined industries in accordance with the classification of the input-output tables. These 9 industries are l.Foud, beverages & tobacco, 2.Textiles & leather, 3.Lumber & wood products, 4.Paper, printing & publishing, 5.Chemicals & chemical products, 6.Nonmetallic mineral products, 7.Primary metal manufacturing, 8.Metal products & machinery, and 9.Miscellaneous manufacturing in the ~30 manucturing sector. We then aggregated these data for the aggregate analysis of the whole manufacturing sector. We will summarize the characteristics of the data which are provided by KIET. The output is calculated by valuing all outputs at the wholesale prices. The capital stock includes the producers' and consumers' durable equipment, residential and nonresidential structures, inventories and land. Labor inputs are obtained by multiplying the yearly average number of workers by the quality index of labor. The output, capital input, and intermediate input which are calculated by using current prices are converted to a constant price. Empirical Results I have constructed an econometric model from a production function and value shares for each industries. First I estimated the parameters of the translog production function with and without restrictions by alternative methods of estimation. I then calculated the rates of productivity growth, VT, by using the estimated parameters. First we undertake the likelihood ratio test to test constant returns to scale, Hicks neutrality in technical change and the existence of value added function. Next we test Hicks neutrality in technical change and the existence of value-added function maintaining the assumption of constant returns to scale since we obtain more significant results from Table 11-1. Critical values, chi-squared degrees level of significance of freedom 0.100 0.050 0.025 0.010 0.005 0.001 1 2.71 3.84 6.36 6.63 7.88 10.83 2 4.60 6.00 8.90 9.22 10.60 13.82 3 6.25 7.81 9.35 11.35 12.84 15.67 5 9.25 11.05 14.72 15.10 16.75 20.50 the model with the assumption of constant returns to scale than the model without the assumption of constant returns to scale. The likelihood ratio test statistics for each tests are represented at Table 11-2 and 11-3. For the test statistic for Hicks neutrality of technical change, we employ the critical value 11.35 for chisquared with three degrees of freedom at a level of significance of 0.01. At this level of significance, we reject Hicks neutrality for eight industries in Table 11-2. We cannot reject Hicks neutrality for miscellaneous manufacturing and the total manufacturing sector. Under Hicks neutrality, productivity growth does not favor any factor. Therefore, the rejection of Hicks neutrality implies that technological change is biased toward some factors. We next test for constant returns to scale. The constant returns to scale restrictions require five degrees of freedom, so we employ the critical value 15.10 for chis-quared with five degrees of freedom at a level of significance of 0.01. Table 11-2. Test statistics for Constant returns to scale, Hisks neutrality, and the Existence of value-added Hypothesis Industry Hicks Constant Value- Valueneutrality returns added I added II to scale 1. Food, beverages 25.4099 60.1144 43.2148 228.3696 & tobacco 2.Textiles & 47.3477 53.9048 33.3668 137.2213 leather 3.Lumber & wood 23.2858 33.7527 -31.5031 81.4153 products 4.Paper, printing & 48.9642 54.8662 33.5702 128.6722 publishing 5.Chemicals & chemical 15.9575 24.4916 115.7244 334.9333 products 6.Nonmetallic mineral 14.8515 12.3842 85.2620 -4.6601 products 7.Primary metal 35.9080 34.5589 -24.2119 141.2689 manufacturing 8.Metal products & 39.4010 15.5197 95.0416 245.9385 machinery 9.Miscellane -ous 8.6594 32.7385 128.3029 39.7803 manufacturing The total 5.5851 15.6301 73.5605 190.5400 manufacturing Table 11-3. Test statistics for Hicks neutrality and the Existence of value-added maintaining the assumption of Constant returns to scale Hypothesis Industry Hicks Value- Valueneutrality added I added II 1. Food, beverages & tobacco 2.Textiles & leather 3.Lumber & wood products 4.Paper, printing & publishing 5.Chemicals & chemical products 6.Nonmetalic mineral products 7.Primary metal manufacturing 8.Metal products & machinery 9.Miscellane -ous manufacturing The total manufacturing 16.69647 8.82013 0.76572 27.24649 24.76041 39.66202 36.20880 48.99066 13.89905 0.08569 14.01059 34.96957 0.87402 37.04483 40.14688 16.77090 35.96268 47.19305 10.17068 11.56906 10.13010 11.22046 0.26984 3.61691 12.05225 1.15286 34.94168 30.75528 4.16483 8.70789 Constant return to scale can be rejected at this level of significance for all industries except Nonmetallic mineral products in Table 11-2. Next we test for the existence of a value-added functions. For the test for the existence of a value-added functions, the first set of restrictions require three degrees of freedom, and the second set of restrictions require two degrees of freedom. The critical value 11.35 for the first set of restrictions and 9.22 for the second set of restrictions are employed for the chi-squared at a level of significance of 0.01. The two sets of restrictions for the existence of valueadded funCtions can be rejected at a level of significance of 0.01 for each industry and the total manufacturing sector in Table 11-2. Here we obtain negative statistics in the case that the convergence cannot be achieved. Now we test Hicks neutrality and the existence of valueadded function maintaining the assumption of constant returns to scale. Test statistics for three hypotheses are represented in Table 11-3. The restrictions to Hicks neutrality require two degrees of freedom, so we employ the critical 9.22 for chi squared with two degrees of freedom at a level of significance of 0.01. Hicks neutrality is not rejected for two industries: Textiles & leather and Lumber & wood products. Hicks neutrality is not rejected for the total manucturing either. The first set of restrictions to the existence of a value-added function maintaining the assumption of constant 35 returns to scale requires two degrees of freedom, so the critical value 9.22 is employed for chi-squared with two degrees of freedom at a level of significance of 0.01. The hypothesis that the production function is separable in Ki,Li and T f rom M, cannot be rejected for one industry: Lumber & wood products in Table 11-3. For the second set of restrictions to the existence of value-added function, we employ the critical value 6.63 for chi-squared with one degree of freedom at a level of significance of 0.01. We cannot reject the hypothesis that output is a linear logarithmic function of intermediate input and value-added at a level of significance of 0.01 for four industries: Lumber & wood products, Paper, printing & publishing, Nonmetallic mineral products, and Miscellaneous manufacturing in Table 11-3. The rejection of the hypothesis that a value-added function exists implies that we would rather abandon measuring TFP from valueadded. We evaluate estimates in the same model which are estimated by different methods of estimation ( FIML and SUR ) These estimates are presented in Table 11-4 and Tables 11-14 to 11-19, which are given in the appendix. We obtain smaller standard error with the SUR method than with the FIML method. In addition to significance, convergence is achieved more easily by SUR than by FIML. For large sample properties, however, w.e cannot conclude that SUR provides more efficient estimates than FIML, and convergence is achieved more easily by SUR tin- by FIML. Let us compare the estimates under different assumptions by SUR. The model under constant return to scale provides more efficient estimates than the one under the other assumptions: Hicks neutrality and existence of value-added function. So far we have evaluated and compared the estimates based on econometric properties. Now we evaluate estimates based on the production theory in order to see which model describes the Korean economy best and in order to measure TFP correctly. If we check the necessary conditions for monotonicity by examining estimated parameters ( AM', AK1, AL' } in Table 11-4 and Table 11-15 to 11-20 in the appendix, we find that models under constant return to scale which are estimated by SUR satisfy these conditions since the estimated parameters { Am', AK', AL' % are all significantly positive in Table 11-4. To check the concavity of the production functions, the diagonal matrix in the Cholesky factorization of the matrix of share elasticities is illustrated in Table 11-8 given in appendix. We check the condition of the concavity for the sector's production function under the different restrictions. By the method of FIML, the concavity of the production function can be accepted for two industries in the generalized model, while this condition can be guaranteed for five industries in the model restricted to constant returns to scale. Similarly by the method of SUR the condition of concavity of production function can be guaranteed for four 37 industries in the model restricted by constant returns to scale. For Nonmetalic mineral products and Metal products & machinery, constant returns to scale can be guaranted by both methods. Constant returns to scale is a special case of production function, given convex isoquants. Therefore the condition for the concavity of production function is well guaranteed by the assumption of constant returns to scale. Based on statistical significance of estimates and production theory, we obtain the best results from the model restricted to constant returns to scale by the estimation method of SUR. Now we interpret the parameter estimates which are represented in Table 11-4. The estimated share elasticities ( Bm, BM' BmJ, B&, BKLi, BLL provide the implications of patterns of substitution for the relative distribution of the value of output among intermediate, capital, and labor inputs. If share elasticities are positive, then the value shares increase with an increase of the corresponding input; if share elasticities are negative, the value shares decrease with an increase of the input; if share elasticities are equal to zero, value shares are independent of the change of input. Under the necessary and sufficient conditions for concavity of the production function for each sector, the estimated share elasticities of each input with respect to the quantity of the input itself ( Bm, BK', BLLi 1 are nonpositive. This implies that the share of each input is not Table 11-4. Parameter Estimates under Constant Return to Scale by SUR Industry 1.Food, 2.Textiles 3.Lumber Parameter beverages & & wood & tobacco leather products -0.4167 (-21.7500) 0.4026 (21.9890) 0.0983 (7.1444) 0.4990 (21.0140) 0.0365 (9.2268) -0.0617 (-1. 6493) 0. 0669 (2.8338) -0.0052 (-0.2221) 0.0033 (1.4533) -0.0413 (-1.7225) -0.0255 (-2.0003) -0.0015 (-0.8255) 0.0307 (1.7032) - (). )018 -. 3941) 0.0002 (0.7561) -0.1380 (-2.4045) 0.2098 (4.5973) 0.1544 (9.4574) 0.6356 (13.9630) 0.0071 (0.6114) -0.0034 (-0.0746) 0.0102 (0.2359) -0.0067 (-0.4109) 0.0053 (1.3947) -0.0309 (-0.6722) 0.0207 (1.2430) -0.0049 (-1.2939) -0.0139 (-1.1575) -0.0004 (-0.3070) 0.0009 (0.9661) -0.2665 (-6.4856) 0.0840 (2.2548) 0.1531 (11.2560) 0.7628 (26.7960) 0.0371 (4.6655) 0. 1060 (4.0230) -0.1114 (-3.1315) 0.0054 (0. 4109) -0.0020 (-0.9673) 0.1359 (2.5645) -0.0245 (-1.1029) 0.0026 (0.9259) 0.0191 (1.6262) -0.0005 (-0.5470) -0.0020 (-3.0137) A'T Bl1v B'MK B1 KL B'KT B'LT B'L Industry 4.Paper, 5.Chemicals 6.Nonmetalic Parameter printing & & chemical mineral publishing products products -0.0810 (-4.9685) 0.1658 (26.2230) 0.1913 (39. 1810) 0.6427 (119.9600) 0.0006 (0.1786) -0.0069 (-0.5632) -0.0065 (-0.6684) 0.0135 (0.9366) 0.0030 (5. 7375) -0.0076 (-0.5889) 0.0142 (1.1586) -0.0026 (-4.0810) -0.0277 (-1.2636) -0.0003 (-0.8100) 0.0011 (3.8449) -0.7670 (-7.4796) 0.2544 (9.7568) 0.1102 (11.8330) 0.6352 (20. 1130) 0.1078 (5.0653) -0.0719 (-2.4548) 0.0684 (2.8826) 0.0034 (0.4274) 0.0102 (3.4811) -0.0405 (-1.5005) -0.0278 (-1.7119) -0.0083 (-3.3897) 0.0243 (1.9440) -0.0018 (-1.9786) -0.0091 (-4.7856) -0.4109 (-13.7140) 0.3098 (18.4240) 0.1709 (18.5460) 0.5192 (27.9110) 0.0454 (7.6512) -0.0186 (-0.8351) 0.0151 (0.9403) 0.0034 (0.3376) 0.0066 (4.6585) -0.0557 (-3.7295) 0.0405 (5.0015) -0.0082 (-6.4241) -0.0440 (-6.0016) 0.0015 (2.2123) -0.0017 (-3.3756) AT Bln BMK B1ML BIMT BIKL B1KT B1LL B1LT B'TT Industry Parameter 7. Primary metal manufacturing 8. Metal products & machinery 9.Miscellaneous manufacturing -0.3587 (-9.9276) 0.1339 (3.0703) 0. 0459 (3. 5713) U. 8201 (19.7180) 0.0366 (5.9726) 0.0668 (2.3428) -0.0388 (-1. 3621) -0.0280 (-3.2416) -0.0020 (-0. 6223) U 004 5 (-U. 1464) 0.0433 (4.6146) -0.0009 (-0.2603) -0.0153 (-2.9489) 0.0029 (2 .8327) -0.0013 (-2 .7374) -0.3898 (-11.5760) 0.3365 (13.0700) 0.0865 (6. 3743) 0.5769 (16.0220) 0.0446 (6.8688) -0.1490 (-4.1882) 0.1473 (5.9170) 0.0016 (0. 1194) 0.0189 (5. 7329) -0. 1814 (-9.4625) 0.0341 (3.4866) -0.0187 (-7.8888) -0.0357 (-4.0535) -0. 0002 (-0. 1628) -0.0019 (-3.3505) -0.2993 (-10.1830) 0.2209 (8.1721) 0.1534 (17.4260) 0.6256 (26.3610) 0.0273 (4.6190) 0.0006 (0.0167) -0.0093 (-0.2850) 0.0087 (0.7409) 0.0028 (0.9592) -0.0077 (-0.2523) 0.0171 (1.7552) -0.0036 (-1.3696) -0.0258 (-3.0274) 0.0007 (0.9121) -0.0002 (-0.4300) BIML BMT B1KL B' KI BLL B1LT BITT Industry The Parameter total manucturing A1o -0.3607 (-12.3520) A'K 0.1930 (24 .7250) AIL 0.1086 (15.1540) A'm 0.6983 (87.9140) A'T 0.0407 (6.7934) B'm 0.0662 (5.7552) BtK -0.0144 (-1.1453) B'ML -0.0517 (-7.4077) B1MT -0.0020 (-3.0507) B'KK -0.0063 (-0.4107) B1KL 0.0208 (3.1875) BKT -0.0006 (-0.9923) B'LL 0.0309 (3.2534) B1,, 0.0027 (3.9595) B'TT -0.0020 (-3.9515) increasing with the increase of the input itself. The estimated elasticities of the share of intermediate input with respect to the quantity of the input itself { BMM' 4 are significantly negative for Chemicals & chemical products and Metal products & machinery. The estimated elasticities of the share of capital input with respect to the input itself { BKK' ) are significantly negative for Nonmetalic mineral products ind Metal products & machinery. The estimated elasticities of the share of capital input with respect to the input itself BLLi 4 are significantly negative for Nonmetalic mineral products, Primary metal manufacturing, Metal products & machinery, and Miscellaneous manufacturing. The estimated elasticities of the share of labor with respect to the quantity of capital J BKL ) are significantly positive for Nonmetalic mineral products, Primary metal manufacturing, Metal products & machinery, and The total manufacturing. For these industries, the share of labor does not decrease with an increase in the quantity of capital, holding quantities of labor and intermediate inputs and time constant. ()f course, this parameter can also be interpreted as the elasticities of the share of capital with respect to the quantity of labor, so the share of capital does not decrease with an increase in the quantity of labor. Meanwhile, the estimated elasticity of the share of labor with respect to the quantity of capital is significantly negative for Food beverage; 6 tobacco. 43 The estimated elasticities of the share of intermediate input with respect to the quantity of capital { BmK ) are significantly positive for Food beverages & tobacco, Chemicals & chemical products, and Metal products & machinery, and significantly negative for Lumber & wood products on the other hand. This parameter can also be interpreted as the elasticity of the share of capital with respect to the quantity of intermediate input. The estimated elasticities of the share of intermediate input with respect to the quantity of labor { BmL ) are significantly negative for Primary metal manucturing, and The total manufacturing. For the other industries, the estimated parameters for elasticities of the share of intermediate input with respect to the quantity of labor are not significant. The estimated biases of productivity growth ( BMTi,BKTi,BLTi 4 can be considered as the change in the share of each input with respect to time, holding all inputs constant. Also the biases of productivity growth can be interpreted as changes in the rate of productivity growth with respect to proportional changes iii input quantities. For example, if the bias with respect to labor input { BLTi ) is positive,the rate of productivity growth increases with the increase of the labor input. If the bias is negative, the productivity growth decreases with the increase of the labor input. We derive the following interpretations about biases of productivity growth based on Binswanger's concept of biases of productivity 44 growth.12 If the estimated value of the bias of productivity growth withl respect to intermediate input is positive { BMTi ), productivity growth is intermediate-using; if the value is negative, productivity growth is intermediate-saving. In the same way the estimated value of the biases of productivity growth with respect to capital input and labor input { BKTi,BLTi } implies capital-using or capital-saving, and labor-using or labor-savingJ. All the industries can be classified by their patterns 0f the biases of productivity. If we assume constant returns to scale in production, we can rule out the possibility that the three biases are either all negative or all positive. A classification of industries by their patterns of biases of productivity growth is represented in Table 11-5. The different estimation methods (FIML and SUR) provide different estimates of biases of productivity growth. FIML estimation shows in Table 11-15 given in appendix that most of estimated biases of productivity growth are not significant. However, SIUP estimation represented in Table 11-4 shows that more e- t ei i coefficients for biases of productivity growth are significant. Therefore we use the results from the SUR method to classify industries according to the biases of productivity growth. Here we eliminate two industries, Textiles & leather and Lumber & wood products, and the total 12 Binswanicer (1974). Table II-5. Classification of Industries by Biases of Productivity Growth under Constant Returns to Scale by SUR Pattern of biases Intermediate-using Capital-saving Labor-saving Intermediate-using Capital-saving Labor-using Intermediate-using Capital-using Labor-saving Intermediate-saving Capital-saving Labor-using Intermediate-saving Capital-using Labor-using Intermediate-saving Capital-using Labor-saving Industries Food, beverages & tobacco Paper, printing & publishing Chemicals & chemical products Metal products & machinery Nonmetalic mineral products Miscellaneous manufacturing Primary metal manufacturing manufacturing in classifying industries according to the biases of productivity growth since Hicks neutrality cannot be rejected at a level of significance of 0.01 for these industry: ind the total manufacturing. The pattern which occurs with greatest frequency in Table 11-5 is intermediate-using, capital-saving, and labor-saving. This pattern characterizes four industries. Meanwhile, the patterns that occur most frequently in the classification of industries which is given by Jorgenson, Gollop, and Fraumeni(1987) are intermediate-using and labor-saving in combination with capital-using and capital-saving. An alternative interpretation of biases of productivity growth is that they represent changes in the rate of productivity growth with respect to proportional changes in input quantities. The rate of productivity growth increases with the increase of corresponding input if the bias of productivity growth is positive. The rate of productivity growth increases in the quantity of intermediate input for six of the nine industries and decreases for one in Table 11-5. The rate oi productivity growth decreases in the quantities of capital for seven industries. This fact raises us doubt about the role ul capital accumulation which traditional growth theory emphasizes in the development processes of developing countries. The rate of productivity growth decreases in the quantities of labor for four industries. Final Ly, let us examine the TFP's in Table 11-6 and Table Table 11-6. Total Factor Productivity under Constant Return to Scale by SUJR Industry 1.Food, 2.Textiles 3.Lumnber Year beverages & & wood & tobacco leather products 1963 0.03517 0.00428 0.03724 1964 0.03559 0.00602 0.03460 1965 0.03594 0.00704 0.03243 1966 0.03632 0.00531 0.03031 1967 0.03680 0.00911 0.02835 1960' 0.03728 0.01018 0.02633 1969 0.03771 0.01126 0.02412 1970 0.03811 0.01281 0.02144 1971 0.03858 0.01431 0.01909 1972 0.03906 0.01645 0.01635 1973 0.03949 0.01807 0.01430 1974 0.03993 0.01982 0.01208 1975 0.04043 0.02131 0.01006 1976 0.04099 0.02263 0.00768 1977 0.04155 0.02395 0.00538 1978 0.04204 0.02506 0.00332 1979 0.04245 0.02639 0.00138 1980 0.04284 0.02772 -0.00060 1981 0.04330 0.02899 -0.00285 1982 0.04383 0.03013 -0.00525 1983 0.04425 0.03176 -0.00747 mean 0.03960 0.01774 0.01468 Industry 4.Paper, 5.Chemicals 6.Nonmetalic Year printing & & chemical mineral publishing products products 1963 0.00117 0.08758 0.03479 1964 0.00222 0.07962 0.03427 1965 0.00331 0.07249 0.03342 1966 0.00434 0.06492 0.03198 1967 0.00544 0.05710 0.03004 1968 0.00657 0.04944 0.02890 1969 0.00784 0.04095 0.02812 1970 0.00920 0.03252 0.02793 1971 0.01053 0.02425 0.02728 1972 u.U1200 0.01659 0.02701 1973 0.01336 0.00757 0.02620 1974 0.01464 0.00451 0.02488 1975 0.01588 -0.00496 0.02346 1976 0.01727 -0.01360 0.02251 1977 0.01871 -0.02201 0.02139 1978 0.02014 -0.03090 0.01986 1979 0.02150 -0.04015 0.01804 1980 0.02297 -0.04987 0.01638 1981 0.02442 -0.05938 0.01492 1982 0.02593 -0.06874 0.01391 1983 0.02734 -0.07695 0.01296 mean 0.01356 0.00814 0.02468 Industry 7 Primary metal manufacturing 0.03723 0.03550 0.03390 0.03217 0.03031 0.02842 0.02702 0.02571 0.02430 0.02263 0.02132 0.02031 0.01920 0.01803 0.01664 0.01540 0.01427 0.01313 0.01195 0.01062 0.00922 8 .Metal products & machinery 0.02410 0.02445 0.02554 0.02522 0.02478 0.02423 0.02307 0.02151 0.02012 0.02163 0.02353 0.02380 0.02450 0.02494 0.02687 0.02690 0.02564 0.02454 0.02398 0.02485 0.02557 9. Miscellaneous manufacturing 0.02571 0.02521 0.02489 0.02463 0.02479 0.02495 0.02523 0.02505 0.02485 0.02480 0.02484 0.02489 0.02501 0.02514 0.02536 0.02548 0.02559 0.02583 0.02584 0.02584 0.02580 mean 0.02225 0.02427 0.02523 Year 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 Industry The Year total manucturing 1963 0.04036 1964 0.03812 1965 0.03590 1966 0.03389 1967 0.03150 1968 0.02925 1969 0.02702 1970 0.02471 1971 0.02244 1972 0.02001 1973 0.01774 1974 0.01515 1975 0.01295 1976 0.01068 1977 0.00835 1978 0.00607 1979 0.00379 1980 0.00151 1981 -0.00077 1982 -0.00307 1983 -0.00531 mean 0.01763 51 11-9 to 11-14 in appendix which are calculated by using the estimated coefficients in the different models. The TFP from the generalized model fluctuates highly. However, the TFP from the models under constant returns to scale by the estimation method of SUR show the similar result with the one from the model under constant returns to scale by FIML. TFP's from the model under constant returns to scale which is estimated by SUR show a deceleration of productivity growth, that is, the estimated accelerations of productivity growth ( BTTi } are significantly negative for five industries. Also TFP for the total manufacturing exhibits a deceleration of productivity growth. Now we compare our measurement of TFP to what others have measured. Kim and Park have measured TFP for the same sectors in Korean manufacturing based on the methodology of growth accounting. The growth accounting was introduced by Solow (1957) and has been discussed by Hulten (1973), Jorgenson and Griliches (1967,1971). I explain their methodology briefly in terms of the same notations in our model. The growth accounting equation starts from a production function: Xi=F 1(Mi, Ki, Li, T) (i=i,2,...,n). (1) TFP in growth accounting is defined as rate of growth of output with respect to time, holding intermediate, capital, and labor inputs constant: i alnxi VT = aT (M, Ki, Li, T) (10) Under constant returns to scale, the rate of technical change for each sector can be expressed as the rate of growth of the corresponding sectoral output less a weighted average of the rates of growth of intermediate input, capital input, and labor input, where the weights are given by the corresponding value shares: dlnX1 _lnX dlnMi + 8X dlnKi dT 81nM dT l81nK. dT 81nXi dlnL 81anX. + +_81nLi dT aT dlnM i dlnK lInL, VM dT + VK dT dT + T The comparisons of TFP's measured by different methods are represented in Table II-7. TFP's measured by growth accounting are greater than TFP's measured by translog production function for five of nine industries and the total industries, and less for the other. Since TFP measured by growth accounting is based on the assumption of Hicks neutrality, it cannot explain the effect of bias of (i=1,2,...,n). (i=1,2, ...,n) Table II-7. Comparison of TFP's measured by different methods: growth accounting and translog production function TFP measured by TFP measured by Industry growth accounting translog production function l.Food, beverages 0.0231 0.0396 & tobacco 2.Textiles & 0.0201 0.0177 leather 3.Lumber & wood 0.0239 0.0146 products 4.Paper, printing & 0.0223 0.0135 publishing 5.Chemicals & chemical 0.0016 0.0081 products 6.Nonmetalic mineral 0.0191 0.0246 products 7.Primary metal 0.0180 0.0225 manufacturing 8.Metal products & 0.0374 0.0242 machinery 9.Miscellane -ous 0.0318 0.0252 manufacturing The total 0.0208 0.0176 manufacturing 54 productivity growth on TFP. However, TFP measured by translog production function reflects the effect of bias of productivity growth as denoted in equation +B LnL,+BT (i=l,2, . ,n). (70) If we assume Hicks neutrality in our flexible model, the rate of productivity growth is determined as denoted in equation VT=Aj+B;T (i=l,2,...,n) (72) It is known that the Korean economy accomplished the rapid growth during the last two decades. However, our estimation of TFP's implies that the outstanding characteristic of the Korean economy is the decelerating TFP. The industrialization of the Korean economy is not due to technological progress. If we observe the normalized variables of X, L, K, and M in data set, the intermediate input is the fastest growing input. In this observation, we can conclude that much of the industrialization in Korea is attributable to the growth of the intermediate input. CHAPTER 3 THE MEASUREMENT OF SOURCES OF GROWTH The Model: Input-Output Analysis The starting point for measuring contributions of demandside factors to growth is the material balance equation of input-output analysis. The input-output model can be used as a tool to disentangle the relative contributions to growth and structural change of different components of changes in the final demand. The material balance equations for the supply of and the demand for domestically produced goods can be written as Xt =ACX, +Ft +Et-MC (88) where X, = domestic production vector in year t At- input-output coefficients matrix such that j is composite intermediate demand of sector i per unit of domestic output in sector j in year t -,, intermediate demand vector in year t (composite of imported and domestic goods) Ft =domestic final demand vector in year t (composite of imported and domestic goods) Et=export vector of domestic goods in year t Mt import vector in year t. The problem with the definition of the above variables is how to treat imports. Imports can be classified as either competitive or as noncompetitive. If they are noncompetitive, then they are not grouped with domestic products but are viewed as a nonproduced input into a sector, analogous to labor and capital. But in this model, I regarded all imports as competitive so that they are included in the same sector classification as domestic production. Let's assume that the ratio of domestic demand for domestically produced goods to total domestic demand is fixed by sectors. These domestic demand ratios in year t are given by di, i C(89) where Vt = A, Xt. Defining a diagonal Matrix Dt of the d, parameters, the material balance equation for domestic goods is given by Xt:D V, D +Ec (90) This equation can be derived by the following procedure. Let's consider the ith row in the material balance equation. Xit : g* g+Fc+ Mi (91) We express this equation in terms of the domestic demand ratio as follows. )M iC = (1- MI ) (Vit+Fit) +Ec =d1: (Vic+Fic) +Eit (92) If we diagonalize di, and vectorize the other variables, then we can get the matrix expression of equation (93). Xc=D (V,+F,) +Et (93) Noting that Vt = AtXt, the material balance equation can be written as Xt= (I-DcA ) -1 (DeFe+Ec) (94) The production of output Xt, is determined by the domestic final demand Ft and exports Et according to this expression of the material balance equation. The demand-side growth accounting can be established by using this equation. As will be explained, there are two methods of decomposing the sources of growth. One is the method based on absolute growth, and the other is the method based on proportional growth. Decomposition of Output Growth based on Absolute Growth Syrquin formulated the method in terms of absolute change in output and used it for the decomposition of industrial output growth. Kubo and Robinson reformulated the Syrquin Method.' Denoting the change in a variable between two periods by A [ AXt = X Xt ,] the change in sectoral output can be written (after some algebraic manipulation) as shown below AXt=Rt1De(AF,) +Rc- (A F,) +R-t_(ADt) (FA+VA) +Re-IDr__ (AAC) Xt. (a) (b) (c) (95) (a) Effects of domestic changes in domestic demand in all sectors(DD), (b) Effects of changes in exports in all sectors (EE), (c) Effects of changes in the import structure of intermediate and final goods (IS), (d) Effects of changes in the matrix of input-output coefficients (IO). The above decomposition equation can be derived from equation (94). If we denote Rt = (I DtAt )-, then equation (94) can be written as (96) Let's take the first difference from this equation, then we obtain Ax~=R~ ,(D~ ,AF~+AE~ +AD~F~ ,) +AR~(D~ ,F~ 1+E~ 1) (97) 1 Dervis, K., J. D. Melo, and S. Robinson (1982). pp92-110. Xt=Rt (DeFc+Et) The first difference of an inverse matrix is given by ARt=A [I-DtAC] -1 = -RtA U I-DA ) Rt =R,-i (ADAJ +D,_ AA.) Rti (98) Substituting this equation into the above equation, we get the decomposition equation (95) AX =R I _1 I(A F O)+R CI(AE ,) +R _, (AD ) (F _, + V _)+R _,D _, (AA d)X CI This equation gives the basic decomposition of the change in sectoral output into different sources (i.e., AF,, AEt, ADt, and AAt). The first two terms on the right-hand side of the above equation are changes in the output of sector i induced by the expansion of domestic demand and exports in all sectors, given a constant import structure. The third and fourth terms measure the direct and indirect effects of changes in the import structure of final and of intermediate goods. The last term gives the direct and indirect effects of changes in the total (domestic and imported) matrix of inputoutput coefficients, which represent the widening and deepening of interindustry relations brought about by the changing mix of intermediate input requirements. The changes in input-output coefficients are caused, in turn, by changes in production technology as well as by substitution among 60 various inputs (perhaps in response to changes in relative prices) although we cannot separate these two effects without more information. Decomposition of Output Growth based on Proportional Growth Chenery provided the decomposition method by using the differences which are called the "deviations from proportional expansion".2 Let's define the deviation from proportional growth of output of sector I as 6Xit = Xi AXi ,1, where A is the ratio of GNP in period t to GNP income in period t-1. 6Xit Xit A Xi- t A 6Fit = Fit A Fi t 6Vit Vir Vi't 1 6EI1 El= A Ei tUsing these definitions, the alternative decomposition equation can be derived from the material balance equations analogous to the decomposition equation (95). After some algebraic manipulations, the decomposition (in matrix notations) is given by 8Xt=Re-IDei 6FC (a) +R-18EC (b) +Rt-1IADl (F-1 +Ve_4) (c) +R -1D -1AAXX, (d). (99) 2 Chenery, H. B., S. Shishido, and T. Watanabe (1962) 61 The deviation from proportional growth in output in sector i is seen to be the sum of four sets of structural changes: (a) Effects of deviations in domestic demand in all sectors(DD), (b) Effects of deviations in exports in all sectors(EE), (c) Effects of changes in the import structure of intermediate and final goods(IS), (d) Effects of changes in the matrix of input-output coefficients(IO). In equation (99), the material balance equation in the terminal year is compared not with its counterpart in the initial year but with the hypothetical material balance equation in the terminal year under the assumption of balanced growth. Difference between two Methods: A Graphic Representation The figure 1 is a graph of growth and structural change in a two-sector model. Initially, the economy is at point I and is producing X1,,- and X2,t1 ( the subscript refers to the sector and the superscript to the period ). Later, the economy is at point II and is producing X1, and X21. Aggregate output has grown from Xt-1 = Xlt11 + X,11 to Xt = Xlt + X2t, where Figure 1 Measures of Growth and Structural Change real output is defined simply as the sum of sectoral outputs in constant prices. The change in aggregate output is given by the sum of the changes in sectoral output: AX = A X1 + A X2 (where AX = X1t Xit t) The change in aggregate output, however, conceals significant changes in the structure of production. To measure this structural change, the movement from point I to point II is decomposed into two steps. First, the economy is assumed to grow so that all sectors expand proportionately. This balanced growth takes the economy from point I to point II', with outputs X1, and X21, and the same aggregate output as at point II. Then, holding aggregate output fixed, the structure of production is changed; the changes in sectoral production generated by moving from point II' to point II are given by 6X1 and 6X2. Therefore, the method based on absolute 63 growth measures the change A in variables and the method based on proportional growth measures the change S in variables. In the decompositions of the deviation measure, let's compare equation (95) with equation (99) to examine the difference between the AX decomposition and the 45X decomposition. The last two terms in equation (95) are nearly identical with the corresponding terms in equation (99). Given that the nonproportional components of domestic demand and export growth are generally smaller than their increments, the relative importance of import substitution and of changes in input-output coefficients will be greater in accounting for S changes than in accounting for A changes. Input-output Data base I focused on an input-output accounting framework to measure the degree to which domestic demand, exports, import substitution, and technological change have each contributed to output growth. Since this accounting can be done at either a broad macroeconomic level or for narrowly defined industrial sectors, it provides a rich set of insights into the detailed workings of the Korean economy. This analysis of the sources of industrial growth and structural change is based on five input-output tables: 1975, 1978, 1980, 1983, and 1985. Although the input-output tables are available for four additional years (1960, 1966, and 1968, 1970) in Korea, I used only five tables to economize on data 64 and computing costs since I focused on the analysis of policy change of the period in which Korea experienced the economic recession because of the second oil shock and the subsequent recession in the advanced countries. The Bank of Korea has provided f ive tables which have about 60 sectors. All the tables are compiled in terms of current producers'I prices. The measurement of sources of growth is most meaningfully conducted in terms of constant price. Thus it is necessary to deflate the current price input-output statistics to obtain constant price figures. For this I deflated all the tables with IMF wholesale price indices. While this procedure suffices to insure that, on the average, changes over time are not mis-stated because of price level changes, it fails to account for relative price changes. The changes of relative prices can take place owing to the price level of imported commodities, the price level of exports and the exchange rates on imports and exports. Except for the two tables for 1980 and 1983, which have 19 sectors, all tables have about 60 sectors. So I had to make all the tables into 19 sectors by aggregating the detailed sectors. Estimation of Sources of Growth: SAS/IML I estimated the sources of growth on the demand side by using SAS/IML (Interactive Matrix Languages) The total change in sectoral output is decomposed into its sources by category 65 of demand. The total change in output equals the sum of the changes in each sector and can also be decomposed either by sector or by category of demand. The relations can be shown schematically as follows: Notations DD = effect of deviations in Domestic Demand expansion EE = effect of deviations in Export Expansion IS = effect of changes in Import Substitution 10 = effect of the changes in Input-Out coefficients. DD1 + EE1 + is, + I01 = A X, DD2 + EE2 + IS2 + 102 = A X2 DD, + EE1 + ISn + I01 = AXn F DD, + Z EE1 + Z IS1 + Z IO1 = Z A Xi Reading down columns gives the sectoral composition of each demand category; reading across rows gives the decomposition of changes in sectoral demand by different demand categories. Growth contributions in each period were first calculated at the 19 sector level and then aggregated before converting to percentage. While the tables of the 19 sector model are presented in Appendix, the summary tables, i.e. sources of aggregated output growth, sources of sectoral output growth, and the sectoral comparison of EE and IS in AX and 6X are summarized in Table 111-2, 111-4, 111-6, and 111-7. Interpretation of the Results While it is apparent from some research results that Korea's industrial development has clearly been export-led, this stands out even more dramatically when the sources of Korea's industrialization are compared with international norms on the demand side. Before I examine the results of my calculation of the sources of growth in the period 1975-1985, I refer to the results from Frank, Kim and Westphal (1975) to compare the Korea's development pattern with the norms on the demand side. The sources of Korea's industrialization from 1960 to 1968 are compared in Table 111-1 with crudely estimated crosscountry norms for the growth of per capita income from $100 to Table III-1. Sources of Industrialization' DD EE(%) is Korea (1960-68) 60 38 2 Large Country Norm 55 24 21 All Country Norm 50 18 32 3Frank, Ch. R., K. S. Kim, and L. E. Westphal (1975), p95. 67 $200. While import substitution contributed very little to Korea's industrialization, the growth of exports contributed more than twice the relative amount that is typically associated with the doubling of per capita income from $ 100 to $ 200. The analysis of Frank, Kim and Westphal, however, had an analytic problem in that a fixed coefficient inputoutput table was assumed. Furthermore these results are unfortunately not comparable to ours because of differences in classification and level of aggregation. Table 111-2 highlights the impact of the shift in Korea's development strategy and the technological change in the early 1980s. According to the AX based estimates found in Table 111-2, the EE effects on the growth of output dominated over the IS effect except during the period 1978-1980. In the period 1978-1980, the IS effect was a little greater than the EE effect in AX. Until 1978, Korea pursued export-oriented economic growth. However, Korea faced some major constraints to the promotion of exports. The advanced countries underwent a prolonged recession after the second oil shock. This led to increased protectionism in the advanced countries. In this period, the greatest effect on the growth of output in Korea was the change in input-output coefficients. This fact reflects that Korea experienced the technological change in the face of the second oil shock and world-wide recession to achieve steady economic growth. Moreover, the resource misallocation which was led by the government's overambitious Table 111-2. Sources of Aggregated Output Growth (in percent) A X 6 X DD EE is I0 DD EE is 10 1975-1978 76. 78 28.34 3.06 -8.18 54.69 -3.80 -65.07 110.76 1978-1980 11.88 11. 34 12.98 63.79 23.04 15.54 10.73 50.69 1980-1983 71.24 43.54 10.23 -25.01 75.54 -24.55 -27.97 76.98 1983-1985 65.21 33.02 3.79 -2.02 -54.36 -1.44 15.49 -16.59 Note) A X: the incremental measured by the method based on absolute growth 6 X: the incremental measured by the method based on proportional grow promotion of heavy and chemical industries since the midseventies accelerated the changes in the input-output coefficients. After these big changes in the input-output coefficient, the difficulties that Korea encountered during the 1979-1981 had been largely overcome by the middle of 1984. If we examine the estimates based on the 6X decomposition, we find that export promotion no longer contributes to the growth of output. In Table 111-2, we can observe the contribution of changes in the input-output coefficients to the growth of output in the decompositions of 6X. To examine the structural changes, let examine the Table 69 111-4 which classifies output into five sectors: primary industry, light industry, heavy industry, social overhead and services, and dummy sector. The aggregation scheme of nineteen industries into five sectors is shown in Table 111-3. According to Table 111-4, domestic demand expansion was a dominant factor in primary industry's output over the entire period (1975-1985) The export expansion contributed to output growth positively, but Table 111-4 showed the great reduction of the EE effect in the decomposition of SX. In the decomposition of SX, the contributions of the changes of technology in manufacturing to the growth of output have different patterns between light industry and heavy industry in the entire period (1978-1985) The contributions of the changes in the input-output coefficients of light industry did not vary sharply from period to period. In contrast, the contributions of the changes of heavy industry changed radically from period to period. In the period 1978-1980, for example, the contributions of the changes in the input-output coefficients of heavy industry was the greatest one among factors of decompositions. In the period 1980-1983, however, the changes in the coefficients of heavy industry contributed by minus 566.8%. These empirical results indicate that the heavy industry experienced the radical change in the government's development policy. The government's overambitious promotion of heavy and chemical industries took place since the mid-seventies. The IS effects were minor Table 111-3. Sector Classification for Five Sectors 5 Aggregated Sector 19 Aggregated Sector classification classification 1. Primary industry 1. Agriculture, forestry and fisheries 2. Mining 2. Light industry 3. Food, beverages and tobacco 4.Textiles and leather 5. Lumber and wood products 6. Paper, printing and publishing 8. Nonmetalic mineral products 11. Miscellaneous manufacturing 3. Heavy industry 7. Chemicals and chemical products 9. Primary metal manufacturing 10. Metal products and machinery 4. Social overhead 12. Construction & services 13. Electric, gas and water services 14. Wholesale and retail trade 15. Transportation, warehousing and communications 16. Finance, insurance and real estate 17. Public administration and defence 18. Restaurants, hotels and other services 5. Dummy sector 19. Dummy sector Table 111-4. Sources of Sectoral Output Growth: 5 Sector Model (in percent) AX 6X DD EE IS 10 DD EE IS IO 1975-1978 1. Primary Indu.t:. 10 o06 23 3 7 -303 1 -79.4 317 .4 -34.9 2. Light Industry 71.7 40.3 -1.2 -10.9 33.0 39.4 2.7 25.0 3. Heavy Industry 71.9 52.4 -.7 -23.7 390.6 640.6 -20.2 -911.0 4. Social Overhead & Services 84.2 15.7 -.3 .4 48.9 23.2 -2.2 30.1 5. Dummy sector 85.9 37.5 -6.1 -17.4 39.6 18.2 16.5 25.7 1978-1980 1. Primary Industry 177.3 7.8 42.5 -127.7 125.9 -3.6 34.4 -63.9 2. Light Industry 50.5 1.0 10.4 38.2 56.2 4.5 7.2 32.0 3. Heavy Industry -12.8 19.0 32.1 61.8 -7.5 25.1 31.1 51.3 4. Social Overhead & Services 43.2 12.1 .8 43.9 51.4 13.4 .9 34.3 5. Dummy sector 6,7 -11.8 33.3 71.7 23.8 -5.2 31.5 49.9 1980-1983 1. Primary Industry 100.5 10,5 28.2 -39.1 33.5 39.2 -76.2 103.5 2. Light Industry 101.9 84.1 -3.3 -82.7 56.1 14.6 3.5 25.8 3. Heavy Industry 41.3 65.7 17.7 -24.8 -305.8 612.1 360.5 -566.8 4. Social Overhead & Services 84.0 23.8 2.9 -10.7 81.2 -53.7 -23.1 95.6 5. Dummy sector 85.7 67.9 18.9 -72.5 53.0 -44.7 -29.1 120.8 1983-1985 1. Primary Industry 69.9 14.7 18.8 -3.4 143.1 26.8 -49.8 11.2 2. Light Industry 43.3 40.3 4.7 14.8 -211 8 7.6 31.8 74.7 3. Heavy Industry 50.4 63.8 5.6 -19.8 -16.4 15.1 8.1 -33.6 4. Social Overhead & Services 87.3 13.2 1i -.6 3.6 -30.4 2.3 -13.9 5. Dummy sector 73.6 14.9 -4.2 15.7 -8,7 -56.3 -10.2 28.0 72 except the recession period. The 10 effects of all industries except primary industry are high just in the recession period. It is interesting to compare these findings of proportional method on Korean economy to the results which are obtained in the analysis of the patterns of Japanese Growth, 1935-1954 by H. B. Chenery, S. Shishido, and T. Watanabe (1962). The relative contribution of export expansion is not emphasized by the proportional method in the case of Korean economy. The similar phenomenon can be found from Table 111-5. For direct comparisons, the analysis of Chenery et al. has some limitations since they assumed that the coefficient matrix of the input-output table was fixed, that is, there was no technological change. However, their results imply the following fact. Many people assumed that the Japanese pattern would be export-led, but the fact is that it was led by import substitution. It is also believed that the pattern of Korean development is export-led. But the results based on the proportional method do not support this conclusion. Most of the major manufacturing subsectors displays a pattern consistent with that for manufacturing as a whole except several subsectors. If we focus on the comparisons of trade policy of each sector, we can compare the relative importance of export expansion and import substitution in Tables 111-6 and 111-7. Table 111-5. Relative Importance of Changes in Final Demand and Trade, 1935-19544 (Billions of 1951 yen) Final Demand Exports Imports Total I A. Agriculture 50 -268 397 179 I B. Mining -43 -48 62 -29 II A. Food 123 -86 8 45 II B. Textiles -16 -807 93 -730 II C. Other Finished -113 -81 44 -150 Goods II D. Intermediate -271 -280 535 -15 Products III. Services 378 -451 152 79 Table 111-6 shows that the relative importance of EE and IS in some subsectors changed dramatically in the recession period. Specifically the heavy and chemical industries experienced the reverse of relative importance between EE and IS. If we compare the relative importance of EE and IS between AX and SX, the EE is of less importance in SX than in AX. During the past ten years much research results about export expansion and economic growth has confirmed the positive relationship. However, while the high positive correlation between export performance and economic growth is 4 H.B.Chenery, S.Shishido, and T.Watanabe (1962), pp 112. Table 111-6. Sectoral Comparison of EE and IS in AX (Method based on absolute growth) (in percent) 75-78 78-80 80-83 83-85 EE is EE is EE is EE is 1. 9.9 <14.0 9.6 < 18.3 6.4 < 27.8 9.6 < 17.0 2. 14.8 <- 77.4 -19.2 <423.5 177.6 > 41.5 65.9 > 37.3 3. 4.1 > -1.8 -0.6 < 8.3 13.4 < 32.6 11.1 > 10.5 4. 59.1 > .3 610.6 >363.4 229.7 >-87.0 63.0 > 4.9 5. 42.6 > -1.4 131.1 > 12.4 -316.8 <-32.4 22.4 >-32.5 6. 30.2 > 3.0 8.1 > 7.0 -304.5 <551.6 25.7 > -5.5 7. 57.4 > -.4 12.8 < 20.3 118.9 >-15.7 73.8 > -7.1 8. 35.3 > -7.5 9.0 < 11.9 57.8 >-30.9 8.1 > .0 9. 104.7 >-20.7 33.9 < 41.0 90.2 > 45.7 458.8 > 66.8 10. 41.8 > 2.3 7.5 <142.8 48.9 > 19.5 47.2 > 11.7 11. 75.3 -> -4.5 -390.1 <126.1 68.3 > -2.8 116.9 > 1.9 12. .7 > 0 1.2 > 1.0 4.5 > .3 4.1 > .1 13. 34.5 >4.8 7.2 < 7.9 28.4 > 4.4 66.5 > 4.6 14. 30.4 ~> .3 164.8 > 93.3 91.6 > -.4 22.0 > 5.8 15. 41.8 > -3.8 50.6 >-13.8 42.3 > 9.7 26.7 > -6.3 16. 12.0 > 1.5 4.2 < 8.2 31.1 > 7.5 7.8 > -1.0 17. 0 0 .5 >-3.0 1.4 > 1.1 -.3 < 8.5 18. 6.0 > -.6 2.9 > -3.4 11.1 > -.8 25.0 > -5.4 19. 37.5 > -6.1 -11.8 < 33.3 67.9 > 18.9 14.9 > -4.2 Table 111-7. Sectoral Comparison of EE and IS in 6X (Method based on proportional growth) (in percent) 75-78 78-80 80-83 83-85 EE IS EE IS EE IS EE IS 1. -11.7< 90.8 5.2< 21.9 55.6>-116.0 45.1>-89.8 2. 1.1< 113.7 137.5>-1296.5 6.5> -10.6 42.5< 81.3 3. 113.8> 14.6 -.2< 5.1 5.6> -13.3 -3.7>-76.1 4. 97.6> -24.4 131.6> 42.1 14.1< 30.6 19.7> 5.7 5. 31.1> -2.7 194.6> 17.0 129.7> 7.9 13.4> 9.5 6. -125.9>-279.7 10.2> 6.5 5.8> -33.0 23.1>-24.4 7. -134.0< 1.2 16.7< 17.2 -13.1< 13.3 59.9>-14.8 8. 59.3> -25.6 11.5> 10.8 12.2< 13.7 -67.6< .6 9. 180.7> -45.5 40.7< 43.4 -87.5>-187.0 -142.9< 83.3 10. 45.7> 2.9 29.0< 151.7 60.8> 34.4 16.3> 10.6 11. 80.0> -5.2 -170.7< 51.1 146.0> -36.7 66.1> 2.7 12. .1> .0 1.4> .9 56.9> 5.2 15.4> 2.4 13. 71.9> 34.1 9.3> 7.8 23.7> 13.8 -47.5<-21.5 14. 79.2> 3.5 50.9> 18.2 -15.0< 2.3 -3.7< 9.9 15. 70.0> -12.1 50.9> -10.6 55.8> 55.5 -129.2<-18.1 16. 10.0> 2.8 5.9< 7.3 -2.2> -8.6 3.4> -.5 17. .0 .0 .5> -1.4 12.0< 13.2 1.0> -6.5 18. 4.4> -1.1 4.1> -2.7 24.5> -4.5 -7.6< 5.0 19. 68.4> -50.8 -7.0< 33.4 -53.2< -32.4 -25.3< -6.5 an accepted fact in development economics, recent studies fail to confirm that the former causes the latter. This analysis indicates that domestic demand and export expansion were two major factors contributing to growth and structural change. However, import substitution and technological change were more important than export expansion in the recession period (1979-1981) in explaining growth. In addition, if we take the method of measurement based on proportional growth, export expansion no longer plays the consistent role that is attributed to it by the method based on absolute growth. CHAPTER 4 SUMMARY AND CONCLUSION I have analyzed the productivity change and pattern of production for industrial sectors in Korean manufacturing by estimating translog production functions and value shares and testing restrictions which are imposed by producer's theory in the supply-side analysis. In the demand-side analysis, I have measured the effect of changes in demand on the growth of outputs of industrial sectors and derived some implications about trade policies: export promotion policy and import substitution policy. In the supply-side analysis, we obtain the best results from the model restricted to constant returns to scale by the estimation method of seemingly unrelated regression based on statistical significance of estimates and production theory. The parameter estimates of translog production function provide implications about share elasticities and biases of productivity. We classify the industries according to the biases of productivity growth. The remarkable characteristic in our classification is capital-saving. This fact raises doubt about the role of capital accumulation which traditional growth theory emphasizes in the development process of developing countries. If we compare the TFP measured by translog production function to the TFP which others have measured by growth accounting, we obtain different results according to the industry. For some industries TFP's measured by translog production function are greater than TFP's measured by growth accounting, and for other industries less. This phenomenon is due to the fact that TFP measured by growth accounting cannot explain the effect of bias of productivity growth on TFP, while TEP measured by translog production function reflects the effect of bias of productivity growth. In the demand-side analysis, domestic demand and export expansion were two major factors contributing to growth and structural change. However, import substitution and technological change were more important than export expansion in the recession period. Besides, if we measure the relative contribution of export expansion by the method based on proportional growth, we do not observe the role of export expansion which is attributed by the method based on absolute growth. If we relate productivity changes of industrial sectors in manufacturing during 1975-83 to the measurement of sources of growth for the same industrial sectors in manufacturing during the same period, we do not find any correlation between the increase of TFP and trade policies. Our observations on total factor productivity implies that the technical progress takes 79 a relatively small role in the industrialization process since the rate of productivity growth is decelerating. APPENDIX Table II-8. Diagonal Matrix of Cholesky Factorization I.FIML 1) Generalized Model l.Food, beverages & tobacco 0.06028 4.63966 -0.10437 2.Textiles & leather 0.04309 2.38705 -0.04185 3.Lumber & wood products 0.11556 3.81398 -0.01627 4.Paper, printing & publishing -0.10252 0.82301 0.13600 5.Chemicals & chemical products -0.07557 36.88665 0.02415 6.Nonmetalic mineral products -0.18428 -2.79678 -0.04545 7.Primary metal manufacturing -0.12738 -1.14135 -0.01693 8.Metal products & machinery -0.22741 1.14399 -0.04406 9.Miscellaneous manufacturing -0.07471 3.86755 -0.03126 10.The whole manufacturing 0.05539 22.15497 -0.01212 2) The Model under Constant Return to Scale 1.Food, beverages & tobacco -0.16665 -0.00051 -0.00000 2.Textiles & leather 0.02607 -0.03638 0.00000 3.Lumber & wood products 0.10554 0.01813 0.00000 4.Paper, printing & publishing -0.08747 0.00288 -0.00000 5.Chemicals & chemical products -0.04982 0.02171 0.00000 6.Nonmetalic mineral products -0.10075 -0.04577 0.00000 7.Primary metal manufacturing -0.18127 -0.01470 -0.00000 8.Metal products & machinery -0.15002 -0.03652 -0.00000 9.Miscellaneous manufacturing -0.17455 -0.01737 -0.00000 10.The whole manufacturing 0.05166 -0.01500 -0.00000 II.SUR 1) Generalized model l.Food, beverages & tobacco 0.08910 4.10452 -0.07681 2.Textiles & leather -0.02319 2.03831 -0.00648 3.Lumber & wood products 0.11146 3.94681 -0.02522 4.Paper, printing & publishing -0.06844 3.40890 0.04821 5.Chemicals & chemical products -0.11675 8.76096 0.02159 6.Nonmetalic mineral products 0.00725 1.81824 -0.05631 7.Primary metal manufacturing 0.13119 -0.01649 -0.01653 8.Metal products & machinery -0.22888 3.76045 -0.04245 9.Miscellaneous manufacturing 0.02431 0.08809 -0.04082 10.The whole manufacturing 0.06293 18.14782 -0.00990 2) The Model under Hicks Neutrality 1.Food, beverage & tobacco -0.05375 0.96644 -0.00939 2.Textiles & leather -0.04362 -0.02710 -0.00517 3.Lumber & wood products 0.11753 0.01442 -0.03530 4.Paper, printing & publishing 0.01825 0.38384 -0.01479 5.Chemicals & chemical products -0.06181 1.16399 0.01749 6.Nonmetalic mineral products 0.04505 0.50963 -0.06598 7.Primary metal manufacturing 0.15134 0.72318 -0.02119 8.Metal products & machinery -0. 23177 -0.42738 -0.03218 9.Miscellaneous manufacturing 0.05039 0.21689 -0.02169 10.The whole manufacturing 0.05836 0.36004 -0.01155 3) The Model under Constant Return to Scale l.Food, beverage & tobacco -0.06170 0.03119 -0.00000 2.Textiles & leather -0.00343 -0.00051 -0.00000 3.Lumber & wood products 0.10603 0.01883 -0.00000 4.Paper, printing & publishing -0.00697 -0.00156 -0.00000 5.Chemicals & chemical products -0.07193 0.02454 -0.00000 6.Nonmetalic mineral products -0.01860 -0.04337 -0.00000 7.Primary metal manufacturing 0.06685 -0.02712 0.00000 8.Metal products & machinery -0.14904 -0.03575 -0.00000 9.Miscellaneous manufacturing 0.00064 -0.14484 0.00000 10.The whole manufacturing 0.06623 -0.00954 0.00000 4) The Model under Existence of Value-added function l.Food, beverage & tobacco -0.01198 4.25468 -0.03367 2.Textiles & leather 0.02774 1.52091 -0.00838 3.Lumber & wood products 0.04432 4.22041 -0.00850 4.Paper, printing & publishing 0.02282 3.51295 0.06909 5.Chemicals & chemical products 0.01520 -8.99473 0.01948 6.Nonmetalic mineral products 0.03370 2.04482 -0.05155 7.Primary metal manufacturing 0.01434 1.16434 -0.01796 8.Metal products & machinery 0.01304 2.17598 -0.04084 9.Miscellaneous manufacturing 0.01516 0.16856 -0.03078 10.The whole manufacturing 0.01757 10.80001 -0.03258 Table 11-9. Total Factor Productivity by FTML Industry l.Food, 2.Textiles 3.Lumber Year beverages & & wood & tobacco leather products 1963 0.13287 -0.02661 0.09446 1964 0.11786 -0.03156 0.07365 1965 0.10402 -0.03667 0.05380 1966 0.09443 -0.04253 0.03457 1967 0.08771 -0.05317 0.01083 1968 0.08114 -0.05652 -0.01363 1969 0.07102 -0.05149 -0.02972 1970 0.06401 -0.04034 -0.02924 1971 0.05471 -0.03096 -0.01824 1972 0.04334 -0.03127 -0.01134 1973 0.03186 -0.03966 -0.01050 1974 0.02558 -0.05018 -0.00972 1975 0.02628 -0.06157 -0.00917 1976 0.02648 -0.06885 -0.01484 1977 0.02404 -0.06707 -0.02847 1978 0.01968 -0.05067 -0.03734 1979 0.02157 -0.02299 -0.03123 1980 0.03013 0.00563 -0.01125 1981 0.04174 0.03067 0.01517 1982 0.04844 0.05118 0.03285 1983 0.04940 0.06419 0.04048 mean 0.05697 -0.02907 0.00481 Industry 4.Paper, 5.Chemicals 6.Nonmetalic Year printing & & chemical mineral publishing products products 1963 0.04206 0.57985 -0.04764 1964 0.03788 0.58364 -0.03479 1965 0.03389 0.57856 -0.02270 1966 0.02917 0.59733 -0.00141 1967 0.02655 0.59024 0.02275 1968 0.02426 0.51129 0.04053 1969 0.02310 0.42549 0.04461 1970 0.02257 0.40190 0.03747 1971 0.02201 0.42508 0.02444 1972 0.02308 0.38831 0.01594 1973 0.02361 0.29622 0.01764 1974 0.02298 0.16844 0.02471 1975 0.02173 0.04931 0.02920 1976 0.02144 -0.05434 0.03357 1977 0.02191 -0.10424 0.04547 1978 0.02245 -0.09283 0.06173 1979 0.02288 -0.02917 0.06730 1980 0.02485 0.05203 0.05907 1981 0.02687 0.16301 0.04233 1982 0.02906 0.12258 0.03131 1983 0.02971 0.39529 0.02850 mean 0.02631 0.28800 0.02476 Industry 7 Primary metal manufacturing -0.06482 -0.05867 -0.05320 -0.04513 -0.03677 -0.02760 -0.02391 -0.02029 -0.01588 -0. 00128 0.01223 0.02023 0.02702 0.03451 0.04640 0.05574 0.06194 0.06565 0.06659 0.06544 0.06224 8. Metal products & machinery -0. 11721 -0.10649 -0.09579 -0.08807 -0.08018 -0.07357 -0.06532 -0.05306 -0. 04148 -0.03490 -0.03498 -0.03432 -0.03320 -0.03243 -0.03212 -0.02863 -0.01679 0.00132 0.02226 0.03964 0.05282 9 .Miscellaneous manufacturing 0.43187 0.31717 0.21876 0.14428 0.10581 0.05619 -0.00195 -0.02582 -0.02553 -0.01277 0.01511 0.06294 0.09813 0.09504 0.09568 0.13435 0.20722 0.27897 0. 33497 0.37442 0.40861 mean 0.00812 -0.04060 0.15778 Year 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 Industry The Year whole manufacturing 1963 0.08492 1964 0.13445 1965 0.12134 1966 0.12523 1967 0.10519 1968 0.10798 1969 0.12306 1970 0.17909 1971 0.27182 1972 0.29487 1973 0.22334 1974 0.10988 1975 0.02799 1976 -0.06102 1977 -0.11849 1978 -0.16032 1979 -0.19949 1980 -0.21949 1981 -0.20048 1982 -0.12060 1983 0.30399 mean 0.05396 Table II-10. Total Factor Productivity under Constant Return to Scale by FIML Industry l.Food, 2.Textiles 3.Lumber Year beverages & & wood & tobacco leather products 1963 0.02884 -0.07969 0.03795 1964 0.03006 -0.06977 0.03525 1965 0.03098 -0.06026 0.03303 1966 0.03188 -0.05241 0.03083 1967 0.03294 -0.04112 0.02879 1968 0.03406 -0.03140 0.02665 1969 0.03509 -0.02163 0.02435 1970 0.03605 -0.01160 0.02159 1971 0.03729 -0.00165 0.01918 1972 0.03855 0.00866 0.01637 1973 0.03966 0.01862 0.01426 1974 0.04070 0.02863 0.01199 1975 0.04182 0.03845 0.00990 1976 0.04313 0.04818 0.00748 1977 0.04446 0.05795 0.00512 1978 0.04564 0.06768 0.00299 1979 0.04649 0.07760 0.00097 1980 0.04718 0.08750 -0.00107 1981 0.04802 0.09733 -0.00337 1982 0.04912 0.10705 -0.00582 1983 0.04993 0.11522 -0.00809 mean 0.03961 0.01825 0.01468 Industry 4.Paper, 5.Chemicals 6.Nonmetalic Year printing & & chemical mineral publishing products products 1963 0.00235 0.06469 0.03464 1964 0.00328 0.05897 0.03417 1965 0.00421 0.05391 0.03335 1966 0.00507 0.04850 0.03173 1967 0.00600 0.04289 0.02926 1968 0.00698 0.03740 0.02795 1969 0.00820 0.03126 0.02719 1970 0.00953 0.02516 0.02738 1971 0.01082 0.01918 0.02691 1972 0.01221 0.01370 0.02709 1973 0.01339 0.00713 0.02659 1974 0.01451 0.00532 0.02535 1975 0.01560 -0.00160 0.02390 1976 0.01693 -0.00787 0.02313 1977 0.01831 -0.01396 0.02222 1978 0.01966 -0.02042 0.02073 1979 0.02086 -0.02718 0.01863 1980 0.02215 -0.03430 0.01664 1981 0.02344 -0.04126 0.01489 1982 0.02484 -0.04811 0.01394 1983 0.02612 -0.05402 0.01316 mean 0.01355 0.00759 0.02471 |

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PAGE 1 THE MEASUREMENT OF PRODUCTIVITY CHANGE AND SOURCES OF GROWTH: THE CASE OF KOREA By CHIANG KIM A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULLFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1991 PAGE 2 ACKNOWLEDGEMENTS This thesis could not have been completed without an unusual amount of excellent advice by the committee. I am particularly grateful to the surpervisor G.S. Maddala, who provided valuable and detailed comments. I also acknowledge the helpful comments of Dr. Leonard Cheng, Dr. Lawrence Kenny, and Dr. John Shonkwiler. I am thankful too to Dr. Yasushi Toda and Dr. Mark Rush. Finally, I thank my wife Misook for her patience and encouragement. PAGE 3 TABLE OF CONTENTS ACKNOWLEDGEMENTS ii ABSTRACT V CHAPTERS 1 INTRODUCTION 1 Research Background 1 Purposes of the Study 3 2 THE MEASUREMENT OF PRODUCTIVITY CHANGE 6 The Model : the Producer s Behavior 6 Value Shares and Rate of Productivity Growth 6 Share Elasticities and Substitution 8 Biases of Productivity Growth and Pattern of Production 11 Acceleration of Productivity Growth 13 Restrictions Based on Producer Theory 14 Hicks neutrality 14 Constant return to scale 15 Concavity of production function 15 Existence of value-added function 19 Econometric Models: Translog Production Function 23 Estimation and Hypothesis Testing: Full Information Maximum Likelihood (FIML) and Seemingly Unrelated Regression (SUR) 27 Data Sources 29 Empirical Results 30 3 THE MEASUREMENT OF SOURCES OF GROWTH 55 The Model: Input-output Analysis 55 Decomposition of Output Growth Based on Absolute Growth 57 Decomposition of Output Growth Based on Proportional Growth 60 Difference Between Two Methods: A Graphic Representation 61 PAGE 4 Input-output Data Base 63 Estimation of Sources of Growth: SAS/IML 64 Interpretation of the Results 66 4 SUMMARY AND CONCLUSION 77 APPENDIX 80 REFERENCES 137 PAGE 5 Abstract of Dissertation Presented to Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THE MEASUREMENT OF PRODUCTIVITY CHANGE AND SOURCES OF GROWTH: THE CASE OF KOREA By Chiang Nam Kim December 1991 Chairperson: Professor G.S. Maddala Major Department: Economics In this dissertation I measure and analyze the productivity change on the supply-side and the sources of growth on the demand-side in the economy of South Korea. On the supply-side I measure total factor productivity (TFP) of industrial sectors by estimating their translog production functions and value shares simultaneously. In addition to measuring TFP, useful indexes for share elasticities, biases of productivity growth and acceleration of productivity growth are obtained. Share elasticities are used for checking the concavity of the production function, and biases of productivity growth for determining the pattern of production. On the demand-side, using growth accounting through material balance equations, the increase of output is decomposed into the effect of deviations in domestic demand, v PAGE 6 exports, changes in the import structure of intermediate and final goods, and the effect of changes in the matrix of inputoutput coefficients. The demand-side analysis will yield estimates of the contribution of import substitution and export promotion to the economic growth. The results indicate that domestic demand and export expansion were the two major factors contributing to growth and structural change. However, import substitution and technological change were quite substantial and much more important than export expansion in the recession period (19791981) In contrast, our results on total factor productivity imply that technical progress played a relatively small role in the industrialization process. PAGE 7 CHAPTER 1 INTRODUCTION Research Background Different countries have followed different growth paths, determined partly by initial conditions and resource endowments, and partly by government policies. Some have emphasized import-substitution strategies, others exportpromotion strategies. The strategy of encouraging domestic industry by limiting imports of manufactured goods is known as the strategy of import substitution. Another way to promote manufacturing is called an export promotion strategy. 1 It is known that Korea accomplished rapid growth by export promotion policies during 1962-1978. 2 After having achieved success through export promotion strategies for nearly two decades, Korea encountered severe economic difficulties in 1979-1982, as indicated in Table 1-1. What were the cause of this sudden economic recession? It may be 1 Krugman, P. R. and M. Obsfeld (1988), pp 229-238. Corbo, V., A. 0. Krueger, and F. Ossa (1985), Ch. 4. Kim, K. S., and M. Roemer (1979), Ch 5. Frank, C. R., K. S. Kim, and L. E. Westphal (1975), Ch. 6, Westphal, L. E., (1978), pp 347-382. Krueger, A. 0., H. B. Lary, T. Monson, and N. Akrasanee (1981) pp 341-392. PAGE 8 2 argued that the second oil shock and the subsequent recession in the advanced countries were the major causes. In view of the uninterrupted rapid growth observed in the other Asian Countries of Table 1-1, however, domestic factors were also responsible Table 1-1. GDP Growth Rate at Constant Prices. Period Korea Japan ThailSingIndustrial Developing land apore countries countries 1975 PAGE 9 3 characterize the pattern of production on the supply-side? What has been the role of changes in the input-output coefficients? This thesis will attempt to answer these questions through input-output analysis. Purposes of the Study In this study I measure and analyze productivity change and the sources of growth in South Korea's manufacturing sector. Specifically I follow two complementary approaches. One is to measure total factor productivity in manufacturing and test restrictions usually imposed on production functions. The other is to measure the contributions of the various components of intermediate and final demand to growth and structural change. In order to retain flexibility in production functions for the manufacturing sectors in Korea, I adopt the transcendental logarithmic (translog) production functions for the first time rather than more restrictive ones such as CobbDouglas or CES production function so that I can test assumptions such as constant return to scale, Hicks neutrality, the concavity of production function, and the existence of value-added. Total factor productivity for the same manufacturing sectors in Korea has been measured by growth accounting which PAGE 10 4 is based on the assumption of Hicks neutrality. 3 Later on we will compare our measurement of TFP to what others have measured for the same sectors in Korean manufacturing. The estimation of total factor productivity (TFP) will be based on gross output, capital, labor, intermediate input and time. In addition to measuring TFP and testing the restrictions which are imposed by the theory of production, we can get some useful indexes for share elasticities, biases of productivity growth and acceleration of productivity growth in estimating the translog production function. On the demandside, the contributions of the various components of intermediate and final demand to the growth and structural change can be estimated. Changes in the composition of demand are useful in providing an understanding of sectoral growth and structural change. Besides, an analysis of demand is needed to answer the question of the relative role of import substition and export promotion in economic growth. Manufacturing in South Korea is disaggregated according to the classification in the country's input-output table. We first constructed the input and output data for production function by aggregating detailed industrial data into broadly defined industries in accordance with the input-output table. The productivity analysis can be done at both the aggregate and disaggregate levels. The supply-side analysis indicates that our measurement Kim, K. S., and S. Y. Park (1989). PAGE 11 5 of total factor productivity is different from what others have measured. In the demand-side analysis, the relative contribution of export expansion to growth and structural change has changed according to different method of measurement PAGE 12 CHAPTER 2 THE MEASUREMENT OF PRODUCTIVITY CHANGE The Model: the Producer's Behavior The starting point for our model is a production function for each industrial sector in the manufacturing. Let the production functions for each of the n industrial sectors be given by X i =F i (M i ,K i ,L i ,T) (i=l,2, . ,n) (1) where X, is the output, M 1 K\ h it and T are the intermediate, capital, and labor inputs and time. Firms are assumed to maximize profits under perfect competition. Value Shares and Rate of Productivity Growth The value shares of intermediate, capital, and labor inputs, say V M V K X V L L in the value of output can be defined by V>^(2) q i X i V*-*^ (3) PAGE 13 Vl = ^- (1=1,2, .. ,n) (4) where q 1 p M p k l and Pl 1 denote the prices of outputs and intermediate, capital, and labor inputs, respectively. Profit maximization in the market of perfect competition implies the equality between the share of each input in the value of output and the elasticity of output with respect to that input: i dlnX. : v = aI^ ,M "^' L r) (5) i dlnX: .,. K dlnK i 2 2 x i dln.X v V^ = ^-Â—{M 1 ,K 1 ,L 1 ,T) (1=1,2, n) (7) olnL, These conditions can be obtained from the following procedure. Profits, II 1 are defined in value terms as W = q 1 X 1 -p^M 1 -p^K 1 -ptL i (i=l,2, . ,n) (8) Assuming that producers wish to maximize profits, II 1 ", will be defined as: W*=m&x[W-\{X i -F i (M i ,K i ,L i> T)}} (i = l,2, . ,n) (9) We can differentiate equation (9) with respect to X, X lt p M \ p K L p L ; and T to derive the conditions for profit maximization in perfect competition: PAGE 14 dip* (a) PAGE 15 9 by share elasticities. 2 Share elasticities are defined as the derivatives of the value shares with respect to the logarithms of intermediate, capital, and labor inputs: U ^-^ iM K L T) (11) U ^-Â§^. {M iK i' L i> T) > (12) ^ = a!nf: (M ^'^' r) (13) ^ = aInV^'^' Li r) (14) UL-^iM^K^L^T), (15) U[ L = V -^Â—AM 1 ,K i ,L il T) l (i=l,2,...,n). (16) alnL J If we set the elasticity of output with respect to each input equal to the corresponding value share, then we can get the share elasticities with respect to each input by differentiating the production function { F 1 } logarithmically twice with respect to the logarithms of intermediate, capital, and labor inputs: 2 The concept of share elasticities was introduced first by Christenson, Jorgenson, and Lau (1971, -1973) and P.A.Samuelson(1973) PAGE 16 10 Um= Â—(M^K^L^T) (17) dlnMi uL=^ =r^ (M,, K,, L,,T) (18) MK dlnM i dlnK 1 J l i a 2 ln,Y, t Â„ n u ^ di^iW Mi Ki,Li T) (19) UL= J~ UX : (M^K^L^T) (20) olnK* u ^ dZ^ Ll {M K L T) (2i) UL= ^ (M^K^L^T) (i=l,2, .. ,n) (22) dlnLJ Interchanging the order of differentiation, we can observe that the share elasticities with respect to each input are symmetric. a 2 lnX_j a 2 lnX i dlnM.dlnK, dlnK.dlnM, UL= -, .. V... = ~ ,,'... =UL (23) 5 2 lnX i a^in^ 3lnM,dlnL," dlnL,dlnM, Uml= ^ ... ^ 1 = ^.. r ^L. = u l>. ( 24 ) tflnXi d 2 lx\X i dlnX.dlnL. dlnl^dlni^ Uk= Â„_.,;;:. = Â„.., ^ =^A (25) These relationships hold for all values of intermediate, capital, and labor inputs, and time. PAGE 17 11 We can analyze the share elasticities to derive implications of patterns of substitution for the relative distribution of the value of output among the three inputs. If a share elasticity is positive, the value share increases with an increase in the quantity of the corresponding input. If a share elasticity is negative, the value share decreases with the increase of the corresponding input. Finally, if a share elasticity is zero, the value share is independent of the quantity Biases of productivity growth and Pattern of Production The concept of Hicks neutrality leads to a definition of biases in terms of factor shares. 3 Hicks' definition is as follows: Technical change is said to be neutral, labor-saving, or labor-using depending on whether, at a constant capitallabor ratio, the marginal rate of substitution stays constant, increases, or decreases. If the marginal rate of substitution is rising, then the labor share is declining. This leads immediately to the following definition of biases. The biases of productivity growth can be defined as derivatives of the value shares with respect to time: U^^iM^K^L^T) (26) Binswanger (1974) PAGE 18 12 U^^iM^K^L^T) (27) dvÂ£ Viar-gfW i ,K i .L il 'n (i=l 2 . n) (28) Alternatively, the biases of productivity growth can be defined as derivatives of the rate of productivity growth with respect to the logarithms of intermediate, capital, and labor inputs : u *^ink: lMi Ki Li,T) (29) u Â™ = -dIEK'. {Mi Kl Ll,T) (30) u TL=-d^r. {M i' K i' L i' T) (31) If we set the elasticity of output with respect to each input equal to the corresponding value share and interchange the order of differentiation, we find that the two definitions are equivalent: i <3~ln.\\. a^lnA. i /oo ^ [/'= Â— J_ = __ Â—=UL (33) KT dlnK.dr dTdlnK, TK PAGE 19 13 i d z lnA', d z lnX i i ,. N Ptr 85 -^ t-'-t-^ Â— -=^rÂ£ (1=1,2, ... ,n (34) LT BlnL.dT dTdlnL, The implications for the relative distribution of the value of output among the three inputs can be provided by the biases of productivity growth. If a bias is positive, the corresponding value share increases with time. If a bias is negative, the value share decreases with time. Lastly, the value share is independent of time if a bias is zero. Acceleration of Productivity Growth Finally, the acceleration of productivity growth can be defined as the derivative of the rate of productivity growth with respect to time, since the logarithmic derivative of the production function is equal to the rate of productivity growth: t d z lnA\ dvi Ut T = =-^(M i ,K i ,L i ,T) (1=1,2, ... ,n) (35) PitoT The biases and the acceleration of productivity growth are independent of the changes of the inputs and time because they are the second-order logarithmic derivatives of the production function with respect to the logarithms of the inputs and time. Jorgenson, Gollop, and Fraumeni (1987) PAGE 20 14 Restrictions based on Producer Theory We can derive restrictions on share elasticities and biases of productivity growth implied by the producer's theory. Hicks neutrality First we derive restrictions which are implied by Hicks neutrality of productivity growth. The production function is Hicks neutral if and only if T is separable from intermediate, capital, and labor inputs, that is, X i =F i (G i (M 1 ,K i ,L i ) ,T) (i = l,2, . ,n) (36) From this eguation we can derive the restrictions on the biases of productivity growth which are imposed by Hicks neutrality : Umt=Uxt=L!,:t=0 (i = l,2, . ,n) (37) Under Hicks neutrality the rate of productivity growth depends only on the time term. Vt=At+Bt T T (i=l,2, . n) (38) I will test to ascertain whether production functions in Korean manufacturing can be characterized as having Hicks PAGE 21 15 neutral technological change. Constant returns to scale Next we express the assumption for constant return to scale in terms of share elasticities and biases of productivity growth. First, the sum of the share elasticities for a given value share, defined by the corresponding second-order logarithmic derivatives, is egual to zero under constant return to scale since all the value shares of the production function add up to unity under constant returns to scale. Um+uÂ£ K +uÂ£ L =0 (39) UJh+U^uL^O (40) uL + ut K +Ul L = Q (i=l,2, . .,n) (41) In addition, the sum of the biases of productivity growth is equal to zero: UJir+UJcr+ulrO ( i=l 2 . n) (42) Concavity of production function We can derive the restrictions for the concavity of the production function in terms of share elasticities. The share elasticities can be expressed in terms of the second-order partial derivatives of the production { F 1 } with PAGE 22 16 respect to the inputs: TJ i d 2 lnF i M i K i d 2 F i ,.i,,i .... U ^ di^dinKr ^-dM&rrw* (44) i d 2 lnF i M,Lj d 2 F i i i u ^ a inM^nLr ^^kr v vt <45) TT i 5 2 lnF 2 K i d 2 F 1 ,.i,..i , ,.,. ^k-jc= r = Â— 7 3"-Vr(Vir-l) ( 46 ) ain/c F 1 a^ 6 2 lnF i K 1 L 1 d 2 F ] -VkV[ (47) Ui L =^K--^^4-Vi(vi-l) (48) ain^ainLj F i dK i dL i d 2 lnF 1 L \ d 2 F dlnLJ F 1 dLf where i_ ainF : M. dF 1 M dlnM f 1 dM i v i_ dlnF' Ki dF 1 K dlnK. f 1 dK i Vi = ^=h:^ (i=l,2,...n) ainLj f 1 5L i To derive the restrictions for the concavity of production functions, we construct the matrix of share elasticities U 5 The relationship between share elasticities and the condition of concavity is represented in Jorgenson (1986) The conditions for concavity in terms of the Cholesky factorization is represented in Lau ( 1978 ; 1979) PAGE 23 17 U= "mm Umk U ml UL U* K (ji L uL uiL ui L (i=i,2, ...,n) (49) And we can express the matrix of share elasticities U 1 by the Hessian matrix of second-order partial derivatives of the production functions H, in the form U 1 = -^N 1 H 1 N 1 -v 1 v 1 +V 1 (50) where H 2 = N 1 -V a = f mm f mk f ml F KM F KK F KL f lm f lk f ll M i PAGE 24 18 The Hessian matrix H can be denoted in the form 1 F 1 N 1 H 1 N 2 =U 1 + v 1 v 2 -V 1 (1 = 1,2 ,n) (51) The Hessian matrix H should be negative semidefinite under the concavity of the production function. Therefore if the production function is concave, then the matrix { U 1 + v^ 1 V 1 ) is negative semidefinite. Sufficient conditions for the matrix { U 1 + v'v 1 V 1 } to be negative semidefinite are that the matrices of share elasticities U are negative semidefinite since the matrices { v 1 v 1 V 1 } are negative semidefinite for all nonnegative value shares which are greater than zero and less than one. To check the concavity of the production functions in terms of the matrices { U 1 } we can transform the matrix { U 1 } in terms of its Cholesky factorization U 1 =Q 1 D 1 Q 1 (52) where Q 1 1 PAGE 25 19 matrix D are nonpositive the matrix U is negative semidef inite These conditions must holds if production functions are concave. Existence of value-added function: 6 Value-added refers to the addition to the value of product at a particular stage of production. All intermediate inputs are netted out of the calculation. Some researchers have used value-added indices to measure total factor productivity across countries. 7 In order to measure TFP in terms of value-added, a value-added function relating net output to the inputs of capital and labor must exist. For this to be true, capital, labor, and time must be separable from intermediate inputs. If this separability assumption is testable and rejected, we would rather abandon the calculation of value-added TFP. A value-added function, where three inputs, capital, labor, and time, produce value-added, exists if and only if the production function is separable in capital, labor inputs, and time from intermediate input. There are two alternative sets of restrictions that are jointly necessary and sufficient for the existence of a value6 Jorgenson and Lau (1975) Blackorby, Primont, and Russel (1977) and Denny and Fuss (1977) 7 Jorgenson and Nishimuzu (1978), and Christensen, Cummings, and Jorgenson (1980). PAGE 26 20 added function. The first set of jointly necessary and sufficient conditions for the existence of a value-added function can be derived by the following procedure. 8 The production function for each sector can be written in the following form, if the production function is separable in Ki, L x and T from M, : K i *F i (G(K i ,L 1 T) ,M ) ( i=l 2 . n) (53) Under this restriction the value shares of capital and labor inputs and the rate of productivity growth are given by dlnZ 1 dlnF 1 dlnG 1 ,^ AS "-= : Â— ^Â„ v (54) (55) (i=l, 2, . n) (56) ainTj dlnG 1 dlriTi K ' ' K Next if we differentiate logarithmically the above production function twice, first with respect to the logarithm of intermediate input and then with respect to the logarithms of capital, labor, and time, we obtain the second-order logarithmic derivatives as functions of these inputs and time. We express these second-order logarithmic derivatives as i dlnZ 1 PAGE 27 21 follows i d-lnX i d 2 lnX i Qq i Umk= dlnM : dlnK 1 = dlnM 1 dG~dlEk~ i =rlVK (57) ,_ d 2 lnX z d 2 lnX 1 dG ML dlnM^lnL, dlnM.dG dlnL, L K t B 2 lnX i d 2 lnX i Qq i Um= dinM,dr = dImM^r =r Vt (59) where a 2 inFdlnM.-dlnGairiFdlnG J (i=l,2, . ,n) The necessary condition for the existence of a valueadded function is that there is a common factor of proportionality between the two share elasticities and the bias of productivity growth and the corresponding value shares and the rate of productivity growth. The sufficient condition requires that the common factor r 1 is equal to zero. The second set of necessary and sufficient conditions for the existence of value-added functions comes from weak separability, since weak separability and the existence of a PAGE 28 22 consistence aggregate index are equivalent restrictions. 9 The production function { F 1 } is said to be weakly separable if and only if the marginal rate of substitution (MRS) between any two inputs from the input subset { K lf L it T } is independent of the quantities of the intermediate input { Mi }. dF 1 d 2 F : dK i PAGE 29 vi uL 23 (i=l,2, . ,n) (65) Econometric Models: Transloq Production function We can specify the production function as the exponential function of second-order Taylor series. 10 X i =exp Uo 1 +A^lnM i +AKlnK 1 +AilnL+ATT + jB ^,(lnM i ) 2 +B^ K lnM i lnK i +B^ L lnM i lnL i +B^ r lnM 1 T + Bi K (lxiK i ) 2 +Bi L lnK i lnL i +BÂ£ T lnK i T (i=l,2, . ,n) (66) + |B/ L (lnL I ) 2 + ^ T lnL i r The value shares of intermediate, capital, and labor inputs are given by the derivatives of the logarithm of the production function with respect to the logarithms of intermediate, capital, and labor inputs. V* =A^ +B^ M lnM i +B^ K lnK i +B^ L lnL i +B^ T T ( 67 ) VÂ£ -Ak ^By K ltiM+Bl CK lnK i +B^ L lnL i +B^ T T ( 68 ) vi=AÂ£+BÂ£ L lnM i +Bl K lnK i +BÂ£ L lnL i +Bl; T T (i=l 2 . n) (69) The rates of productivity growth are given by the derivatives of logarithm of production function with respect 10 Christenson, Jorgenson, and Lau ( 1971 ; 1973 ) PAGE 30 24 to time: Vt =AT+B^ T lnM i +BÂ£ T LMC i +BÂ£ r lnL i +B^T (i=l,2,...,n). (70) From this specific form of the production function we can derive the restrictions on the parameters imposed by production theory. First, if we set the inputs equal to unity and time equal to zero, we obtain necessary conditions for the production functions to be increasing: A^>0 A*>0 Ai>0 (i=l,2,...,n) From the translog production functions we can derive the restrictions for Hicks neutrality, that is, each input has no bias in technological change: B^=B^BÂ£ T =0 (i=l,2, n) (71) Under Hicks neutrality the rate of productivity growth depends only on the time term. Vt=At+B^tT (i=l, 2 . ,n) (72) The translog production function for an industrial sector is constant return to scale if and only if the parameters satisfy the conditions: PAGE 31 25 A2+AÂ£+At=l (73) B^B^B^O (74) B&B&B^O (75) BÂ£ L + B^B[ L = (76) B^+B^Bi T =0 (i=l,2,...,n) (77) We obtain the first set of necessary conditions for the existence of value-added functions from equation (57), (58), and (59) Evaluating these equations where the three inputs are equal to unity and time is equal to zero, we obtain the following restrictions: B&rpW (78) Btar^At (79) B^P^t (80) These equations imply that the value shares of capital and labor inputs and the rate of productivity growth are proportional to the corresponding elasticities of the share of capital and labor with respect to intermediate input and the bias of productivity growth with respect to intermediate input The sufficient conditions require PAGE 32 26 The second set of restrictions for the existence of value-added functions result from the fact that output is a linear logarithmic function of intermediate input and valueadded : JTj-explAo+AiftnAfj+AylnVj] (i=l, 2 . ,n) (81) where + Â— Br K ( lnK i ) 2 +B^ L lnK i lnL i +B^ T lnK i T The value shares of capital, and labor and the rate of productivity growth can be expressed as i i aim/, v 'A 'jnst L (82) i i aim/, Vt'Ai^ (83) i i ainl/,Vr=^vÂ— -^ (i = l,2, . .,n) (84) If these equations are substituted into equations which are the conditions for weak separability, a second set of restriction are obtained: A I bL Â— =Â— (85) Ar 1 Bi, PAGE 33 27 Ai bL Â— -.= Â— (86) A 1 B 1 -7=-y (i=l,2, n) (87) At Evrr Estimation and Hypothesis testing: Full Information Maximum Li kelihood (FIML) and Seemingly Unrelated Regression Since our model of production is a system of equations with cross equation parameter restrictions, it is likely that the disturbances of the individual equations are correlated. If so, the technique of joint estimation gives more efficient estimates than separate regression of each equation. Jorgenson, Gollop, and Fraumeni estimated the unknown parameters of the translog production function for the industrial sectors in American economy 11 They formulated the econometric model by combining the first two equations for the value shares with the equations for the rate of productivity growth. They estimated the parameters of the equations for the remaining value shares from estimates of the parameters of the first two value shares, using the restrictions on these parameters given by the assumption of constant returns to scale Jorgenson, Gollop, and Fraumeni (1987) PAGE 34 28 With their method we cannot estimate the parameters (A/jBt/) in the translog production. In addition to this weakness, we have to assume constant returns to scale in production. Based on these facts, I estimate the system of equations, logX, V M V k with the method of full information maximum likelihood (FIML) and seemingly unrelated regression (SUR) The FIML and SUR estimators have identical efficiencies asymptotically for large sample properties. The SUR takes account of the fact that the structural equations may be correlated in cross equation disturbance term and makes use of the covariance matrix of the disturbances among the equations. The asymptotic covariance matrix of the SUR estimator is identical with that of the FIML estimator. In terms of computational ease, the SUR method is simpler than the FIML method, because the latter results in nonlinear equations in unknown parameters that must be solved. With FIML, however, we can use the likelihood ratio test for testing hypotheses. Regardless of the large sample properties of two estimators, we obtain smaller standard errors with the SUR method than the FIML method for the data of Korean manufacturing. But the TSP software package does not print some test statistics for the SUR method. Therefore we used both methods to estimate the system of eguations model and compare the empirical results. First we started our estimation from the generalized PAGE 35 29 model and move to increasingly more restricted ones to test the restrictions which are imposed by the production theory. In our model the rates of productivity growth, V T ,can not be observable. Therefore, we computed the rates of productivity growth (TFP) by using the estimated coefficients. One of value shares in estimation is ommitted in order to avoid perfect multicol linearity. Data Sources The data for the Korean manufacturing sector were compiled by KIET (Korea Institute for Economics & Technology) They estimate the annual time series data of output as well as the intermediate, capital, and labor inputs for 39 industries of the manufacturing sector from 1963 to 1983. These data are based on the Report on Mining and Manufacturing Survey and Input-output tables. We use the data from 1963 to 1983 because these are the only years for which data are available. First we aggregated data for 39 industries to 9 more broadly defined industries in accordance with the classification of the input-output tables. These 9 industries are 1 Food beverages & tobacco, 2. Textiles & leather, 3. Lumber & wood products, 4. Paper, printing & publishing, 5. Chemicals & chemical products, 6 Nonmetallic mineral products, 7 Primary metal manufacturing, 8. Metal products & machinery, and 9 .Miscellaneous manufacturing in the PAGE 36 30 manucturing sector. We then aggregated these data for the aggregate analysis of the whole manufacturing sector. We will summarize the characteristics of the data which are provided by KIET. The output is calculated by valuing all outputs at the wholesale prices. The capital stock includes the producers' and consumers' durable equipment, residential and nonresidential structures, inventories and land. Labor inputs are obtained by multiplying the yearly average number of workers by the quality index of labor. The output, capital input, and intermediate input which are calculated by using current prices are converted to a constant price. Empirical Results I have constructed an econometric model from a production function and value shares for each industries. First I estimated the parameters of the translog production function with and without restrictions by alternative methods of estimation. I then calculated the rates of productivity growth, V T by using the estimated parameters. First we undertake the likelihood ratio test to test constant returns to scale, Hicks neutrality in technical change and the existence of value added function. Next we test Hicks neutrality in technical change and the existence of value-added function maintaining the assumption of constant returns to scale since we obtain more significant results from PAGE 37 31 Table II-l. Critical values, chi-squared degrees level of significance of freedom 0.100 0.050 0.025 0.010 0.005 0.001 1 2.71 3.84 6.36 6.63 7.88 10.83 2 4.60 6.00 8.90 9.22 10.60 13.82 3 6.25 7.81 9.35 11.35 12.84 15.67 5 9.25 11.05 14.72 15.10 16.75 20.50 the model with the assumption of constant returns to scale than the model without the assumption of constant returns to scale. The likelihood ratio test statistics for each tests are represented at Table II-2 and II-3. For the test statistic for Hicks neutrality of technical change, we employ the critical value 11.35 for chisquared with three degrees of freedom at a level of significance of 0.01. At this level of significance, we reject Hicks neutrality for eight industries in Table II-2. We cannot reject Hicks neutrality for miscellaneous manufacturing and the total manufacturing sector. Under Hicks neutrality, productivity growth does not favor any factor. Therefore, the rejection of Hicks neutrality implies that technological change is biased toward some factors. We next test for constant returns to scale. The constant returns to scale restrictions require five degrees of freedom, so we employ the critical value 15.10 for chis-quared with five degrees of freedom at a level of significance of 0.01. PAGE 38 32 Table II-2. Test statistics for Constant returns to scale, Hisks neutrality, and the Existence of value-added Hypothesis Industry Hicks Constant ValueValueneutrality returns added I added II to scale l.Food, beverages 25.4099 60.1144 43.2148 228.3696 & tobacco 2 .Textiles & 47.3477 53.9048 33.3668 137.2213 leather 3 Lumber & wood 23.2858 33.7527 -31.5031 81.4153 products 4 Paper, printing & 48.9642 54.8662 33.5702 128.6722 publ ishing 5 Chemicals & chemical 15.9575 24.4916 115.7244 334.9333 products 6 .Nonmetall ic mineral 14.8515 12.3842 85.2620 -4.6601 products 7 Primary metal 35.9080 34.5589 -24.2119 141.2689 manufacturing 8. Metal products & 39.4010 15.5197 95.0416 245.9385 machinery 9 .Miscellane -ous 8.6594 32.7385 128.3029 39.7803 manufacturing The total 5.5851 15.6301 73.5605 190.5400 manufacturing PAGE 39 33 Table II-3. Test statistics for Hicks neutrality and the Existence of value-added maintaining the assumption of Constant returns to scale Hypothesis Industry Hicks ValueValueneutrality added I added II l.Food, beverages 16.69647 14.01059 10.13010 & tobacco 2 .Textiles & 8.82013 34.96957 11.22046 leather 3 Lumber & wood 0.76572 0.87402 0.26984 products 4 Paper printing & 27.24649 37.04483 3.61691 publishing 5 Chemicals & chemical 24.76041 40.14688 12.05225 products 6 .Nonmetal ic mineral 39.66202 16.77090 1.15286 products 7 Primary metal 36.20880 35.96268 34.94168 manufacturing 8. Metal products & 48.99066 47.19305 30.75528 machinery 9 .Miscellane -ous 13.89905 10.17068 4.16483 manufacturing The total 0.08569 11.56906 8.70789 manufacturing PAGE 40 34 Constant return to scale can be rejected at this level of significance for all industries except Nonmetallic mineral products in Table II-2. Next we test for the existence of a value-added functions. For the test for the existence of a value-added functions, the first set of restrictions require three degrees of freedom, and the second set of restrictions require two degrees of freedom. The critical value 11.35 for the first set of restrictions and 9.22 for the second set of restrictions are employed for the chi-squared at a level of significance of 0.01. The two sets of restrictions for the existence of valueadded functions can be rejected at a level of significance of 0.01 for each industry and the total manufacturing sector in Table II-2. Here we obtain negative statistics in the case that the convergence cannot be achieved. Now we test Hicks neutrality and the existence of valueadded function maintaining the assumption of constant returns to scale. Test statistics for three hypotheses are represented in Table II-3. The restrictions to Hicks neutrality require two degrees of freedom, so we employ the critical 9.22 for chi squared with two degrees of freedom at a level of significance of 0.01. Hicks neutrality is not rejected for two industries: Textiles & leather and Lumber & wood products. Hicks neutrality is not rejected for the total manucturing either. The first set of restrictions to the existence of a value-added function maintaining the assumption of constant PAGE 41 35 returns to scale requires two degrees of freedom, so the critical value 9.22 is employed for chi-squared with two degrees of freedom at a level of significance of 0.01. The hypothesis that the production function is separable in K LI h L and T from M i cannot be rejected for one industry: Lumber & wood products in Table II-3. For the second set of restrictions to the existence of value-added function, we employ the critical value 6.63 for chi-squared with one degree of freedom at a level of significance of 0.01. We cannot reject the hypothesis that output is a linear logarithmic function of intermediate input and value-added at a level of significance of 0.01 for four industries: Lumber & wood products, Paper, printing & publishing, Nonmetallic mineral products, and Miscellaneous manufacturing in Table II-3. The rejection of the hypothesis that a value-added function exists implies that we would rather abandon measuring TFP from valueadded We evaluate estimates in the same model which are estimated by different methods of estimation ( FIML and SUR ) These estimates are presented in Table II-4 and Tables 11-14 to 11-19, which are given in the appendix. We obtain smaller standard error with the SUR method than with the FIML method. In addition to significance, convergence is achieved more easily by SUR than by FIML. For large sample properties, however, we cannot conclude that SUR provides more efficient estimates than FIML, and convergence is achieved more easily PAGE 42 36 by SUR than by FIML. Let us compare the estimates under different assumptions by SUR. The model under constant return to scale provides more efficient estimates than the one under the other assumptions: Hicks neutrality and existence of value-added function. So far we have evaluated and compared the estimates based on econometric properties. Now we evaluate estimates based on the production theory in order to see which model describes the Korean economy best and in order to measure TFP correctly. If we check the necessary conditions for monotonicity by examining estimated parameters { A M X A K X Al 1 } in Table II-4 and Table 11-15 to 11-20 in the appendix, we find that models under constant return to scale which are estimated by SUR satisfy these conditions since the estimated parameters { Am 1 A K A L are all significantly positive in Table II-4. To check the concavity of the production functions, the diagonal matrix in the Cholesky factorization of the matrix of share elasticities is illustrated in Table II-8 given in appendix. We check the condition of the concavity for the sector's production function under the different restrictions. By the method of FIML, the concavity of the production function can be accepted for two industries in the generalized model, while this condition can be guaranteed for five industries in the model restricted to constant returns to scale. Similarly by the method of SUR the condition of concavity of production function can be guaranteed for four PAGE 43 37 industries in the model restricted by constant returns to scale. For Nonmetalic mineral products and Metal products & machinery, constant returns to scale can be guaranted by both methods. Constant returns to scale is a special case of production function, given convex isoquants. Therefore the condition for the concavity of production function is well guaranteed by the assumption of constant returns to scale. Based on statistical significance of estimates and production theory, we obtain the best results from the model restricted to constant returns to scale by the estimation method of SUR. Now we interpret the parameter estimates which are represented in Table II-4. The estimated share elasticities { E^, 1 B^ 1 B^ 1 B^ 1 b ki/ / b il provide the implications of patterns of substitution for the relative distribution of the value of output among intermediate, capital, and labor inputs. If share elasticities are positive, then the value shares increase with an increase of the corresponding input; if share elasticities are negative, the value shares decrease with an increase of the input; if share elasticities are equal to zero, value shares are independent of the change of input. Under the necessary and sufficient conditions for concavity of the production function for each sector, the estimated share elasticities of each input with respect to the quantity of the input itself ( B m B KK B L1 / } are nonpositive. This implies that the share of each input is not PAGE 44 Table II-4. Parameter Estimates under Constant Return to Scale by SUR 38 PAGE 45 39 PAGE 46 Industry 40 7 Primary 8. Metal 9 .Miscellaneous Parameter metal products & manufacturing manufacturing machinery A x PAGE 47 41 Parameter Industry The total manucturing A x A 1 A\ A'm B tw B ML B MT B'nc BV Bl KT B\ L B\t -0 -12 (24 (15 (87 (6 0. (5 -0. (-1 -0 (-7 -0. ("3 -0. (-0 0. (3 -0. (-0 0. (3 0. (3 -0. (-3 3607 3520 1930 .7250 1086 1540 6983 .9140 0407 7934 0662 7552 0144 1453 0517 4 07 7 0020 0507 0063 4107 0208 1875 0006 9923 0309 .2534 0027 9595 0020 9515 PAGE 48 42 increasing with the increase of the input itself. The estimated elasticities of the share of intermediate input with respect to the quantity of the input itself { B^ 1 } are significantly negative for Chemicals & chemical products and Metal products & machinery. The estimated elasticities of the share of capital input with respect to the input itself { EW ) are significantly negative for Nonmetalic mineral products and Metal products & machinery. The estimated elasticities of the share of capital input with respect to the input itself j B^ 1 ) are significantly negative for Nonmetalic mineral products, Primary metal manufacturing, Metal products & machinery, and Miscellaneous manufacturing. The estimated elasticities of the share of labor with respect to the quantity of capital { B KL ; } are significantly positive tor Nonmetalic mineral products, Primary metal manufacturing, Metal products & machinery, and The total manufacturing. For these industries, the share of labor does not decrease with an increase in the quantity of capital, holding quantities of labor and intermediate inputs and time constant. Of course, this parameter can also be interpreted as the elasticities of the share of capital with respect to the quantity of labor, so the share of capital does not decrease with an increase in the quantity of labor. Meanwhile, the estimated elasticity of the share of labor with respect to the quantity of capital is significantly negative for Food beverages & tobacco. PAGE 49 43 The estimated elasticities of the share of intermediate input with respect to the quantity of capital { B^ 1 } are significantly positive for Food beverages & tobacco, Chemicals & chemical products, and Metal products & machinery, and significantly negative for Lumber & wood products on the other hand. This parameter can also be interpreted as the elasticity of the share of capital with respect to the quantity of intermediate input. The estimated elasticities of the share of intermediate input with respect to the quantity of labor { B^ 1 } are significantly negative for Primary metal manucturing, and The total manufacturing. For the other industries, the estimated parameters for elasticities of the share of intermediate input with respect to the quantity of labor are not significant. The estimated biases of productivity growth { B^ 1 Bj;/ B^ 1 } can be considered as the change in the share of each input with respect to time, holding all inputs constant. Also the biases of productivity growth can be interpreted as changes in the rate of productivity growth with respect to proportional changes in input quantities. For example, if the bias with respect to labor input { B^ 1 1 is positive, the rate of productivity growth increases with the increase of the labor input. If the bias is negative, the productivity growth decreases with the increase of the labor input. We derive the following interpretations about biases of productivity growth based on Binswanger's concept of biases of productivity PAGE 50 44 growth. 1 If the estimated value of the bias of productivity growth with respect to intermediate input is positive { B^ 1 }, productivity growth is intermediate-using; if the value is negative, productivity growth is intermediate-saving. In the same way the estimated value of the biases of productivity growth with respect to capital input and labor input { B^ 1 B^ 1 } implies capital-using or capital-saving, and labor-using or labor-saving. All the industries can be classified by their patterns ui the biases of productivity. If we assume constant returns to scale in production, we can rule out the possibility that the three biases are either all negative or all positive. A classification of industries by their patterns of biases of productivity growth is represented in Table II-5. The different estimation methods (FIML and SUR) provide different estimates of biases of productivity growth. FIML estimation shows in Table 11-15 given in appendix that most of estimated biases of productivity growth are not significant. However, SUR estimation represented in Table II-4 shows that more estimated coefficients for biases of productivity growth are significant. Therefore we use the results from the SUR method to classify industries according to the biases of productivity growth. Here we eliminate two industries, Textiles & leather and Lumber & wood products, and the total Binswanger (1974) PAGE 51 45 Table II-5. Classification of Industries by Biases of Productivity Growth under Constant Returns to Scale by SUR Pattern of biases Industries Intermediate-using Food, beverages & tobacco Capital-saving Paper, printing & publishing Labor-saving Chemicals & chemical products Metal products & machinery Intermediate-using Nonmetalic mineral products Capital-saving Miscellaneous manufacturing Labor-using Intermediate-using Capital-using Labor-saving Intermediate-saving Primary metal manufacturing Capital -saving Labor-using Intermediate-saving Capital -using Labor-using Intermediate-saving Capital-using Labor-saving PAGE 52 46 manufacturing in classifying industries according to the biases of productivity growth since Hicks neutrality cannot be rejected at a level of significance of 0.01 for these industries and the total manufacturing. The pattern which occurs with greatest freguency in Table II-5 is intermediate-using, capital-saving, and labor-saving. This pattern characterizes four industries. Meanwhile, the patterns that occur most freguently in the classification of industries which is given by Jorgenson, Gollop, and Fraumeni ( 1987 ) are intermediate-using and labor-saving in combination with capital-using and capital-saving. An alternative interpretation of biases of productivity growth is that they represent changes in the rate of productivity growth with respect to proportional changes in input quantities. The rate of productivity growth increases with the increase of corresponding input if the bias of productivity growth is positive. The rate of productivity growth increases in the guantity of intermediate input for six of the nine industries and decreases for one in Table II-5. The rate of productivity growth decreases in the guantities of capital for seven industries. This fact raises us doubt about the role ui capital accumulation which traditional growth theory emphasizes in the development processes of developing countries. The rate of productivity growth decreases in the quantities of labor for four industries. Final Ly, let us examine the TFP's in Table II-6 and Table PAGE 53 47 Table II-6. Total Factor Productivity under Constant Return to Scale by SUR PAGE 54 48 Industry 4. Paper, 5. Chemicals 6 Nonmetalic Year printing & & chemical mineral publishing products products 1963 0.00117 0.08758 0.03479 1964 0.00222 0.07962 0.03427 1965 0.00331 0.07249 0.03342 1966 0.00434 0.06492 0.03198 1967 0.00544 0.05710 0.03004 1968 0.00657 0.04944 0.02890 1969 0.00784 0.04095 0.02812 1970 0.00920 0.03252 0.02793 1971 0.01053 0.02425 0.02728 1972 O.U1200 0.01659 0.02701 1973 0.01336 0.00757 0.02620 1974 0.01464 0.00451 0.02488 1975 0.01588 -0.00496 0.02346 1976 0.01727 -0.01360 0.02251 1977 0.01871 -0.02201 0.02139 1978 0.02014 -0.03090 0.01986 1979 0.02150 -0.04015 0.01804 1980 0.02297 -0.04987 0.01638 1981 0.02442 -0.05938 0.01492 1982 0.02593 -0.06874 0.01391 1983 0.02734 -0.07695 0.01296 mean 0.01356 0.00814 0.02468 PAGE 55 49 Industry 7 Primary 8. Metal 9 .Miscellaneous Year metal products & manufacturing manufacturing machinery 1963 0.03723 0.02410 0.02571 1964 0.03550 0.02445 0.02521 1965 0.03390 0.02554 0.02489 1966 0.03217 0.02522 0.02463 1967 0.03031 0.02478 0.02479 1968 0.02842 0.02423 0.02495 1969 0.02702 0.02307 0.02523 1970 0.02571 0.02151 0.02505 1971 0.02430 0.02012 0.02485 1972 0.02263 0.02163 0.02480 1973 0.02132 0.02353 0.02484 1974 0.02031 0.02380 0.02489 1975 0.01920 0.02450 0.02501 1976 0.01803 0.02494 0.02514 1977 0.01664 0.02687 0.02536 1978 0.01540 0.02690 0.02548 1979 0.01427 0.02564 0.02559 1980 0.01313 0.02454 0.02583 1981 0.01195 0.02398 0.02584 1982 0.01062 0.02485 0.02584 1983 0.00922 0.02557 0.02580 mean 0.02225 0.02427 0.02523 PAGE 56 50 Industry Year The total manucturing 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 0. 04036 0. 03812 0. 03590 0. 03389 0.03150 0.02925 0. 02702 0. 02471 0. 02244 0. 02001 0. 01774 0. 01515 0. 01295 0. 01068 0. 00835 0. 00607 0. 00379 0.00151 -0 00077 0. 00307 0. 00531 0. 01763 PAGE 57 51 II-9 to 11-14 in appendix which are calculated by using the estimated coefficients in the different models. The TFP from the generalized model fluctuates highly. However, the TFP from the models under constant returns to scale by the estimation method of SUR show the similar result with the one from the model under constant returns to scale by FIML. TFP's from the model under constant returns to scale which is estimated by SUR show a deceleration of productivity growth, that is, the estimated accelerations of productivity growth { B^ 1 } are significantly negative for five industries. Also TFP for the total manufacturing exhibits a deceleration of productivity growth. Now we compare our measurement of TFP to what others have measured. Kim and Park have measured TFP for the same sectors in Korean manufacturing based on the methodology of growth accounting. The growth accounting was introduced by Solow (1957) and has been discussed by Hulten (1973) Jorgenson and Griliches (1967,1971) I explain their methodology briefly in terms of the same notations in our model. The growth accounting equation starts from a production function: i 'ifljt X i -F x (M 1 ,K i ,L i ,T) (i=l,2, . ,n) (1) TFP in growth accounting is defined as rate of growth of output with respect to time, holding intermediate, capital, and labor inputs constant: PAGE 58 52 V^Â—^iM^K^L^T) (i=l,2,...,n). (10) Under constant returns to scale, the rate of technical change for each sector can be expressed as the rate of growth of the corresponding sectoral output less a weighted average of the rates of growth of intermediate input, capital input, and labor input, where the weights are given by the corresponding value shares: din A',dlnA,. dlnA/,dA, dlnA,dT dlnMv dT dlnK i dT dlnA, dlnL, dlnA,dlnL 1 dT dT (i=l,2, ...,n) i dlnM, dlnKi ; lnL ; M dT K dT L dT + Vr The comparisons of TFP s measured by different methods are represented in Table II-7. TFP s measured by growth account incj are greater than TFP's measured by translog production function for five of nine industries and the total industries, and less for the other. Since TFP measured by growth accounting is based on the assumption of Hicks neutrality, it cannot explain the effect of bias of PAGE 59 53 Table II-7. Comparison of TFP's measured by different methods: growth accounting and translog production function TFP measured by Industry growth accounting TFP measured by translog production function l.Food, beverag & tobac 2 .Textile & leather 3 Lumber & wood product 4 Paper, printin publish 5 Chemica & chemi product 6 Nonmeta mineral product 7 Primary metal manuf actu 8. Metal product machine 9 .Miscell -ous manufactu The total manufactu es CO g & ing Is cal lie ring s & ry ring ring 0.0231 0. 0201 0.0239 0. 0223 0. 0016 0. 0191 0. 0180 0.0374 0. 0318 0. 0208 0. 0396 0. 0177 0.0146 0.0135 0. 0081 0.0246 0. 0225 0.0242 0.0252 0.0176 PAGE 60 54 productivity growth on TFP. However, TFP measured by translog production function reflects the effect of bias of productivity growth as denoted in equation ^y=Ar+B^ r lnAf i +B^ T li\K 1 +BÂ£ T lnL i +BÂ£ T T ( i=l 2 . n) (70) If we assume Hicks neutrality in our flexible model, the rate of productivity growth is determined as denoted in equation V^At+B^T (i=l,2, . ,n) (72) It is known that the Korean economy accomplished the rapid growth during the last two decades. However, our estimation of TFP's implies that the outstanding characteristic of the Korean economy is the decelerating TFP. The industrialization of the Korean economy is not due to technological progress. If we observe the normalized variables of X, L, K, and M in data set, the intermediate input is the fastest growing input. In this observation, we can conclude that much of the industrialization in Korea is attributable to the growth of the intermediate input. PAGE 61 CHAPTER 3 THE MEASUREMENT OF SOURCES OF GROWTH The Model: Input-Output Analysis The starting point for measuring contributions of demandside factors to growth is the material balance equation of input-output analysis. The input-output model can be used as a tool to disentangle the relative contributions to growth and structural change of different components of changes in the final demand. The material balance equations for the supply of and the demand for domestically produced goods can be written as X t =A c X r + F r +E c -M c (88) where X t = domestic production vector in year t A. = input-output coefficients matrix such that A^ is composite intermediate demand of sector i per unit of domestic output in sector j in year t A t X t = intermediate demand vector in year t (composite of imported and domestic goods) F t = domestic final demand vector in year t (composite of imported and domestic goods) EÂ„ = export vector of domestic goods in year t M t = import vector in year t. The problem with the definition of the above variables is 55 PAGE 62 56 how to treat imports. Imports can be classified as either competitive or as noncompetitive. If they are noncompetitive, then they are not grouped with domestic products but are viewed as a nonproduced input into a sector, analogous to labor and capital. But in this model, I regarded all imports as competitive so that they are included in the same sector classification as domestic production. Let's assume that the ratio of domestic demand for domestically produced goods to total domestic demand is fixed by sectors. These domestic demand ratios in year t are given by d 2 = K i-*~ Ei -t (89) where V t = A t X t Defining a diagonal Matrix D t of the d 1 parameters, the material balance equation for domestic goods is given by ^t=D r V L+ D : F c+ E c (90) This equation can be derived by the following procedure. Let's consider the ith row in the material balance equation. Xit=Vit + F 1 c + E 1 t-M ic (91) We express this equation in terms of the domestic demand ratio as follows. PAGE 63 57 M=d it (V it +F it )+Â£ it (92) If we diagonalize d i7 and vectorize the other variables, then we can get the matrix expression of equation (93). X t =D t (V t +F c ) +E t (93) Noting that V t = A t X t the material balance equation can be written as X^d-D^rMD.F,^) (94) The production of output X t is determined by the domestic final demand F t and exports E t according to this expression of the material balance equation. The demand-side growth accounting can be established by using this equation. As will be explained, there are two methods of decomposing the sources of growth. One is the method based on absolute growth, and the other is the method based on proportional growth. Decomposition of Output Growth based on Absolute Growth Syrquin formulated the method in terms of absolute change in output and used it for the decomposition of industrial output growth. Kubo and Robinson reformulated the Syrquin PAGE 64 58 Method. 1 Denoting the change in a variable between two periods by A [ AX t = X t X t : ] the change in sectoral output can be written (after some algebraic manipulation) as shown below AX^R^D^iAF,) (a) + t -i(AF t ) (b) +R t 1 (AD r ) (F t +V c ) (c) +R t 1 D L j (AA r )X c (d) (95) (a) Effects of domestic changes in domestic demand in all sectors(DD), (b) Effects of changes in exports in all sectors (EE) (c) Effects of changes in the import structure of intermediate and final goods (IS), (d) Effects of changes in the matrix of input-output coefficients (10). The above decomposition equation can be derived from equation (94). If we denote R t = (I D t A t )~ 1 then equation (94) can be written as X t =R r {D t F r +E t ) (96) Let's take the first difference from this equation, then we obtain AJr t =i? t 1 (D t 1 AF t +A^ t +Al? t F t 1 )+Ai? t (Z3 t 1 F e 1 +Â£ e 1 ) (97) 1 Dervis, K. J. D. Melo, and S. Robinson (1982). pp92-110. PAGE 65 59 The first difference of an inverse matrix is given by AR^MI-D.A,}1 = -R r A(I-D c A c )R c ^^(AZVVi+ZVi^t^t-i (98) Substituting this eguation into the above equation, we get the decomposition equation (95) ^X^R^D^^Ft) *R t 1 (AE t ) t-R^/iD,.) (F t 1 + ^ t 1 ) *R t 1 D t 1 {LA t )X t x This equation gives the basic decomposition of the change in sectoral output into different sources (i.e., AF t AE t AD t and AAJ The first two terms on the right-hand side of the above equation are changes in the output of sector i induced by the expansion of domestic demand and exports in all sectors, given a constant import structure. The third and fourth terms measure the direct and indirect effects of changes in the import structure of final and of intermediate goods. The last term gives the direct and indirect effects of changes in the total (domestic and imported) matrix of inputoutput coefficients, which represent the widening and deepening of interindustry relations brought about by the changing mix of intermediate input requirements. The changes in input-output coefficients are caused, in turn, by changes in production technology as well as by substitution among PAGE 66 60 various inputs (perhaps in response to changes in relative prices) although we cannot separate these two effects without more information. Decomposition of Output Growth based on Proportional Growth Chenery provided the decomposition method by using the differences which are called the "deviations from proportional expansion". 2 Let's define the deviation from proportional growth of output of sector i as <5X lL = X lt XX X t lf where A is the ratio of GNP in period t to GNP income in period t-1. 5^it = x it A ^i,t-i 5F it = F it ~ ^ F i,t-i 5V it = V it A V liW 5E lt = E 1L ^ Ei,t-i Using these definitions, the alternative decomposition equation can be derived from the material balance equations analogous to the decomposition equation (95) After some algebraic manipulations, the decomposition (in matrix notations) is given by +J R t 1 AD t X(F t 1 + y t 1 ) (c) (d). (99) Chenery, H. B. S. Shishido, and T. Watanabe (1962) PAGE 67 61 The deviation from proportional growth in output in sector i is seen to be the sum of four sets of structural changes: (a) Effects of deviations in domestic demand in all sectors (DD) (b) Effects of deviations in exports in all sectors (EE), (c) Effects of changes in the import structure of intermediate and final goods(IS), (d) Effects of changes in the matrix of input-output coefficients (10) In equation (99), the material balance equation in the terminal year is compared not with its counterpart in the initial year but with the hypothetical material balance equation in the terminal year under the assumption of balanced growth Difference between two Methods: A Graphic Representation The figure 1 is a graph of growth and structural change in a two-sector model. Initially, the economy is at point I and is producing X 1)t -! and X 2it -i ( the subscript refers to the sector and the superscript to the period ) Later, the economy is at point II and is producing X lt and X 2t Aggregate output has grown from X t x = X lit -! + X 2it -i to X t = X lt + X 2t where PAGE 68 62 PAGE 69 63 growth measures the change A in variables and the method based on proportional growth measures the change 6 in variables. In the decompositions of the deviation measure, let's compare equation (95) with equation (99) to examine the difference between the AX decomposition and the PAGE 70 64 and computing costs since I focused on the analysis of policy change of the period in which Korea experienced the economic recession because of the second oil shock and the subseguent recession in the advanced countries. The Bank of Korea has provided five tables which have about 60 sectors. All the tables are compiled in terms of current producers' prices. The measurement of sources of growth is most meaningfully conducted in terms of constant price. Thus it is necessary to deflate the current price input-output statistics to obtain constant price figures. For this I deflated all the tables with IMF wholesale price indices. While this procedure suffices to insure that, on the average, changes over time are not mis-stated because of price level changes, it fails to account for relative price changes. The changes of relative prices can take place owing to the price level of imported commodities, the price level of exports and the exchange rates on imports and exports. Except for the two tables for 1980 and 1983, which have 19 sectors, all tables have about 60 sectors. So I had to make all the tables into 19 sectors by aggregating the detailed sectors. Estimation of Sources of Growth: SAS/IML I estimated the sources of growth on the demand side by using SAS/IML (Interactive Matrix Languages) The total change in sectoral output is decomposed into its sources by category PAGE 71 65 of demand. The total change in output equals the sum of the changes in each sector and can also be decomposed either by sector or by category of demand. The relations can be shown schematically as follows: Notations DD = effect of deviations in Domestic Demand expansion EE = effect of deviations in Export Expansion IS = effect of changes in Import Substitution 10 = effect of the changes in Input-Out coefficients. DD : + EE : + ISj + IOj = A X : DD, + EE, + IS, + 10, = AX, DDÂ„ + EEÂ„ + IS,, + I0Â„ = A X,. E DD, + S EE, + E IS, + E 10, = E A X H Reading down columns gives the sectoral composition of each demand category; reading across rows gives the decomposition of changes in sectoral demand by different demand categories. Growth contributions in each period were first calculated at the 19 sector level and then aggregated before converting to percentage. While the tables of the 19 sector model are presented in Appendix, the summary tables, i.e. sources of aggregated output growth, sources of sectoral output growth, and the sectoral comparison of EE and IS in AX and 6X are summarized PAGE 72 66 in Table III-2, III-4, III-6, and III-7. Interpretation of the Results While it is apparent from some research results that Korea's industrial development has clearly been export-led, this stands out even more dramatically when the sources of Korea's industrialization are compared with international norms on the demand side. Before I examine the results of my calculation of the sources of growth in the period 1975-1985, I refer to the results from Frank, Kim and Westphal (1975) to compare the Korea's development pattern with the norms on the demand side. The sources of Korea's industrialization from 1960 to 1968 are compared in Table III-l with crudely estimated crosscountry norms for the growth of per capita income from $100 to Table III-l. Sources of Industrial ization J DD EE(%) IS Korea (1960-68) Large Country Norm All Country Norm 60 55 50 38 24 18 2 21 32 Frank, Ch R. K. S. Kim, and L. E. Westphal (1975), p95, PAGE 73 67 $200. While import substitution contributed very little to Korea's industrialization, the growth of exports contributed more than twice the relative amount that is typicallyassociated with the doubling of per capita income from $ 100 to $ 200. The analysis of Frank, Kim and Westphal, however, had an analytic problem in that a fixed coefficient inputoutput table was assumed. Furthermore these results are unfortunately not comparable to ours because of differences in classification and level of aggregation. Table III-2 highlights the impact of the shift in Korea's development strategy and the technological change in the early 1980s. According to the AX based estimates found in Table III-2, the EE effects on the growth of output dominated over the IS effect except during the period 1978-1980. In the period 1978-1980, the IS effect was a little greater than the EE effect in AX. Until 1978, Korea pursued export-oriented economic growth. However, Korea faced some major constraints to the promotion of exports. The advanced countries underwent a prolonged recession after the second oil shock. This led to increased protectionism in the advanced countries. In this period, the greatest effect on the growth of output in Korea was the change in input-output coefficients. This fact reflects that Korea experienced the technological change in the face of the second oil shock and world-wide recession to achieve steady economic growth. Moreover, the resource misallocation which was led by the government's overambitious PAGE 74 68 Table III-2. Sources of Aggregated Output Growth (in percent) AX 6 X 1975-1978 76.78 28.34 J. 06 -8.18 5*. 69 -3.80 -65.07 110.76 1978-1980 11.88 11.34 12.98 63.79 23. 04 15.54 10.73 50.69 1980-1983 71.24 43.54 10.23 -25.01 75.54 -24.55 -27.97 76.98 1983-1985 65.21 33.02 3.79 -2.02 -54.36 -1.44 15.49 -16.59 Note) A X: the incremental measured by the method based on absolute growth 5 X: the incremental measured by the method based on proportional grow promotion of heavy and chemical industries since the midseventies accelerated the changes in the input-output coefficients. After these big changes in the input-output coefficient, the difficulties that Korea encountered during the 1979-1981 had been largely overcome by the middle of 1984. If we examine the estimates based on the SX decomposition, we find that export promotion no longer contributes to the growth of output. In Table III-2, we can observe the contribution of changes in the input-output coefficients to the growth of output in the decompositions of SX. To examine the structural changes, let examine the Table PAGE 75 69 III-4 which classifies output into five sectors: primary industry, light industry, heavy industry, social overhead and services, and dummy sector. The aggregation scheme of nineteen industries into five sectors is shown in Table III-3. According to Table III-4, domestic demand expansion was a dominant factor in primary industry's output over the entire period (1975-1985) The export expansion contributed to output growth positively, but Table III-4 showed the great reduction of the EE effect in the decomposition of <5X. In the decomposition of <5X, the contributions of the changes of technology in manufacturing to the growth of output have different patterns between light indusry and heavy industry in the entire period (1978-1985). The contributions of the changes in the input-output coefficients of light industry did not vary sharply from period to period. In contrast, the contributions of the changes of heavy industry changed radically from period to period. In the period 1978-1980, for example, the contributions of the changes in the input-output coefficients of heavy industry was the greatest one among factors of decompositions. In the period 1980-1983, however, the changes in the coefficients of heavy industry contributed by minus 566.8%. These empirical results indicate that the heavy industry experienced the radical change in the government's development policy. The government's overambitious promotion of heavy and chemical industries took place since the mid-seventies. The IS effects were minor PAGE 76 Table III-3. Sector Classification for Five Sectors 70 5 Aggregated Sector Classification PAGE 77 71 Table III-4. Sources of Sectoral Output Growth: 5 Sector Model (in percent) AX 5 X 1975-1978 Primary Industry Light Industry Heavy Industry Social Overhead & Services Dummy sector 1978-1980 Primary Industry Light Industry Heavy Industry Social Overhead U Services Dummy sector 1980-1983 Primary Industry Light Industry Heavy Industry Social Overhead & Services Dummy sector 1. Primary Industry 69.9 14.7 18.8 -3.4 143.1 26.8 -49.8 2. Light Industry 43.3 40.3 4.7 14.8 -211.8 7.6 31.8 3. Heavy Industry 50.4 63.8 5.6 -19.8 -16.4 15.1 8.1 4. Social Overhead & Services 87.3 13.2 .1 -.6 3.6 -30.4 2.3 5. Dummy sector 73.6 14.9 -4.2 15.7 -8.7 -56.3 -10.2 56 PAGE 78 72 except the recession period. The 10 effects of all industries except primary industry are high just in the recession period It is interesting to compare these findings of proportional method on Korean economy to the results which are obtained in the analysis of the patterns of Japanese Growth, 1935-1954 by H. B. Chenery, S. Shishido, and T. Watanabe (1962) The relative contribution of export expansion is not emphasized by the proportional method in the case of Korean economy. The similar phenomenon can be found from Table III-5. For direct comparisons, the analysis of Chenery et al. has some limitations since they assumed that the coefficient matrix of the input-output table was fixed, that is, there was no technological change. However, their results imply the following fact. Many people assumed that the Japanese pattern would be export-led, but the fact is that it was led by import substitution. It is also believed that the pattern of Korean development is export-led. But the results based on the proportional method do not support this conclusion. Most of the major manufacturing subsectors displays a pattern consistent with that for manufacturing as a whole except several subsectors. If we focus on the comparisons of trade policy of each sector, we can compare the relative importance of export expansion and import substitution in Tables III-6 and III-7. PAGE 79 73 Table III-5. Relative Importance of Changes in Final Demand and Trade, 1935-1954 A (Billions of 1951 yen) Final Demand Exports Imports Total I PAGE 80 74 Table III-6. Sectoral Comparison of EE and IS in AX (Method based on absolute growth) (in percent) PAGE 81 75 Table III-7. Sectoral Comparison of EE and IS in PAGE 82 an accepted fact in development economics, recent studies fail to confirm that the former causes the latter. This analysis indicates that domestic demand and export expansion were two major factors contributing to growth and structural change. However, import substitution and technological change were more important than export expansion in the recession period (1979-1981) in explaining growth. In addition, if we take the method of measurement based on proportional growth, export expansion no longer plays the consistent role that is attributed to it by the method based on absolute growth. 76 PAGE 83 CHAPTER 4 SUMMARY AND CONCLUSION I have analyzed the productivity change and pattern of production for industrial sectors in Korean manufacturing by estimating translog production functions and value shares and testing restrictions which are imposed by producer's theory in the supply-side analysis. In the demand-side analysis, I have measured the effect of changes in demand on the growth of outputs of industrial sectors and derived some implications about trade policies: export promotion policy and import substitution policy. In the supply-side analysis, we obtain the best results from the model restricted to constant returns to scale by the estimation method of seemingly unrelated regression based on statistical significance of estimates and production theory. The parameter estimates of translog production function provide implications about share elasticities and biases of productivity. We classify the industries according to the biases of productivity growth. The remarkable characteristic in our classification is capital-saving. This fact raises doubt about the role of capital accumulation which traditional growth theory emphasizes in the development process of 77 PAGE 84 78 developing countries. If we compare the TFP measured by translog production function to the TFP which others have measured by growth accounting, we obtain different results according to the industry. For some industries TFP's measured by translog production function are greater than TFP's measured by growth accounting, and for other industries less. This phenomenon is due to the fact that TFP measured by growth accounting cannot explain the effect of bias of productivity growth on TFP, while TFP measured by translog production function reflects the effect of bias of productivity growth. In the demand-side analysis, domestic demand and export expansion were two major factors contributing to growth and structural change. However, import substitution and technological change were more important than export expansion in the recession period. Besides, if we measure the relative contribution of export expansion by the method based on proportional growth, we do not observe the role of export expansion which is attributed by the method based on absolute growth. If we relate productivity changes of industrial sectors in manufacturing during 1975-83 to the measurement of sources of growth for the same industrial sectors in manufacturing during the same period, we do not find any correlation between the increase of TFP and trade policies. Our observations on total factor productivity implies that the technical progress takes PAGE 85 79 a relatively small role in the industrialization process since the rate of productivity growth is decelerating. PAGE 86 APPENDIX Table II-8. Diagonal Matrix of Cholesky Factorization I.FIML 1) Generalized Model l.Food, beverages & tobacco 0.06028 4.63966 -0.10437 2. Textiles & leather 0.04309 2 38705 -0.04185 3 Lumber & wood products 0. 11556 3.81398 -0.01627 4. Paper, printing & publishing -0. 10252 0.82301 0.13600 5. Chemicals & chemical products -0. 07557 36.88665 0.02415 6.Nonmetalic mineral products -0. 18428 -2.79678 -0.04545 80 PAGE 87 81 7. Primary metal manufacturing -0. 12738 -1.14135 -0. 01693 8. Metal products & machinery -0.22741 1.14399 -0.04406 9 .Miscellaneous manufacturing -0.07471 3 .86755 -0.03126 10. The whole manufacturing 0.05539 22 15497 -0.01212 2) The Model under Constant Return to Scale l.Food, beverages & tobacco -0. 16665 -0.00051 -0.00000 2. Textiles & leather 0.02607 -0.03638 0. 00000 3 Lumber & wood products 0. 10554 0.01813 0.00000 PAGE 88 82 4. Paper, printing & publishing -0. 08747 0.00288 -0.00000 5. Chemicals & chemical products -0. 04982 0.02171 0.00000 6.Nonmetalic mineral products -0. 10075 -0.04577 0. 00000 7 Primary metal manufacturing -0. 18127 -0.01470 -0. 00000 8. Metal products & machinery -0. 15002 -0.03652 -0.00000 9 .Miscellaneous manufacturing -0. 17455 -0.01737 -0.00000 10. The whole manufacturing 0. 05166 -0. 01500 -0. 00000 PAGE 89 83 II.SUR 1) Generalized model l.Food, beverages & tobacco 0.08910 4.10452 -0.07681 2. Textiles & leather -0.02319 2.03831 -0.00648 3 Lumber & wood products 0. 11146 3 .94681 -0.02522 4. Paper, printing & publishing -0. 06844 3.40890 0.04821 5. Chemicals & chemical products -0. 11675 8.76096 0.02159 6.Nonmetalic mineral products 0. 00725 1.81824 -0.05631 PAGE 90 84 7 Primary metal manufacturing 0. 13119 -0. 01649 -0.01653 8. Metal products & machinery -0. 22888 3.76045 -0. 04245 9 .Miscellaneous manufacturing 0. 02431 0. 08809 -0.04082 10. The whole manufacturing 0. 06293 18. 14782 -0.00990 2) The Model under Hicks Neutrality l.Food, beverage & tobacco -0.05375 0. 96644 -0.00939 2. Textiles & leather -0.04362 -0. 02710 -0.00517 3 Lumber & wood products 0. 11753 0. 01442 -0.03530 PAGE 91 85 4. Paper, printing & publishing 0. 01825 0.38384 -0.01479 5. Chemicals & chemical products -0. 06181 1. 16399 0.01749 6.Nonmetalic mineral products 0.04505 0.50963 -0.06598 7 Primary metal manufacturing 0. 15134 0.72318 -0.02119 8. Metal products & machinery -0.23177 -0.42738 -0.03218 9 .Miscellaneous manufacturing 0. 05039 0.21689 -0.02169 10. The whole manufacturing 0.05836 0. 36004 -0. 01155 PAGE 92 86 3) The Model under Constant Return to Scale l.Food, beverage & tobacco -0.06170 0.03119 -0.00000 2. Textiles & leather -0.00343 -0.00051 -0.00000 3 Lumber & wood products 0. 10603 0.01883 -0.00000 4. Paper, printing & publishing -0. 00697 -0.00156 -0.00000 5 Chemicals & chemical products -0.07193 0.02454 -0.00000 6 Nonmetalic mineral products -0. 01860 -0.04337 -0. 00000 7. Primary metal manufacturing 0.06685 -0. 02712 0. 00000 PAGE 93 87 8. Metal products & machinery -0.14904 -0.03575 -0.00000 9 .Miscellaneous manufacturing 0. 00064 -0. 14484 0.00000 10. The whole manufacturing 0.06623 -0.00954 0.00000 4) The Model under Existence of Value-added function l.Food, beverage & tobacco -0.01198 4.25468 -0.03367 2. Textiles & leather 0. 02774 1. 52091 -0.00838 3 Lumber & wood products 0. 04432 4 .22041 -0. 00850 4. Paper, printing & publishing 0.02282 3.51295 0.06909 PAGE 94 5. Chemicals & chemical products 0.01520 -8.99473 0.01948 6.Nonmetalic mineral products 0.03370 2.04482 -0.05155 7. Primary metal manufacturing 0.01434 1. 16434 -0.01796 8. Metal products & machinery 0. 01304 2. 17598 -0. 04084 9 .Miscellaneous manufacturing 0.01516 0.16856 -0.03078 10. The whole manufacturing 0.01757 10.80001 -0. 03258 PAGE 95 Table II-9. Total Factor Productivity by FIML 89 PAGE 96 90 IndustryYear 4 Paper, printing & publishing 5 Chemicals & chemical products 6 .Nonmetalic mineral products 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 0.04206 0.03788 0.03389 0.02917 0.02655 0. 02426 0. 02310 0. 02257 0. 02201 0.02308 0.02361 0.02298 0.02173 0.02144 0.02191 0.02245 0.02288 0.02485 0.02687 0.02906 0. 02971 0. 57985 0.58364 0.57856 0.59733 0. 59024 0.51129 0.42549 0.40190 0.42508 0.38831 0.29622 0. 16844 0.04931 -0.05434 -0. 10424 -0. 09283 -0.02917 0.05203 0. 16301 0.12258 0.39529 -0.04764 -0.03479 -0.02270 -0.00141 0.02275 0.04053 0.04461 0.03747 0.02444 0.01594 0.01764 0.02471 0.02920 0.03357 0. 04547 0.06173 0.06730 0.05907 0.04233 0.03131 0.02850 mean 0.02631 0.28800 0.02476 PAGE 97 91 PAGE 98 92 Industry PAGE 99 93 Table 11-10. Total Factor Productivity under Constant Return to Scale by FIML PAGE 100 94 Industry 4. Paper, 5. Chemicals 6.Nonmetalic Year printing & & chemical mineral publishing products products 1963 0.00235 0.06469 0.03464 1964 0.00328 0.05897 0.03417 1965 0.00421 0.05391 0.03335 1966 0.00507 0.04850 0.03173 1967 0.00600 0.04289 0.02926 1968 0.00698 0.03740 0.02795 1969 0.00820 0.03126 0.02719 1970 0.00953 0.02516 0.02738 1971 0.01082 0.01918 0.02691 1972 0.01221 0.01370 0.02709 1973 0.01339 0.00713 0.02659 1974 0.01451 0.00532 0.02535 1975 0.01560 -0.00160 0.02390 1976 0.01693 -0.00787 0.02313 1977 0.01831 -0.01396 0.02222 1978 0.01966 -0.02042 0.02073 1979 0.02086 -0.02718 0.01863 1980 0.02215 -0.03430 0.01664 1981 0.02344 -0.04126 0.01489 1982 0.02484 -0.04811 0.01394 1983 0.02612 -0.05402 0.01316 mean 0.01355 0.00759 0.02471 PAGE 101 95 PAGE 102 96 Industry The Year whole manucturing 1963 0.04405 1964 0.04140 1965 0.03876 1966 0.03616 1967 0.03350 1968 0.03085 1969 0.02822 1970 0.02557 1971 0.02293 1972 0.02026 1973 0.01762 1974 0.01493 1975 0.01230 1976 0.00966 1977 0.00701 1978 0.00438 1979 0.00175 1980 -0.00087 1981 -0.00349 1982 -0.00613 1983 -0.00879 mean 0.01762 PAGE 103 Table 11-11. Total Factor Productivity by SUR 97 PAGE 104 98 Industry Year 4 Paper, printing & publishing 5 Chemicals & chemical products 6 .Nonmetalic mineral products 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 0.07922 0.06284 0.04746 0.03368 0. 02395 0.01810 0.01146 0. 00453 0. 00119 0.00120 0.00787 0. 00883 0.00653 0. 00203 0. 00055 0. 00075 0.00581 0. 01839 0. 03129 0. 04122 0.04503 0.55934 0.54421 0. 52478 0.51112 0.49342 0.46196 0.43181 0.41307 0.40258 0.37903 0.34934 0.29458 0. 26120 0. 22816 0.20440 0. 19346 0. 19335 0. 19794 0.20741 0.18841 0.22394 0.11636 0.10606 0.09569 0.07886 0.05881 0. 04436 0.03851 0.04064 0. 04488 0.04788 0.04408 0.03601 0.02891 0. 02311 0. 01298 -0. 00058 -0.00948 -0.01068 -0.00678 -0.00448 -0.00633 mean 0. 02141 0.345i 0.03709 PAGE 105 99 Industry 7 Primary 8. Metal 9 .Miscellaneous Year metal products & manufacturing manufacturing machinery 1963 PAGE 106 Industry 100 Year The whole manucturing 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 0.08315 0. 12364 0. 11277 0. 11592 0.09931 0. 10148 0. 11374 0. 15958 0. 23553 0.25426 0. 19547 0. 10217 0. 03490 Â•0. 03823 0.08551 Â•0. 11993 0. 15214 Â•0. 16860 Â•0. 15308 Â•0. 08766 0.26050 0.05654 PAGE 107 Table 11-12. Total Factor Productivity under Hicks Neutrality by SUR 101 PAGE 108 102 Industry 4. Paper, 5 Chemicals 6.Nonmetalic Year printing & & chemical mineral publishing products products 1963 0.02440 0.51688 0.08417 1964 0.02332 0.49496 0.07900 1965 0.02224 0.47305 0.07384 1966 0.02116 0.45114 0.06867 1967 0.02008 0.42923 0.06351 1968 0.01900 0.40732 0.05834 1969 0.01792 0.38541 0.05318 1970 0.01684 0.36350 0.04801 1971 0.01576 0.34159 0.04285 1972 0.01468 0.31967 0.03768 1973 0.01360 0.29776 0.03252 1974 0.01252 0.27585 0.02735 1975 0.01144 0.25394 0.02219 1976 0.01036 0.23203 0.01702 1977 0.00928 0.21012 0.01186 1978 0.00820 0.18821 0.00669 1979 0.00712 0.16630 0.00153 1980 0.00604 0.14438 -0.00364 1981 0.00496 0.12247 -0.00880 1982 0.00388 0.10056 -0.01397 1983 0.00280 0.07865 -0.01913 mean 0.01360 0.29776 0.03252 PAGE 109 103 PAGE 110 Industry 104 Year The whole manucturing 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 0.20726 0.19856 0. 18986 0.18116 0. 17245 0.16375 0. 15505 0. 14635 0. 13765 0. 12895 0. 12025 0. 11154 0. 10284 0.09414 0.08544 0.07674 0.06804 0. 05934 0. 05063 0. 04193 0.03323 0. 12025 PAGE 111 105 Table 11-13. Total Factor Productivity under Existence of Value-added by SUR PAGE 112 106 Industry Year 4 Paper, printing & publishing 5. Chemicals & chemical products 6 .Nonmetalic mineral products 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 0.07619 0.05934 0. 04327 0.02951 0.02001 0. 01497 0. 00814 0.00059 -0. 00551 -0. 00357 0. 00380 0. 00505 0. 00314 -0. 00234 -0. 00458 -0. 00491 0. 00060 0.01394 0.02783 0.03809 0. 04192 0.51294 0.48729 0.46362 0.43355 0.41095 0.40851 0.40852 0. 39089 0.35992 0.34547 0. 34765 0. 35581 0. 36597 0. 37120 0. 36107 0. 33396 0.29235 0.24612 0. 19131 0. 17911 0. 07767 0. 12003 0. 10906 0.09815 0.08036 0.05953 0. 04434 0.03854 0.04118 0. 04662 0. 05015 0. 04634 0. 03813 0.03122 0.02534 0.01455 0.00022 -0.00828 -0.00800 -0.00203 0.00150 0. 00012 0. 01740 0. 34971 0.03938 PAGE 113 107 PAGE 114 108 Industry The Year whole manucturing 1963 0.17851 1964 0.19513 1965 0.18206 1966 0.17690 1967 0.16067 1968 0.15515 1969 0.15542 1970 0.17512 1971 0.21218 1972 0.21636 1973 0.17565 1974 0.11532 1975 0.06965 1976 0.02066 1977 -0.01336 1978 -0.04005 1979 -0.06551 1980 -0.08190 1981 -0.07981 1982 -0.04886 1983 0.14537 mean 0.09546 PAGE 115 109 Table 11-14. Parameter Estimates by FIML PAGE 116 110 PAGE 117 Ill Industry 7 Primary 8. Metal 9 .Miscellaneous Parameter metal products & manufacturing manufacturing machinery A" -0.9109 2.3381 5.0015 (-0.2449) (0.0483) (4.7822) A\ -0.6090 2.9742 7.0222 (-0.1256) (0.0429) (6.8838) A\ 0.0886 0.0287 0.1682 (1.0085) (0.3715) (3.2579) A'm 0.2929 0.7118 0.5039 (0.7029) (4.0644) (7.7526) A\ 0.1415 -0.3925 -0.9249 (0.2231) (-0.0444) (-7.5348) B 1 ^ -0.1273 -0.2274 -0.0747 (-6.3180) (-1.1167) (-3.6923) B x m -0.0764 0.3399 0.0059 (-0.2303) (0.9522) (0.1173) B X ML -0.0071 0.0379 0.0287 (-0.7849) (0.5428) (2.1120) B\ T 0.0428 0.0061 0.0134 (1.1168) (0.3858) (2.7192) B 1 ^ -1.1872 0.6357 3.8670 (-0.3832) (0.0127) (6.1434) B X KL 0.0386 -0.0544 0.0151 (0.5577) (-0.3735) (0.7518) B\ r 0.0806 -0.2158 -0.6592 (0.1970) (-0.0341) (-8.7324) B\ L -0.0189 -0.0503 -0.0422 (-4.4165) (-2.3942) (-1.3927) B x u -0.0005 0.0052 -0.0004 (-0.0687) (0.7301) (-0.1049) B 1 ^ -0.0117 0.0325 0.0854 (-0.2180) (0.0404) (10.9636) PAGE 118 112 Industry The Parameter whole manucturing A l 20.9349 (0.4962) A\ 30.9216 (0.573 5) A\ 0.1343 (3.7281) A\ 0.7110 (3.8188) A\ -4.0321 (-0.5186) B L m 0.0553 (0. 6237) B 1 ^ -0.0025 (-0.0186) B\ L -0.0354 (-0. 8086) B x m -0.0032 (-0. 1904) B\ K 22.1551 (0. 6504) B X KL 0.0308 (1.3993) B\ t -2.9370 (-0.5919) B\ L 0.0105 (0.2253) B^x 0.0002 (0.0833) B'xx 0.3868 (0. 5397) PAGE 119 Table 11-15. Parameter Estimates under constant return to scale estimated by FIML 113 PAGE 120 114 Industry Parameter 4 Paper, printing & publishing 5 Chemicals & chemical products 6 .Nonmetalic mineral products AV A 1 A\ A : B\ B\ B\, B\ B\ BS B-B ; : B 1 0.3191 (7.3991) 0. 1152 (2.7638) 0.3721 (5.9772) 0. 5127 (14. 1154) -0.0006 (-0. 1656) -0.0881 (-4.8007) -0.0370 (-1.6787) 0. 1251 (6.9424) 0.0040 (5. 1185) -0.0131 (-0.5585) 0.0501 (1.7115) -0.0020 (-1.8308) -0. 1752 (-4.2925) -0.0019 (-1.9780) 0.0010 (2.2599) 0.5664 (3.2122) 0.1612 (6.3651) 0.0524 (3.6735) 0.7864 (24.3563) 0.0623 (1. 7583) -0.0489 (-1.9725) 0. 0490 (2 .4855) -0.0001 (-0.0186) 0. 0082 (2 .8613) -0. 0274 (-1.8684) -0.0216 (-2.9907) -0.0067 (-2.9291) 0.0217 (4.3645) -0.0015 (-2.2117) -0.0067 (-1.6187) 0.2918 (3.8805) 0. 1681 (7.2149) 0.2697 (32.2569) 0. 5622 (29.9434) 0.0275 (1.9445) -0.0871 (-2.6671) 0.0568 (2.4815) 0.0303 (2.8898) 0.0103 (5. 1731) -0.0815 (-3.7453) 0.0246 (3.3754) -0.0104 (-8.0114) -0.0549 (-6.0009) 0.0002 (0. 1484) -0.0019 (-2.0125) PAGE 121 Industry 115 7 Primary 8. Metal 9 .Miscellaneous Parameter metal products & manufacturing manufacturing machinery A'o PAGE 122 116 Industry The Parameter whole manucturing A x 0.2217 (2.3887) A\ 0.2351 (5.2244) A\ 0.1303 (7.7499) A X M 0.6346 (16. 3433) A\ 0.0468 (2 .6885) B 1 ,^ 0.0518 (1.0209) B 1 ,^ -0.0244 (-0.4999) BV -0.0274 (-2 5726) B 1 ,^ -0.0004 (-0. 1408) B\ K -0.0031 (-0.0584) B' KL 0.0275 (3.8396) B X KT 0.0001 (0.0500) B\ L -0.0002 (-0.0109) B i LT 0.0003 (0.2126) B\ T -0.0026 (-2.2333) PAGE 123 Table 11-16. Parameter Estimates estimated by SUR 117 PAGE 124 118 Industry Parameter 4 Paper, printing & publishing 5 Chemicals & chemical products 6 .Nonmetalic mineral products AV A\; A\ A 1 A 1 B t B> B\ B\ bS B 1 B\ B\ 0.7122 (2.3944) 2.7743 (4.2707) 0.1717 (1.9287) 0. 4603 (7.2247) -0. 1367 (-2.8612) -0.0684 (-2.8432) -0.0444 (-3.0700) -0.0366 (-1.3908) 0.0196 (3.3713) 3 3800 (4.7060) -0.0005 (-0.0312) -0.2295 (-4.2754) 0. 0286 (0.6365) 0.0012 (0. 1564) 0.0132 (3 .4557) -0.9709 (-0.1002) 3.5637 (0.1997) 0. 0372 (1.0917) 1. 1499 (8.9050) -0. 1881 (-0. 1056) -0. 1167 (-4.5641) 0. 5939 (4.1830) 0.0117 (1.8211) -0.0363 (-3.1115) 5.7392 (0. 3453) -0. 1030 (-2.9371) -0.6081 (-0.3687) 0.0206 (2.1519) 0.0047 (1.5244) 0.0488 (0. 2975) -0.4396 (-2.0782) 1.1400 (1.7526) 0. 1748 (15.9541) 0. 5299 (18.2730) 0. 0362 (0.8222) 0.0072 (0.3202) -0.0348 (-1.5344) 0.0040 (0.4664) 0.0062 (2.4574) 1.9861 (2. 1496) 0.0599 (6.0519) -0.1050 (-1.5776) -0.0505 (-9.5764) 0.0010 (1.0634) 0.0007 (0. 1553) PAGE 125 119 Industry 7. Primary 8. Metal 9 .Miscellaneous Parameter metal products & manufacturing manufacturing machinery A x PAGE 126 120 Industry The Parameter whole manucturing A x 17.0329 (2.4388) A X K 25.3316 (2.6296) A\ 0.1317 (8.2338) A\ 0.7122 (18.2734) A\ -3.2948 (-2.5341) B L m 0.0629 (5. 3928) B 1 ^ -0.0042 (-0. 1500) B 1 ^ -0.0462 (-6.3483) B^i -0.0033 (-0.9217) B 1 ^ 18.1481 (2.7252) B\ L 0.0341 (2.9537) B'kt -2.4091 (-2 .6831) B\ L 0.0241 (2 .4017) B 1 ^ 0.0005 (0. 3495) B\ T 0.3173 (2.6222) PAGE 127 Table 11-17. Parameter Estimates under Hicks Neutrality estimated by SUR 121 PAGE 128 122 PAGE 129 123 Industry 7. Primary 8. Metal 9 .Miscellaneous Parameter metal products & manufacturing manufacturing machinery 0.7420 -0.2965 (1.1920) (-2.2594) 0.6089 0.3891 (2.6513) (4.9595) 0.0842 0.1623 (71.2490) (117.2134) 0.7794 0.6513 (287.0511) (141.3076) -0.1018 0.0400 (-1.1924) (2.6083) -0.2317 0.0503 (-5.0828) (2.9223) 0.4097 -0.0643 (5.8614) (-2.6865) 0.0273 0.0054 (1.6370) (0.7197) 0.0000 0.0000 (0.0000) (0.0000) -1.1519 0.2991 (-3.0364) (6.8691) -0.0104 0.0184 (-0.4485) (2.7024) 0.0000 0.0000 (0.0000) (0.0000) -0.0387 -0.0181 (-3.5523) (-1.9973) 0.0000 0.0000 (0.0000) (0.0000) 0.0060 -0.0024 (1.1052) (-3.7716) A\, PAGE 130 124 Industry The Parameter whole manucturing A'q -1.8557 (-3. 1549) A* K -0.5911 (-2.4368) A\ 0.1373 (200.9108) A^ 0.6763 (408.4364) A l T 0.2159 (2.7489) BV, 0.0 58 3 (4 .9245) BV -0.0254 (-1.6531) BV -0.0425 (-5.5584) BV 0.0000 (0.0000) BV 0.3710 (1.3484) BV 0.0 3 56 (5.8370) BV 0.0000 (0. 0000) B\ L 0.02 02 (1.9393) BV 0.0000 (0.0000) BV -0.8701 (-1.8609) PAGE 131 125 Table 11-18 Parameter Estimates under Existence of Value-added Function by SUR PAGE 132 126 PAGE 133 127 Industry 7 Primary 8. Metal 9 .Miscellaneous Parameter metal products & manufacturing manufacturing machinery A i -0.9379 3.4018 -0.3520 (-0.2989) (0.7733) (-1.8249) A 1 0.4286 4.3618 0.3345 (0.0842) (0.7018) (1.5061) A\ 0.0480 0.0199 0.1377 (1.9023) (1.3434) (12.9115) A\ 0.7823 0.7779 0.6607 (206.2660) (190.7199) (179.6206) A' T 0.0925 -0.5869 0.0493 (0.1589) (-0.7208) (1.6874) B 1 ^ 0.0143 0.0130 0.0151 (5.3407) (4.5724) (5.2779) BV 0.0000 0.0000 0.0000 (0.0000) (0.0000) (0.0000) B\ AL 0.0000 0.0000 0.0000 (0.0000) (0.0000) (0.0000) BV 0.0000 0.0000 0.0000 (0.0000) (0.0000) (0.0000) B 1 ^ 1.1643 2.1759 0.1685 (0.2816) (0.4906) (1.2410) B 1 ^ -0.0117 -0.0041 0.0228 (-0.5560) (-0.3223) (3.5170) B 1 ^ -0.0675 -0.3414 0.0034 (-0.1428) (-0.5915) (0.1781) B\ L -0.0178 -0.0408 -0.0276 (-4.7122) (-6.3158) (-2.8682) B\ T 0.0033 0.0060 0.0022 (1.4291) (4.3641) (2.2368) B 1 ^ -0.0018 0.0501 -0.0032 (-0.0339) (0.6648) (-1.4071) PAGE 134 128 Parameter Industry The whole manucturing AS, A\ A\ A 1 B [^ MK B ML B MT B'kk B l KL Bl KT B\ L B | T (1 14 (1 (12 (424. -1, (-10. (12. 0. (0. 0. (0. 0. (0. 10. (1. 0. (2. -1. (-1-0. (-7. -0. (-0. 0. (1. .7194 ,0731) .2764 .2730) 1463 .5811) 6759 .7895) 7624 1646) 0175 2801) 0000 0000) 0000 0000) 0000 0000) 8000 3925) 0214 5933) 3909 3304) 0325 1107) 0008 7931) 1761 2506) PAGE 135 129 Table III-8. Sources of Sectoral Output Growth: 19 Sectors Model (in percent) 1975-1978 A X Industry DD EE IS 10 1. Agri, Forest & fish 2 Mining 3 Food & beverages 4. Textiles & leather 5. Lumber & wood prod 6. Paper, print & publ 7 Chems & chem prods 8. Nonmetal min prods 9. Prim metal manufac 10. Metal prods & mach 11. Misc manufacturing 12 Construction 13. Elec, gas &wtr serv 14. Wholesale & retail 15. Transp,wrhs & comm 16. Fin, ins & real est 17. Publ admin & defen 18. Restrnt & hotl,etc 19. Dummy sector 77 .4 PAGE 136 130 Table III-9. Sources of Sectoral Output Growth: 19 Sectors Model (in percent) 1978-1980 A X Industry DD EE IS 10 1. Agri, forest & fish 2 Mining 3 Food & beverages 4. Textiles & leather 5 Lumber & wood prod 6. Paper, print & publ 7 Chems & chem prods 8. Nonmetal min prods 9. Prim metal manufac 10. Metal prods & mach 11. Misc manufacturing 12. Construction 13. Elec,gas &wtr serv 14. Wholesale & retail 15. Transp,wrhs & comm 16. Fin, ins & real est 17. Publ admin & defen 18. Restrnt & hotl,etc 19. Dummy sector 187 PAGE 137 131 Table 111-10. Sources of Sectoral Output Growth: 19 Sector Model (in percent) 1980-1983 A X Industry DD EE IS 10 1. Agri, forest & fish 2. Mining 3 Food & beverages 4 Textiles & leather 5 Lumber & wood prod 6. Paper, print & publ 7 Chems & chem prods 8. Nonmetal min prods 9. Prim metal manufac 10. Metal prods & mach 11. Misc manufacturing 12 Construction 13. Elec,gas &wtr serv 14. Wholesale & retail 15. Transp,wrhs & comm 16. Fin, ins & real est 17. Publ admin & defen 18. Restrnt & hotl,etc 19. Dummy sector 100.8 PAGE 138 132 Table III-ll. Sources of Sectoral Output Growth: 19 Sector Model (in percent) 1983-1985 A X Industry DD EE IS 10 1. Agri, forest & fish 2 Mining 3 Food & beverages 4. Textiles & leather 5 Lumber & wood prod 6. Paper, print & publ 7 Chems & chem prods 8. Nonmetal min prods 9. Prim metal manufac 10. Metal prods & mach 11. Misc manufacturing 12. Construction 13. Elec,gas &wtr serv 14. Wholesale & retail 15. Transp,wrhs & comm 16. Fin, ins & real est 17. Publ admin & defen 18. Restrnt & hotl,etc 19. Dummy sector 66 PAGE 139 133 Table 111-12. Sources of Sectoral Output Growth: 19 Sector Model (in percent) 1975-1978 S X Industry DD EE IS 10 1. Agri, forest & fish 2 Mining 3. Food & beverages 4. Textiles & leather 5 Lumber & wood prod 6. Paper, print & publ 7 Chems & chem prods 8. Nonmetal min prods 9. Prim metal manufac 10. Metal prods & mach 11. Misc manufacturing 12 Construction 13. Elec,gas &wtr serv 14. Wholesale & retail 15. Transp,wrhs & comm 16. Fin, ins & real est 17. Publ admin & defen 18. Restrnt & hotl,etc 19 Dummy sector 23 PAGE 140 134 Table 111-13. Sources of Sectoral Output Growth: 19 Sector Model (in percent) 1978-1980 6 X Industry DD EE IS 10 1. Agri, forest & fish 2. Mining 3 Food & beverages 4. Textiles & leather 5 Lumber & wood prod 6. Paper, print & publ 7 Chems & chem prods 8. Nonmetal min prods 9. Prim metal manufac 10. Metal prods & mach 11. Misc manufacturing 12 Construction 13. elec,gas &wtr serv 14. Wholesale & retail 15. Transp,wrhs & comm 16. Fin, ins & real estm 17. Publ admin & defen 18. Restrnt & hotl etc 19. Dummy sector 123 .4 PAGE 141 135 Table 111-14. Sources of Sectoral Output Growth: 19 Sector Model (in percent) 1980-1983 6 X Industry DD EE IS 10 1. Agri, forest & fish 2. Mining 3 Food & beverages 4. Textiles & leather 5 Lumber & wood prod 6. Paper, print & publ 7 Chems & chem prods 8 Nonmetal min prods 9. Prim metal manufac 10. Metal prods & mach 11. Misc manufacturing 12. Construction 13. Elec,gas &wtr serv 14. Wholesale & retail 15. 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Total Factor Productivity Analysis: A Disaggregated Study if the Korean Mining and Manufacturing Sectors With Explicit Consideration of Intermediate Inputs (Mimeograph) Korea Development Institute. Seoul, Korea. Samuelson, Paul A. 1973. Relative shares and elasticities simplified: Comment. American Economic Review 63: 770771. Sono M. 1961. The effect of price changes on the demand and supply of separable goods. International Economic Review 2: 239-271. Westphal, Larry E.. 1978. The Republic of Korea's Experience with Export-Led Industrial Development. World Development 6-3: 347-382. PAGE 148 I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. s-~-^Zs-& A^-~ s; G.S. Maddala, Chairman Graduate Research Professor of Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doc of Doctor of Philosophy. Leonard Cheng Associate Professor of Econo I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. NLawrence Kenny / Professor of Economics I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Dp.Gtor of Philosophy n <,: IfjL .-Â•/ John Shonkwiler Professor of Food and Resource Economics This dissertation was submitted to the Graduate Faculty of the Department of Economics in the College of Business Administration and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. December, 1991 \o fi ^y C^^i^^^t u ' Dean, Graduate School PAGE 149 UNIVERSITY OF FLORIDA 3 1262 08285 3341 |