RISK PREMIA IN FOREIGN EXCHANGE MARKETS
BY
WENHE LU
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN
PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1986
I dedicate this dissertation to Mr. Li Youchai, Mr. Li Youfu, Mr.
Li Youqien and all of my fellow kinsmen in Xigomen Village,
Duijiugo District, Fengzhen County, Inner Mongolia, China, whose
experience in the last half a century has led me to comprehend the
significance of economic theory.
ACKNOWLEDGEMENTS
I would like to thank my dissertation committee members, Dr. G.S.
Maddala, Dr. S.R. Cosslett, Dr. E. Zabel, and Dr. R.D. Emerson for their
guidance and comments on earlier drafts of this dissertation.
This dissertation would not have been started if this topic had not
been suggested by my committee chairman Professor G.S. Maddala, to whom
I owe all the intuition I have developed in econometrics. I am deeply
grateful that I have had this opportunity of being exposed to his mind.
Gratitude is accorded to Professor Stephen R. Cosslett, whose
patience and guidance have led me through all the tides in my empirical
experimentation. The sacrifice of his time in disciplining this study
into the form it now takes can never be adequately repaid no. His
expertise in econometrics and high standard of academic studies will be
enlightment to me in the years to come.
Dr. Roger Huang provided me with some of the data used in this
dissertation. Dr. Mark Rush and Dr. Leonard Cheng provided some
references. Thanks to them are due.
Special thanks go to Debra Hunter and DeLayne Redding for efficient
and accurate typing of many drafts of this dissertation.
I would not have started this long process of selfeducation and
eventually formal training in the U.S. but for the encouragement,
guidance and discipline from my parents and my uncles. I would like to
think them for their kindness.
Last but not least I thank Lyndall for all the support she has shown
over these four years of graduate study here at the University of Florida.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS . . . . . . . . . .
ABSTRACT . . . . . . . . . . . .
CHAPTER
I INTRODUCTION AND SURVEY OF THE LITERATURE. . . .
II LUCAS MODEL AND ITS EXTENSIONS: AN EMPIRICAL STUDY.
Lucas Model and its Extension .
White's Adjustment and Empirical Results..
White's test . . . . . . .
Engle's ARCH test . . . . .
III A MONETARY APPROACH TO THE FOREIGN EXCHANGE RATE
DETERMINATION . . . . . . . .
The Model . . . . . . . . .
Estimation and Testing . . . . .
ARCH Method of Estimation . . .
GMM Estimation . . . . . .
Variation on the theme . . . .
IV SUMMARY AND CONCLUSIONS . . . . . .
APPENDIX A . . . . . . . . . .
APPENDIX B . . . . . . . . . ..
APPENDIX C . . . . . . . . . ..
APPENDIX D . . . . . . . . . ..
BIBLIOGRAPHY . . . . . . . . . .
BIOGRAPHICAL SKETCH. . . . . . ... . .
PAGE
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II I
*
.
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
RISK PREMIA IN FOREIGN EXCHANGE MARKETS
By
Wenhe Lu
August, 1986
Chairman: Dr. G.S. Maddala
Major Department: Economics
We have attempted to test the existence of timevarying risk premia
in foreign exchange markets under two models that we have developed in
this dissertation. This first one is an extension to Lucas's general
equilibrium model of international finance. By assumption of the Cobb
Douglas utility function of the consumers we are able to derive a closed
form for the risk premia in the foreign exchange markets on the setting
of a twocountry economy model. We used White's test and Engle's test
for homoscedasticity and used White's heteroscedasticityconsistent
variancecovariance matrix to derive the correct standard errors. The
time varying risk premium is tested jointly with the efficiency of the
foreign exchange market, i.e., whether the forward exchange rates are
unbiased predictors of the future spot exchange rates. The empirical
findings indicate that the notion of market efficiency is rejected and
there is no risk premium for any of the three cases we studied.
In the monetary approach, however, we test the existence of time
varying risk premia alone. By PPP and an extension to the uncovered
v
interest parity we introduced the risk premia into our monetary approach
to foreign exchange rate determination. The forward premium is used as
a driving force of the risk premium. A rational expectation hypothesis
is made and the forward solution derived.
Since it is a nonlinear single equation model and there is
evidence of heteroscedasticity we used GMM estimators and the
corresponding variancecovariance matrix and found that there is
constant risk premia in the case of Germany and Japan but not in the
case of Canada.
We also did an empirical study of monetary model with the formation
of risk premium derived before. The findings we have is that there is
timevarying risk premium in the case of Germany but not in the cases of
Japan and Canada.
Since our monetary model relaxes the restriction imposed on the
semielasticity of interest rate the empirical results are based on a
more general setting than most of the monetary models of foreign
exchange rates. The conflicting empirical results from the two attempts
are attributed to the different setting of the models.
Extensions to the current data will test whether the conclusion we
have drawn is valid.
CHAPTER I
INTRODUCTION AND SURVEY OF THE LITERATURE
Since the early 1970s, the foreign exchange rates among all the
major currencies of the industrialized world have been determined
largely by private market forces within a floating exchange rate system.
The enormous volatility of the spot and forward foreign exchange rates
as predictors of the future spot rates indicates the unexpected amount
of speculation in exchange markets and causes concern for policy makers,
financial associations and research economists. One feature of this
volatility of the exchange rates is that it far exceeds the variation in
the price levels and in the inflation rates in all of the developed
countries over the same period. The search for a rational explanation
for this exchange rate behavior in the setting of integrated
international financial markets has been the central thrust of empirical
as well as theoretical research over the last decade.
A huge literature already exists on this topic. R.M. Levich (1983)
gives a comprehensive survey of the existing models and empirical
findings. These empirical studies convey mixed messages about the
validity of the different models proposed. Most of these models fit the
data for the countries and for the length of time the authors proposed,
but they do not fit the data for the others. There is still no simple
consensus on this topic. See Levich (1983).
Many researchers suspect that the failure of the models overall is
due to the simplicity of the models. The relaxation of the restrictions
imposed on the existing models may well provide us with a more realistic
picture and a closer fit to the data.
There arises a question whether the foreign exchange market is
efficient. If the foreign exchange market is efficient and if the
exchange rate is determined in a fashion similar to the determination of
other asset prices, we should expect that current rates reflect all
current and available information. Expectations concerning future
exchange rates should be incorporated and reflected in forward exchange
rates, i.e., in the regression
lnet = a + blnFt_1 + ut (1.1)
where et denotes the spot exchange rate, Ft denotes the forward exchange
rate at time t, a = 0, b = 1 and residual u should contain no
systematic information and should have no serial correlation. Frankel
(1982) does the above regression and a number of other regressions for
the period June 1973 to August 1980 and concludes that the market is
efficient. However, when the data are extended to the 1980s the same
conclusion can not be drawn. Due to difficulty in collecting the
relevant data, we restrain our preliminary investigation to monthly data
of Dollar/Mark, Dollar/Yen and Dollar/Canada from September 1973 to
December 1984. The results are reported in Table 1.
The hypothesis of market efficiency under the context of (1.1)
amounts to the joint hypothesis H0: a0 = 0, al = 1. We observe that
all the OLS parameter estimates are far off the targets. We do a
conventional Ftest, and the null hypotheses are all rejected.
However, we can not reject the hypothesis of the market being
efficient by the results reported, since we implicitly assume that there
exists no risk premium. It is probable that the market efficiency
Table 1
Preliminary test of the hypothesis of market efficiency
Ine = a + a nFt + ut
t+1 0 1 t t
2
a0 a R URSS RSS F2,131
German 0.815 0.180 0.0170 2.733 73.398 1693.5812
(0.018) (0.120)
Canada 0.193 0.088 0.0196 1.149 69.967 3923.0453
(0.046) (0.055)
Japan 2.097 0.618 0.76 0.574 1.295 257.4
(0.167) (0.030)
Note: The numbers in parentheses are standard errors from
the estimation.
notion is rejected because we do not include the riskpremium term,
preferably a timevarying risk premium term. Therefore, we need to
investigate the risk premia's existence to test for market efficiency.
The purpose of this dissertation is to investigate the existence of the
timevarying risk premium by different approaches in the foreign
exchange rate determination. Before my own studies are introduced, a
survey of the established research efforts is in order.
The approaches taken in this area reflect the different viewpoints
of the exchange rates themselves. As Dornbusch (1980) notes, there are
basically three views of foreign exchange rates: that of the exchange
rates being the relative prices of monies, the relative prices of goods,
and the relative prices of different financial assets. Each of these
three views can not help being partial on its own.
Those who view the exchange rates as the relative prices of monies
concentrate their investigations on the foreign exchange markets per se,
i.e., they study only the relationship between the exchange rates of
different sorts and assume that the other economic factors (price
levels, interest rates, money supplies, etc.) are not arguments for the
determination of the foreign exchange rates. Stochastic properties of
the exchange rates under rational expectations constitute the main focus
of studies falling into this category. In the context of rational
expectation, all of the economic factors other than the exchange rates
are excluded in the information sets of the agents in the economy
considered. See Driskill and McCafferty (1982), Hansen and Hodrick
(1980), (1983), Hodrick and Srivastava (1983), M. Kawai (1984) and Huang
(1984) among others. Compared with these theoretical attempts, the
empirical works are relatively scarce. Hansen and Hodrick (1983) treat
the risk premia as not being rejected for some pairs of countries and
rejected for the others.
The theory of purchasing power parity (PPP) views the exchange
rates as the relative prices of goods in the two countries involved.
Although PPP is theoretically appealing, its restrictions reflect
themselves in the empirical studies. Rush and Husted (1985) is referred
to for detailed empirical studies. The major theoretical drawbacks of
PPP are that PPP ignores the notions of governments intervening in the
foreign exchange markets (tariff), and that not all commodities are
involved in the transactions of foreign trade and the existing
transportation costs. This may be one of the reasons why the PPP
approach to the foreign exchange rate determination is not appealing to
research economists. However, we would expect that PPP would fare
better in the long run than in the short run, since in the long run the
intervention and other obstacles to the flow of trade are not
consequential. Woo (1985) proposes a monetary model with lagged
exchange rates as well as a lagged inflation rate, a real income index
and interest rates. He found that the forecasting power of this model
is better than that of random walk model. However, in his model he
implicitly assumed the absence of the risk premium in the foreign
exchange markets.
More recent research follows the popular portfoliobalance model,
which views the exchange rates mainly as relative prices of different
assets for the two countries. See Frankel (1982a), Dooley and Isard
(1983) and Ueda (1983), among others for theoretical models of this type.
Frankel (1982a) does empirical studies in testing the existence of
the riskpremia for the major six currencies. He assumes that the risk
premia depend specifically upon asset supplies and variancecovariance
of the asset supplies. His conclusion is that empirical results fail to
support the existence of the risk premia in foreign exchange markets.
Dooley and Isard (1983) also find from their investigation that the
assumption of risk premia is a weak one.
Among all the theoretical models Lucas's (1982) is the most general.
His model encompasses all the economic factors (besides news). Domowitz
and Hakkio (1985) extend it by a simplifying specification of the utility
function and derive the risk premium as a function of the difference of
variances of the future money supplies of the two countries. However,
they depart from the model by applying Engle's (1982) ARCH (autoregressive
conditional heteroscedasticity) method which changes the specification of
the risk premia into a function of the realized forecasting errors and
therefore undercuts the theoretical base of their attempt. The results
are quite misleading. If interpreted correctly, the hypotheses that risk
premia exist and are time varying are all rejected, contrary to their
conclusions.
We plan to investigate the existence of timevarying risk premia
along two lines. In Chapter II we set out with a derivation of Lucas's
model and an extension is made with some extra assumptions. An
empirical study follows. Since it is a linear model, we introduce
White's (1980) covariance adjustment robust to heteroscedasticity. We
then carry out a series of tests on market efficiency and the existence
of timevarying risk premia. In Chapter III we pursue a monetary
approach to the foreign exchange determination. We also make a general
assumption of time varying risk premium with the forward premium as a
proxy, as suggested by Hansen and Hodrick (1984). Since it is a
nonlinear model, we use the nonlinear least square method of estimation
to get consistent estimates of the parameters and we introduce the
generalized method of moments by Hansen (1982) to correct the covariance
matrix which is designed to be robust against heteroscedasticity and it
is proved to be asymptotically efficient. The reason that we lay so much
emphasis on the robustness of the estimates against heteroscedasticity is
that its presence causes the variances of the estimates to be inefficient
and makes the statistical inference invalid. A summary and concluding
remarks are collected in Chapter IV.
CHAPTER II
LUCAS MODEL AND ITS EXTENSION: AN EMPIRICAL STUDY
Lucas (1982) developed a general twocountry model of international
trade and finance. Since then it has been extended in a number of
empirical studies of foreign exchange models. Notably, Hodrick and
Srivastava (1983) derive a model with risk premia as a linear function
of the forward premia, and Domowitz and Hakkio (1985) derive an
extension by assuming a specific form of utility function for the agent.
The risk premium in that context is a linear function of the difference
between the variances of the forecasting errors of the money supplies
of the two countries involved. However, they departed from their own
model and used Engle's (1982) ARCH method in their estimation.
Although Lucas (1982) is in close parallel with Lucas (1978), it
has not generated as much response in the field of international finance
as the latter. The purpose of this chapter is to pursue where Domowitz
and Hakkio (1985) left off in their extension and to introduce the
rational expectation hypothesis and White's (1980) heteroscedasticity
consistent covariance adjustment to estimate the original Lucas' model
and also to test the null hypothesis of risk premia being timevarying
in the foreign exchange rate determination and the notion of foreign
exchange market efficiency. The derivation of the model is contained in
Section 1. White's adjustment and the empirical results are reported in
Section 2. Some detailed derivations are collected in the Appendix A.
Section 1 Lucas Model and its Extension
Consider a world economy with two countries. These countries have
identical constant populations; all variables will then be expressed in
per (own country) capital terms. Each citizen of country 0 is endowed
each period with E units of a freely transportable, nonstorable
consumption good X. Each citizen of country 1 is endowed with n units
of consumption good Y. These endowments E and n are stochastic
following a Markov process with transition given by
Pr{(+ < 'I = E, n, = ) = F{}',n',=,n}
Assume that the process 9tn t} has a unique stationary distribution
9((,n). The realizations of ,,n are taken to be known at the beginning
of the period, prior to any trading, but no information (other than full
knowledge of F) is available earlier. Each agent in country i wishes to
maximize an intertemporal utility function of the form
E{ ZE t U(xit,yit )}, 0 < B < 1 i = 0,1 (2.1)
t=0
where xit is consumption in country i in the period t of the good X and
yit is consumption of the good Y. The utility function U and discount
factor 8 are common to both countries. In (2.1) U is assumed to be
continuously differentiable, increasing in both arguments, and concave.
Here we specify a CobbDouglas utility function
U(x,y) = Axyla (2.2)
We assume that agents trade in both goods, spot and in advance
contingent on all possible realizations of the shock process { ,nt}.
The preferences of agents have been assumed to be independent of their
nationalities, so that agents differ only in their endowments. Agents
are assumed riskaverse so that in the face of stochastically varying
endowments, one would expect them to use available securities markets to
pool their risks. In this context, pooling must come down to an exchange
of claims on 'home' endowment for claims on 'foreign' endowment in return.
Perfectly pooling in this sense would involve agents of each country
owning half of the claim to 'home' endowment and half of the foreign.
Let s = {,n} be the current state of the system. Take the prices
of all the goods, current and future, to be functions of the current
state s, with the understanding that prices are assumed stationary in
the sense that the same set of prices is established at s independent of
when s is realized. Then the knowledge of the equilibrium price
functions together with knowledge of the transition functions F(s',s) =
F{(',n',~,n} amount to knowledge of the probability distributions of all
the future prices. Therefore, the agents are assumed to have rational
expectations formulated as such.
For a system in any current state s, let the current spot price of
good X be unity, so that all the other prices will be in terms of
current Xunits. Let p (s), qx(s), and q (s) be the spot price of good
Y at state s, the current price of a claim to the entire future (from
the next period on) stream { t} of the endowment of good X, and the
current price of a claim to the future stream {nt}, respectively, all in
Xunits. Therefore p y(s), q(s) and qy(s) are all relative prices.
Consider an agent entering a period endowed with 0 units of wealth,
consisting of claims to current and future goods, valued in Xunits. He
wants to maximize his utility by choosing the current consumption (x,y)
at spot prices (l,p (s)), equity shares x y in future endowments {Et}
and {nt} at the prices per share qx(s) and q (s) respectively. The
budget constraint is
x + py(s)y + qx(s)Ox + qy(s)y = e (2.3)
The corresponding endowed wealth e' valued in Xunits at the
beginning of the next period will be
6' = 6x [' + q (s')] + 6 [p (s')n' + q (s')] (2.4)
since X,Y are assumed to be nonstorable and V' and n' are new transfer
endowments.
The use of money is motivated by two constraints imposed upon all
traders to the effect that goods can be purchased only with currency
accumulated in advance. The idea is that under current circumstances
currency can serve as an inexpensive bookkeeping device for
decentralized transactions, thus enabling a decentralized system to
imitate closely a centralized ArrowDebreu system. See Lucas (1982).
The timing of trading is taken to be the following. At the
beginning of a period, traders from both countries meet in a centralized
marketplace, bring securities and currency holdings previously
accumulated, and engage in perfectly competitive securities trading.
Before the trading opens, the current period's real state s = {(,n} and
current money supply state {M,N} are both known to all. We note here
that the current money supply shocks are also known at this stage. At
the conclusion of securities trading, agents disperse to trade in goods
and currencies. Since any security earns a positive nominal return in
some currency, it is evident that traders will hold noninterestbearing
currency in exactly the amount they need to cover their perfectly
predictable currentperiod goods purchase. In this context there is
only transaction demand for money of the current period. Also, the
consumers are assumed to have no speculative demand for money.
Let Mt,Nt denote nominal dollars per capital for both countries.
Prior to any trading in period t, let each trader's money holdings be
increased by a lumpsum wtMt_ and vtNt1 so that money supply evolves
according to
Mt+ = (1 + wt+l)Mt,
Nt+1 = (1 + vt+ )Nt (2.5)
Let (w } follow a Markov process, possibly related to the real
process (st with transition function
H{w,w',v,v',s,s'} =
P t+1 w' t+t t= ,t+1 = s',st = s) (2.6)
We then have the following financial constraint
M(t) = Px(s,M)
N(t) = p (s,N)n (2.7)
with the equality sign when equilibria are reached. Here px(s,M) and
p (s,N) are nominal prices.
The objective value function for this agent, therefore, is
V(O,s) = max {U(x,y) + 6 f V(O',s') f(s',s)ds'} (2.8)
x,y, x,9
x y
for the consumer in state s with wealth 6. He is assumed to maximize
(2.8) with 6' denoted in (2.4) subject to the constraints (2.3) and
(2.7). We now have Lagrangian function
12
L(x,y,x' y, X,,1'2,3) = {U(x,y) + 8 / V[{ x[' + qx(s')]
+ e [p (s')n' + q (s')]},s] f(s',s)ds'
+ Al[e x py(s)y qx(s) Ox qy(s) y]
+ 2[Mt Px(s,M)S]
+ x3[Nt py(s,N)n]} (2.9)
The first order conditions for the Lagrangian problem are
L = U (x,y) 1 = 0 (2.10.1)
L = U (x,y) A1p (s) = 0 (2.10.2)
L = B f V,,(e',s')[E' + qx(s')] f(s',s)ds'
x
X1q (s) = 0 (2.10.3)
Le = f V ,(6',s')[p (s')n'
y
+ q (s')] f(s',s)ds' Xq y(s) = 0 (2.10.4)
We also know L = 1 as 0 is given and
L = 6 x p(s)y qx(s) yq (s) (2.10.5)
A1 y x A y y
L = Mt p (s,M)E (2.10.6)
L = N p y(s,N)n (2.10.7)
Reorganizing the above conditions, we have
U (x,y) = Xp (S)
Using L, = 1 = Ux(x,y)
U (x,y) U (x,y) U (i,itn)
p(s) = = TTTn (2.11.1)
y x U (x,y) U (i ,I,)
X x
S/f V (e',s')[v' + qx(s')] f(s',s)ds' = 1q x(s)
q (s) = B[U (x,y)]I 1 U (s')[E' + q (s')] f(s',s)ds' (2.11.2)
B / Ve(6',s')[p (s')n' + q (s')] f(s',s)ds' = X1qy(s)
q (s) = B[U (s)]1 / U (s')[p (s')n'
+ q (s')] f(s',s)ds' (2.11.3)
and
M
px(s,M) = t (2.11.4)
Nr
N
p (sN) = (2.11.5)
y n
Equations (2.8) and (2.9) can be solved forward as in Lucas (1978).
However, it is (2.11.4) and (2.11.5) with which we proceed to derive the
timevarying riskpremia.
Equation (2.11.1) means at such an equilibrium, the relative price
of Y in terms of X, p (st) depends only on the real state of the system,
and is given by the ratio of the marginal utility of Y to the marginal
utility of X.
Given the specification of our utility function, we have
U (,,n) A(1a)xYa 1a x a
U x( ), l  A x y y x ( 2 1
Sy = in
y = In
Here the perfect pooling assumption seems to be restrictive. As we see
later, this will not affect our derivation of the timevaryingrisk
premia.
Assuming purchasing power parity we have
p (s ) Mn M.
xM(stNMt) M ttt t 1a M (
e(st'MtNt) ps y(s) = P p(s ( (2.13)
by (2.11.4), (2.11.5) and (2.12).
The imperfect pooling would mean an additional coefficient of the
above. It should be noted that the exchange rate in (2.13) does not
incorporate expectations of the future contrary to many rational
expectations models of exchange rate [see Levich (1983)]. This result
follows from the setup of the model: all decisions are made after the
resolution of uncertainty, so there is no speculation component to the
money demand. In our paper, endowments and money supplies are assumed
to follow conditional Gaussian AR(1) stochastic process
Int = P1lnt1 + ult
Innt = P2nntl + u2t
nt lnM1 + 3t
nNt = Y2nNt1 + ut
ut' = (Ult,u2t,u3t,u4t)
ut It1 I N(0,Ht)
where I indicates the information set at the period t1.
tdiag(h) (2.14)
t= diag(hll,th22,t h33,t'h44,t) (2.14)
Here we assume zero covariance between the stochastic processes. It is
possible to generalize the model to allow for nonzero covariance. This
would lead to the risk premia also depending upon the conditional
covariances of the money supply.
To derive the forward rate we need interest rate parity. First,
consider the homecurrency price in period t of a claim to one unit of
homecurrency with certainty in period t+1. Such a claim is equivalent to
tM 1 t+l (2.15)
t+1 M
Px(St+lMt+1) Mt+l
units of X in period t+l. Similarly
HN t+l (2.16)
t+l Nt+
t+l
Since l and tl are both functions of the future real output and
nominal money supply, there is uncertainty as to their exact values.
The I units of X will be valued by agents in period t+l at the
t+1
marginal utility of X, Ux(st+ ), which must be discounted back to period
t by multiplication by the discount factor. The xunit price of the
claim to one unit of home currency is therefore Et[Ux(st+) n + Ux(St)1]
which is obtained by taking the conditional expectation of the marginal
value of the payoff on the asset and dividing it by the marginal utility
of X in period t, since the opportunity cost of the investment is its
xunit price times the marginal utility of X in period t.
The home currency price of the investment is then obtained by
multiplication of the xunit price by p (st,M) or division by It.
Therefore, the period t discount bill paying one unit of home currency
in period t+l in terms of the home currency price is
Mt+ M
U (s )1M
b(s ) = E[ s 1Mt+1 EQ (2.17)
x t U (s )M t+1
x t t
Similarly, by replacing x with y in the above argument, the period t
foreign currency price of a claim to one unit of foreign currency in t+1
is
BU (s )H+
b (stt) = E[ t+ E N (2.18)
Y t t U (s )N = t+
y t >"t
where U (s ) is the marginal utility of y in period t and HN is the
yt t
purchasing power of one unit of foreign currency in terms of Y. The
intertemporal marginal rate of substitution of money is an index that
weights the change in the purchasing power of one currency by the inter
temporal marginal rate of substitution of goods between the two periods.
Since the exchange rate is the relative price of two monies, each of the
rates of substitution is important in determining the risk premium in
the forward foreign exchange market.
In order to determine the nature of the risk premium in one forward
foreign exchange market, we must derive the forward price of foreign
exchange, that is, the contract price set in period t at which one can
buy and sell foreign exchange in period t+1.
If there is no default risk on either nominal investment discussed
above or on the forward contracts, investors must be indifferent between
investing in the riskless home currency dominated asset, in which case the
return is 1/b (s ,6 ) per unit of home currency invested, and the alterna
tive covered interest arbitrage strategy of converting the home currency
into foreign currency and selling the proceeds in today's forward market
at price F(stOt,Mt,Nt) of home currency in terms of foreign currency.
17
The covered investment in foreign currency yields the return
1
[e(stlMN)111/by(st,6t)]f(st,9tMtNt)
per home currency invested e(st,M,N) is the exchange rate, i.e., the
foreign currency per one unit of the home currency. Equating the two
strategies,
1 1 [ /
bx(stt) e(stM,N) [i/by(St'et)]F(st'et'Mt'Nt)
x t, t t
we have
b (s ,0 )
F(st,et,Mt,N ) = e(st,M,N) b(s (2.19)
x t t
The forward rate formulation is
EN
EtQ t+1
F =e
t = et M
EtQt+1
From (2.14) we have
U (s')(' M
Et+ = B x t f(ul u u )du du du
St+ U (s) M 1,t+l' U2,t+l' U3,t+l) dUlt+1 du2t+1 du3t+1
x t+l1
BU (s ) M
E x t+1 t+1
=E
t U (s )fl
x t t
ca1
t+1 t
t t+l
a 1(
= E t+1 t+1
E B () (t )
t t nt
M <
t t+1
t+1 t
M
t
M
t+1
(2.20)
u (s')n' N
EQ f (u l du du du
Ety B (sn N t f(ult+l,u2,t+l 3,t+l) dltd2tdu4t
y t+1
BU (s )1N
E y t+1 t+1
t 't+1 "t+1
It is shown in Appendix D that
E NNN
InEtQ InEtQ+ = (lY)lnNt + h
(1Y )lnM h3
1 t 33,t
Substituting the above into (2.19) and taking the logarithm, we have
InFt = Inet + [(1Y2)lnNt (1Y )lnMt h33,t + h44,t
= ln[(la)/a] + InMt nNt + (1Y2)lnNt (1Y1)lnMt h33,t
+ 3h
44,t
= ln[(la)/a] + YllnMt Y21nNt 2h33,t + h44,t
Also from (2.13) we have
E tne = ln[(la)/a] + InMt+1 InNt
= ln[(la)/a] + yllnM Y2lnNt + Etu3t Etu4t
The last two terms are zero, hence we have
EInet nFt = (h 33,+ h44+) (2.23)
Equation (2.23) indicates that the risk premium depends upon the condi
tional variances of the forecasting errors of the domestic and foreign
money supplies. An increase in the conditional variance of domestic
money, h33,t+, increases the conditional variance of domestic prices and,
therefore, increases the expected future purchasing power of the foreign
currency. Consequently, the expected return on a long position in foreign
exchange (the risk premium) must rise to compensate investors. Similarly,
there is an increase in the demand for future foreign currency which
drives down the forward rate, leading to an increase in the risk premium.
The model of (2.23) has the term representing relative conditional
variances of the future money supply shock h33,t+ h44,t+ which can
not be observed at time t. We here make a naive rational expectation
assumption, i.e., that the economic agents use the relative variance of
current money supply shocks h33,t h44,t a proxy to that of the future
money supply shocks. There are other ways of formulating the rational
expectation hypothesis, but they are just as, if not more, arbitrary;
hence (2.23) becomes
Etlne nFt = (h33, h44,t) + [i(ht+ 33t
t t 2 33,t 44,t h33,t
(h44, h44,t)] (2.24)
We approximate Et net and InFt by
et etl Ft et
t t1 t t
and
et1 et
and estimate the equation
et etl Ft I etl
et= a0 + aI e + (h33t h44,t) + t (2.25)
et1 t1
There are two implications of equation (2.25) for the behavior of
the risk premium. First, the only time series movement of the risk
premium is due to the movement of the 'relative variance of the money
supply shock.' Second, the risk premium can take both signs and can
switch signs, depending upon the values of a,, a2. This is important
since, for example, Stockman (1978, p. 172) found that 'the point
estimates of the risk premium change signs,' when he estimated a
hypothesized constant risk premium over different subsamples. Suppose
that a, < 0, a2 > 0. Then for small relative variance of money supply
shocks the risk premium will be negative, while for large relative
variance of money supply shocks, the risk premium may change signs.
Equation (2.25) allows tests of several hypotheses concerning the
timeseries behavior of the risk premium. According to the model, al
should be 1 if the market efficiency hypothesis is to hold, and t+l
should be white noise, independent of whether or not a risk premium
exists. A test of the hypothesis that a2 = 0 is a test of whether the
risk premium is timevarying or not, in determining the deviation of the
forward rate from the expected future spot rate.
Maintaining ia = 1 and t+l white noise, a0 = 0, a2 = 0 means a zero
risk premium. a0 e 0, a2 = 0 implies a constant risk premium. a0 z 0,
a2 = 0 means that data dictate that the risk premium is a time varying one.
Section 2 White's Adjustment and Empirical Results
The model of (2.25) is the one we proceed to estimate. From (2.24)
and (2.25) it is clear that t = vt + a2[I(h33,t+l h33,t) + (h44,t 
h44,t)] and is clearly heteroscedastic. The consequence of this approxi
nation is that the error terms are heteroscedastic; hence OLS estimates of
parameters are consistent and unbiased but not efficient. The OLS
estimates are reported in Table 2. The DW statistics show that the first
degree serial correlation is absent for all cases. Therefore we can treat
the heteroscedasticity as being 'crosssectional' in nature. Before we
proceed to estimate the consistent variancecovariance matrix, we do two
tests for heteroscedasticity and the test scores are reported in Table 2.
White's test
The information matrix test of White (1980) is a test of the validity
of the model against any alternative which renders the usual maximum
likelihood inference techniques invalid. When the model is correctly
specified, the information matrix may be expressed either in Hessian form,
 E[2 L/UDE'] or in the outer product form, E[8L/85 WL/W'] where E is
the vector of parameters being estimated. The White procedure tests the
equality of these alternative expressions. In the present context, the
information matrix test for normality is sensitive to skewness or kurtosis
[White (1980)], and can also be interpreted as a test for parameter
constancy [Chesher (1983)]. White (1980) also proves that the test score
2 2 2
is equivalent to TR x k(k+1)/2 where T is the sample size; R is the
constantadjusted squared multiple correlation coefficient from the
regression
^2 t t 2
=2 = I )2 2
ut + 1 e +2 (h33,t 44,t
+ 3 [(h33,t h44,) t 1]
where again ut is the OLS residual term of model (2.25). The results
are contained in Table 2. The test scores indicate that there is
Tests for Serial
with
e et
t t1
e 0 + 1
tI
Table 2
Correlation and Heteroscedasticity
ARCH as a special case
Ft let)
[ e ] + a2[(h33 h44 )] + E
OLS Estimation
critical
score
Germany Japan Canada at 5%
significance
level
a0 0.0313 0.0022 0.0038
(0.0170) (0.0033) (0.0035)
a 0.0560 0.0426 0.0016
(0.0329) (0.0218) (0.0031)
a2 3.425 1.3865 0.2706
(2.612) (2.2926) (0.3503)
R2 0.0329 0.0316 0.0063
DW 2.007 1.863 2.218
ARCH1 8.619 2.769 2.392 5.02
ARCH2 8.656 3.548 2.3607 7.38
ARCH3 8.9984 3.571 2.5344 9.35
ARCH4 9.3345 5.779 2.794 11.1
White's test 9.694 4.1003 0.5371 9.35
Note: The score for ARCHP is equivalent to TR2 with T as sample size and
2 2 P 2
R from regression e = Y + E .. The numbers in parentheses
Rt from regression Yiti.
i=l
are standard errors from the estimation.
heteroscedasticity in the German/U.S. case but not in the Canada/U.S.
and the Japan/U.S. cases.
Engle's ARCH test
We also carry out Engle's test for the presence of ARCH (auto
regressive conditional heteroscedasticity). In a general model of Engle's
yt = f(Xt,B) + ut
where X is a vector of explanatory variables and 6 the parameter vector
with the distribution of the disturbance term assumed conditional normal
as following
ut t1 N(0,o)
where
2 P 2 (2.26)
t 0 + Yiuti26)
i=1
The highlight of Engle's ARCH formulation is to capture the severe
volatility of the error terms in a model with time series data. It is
particularly attractive in the research involving the foreign exchange
rate modeling, since we observe immense volatility of both spot and
foreign exchange rates. The conditional variance of the current time
period is assumed to be a (linear) function of the squared past errors;
therefore, one larger past error tends to be followed by errors with
larger dispersion. One weak point of ARCH is that p in (2.26) is
arbitrary and has no strict economic theoretical backing.
2
Engle (1982) shows that X score for testing the null hypotheses
2
H Y = Y = ... = Y = 0 is equivalent to TR where T is the sample
size, R2 is the constantadjusted squared multiple correlation
coefficient from the regression
^2 P ^2
ut = Y + E Yiuti (2.27)
i=1
The test scores reported in Table 2 indicate that there is no ARCH for
the cases of Canada and Japan. However, ARCH effects of 1st and 2nd
order are significant in the Germany/U.S. case, although longer lags are
not significant.
Since (2.25) is linear, ARCH estimates can be obtained from the OLS
regression (2.27). See Engle (1982). The results are reported in Table
A ^
3b. The estimates show that y0 and yl are significant in the case of
Germany for all the lag lengths p which we tried. This partly confirms the
results we had in White's test and Engle's test, i.e., there is hetero
scedasticity in the case of Germany case and it is of ARCH type.
Table 3a
ARCH Estimates and White's heteroscedasticityconsistent
variance estimates for Mark/$
^2 P ^2
t = Y0 + Yiu ti
i=l
White's heteroscedasticityconsistent estimates and standard errors
a0 1 a2
Germany 0.0313 0.0560 3.425
(0.215) (0.0399) (2.447)
Japan 0.00225 0.04256 1.3865
(0.00356) (0.02448) (2.10544)
Canada 0.0038 0.0016 0.2706
(0.00356) (0.00313) (0.1195)
Note: The figures in the parenthesis are standard errors.
indicates significance at 5% level.
Table 3b
ARCH Estimates and White's heteroscedasticityconsistent
variance estimates for Mark/$
^2 P ^2
ut = Y + 1 Yiuti
i=1
ARCH parameter estimates
YO Y1 Y2 Y3 Y
Germany 0.00074
(0.00018)
0.00076
(0.00019)
0.00081
(0.00021)
0.00082
(0.00022)
0.00087
(0.00019)
0.00096
(0.00021)
0.00092
(0.00023)
0.00076
(0.00024)
0.00015
(0.00041)
0.00016
(0.000043)
0.00015
(0.000046)
0.00016
(0.000048)
0.2574
(0.0851)
0.2651
(0.0887)
0.2633
(0.0893)
0.2634
0.0897
0.14597
(0.08711)
0.15694
(0.08850)
0.15945
(0.08890)
0.14616
(0.08876)
0.1356
(0.0872)
0.13638
(0.08874)
0.13766
(0.08931)
0.14121
(0.09004)
0.0289
(0.0888)
0.0126
(0.0925)
0.0132
(0.0931)
0.08101
(0.08851)
0.07780
(0.08974)
0.06193
(0.08937)
0.00993
(0.08875)
0.01317
(0.09015)
0.01484
(0.09076)
0.9583
(0.0895)
0.0511
(0.0931)
0.0097
(0.08893)
0.0097
(0.08921)
0.03463
(0.08930)
0.03921
(0.0474)
Note: The figures in the parenthesis are standard errors.
indicates significance at 5% level.
Following White (1980), we calculate the heteroscedasticity
consistent covariance matrix. The procedure is to save residuals ut
from regression (2.25) and calculate the following
Japan
Canada
0.0375
(0.0901)
0.14662
(0.08824)
0.04215
(0.08992)
I 1 ^2 1
0 = (X'X/n) (X'(diag(u ))X'/n)(X'X/n) (2.28)
where X is the matrix of the explanatory variables.
Comparing the heteroscedasticity adjusted standard errors with
those from OLS in Table 2, we find that all but one of them are greater
than the OLS estimates. The coefficient of the risk premium (h33,t
h44,t) for Canada is significant.
Maintaining al = 1, we first test the joint hypothesis a0 = 2 = 0.
The results in Table 4 (in the column RP1) indicate that this null hypothe
sis can not be rejected for any currency. We next test the expanded
hypothesis H0: a0 = a2 = 0, al = 1. The results of this test are reported
in Table 4 (in the column RP2). The results indicate that the null hy
pothesis of no risk premium are rejected for Germany, France and Japan.
The third hypothesis we test is a, = 1. This is a test of market
efficiency when the timevarying risk premium is present in the model.
The null hypothesis are rejected for all the cases.
Table 4
Testing scores for existence of the Risk premia
RP1 RP2 RP3
Germany 2.6427 431.9083 409.25
Japan 6.6010 971.5318 1001.98
Canada 1.1785 53017.746 50922.34
Critical value 99.5 26.2 99.5
Note: The numbers reported for RP1 and RP2 are Fstatistics
at 1% significance level.
RP1 is an Ftest of the hypothesis a0 = a2 = 0;
RP2 is an Ftest of the hypothesis a0 = a2 = 0, a = 1.
RP3 is an Ftest of the hypothesis al = 1.
The above tests suggest that there is no empirical evidence in our
model that the foreign exchange market is 'efficient', i.e., the forward
exchange rates is not an unbiased predictors of the future spot rates.
This finding coincides with the results of the models of the other
authors (see Park (1984), Frankel (1982), Domowitz and Hakkio (1985)
Murfin and Ormerod (1984), Baillie, Lippens and MacMahon (1983)).
However, the tests of the other authors for the market efficiency are
based upon one assumption of risk premia being constant. Although they
also rejected the hypothesis that the forward rates are unbiased
predictors for the spot rates, they can not preclude the possibility
that with timevarying risk premia the market is efficient. The test of
our model does not have this shortcoming and the rejection of the market
efficiency is made upon a more general setting than most of the
empirical studies in the literature.
CHAPTER III
A MONETARY APPROACH TO THE FOREIGN EXCHANGE RATE DETERMINATION
In this chapter we derive a model based on a monetary approach to
foreign exchange rate determination with time varying risk premium.
Except for a timevarying risk premium term, this model is a straight
forward extension of Dornbusch (1980) and Woo (1985).
The model is partial in that money supplies, real incomes, price
levels and interest rates in both countries are assumed to be exogenous
to the foreign exchange market. The rational hypothesis is made when
the revised uncovered interest rate parity is assumed. All the
exogenous variables are assumed to be represented by a finite order
autoregressive process. However, the semielasticity of money demand
with respect to real income levels is not assumed to be the same for
both countries. We hope that this relaxation can lend support to the
validity of the model. We use the forward solution to handle the
expectation of the future endogenous variable and the generalized
method of moments to estimate the model. The model is derived in
Section 1. Section 2 contains the estimation and testing procedure.
Some details are provided in Appendix B.
Section 1 The Model
Consider an economy of two countries. The standard money market
equilibrium condition is
mt Pt =
mt Pt = y r + u tl,..., (3.2)
T is the sample size. Here mt pt' Yt stand for the logarithm of
money supply, price level and real income level at time t for the home
country; rt is the nominal interest rate and ut is a white noise
disturbance term, 4 and 3 are unknown coefficients of the real income
and interest rate and are both positive. Similarly, mt, pt, yt, rt, ut
and t are the corresponding variables and parameters for the foreign
country in the model. Note that we here relax the constraint that most
of the models impose upon the coefficients of the real income levels
being the same for both countries. We hope that this relaxation makes
this model more general than the conventional practice.
Subtracting (3.2) from (3.1) we have
(mtmt (Pt)t = t t B(rtrt) + (utut) (3.3)
The cornerstone of the monetary approach, PPP (purchasing power
parity) is assumed, i.e.,
Pt = pt + et (3.4)
where et is the home currency price of the foreign currency. The PPP
says that arbitrage of commodities will make the exchange rate equal to
the ratio of the price levels of the two countries involved. The
underlying assumptions are that all commodities are traded and that
there is neither government intervention nor transportation cost. These
assumptions are of course not realistic in the real world. However,
these distortions in the longrun are not consequental. Officer (1981)
and Rush and Husted (1985) provide evidence in support of this
assumption. See Levich (1983) for further discussion.
Departing from the riskneutrality assumption in Dornbusch (1980)
and Woo (1985), we modify the uncovered interest rate parity by
introducing the risk premium term
S r = E(et+ e RtI)= E(et+) e R (3.5)
where It is the information set the agents in the economy have up to
time t, R(t) is the risk premium term at period t. E(.I t) denotes the
rational expectation of the agents at time t.
Under the assumption of perfect capital mobility, the equation
looks exactly the same as the uncovered interest rate parity with
investors being riskneutral.
The risk premium we introduced shows our assumption of investors in
general being risk averse. Admittedly, there is difficulty in
differentiating the riskneutrality from perfect capital mobility, since
both arrive at the same form of expression of (3.5) without Rt. Here we
choose the former interpretation.
This can also be interpreted as deriving from the perfect state of
capital mobility. Papell (1985) defines this equation as
r rt = E(el e a(e qt)) + v
where et and qt are deviations from the steady state of the exchange rates
and relative price levels. His formulation implies that imperfect capital
mobility is caused by the shortrun deviation from the longrun PPP.
We can interpret the risk premium along the same lines, i.e., risk
premium reflects the shortrun deviation from PPP relating to the
uncovered interest rate parity in a particular way and this deviation is a
function of the past forecasting error on the spot exchange rates.
Substituting (3.4), (3.5) into (3.3) and rearranging, we have
1 4 8 8
e I (m m ) y + y R + E e +v (3.6)
t 1+8 t 1+7 t 1+ t 1+ Rt 1+ Et t+l (3
(utut)
where vt vt is white noise too.
t 1+p t
Now we proceed to formulate the risk premium and the distribution
of the error term. We assume that R has the general form
2 2 2
Rt = f(d ,d ...,d ) (3.7)
t t1t2 tp
where dt is the forward premium, the difference between the realized
future spot rate and the forward rate divided by the future spot rate
f e
te Hodrick and Srivastava (1983) developed an extension to Lucas's
e
(1982) model and derived that the riskpremium is a function of forward
premium. We take this as given and work from there. The equation
(2.23), the risk premium we derived in Chapter II is developed also from
another extension of Lucas's (1982) model. Since the difference between
these two formulations do not affect the rest of the derivations, we
keep our formulation of the risk premium as the former. In a later
section empirical study with (2.23) is done.
This formation of the risk premium departs from the constant risk
premium assumed in most of the empirical and theoretical studies of
exchange rate models. In a period of rampant forward speculation
constant risk premium is less likely to be the case.
In our investigation, we specifically assume the following:
R = a0 + adt2 + (3.8)
where a0 and a are constant unknowns and dt is the forward premium at
time t, i.e., the difference of logarithms of the forward exchange rate
at time t1 and the spot rate at time t; wt is white noise. Although we
observe asymmetry in the above formulation of the risk premium, we do
allow the risk premium to take either sign as the data dictate.
We here assume that the agents have a naive rational expectation,
i.e., use the current forecasting error as estimate of the future
forecasting errors. Therefore we have
ER = a0 + ad
tt 0 1 t1
ERt+i = + a d i=1,2,... (3.9)
t t+i 0 1 t1
Substituting (3.8) into (3.6), we finally have the model
1t 1+ t +B t 1+6 Y 1+8 tt+1 1+R
( + a d _) + v (3.10)
0 1 t1 t
There are usually two ways of handling the rational expectation of
future endogenous variables. The first is Wickens's (1982) errorin
variable method, which replaces the expectation of the future endogenous
variables with the true observation of that variable. One restriction of
this method is that it is not applicable when the realized and expected
variable appears in the same equation, which is the case with our model.
Therefore, we are left with the method of substitution due to Shiller
(1978) and Wallis (1980). In this model B must take a positive value;
therefore, the backwardsolution method is explosive. See Shiller (1978)
and Wallis (1980) for a discussion of the forward and backward solution
methods. Hence, we proceed to simplify the model using the forward
solution method.
Since Etet+1 involves the future values of all the exogenous
*
variables, we assume at the outset that mt, mt, t, yt are all from a
first order autoregressive process.
Inmt = O + Pl nm + t
*
Inmt = PO + llnmt + t
Inyt = k0 + kllnyt + nt
*
Inyt = ko + k lnyt1 + nt (3.11)
*
where Et, Et' qt' qt are all white noises.
The stationary conditions require that
PO + P" 1
*
PO + PI 1
k0 + k1 1
*
k0 + k < 1
The forward solution method leads us to
1 1 *
et = +(1l mt ( ) mt it l +
+B lk Yt Yt
BO 110 1O k o 0 k
B +1 [1l l 1 ]
0 +I l ) 11 1 1 1k
1~**
011 110111
w w
kOkl1 koklp
[1+k(1 k)I(1k ) +
1 1k [1+8(1kl)](1k)
a1 2 a1 2
Bd d + v (3.12)
1+8 t1 +I t t
The detailed derivations are collected in Appendix B. Equation (3.12)
is the model we proceed to estimate.
Section 2 Estimation and Testing
In this section we use both the ARCH (autoregressive conditional
heteroscedasticity) method introduced by Engle (1982) and GMM
(generalized method of moments) introduced by Hansen (1982) to estimate
the model developed in the last section.
When we address the empirical estimation and testing of our model,
we have to consider the plausibility of the assumption that the distur
bance term is homoscedastic. The volatility of the spot exchange rates
in all years since September 1973 suggests that this assumption may not
be valid, and consideration of this possibility should be given in
estimation and testing to prevent the estimates from being inefficient
if heteroscedasticity is truly the case. There are two ways now
available to tackle this problem. One is the ARCH method of estimation
and the other is GMM. ARCH is more suitable if the residuals show signs
of having a distribution that has a fatter tail than the normal
distribution, whereas GMM has the advantage of not having to be this
specific. We shall use both methods. Unfortunately, the ARCH method
fails to produce convergent maximum likelihood estimates. So after the
derivation of both the methods, only the results of GMM are reported.
ARCH Method of Estimation
McNee (1979) says that "large and small errors tend to cluster
together" in the international finance models. This would suggest that
forecasting variance may change over time, and is predicted by past fore
casting errors. Engle's (1982) ARCH method is intended to help solve this
problem in empirical studies. The basic idea is that the conditional
variance of the error term is nonconstant and moves in an autoregressive
fashion with the past forecasting error. This implies that large errors
tend to be followed by large errors and small errors tend to be followed
by small errors, in either direction. We start with the model
Yt = f(xt ) + v (3.13)
where Y is a vector of observations of the endogenous variable and 6 is
a vector of parameters to be estimated; X is a matrix of explanatory
variables; v is the vector of error terms. The conditional distribution
of the error term is assumed to be of the form
vt Itl N(O,o2) (3.14)
where It is the information set at time t1 and var vt is generally
defined by
2 = f(v v2 v2 ) (3.15)
at = f(t t2 Vt (3 5t
Specifically, we formulate a linear function as follows
o2 = Zy (3.16)
t
where
2 2 2
Z= 1, v ,v ,...,v _} (3.17)
t t1 t21 tp t
a = {y0,Y1,..., p} (3.18)
To restrict the variance to be nonnegative, we impose
Yi > 0 i=0,1,2,...,p (3.19)
and to prevent the variance from being explosive we impose
p
E Yi < 1 (3.20)
i=l1
We note that (3.18) is sufficient but not necessary.
The likelihood function is
2
1 2 1 vt
InL =const. In (3.21)
t 2 t 2 2
at
2
where v = Y f(x ,B) and oa is defined as (3.16). This is maximized
t tt
to obtain the MLE of . The first and second order conditions can be
easily derived. However, in our empirical study likelihood functions
fail to converge.
GMM Estimation
The generalized method of moments (GMM) estimator introduced by
Hansen (1982) consists of finding the element of the parameter space
that sets linear combinations of the sample cross products as close to
zero as possible. The GMM estimator is consistent and is asymptotically
normal if the observable variables are stationary and ergodic. Since
many linear and nonlinear econometric estimators reside within this
category, GMM is a good alternative to the conventional maximum likeli
hood method. One advantage of the GMM estimator over MLE is that the
variancecovariance matrix obtained by GMM is robust with respect to the
specification of the disturbance distribution; hence, we can expect to
produce a heteroscedasticityrobust variancecovariance matrix of the
estimated parameters when the researchers are not confident about the
specification of the disturbance distribution and/or when the specifica
tion of one distribution is too complex.
Consider a model similar to (3.12)
y = Xf(5) + e (3.22)
where y is a Txl dependent variable and X a matrix of explanatory varia
bles of dimension TxM; 6 is the unknown hxl parameter vector; f(6) is
MxN a onetoone function (not necessarily linear) taking element 6 of
the parameter space into a space of greater or equal dimension, i.e., M'h.
It is assumed that there exists an integer P having the property that
E{ tlEtp ,t_p_l...XtXtl*** .) = 0 (3.23)
This formulation admits the possibility of serially correlated residuals.
p=l is equivalent to the absence of serial correlation, since (3.23) implies
E{stle t,St2,...,Xt,Xt_,...} = 0 (3.24)
The GMM estimator is the vector 6 that minimizes the quadratic form
$(6) = (y Xf(6))'X 1X'(y Xf(6)) (3.25)
where 0 is a consistent estimator of the positivedefinite matrix
R = lim ( E(X'ce'X)). (3.26)
T+cT
Hansen (1982) proves that
p1 1 T (
= iX'E X ttqXtq} (3.27)
is a consistent estimator of n.
The variancecovariance matrix of the GMM estimator of 6 is
v'X ^1 X'v 1
plim [( T TX 1 (3.28)
af af f
where v = X X [ ... (3.29)
a6 1 36 62 6h *
where 6 is the GMM estimate.
In our model (3.12)
ft {f f2 f3 f4 f5 f6 f7
where
1
1
f 2
f
1 1+BBp1
I+BBv1
f =
*
6I+BBk1
1+BBk1
2
a, 8
f5 
1+B
oilg
6 = 1+
*
^ 0 B0 0 Bk0 O 0k0
f = + + (3.30)
f7 0 + 1+BBy 1++ + _kBk
2 2
and X = (m m y y d2 d 1.)
and Xt = (m t t Yt t td t
6 = (B 4 ) 0 a 1)
^* af
The derivatives evaluated at 6 7, for the model (3.12) are derived in
Appendix C.
Before we estimate (3.12) the rational expectation hypothesis allows
us to impose the first order autoregressive process on the money supply,
and on the income index for the models of two countries (Germany vs. U.S.
Japan vs. U.S. and Canada vs. U.S.) defined in (3.11). The estimates of
P0' il, k0, k1 are reported in Table 5. The U.S. is treated as the
foreign country in all cases, as usually the case in empirical studies of
exchange rate models.
Table 5
Estimations of the firstorder autoregression process
*
on the exogenous variables mt, mt, Yt' Yt.
U.S. Germany Japan Canada
V0 0.00115077 0.09747710 0.30776482 0.00467322
1 1.0078970 0.98287155 0.972608783 1.00037203
k0 0.05466299 0.37540327 0.01169507 0.41615339
k. 0.98914601 0.92667755 0.99814542 0.91531332
Note: The above estimates are from the regressions
mt = + ~imt1 + lt
and Yt = k0 + kYt + v2t
where mtYt are logarithms of money supply and income index
respectively.
Substitute the estimates from the autoregressive processes into
equation (3.12), and then estimate it with NLLS.
Before we set out to adjust the variancecovariance matrix of the
GMM estimator, we first do some diagnostic checking on the residuals we
obtained from the NLLS estimation.
Table 6
Tests of ARCH in equation (3.12)
2 p
2t =0 +
i=1
Germany
Japan
Canada
2
Bi t1
Note: The numbers in parentheses are all t scores
indicates significance at the 5% level.
for H :
i = 0.
1
B0 1 2 B3
0.0035 0.7321
(1.787) (12.255),
0.0037 0.7910 0.0804
(1.889) (8.97) (0.911)
0.0025 0.8101 0.2671 0.2364
(1.341) (9.464) (2.449) (2.759)
0.0043 0.8372
(0.046) (17.708),
0.0027 0.5649 0.3278
(1.342) (6.792), (3.96) ,
0.0022 0.5495 0.2207 0.1233
(1.113) (6.557) (2.396) (1.479)
0.0010 0.8219
(1.719) (16.969),
0.0007 0.5844 0.2981
(1.099) (6.988) (3.605),
0.0008 0.62988 0.2561 0.0221
(1.139) (7.329) (2.688) (0.263)
We first test the existence of serial correlation by the standard
regression
2 P 2
s = 0 + Bti (3.31)
i=l
The results are reported in Table 6. Engle's X2 test of ARCH is
conveniently equivalent to TR2 of (3.31), with T as sample size and R2
as the squared multiple correlation coefficient from (3.12). Table 6
shows that p in (3.31) should be picked as 3 for Germany, 2 for Canada
and Japan. Table 7 contains the GMM estimates.
In Table 7 the estimates of the semielasticity of money with
respect to interest rates B show that they are not significant from zero
for all the cases. The estimates of the semielasticity of money with
respect to the income index for Germany, Japan and Canada are all
significantly different from that of U.S. These findings have confirmed
that the restrictions imposed in the conventional monetary models are
too rigid and the corresponding restrictions should be relaxed.
Therefore the results we have obtained are based on a more general
setting then the conventional practice. Unfortunately, the estimates of
are not the same for the three cases. We concede here that further
research should be made along these lines.
Woo (1985) develops a monetary model for the dollar/deutschmark
rate with a partial adjustment mechanism assumed in the money demand
function. There he also relaxes the restrictions as we do but he
assumes a zero risk premium. His estimate of B is significantly
different from zero but (, i are not. Since he concentrates on the
dollar/deutschmark rate only, we do not know how his model would fare in
the other cases. In contrast, our model is built up with a timevarying
risk premium. The results from our empirical study should have a better
reflection of the reality than Woo's.
The other monetary models are mostly built using the data up until
1980, therefore their results can not be compared in the same light with
ours. See Frankel (1983) for the other empirical studies.
Turning to the terms of timevarying risk premium, GMM estimates
indicate that there are constant risk premia in the case of Germany and
Japan.
Table 7
GMM estimation of (3.12)
B f f 0 a1
Germany 3.9920 2.4402 1.05637, 2.0918 0.4884
(S.E.) (3.6176) (1.4070) (0.2444) (0.9269) (0.4415)
Canada 0.0307 0.9484 7.2775 35.7719 1.8947
(S.E.) (0.1039) (0.2824) (0.2116) (135.921) (5.5671)
Japan 0.0056 0.1257 0.1723 40.0190 0.1697
(S.E.) (0.5483) (0.6316) (0.3458) (0.3958) (0.1413)
Note: S.E. stands for the standard error according to the generalized
method of moments.
indicates significance at 5% level.
In the case of Canada, GMM estimates indicate that risk premia do
not exist. There have been few attempts on modeling timevarying risk
premium into the monetary approach of foreign exchange determination.
One reason is that the monetary approach did not fare well in empirical
studies. Therefore there are not many papers of monetary approach in
the recent five or six years. Another reason is that the source of the
timevarying risk premium is usually outside the system of the monetary
models. It is my belief that incorporating the timevarying risk
premium into the monetary approach may prove to revive the interests of
researchers in this area. The current paper is one attempt.
Variation on the Theme
We proceed to do another empirical study with model (3.12).
Instead of using forward premium as argument of the timevarying risk
premium so far we use (2.23), the risk premium derived in Chapter II,
i.e., the difference of the variances of the money supplies as the
argument of the risk premium.
Parallel to the preceding procedure, NLLS of (3.12) is run with new
formulation of risk premium. Residuals are saved and ARCH test is
taken. The result is reported in Table 8.
The results show evidence of ARCH effect. We choose 2, 2, 1 as
values of p in (3.30) for Japan, Canada and Germany respectively. ARCH
estimation failed to converge again. GMM is used to estimate (3.12).
The results are reported in Table 9.
We note that in the case of Japan the estimate of coefficient of
*
U.S. income index ( hit the bound. As in the preceding empirical
study, the estimates of < ) are significant for the case of Canada
while risk premium is nonexistent. Again, there is empirical evidence
that in the case of Germany there is timevarying risk premium but not
in the case of Japan and Canada. These results partly conform to those
we obtained in the first empirical study of (3.12).
Table 8
Tests of ARCH of equation (3.12) with
risk premium defined as (2.23)
2 P
Et 0 + E
t=1
E2i
i ti
80 81 62 83 TR2
0.0061 0.8280 88.805
(0.0027) (0.0501)
0.0054 0.7288 0.1190 59.706
(0.0027) (0.0877) (0.0889)
0.0049 0.6910 0.0027 0.1441 92.648
(0.0024) (0.0770) (0.095) (0.0779)
0.0029 0.8649 97.595
(0.0016) (0.0444)
0.0021 0.5977 0.3123 100.256
(0.0016) (0.0837) (0.0840)
0.0018 0.5990 0.2647 0.0498 100.736
(0.0016) (0.0867) (0.0977) (0.0875)
0.0014 0.8140 60.892
(0.0008) (0.0487)
0.0009 0.6022 0.2719 92.248
(0.0007) (0.0841) (0.0828)
0.0010 0.6575 0.2478 0.0561 92.288
(0.0007) (0.0862) (0.0969) (0.0838)
Note: The figures in the parentheses are the standard errors. The
2
critical X score is 53.7 at 0.5% significance level.
indicates that the coefficient is significant at 5% level.
Germany
Japan
Canada
Table 9
GMM estimation of (3.12) with (2.23) as risk premium
S0 "1
Germany 0.7083 2.1196 0.6534 11.8076 8.0253
(S.E.) (15.5247 (4.8193) (0.7628) (3.54133) (3.19257)
Canada 0.3728 1.2322 1.2743 6.6495 0.6425
(S.E.) (0.9642) (0.3085) (0.3272) (1134.7) (165.869)
Japan 4.5285 0.2833 0.0 0.4098 0.1427
(S.E.) (1.2580) (0.7046) (0.3293) (0.4405) (3.3414)
Note: S.E. stands for the standard error.
indicates significance at 5% level.
CHAPTER IV
SUMMARY AND CONCLUSIONS
We have attempted to test the existence of timevarying risk premia
in the foreign exchange markets under two models we have developed in
this dissertation. This first one is an extension of the Lucas (1982)
general equilibrium model of international finance. By the assumption
of a CobbDouglas utility function for consumers we are able to derive a
closed form for the risk premia in the foreign exchange markets in the
setting of a twocountry economy model. The time varying risk premium
is tested jointly with the efficiency of the foreign exchange markets,
i.e., whether the forward exchange rates are unbiased predictors of the
future spot exchange rates.
We note that the model we developed in Chapter 2 is an extension to
Lucas (1982) under the strict assumption of CobbDouglas utility
functions. This assumption immensely simplifies our derivation of the
source for the risk premia in our model. We also made the assumptions
of independent Markov processes for the incomes and the money supplies
of both countries. Finally, we used the variance of current money
supply shocks as estimates of the variance of the future money supply
shocks for both countries. Any of the three assumptions can not avoid
being arbitrary and there are other alternatives for each of them.
Further investigations along these lines are topics for future research.
We used White's test and Engle's test for homoscedasticity and used
White's heteroscedasticityconsistent variancecovariance matrix to
derive the correct standard errors. The joint hypothesis of market
efficiency and nonexistence of risk premia in the foreign exchange
market are rejected for Germany, Japan and Canada. Market efficiency is
rejected by the data in our model. Although market efficiency is also
rejected in the models of Park (1984), Frankel (1982), Murfin and
Ormerod (1984), Baillie, Lippens and MacMahon (1983), their models
assumed zero or constant risk premium. Therefore their results are
based on a less general setting than the one we have. Domowitz and
Hakkio (1985), however, did develop an exchange rate model with time
varying risk premium and also tested the market efficiency and the time
varying risk premium. Unfortunately their conclusions were wrongly
drawn. Interpreted correctly, their findings are parallel to what we
have in our model.
In the monetary approach, we tested the existence of timevarying
risk premia alone. The semielasticities with respect to interest rates
in the money demand equation are assumed to be identical. However, the
parameters of the income index term are not assumed identical.
Therefore, our model is estimated on a more general setting than most of
the monetary models of risk premium in the foreign exchange markets. By
PPP and an extension to the uncovered interest parity we introduced the
risk premia into our monetary approach to foreign exchange rate
determination. The forward premium is used as a proxy for the source of
the risk premium. Rational expectation hypotheses are made and the
forward solution derived.
In the first stage of investigation we impose the firstdegree
autoregressive process for all the exogenous variables and we also
impose independence of the disturbance terms. Although these are
conventional practices in the literature with the rational expectation
hypothesis, we must concede that there is arbitrariness in these
formulations. Other rational expectation hypotheses can be incorporated
into our model in future research.
Since it is a nonlinear single equation model, and we found
evidence of the existence of heteroscedasticity in the error term we
used GMM estimators and corresponding variancecovariance matrices and
found that for the case of Germany there is risk premium.
Redefining the risk premium as we derived in the Lucas's model, we
repeat the empirical studies in the monetary approach and find that
there is risk premium in the case of Germany and Japan and no risk
premium in the case of Canada.
There have been few attempts on modeling timevarying risk premium
into the monetary approach of foreign exchange determination. One
reason is that the monetary approach did not fare well in empirical
studies. Therefore there are not many papers of monetary approach in
the recent five or six years. Another reason is that the source of the
timevarying risk premium is usually outside the system of the monetary
models. It is my belief that incorporating the timevarying risk
premium into the monetary approach may prove to revive the interests of
researchers in this area. The current paper is one attempt.
The conflicting empirical results from the two attempts are
attributed to the different settings of the models. However, there is
enough empirical support to the notion that German mark/U.S. Dollar
exchange market generates risk premia.
Extension to the current data will test whether the conclusion we
have drawn is valid.
APPENDIX A
The monthly data used in Chapter II and III are obtained from the
following resources.
Canada
Japan
U.S.
Germany
spot IFS IFS IFS
rate ae ae ae
73.10 78.12 73.10 78.12 73.10 78.12 ,
forward Harris Bank Weekly Harris Bank Weekly Harris Bank Weekly
rate 79.1 84.12 79.1 84.12 79.1 84.12
Financial Times Financial Times Financial Times
price IFS IFS IFS IFS
index 64 64 64 64
income IFS IFS IFS IFS
index 66.c 66.c 66.c 66.c
interest IFS IFS IFS IFS
rates 60c 60b 61 60c
money IFS IFS IFS IFS
supply 34.b 34.b 34.b 34.b
Note: The spot exchange rates and forward exchange rates are all relative
to U.S. Dollars. Interest rates and money supply figures are all
reported figures. Price indices and income indices are all with
1967 as the base year. Forward rates are collected for the last
Friday of each month from the Financial Times from January 1979 to
December 1984.
*
The forward data are obtained from the Harris Bank Weekly Review
for October 1973 to December 1978. Weekly data are available, and
the last week's data of every month is used for tests and
estimations involving 1month forward rate.
International Financial Statistics
Exchange market rate
consumer prices
Industrial Production, Seasonally adjusted
call money rate
treasury bill rate
public authority bond yield
Money, Seasonally adjusted
IFS:
ae:
64:
66.c:
60.b:
60.c:
61:
34.b:
APPENDIX B
We first make the assumption that all the exogenous variables are
from afirstorder autoregressive process, which is the conventional
practice as well as the simpliest assumption in models of rational
expectations. The other types of assumptions of the stochastic process
are certainly just as arbitrary.
mt = 10 + 1mt1 + t
** *
m = 0 + mtl + t
S= k0 + klt1 +t
* *
Yt = k + klYt1 + w t=2,...,T (Bl)
*
where vt, vt, wt, wt are white noise; T is the sample size. Equation
(Bl) and the rational expectation hypothesis lead to
t t+i 111 mt
1
*i
0(1 ) *i *
Em = + mt
t t+i 1 t
i *i
k0(1kl) i k0(lkl ) *i
E y 0 + kly Ey 0 + k y (B2)
tt+i 1k t t t+i k k Yt
The expectations of the e's projected on It are
1
Etet+I 1+ O P"O+ mt
*
1+6
*
 o 1+8t (k ( + klYt
** 2 +
(k0 + klYt) ~T (a0 + aldt) +  Etet+2
1 O0(u ) i
Eet+i + pm
t t+i 1+ 11 t
1
*1 *i
0pl) *i *
1p* 1 t
1
k0(1k )
+ 4 ( 1k +
1 K
*i
i k0(lk1 )
klt) + ( +
lk1
6
+ Etet+i+
1+6 t t+i+1
018 2
Sd2
1+6 t
Substituting (B3) into (3.10) recursively and collecting terms we have
1I
e=
t 1+6B6i
62
a1 2
1+B t
1 4 ,
m TTm Y +
t t 1+Bk t *
1 +BBk
a16 2
d t
1+8 t1
+6 0 ~ 0 k k0
1+B 1P 1k
I 1 1
1
*
4 kO
+ ) a 0
1k
1
**
17 (11PP)(1+61) ( P*)(1+6_ 1
11 )
4kok1 4 k0k1
k1 + k)0k +vt
(1k )(1+66k ) (1k )(1+*6k t
1 (l (lkl)(l+ kl)
which we use in our empirical study of this chapter.
*i *
k Yt)]
(B3)
(B4)
To make the derivation clear, we repeat (B4) and have
1
vt = e +B
t t 1+a6p
y *
SYt
1+g6k
1
1( P"
1+B luI
+ *
(lk )(l+6f k )
The likelihood function is
1 *
m + m + y
t 1+6^ t + 1+8BkI Yt
2
1 B 2 a2 2
1+r t 1+T tl
*0 k0 O k0
S k + +
lv 1 lk
1 1
0 _)1 k 0k1
*l(1k 1)(i++k
1 l 2 1
2 ogat 2
2
v
t
2 + const.
t
we impose here
2 2
t = 2 + avt
and the first order conditions are
and the first order conditions are
af 1
an 2
a
t
St1 t vt
(av) +
(3tI a 2 +
a
t
2
vt
2 )2
(a )
t
tt1
vt1 an 3
2
v tv v av v
t t t1 t1 it
+ 7 ( 1)
2 3n 3 2 an 2
t t t
f(v ) = 
af 1 1
a2 2 2
t
af
3f
3o 3
2
1 vt
2 (2 )2
t
3f 2
 2* v
aa t1
2
*
where n = {6,<,( ,C0,a }.
We need
1plI
= 2 m
(1+66Ul)
* (1k1)
+* 2
(1+6Ok)I )
*
t
*
1pl

*2
(1+88pl)
alB(B+2) 2
(1+B)2 t
* 4(1kI)
m  y
t 2 Yt
(1+88k)
al 2
+ d
(+)2 t1
(1+B)
1 0 0 0ko k 0
+ +
SO2 1 1 1k 
(1+6) I 1 0 1 1k1
1 kO l 1Ol
+ ( 
kokI 0 kok1
(1k )(1+BBk ) + )
1 1 (1kl)(1+B8k)
**
+ 0 + ( +
1+ (l+2 B )2
(1+BBUl) (1+B8pl)
S kk1
(1+6+Bk )
1 B ko kkl1
+Bk t 1+ 1 k1 1+B (lk )(1+BBk)
1+Rkl t + T+ + k1
1
1+BBk1 Yt
k k
S0k 1
+ (1 
1+B 1k 1+6Bk
1 1
av
t
w8
av
t
* *
4 k0k1
1 )
2
(1+SBk1)
**
1 k __ k0k1
t 1+e 1+6 
1+BkI lk1 (1lkl) (l+Bak)
1
1+BBk1
*
ko k
S k(1 
l k1 1+BBk1
2
I a 2 d2 + d2
1+a t 1+6 t1
av
a300
avt
ml
Dv
Appendix C
8f
For (3.28) we derive 2
fi1 (1u)
1 1 1
a8 [ i+f3(li)]2
[1+BC1k) 2
af3 (1k )
^ 2
af4 (lkI)
af5 _l_(2+_ )
S (1+)2
af6
as (1+S)2
Jr6
as following
af7 1 10 "
aB (1+)2 1 1[l
Da [P 
*
(1i1)[ l+B(l1) ]2
+ ^ 2
1+P [I1+e(11l) ]
^
Ik 1
lkl
^* *
+ ko 1__ O1
 0 [2
1k (1+6) (1 1[1+8(1u)]
k0k1 +
0k
(1kl)[l+B(1kl)]
^* *
Skk1k
^ ^
(1k1 (1+8Sk1)
* ^ ^ *
110k O0k 1 k k k
[1+(1p)] [1+(1k)]2 1+6(1k) ]2
^ ]2 [ l+ (llkl
af af2
1 2
af 
af3
af7
afl
af 4
3({
af7
03f
0
af4 af af6
4 = = T = 6
p ( (( 0
1
1+B(1k1)
A
ak
= ^ (1
(l+8)(lk1)
af2 af3
2 3
w*
1
1+8(1kI)
af
~*
*<(
^ *
Sk
(1 
(1+8)(lkI)
af2
2
T0
0
8f 3 f
3 4
0 0
k
^ )
1+B(1k1)
af
 0
*>
k
af5 af6
 5 6T
0 0
af7
7
5 a_ B
0
af2
1
af af 9f
3 4 6
1 1 1
8f
7
=  = 0
1
af
5 6
1 1+8
afl
1
APPENDIX D
From equation (2.19) we know
b (s ,6 )
F(st'tM Nt) = e(stM,N) b t t
x tt
The forward rate formulation is
EtQt+
t t where
where
U (s') '
EtQti + U (s)
x
M
t
Nt+l
6U (s )t+
x t+1 t+l
Et U(s)TM
x t t
t+l1
t E t
t
t
()
t+1
M
t
M
t+1
t+l
Et
a 1a
t+1 t+l t
Et E n M
t t t+1
Et Q =
U (s')n' N
y ) f(u lt tu t) dutdu dut
U (s) f Itu2t' 4t it 2t 4t
y t+1
(DI)
f(ultu2t'u3t) dultdU2tdu3t
(D2)
0 (s ) I
=E y t+1 t+1
 USE
U (s )v
y tt
(t+1)
= E ( t
5t
nt)
nt+l
t+l1
= E5 ()
Et
a a1
n, N
t t
>()
t+ N
t+l t+1
From (2.14)
Ult = Int+l tln t
Ult N(0,hlt)
In t+1 = Ult + P11nt N(Pllnt,hllt)
Hence the probability density function of lnSt+ given hlt is
t~l gvenlilt
(D3)
f(inEt+',hlit)
= 1
1 t
exp[ 2h (ln
lit
 P1lnt)2]
Similarly
f(innt+lh22t
f(1nMt+1,h33t)
f(InNt+ ,h44t )
1
=  exp[
22t
exp[
33t
S 1
44t
2h (1nnt+1
22t
(InMll
2h t t+
2h33t (nMt+l
exp[ (inNt+1
44t
 P21nnt )2
 Yl1nMt)2]
 Y21nNt)2]
N t+l t+l
Et t+1 t Et 
t t
N
t
t+I
nt+
ntt
N
t
t+i
60
S a cn ia N 1
t+1 t+1 t+1
=E ( ) () ()
Et ( N
t t t t
t a a e 1a N
(t+1 t+ 2t+1u
= / ( ) ) ( N ) f(ult,u2tu) dultdu2tdu4t
t t t
Since ult, u2t and u4t are assumed to be uncorrelated, we have
E a t+ 1a
N t+l (t+1 
EQ = 8 (t) f(u t)dult f )
t t+1 t It It nt
N 1
t+1
f(u2t) dut I ( N)
t
f(u ) dut
4t 4t
( t+ l) 1 exp{ n PInE '2} d(lnt )
B t r27 i 2hllt t+i
( t + )I 1 0 e x pt + 2 t d ( in n + 1)
St /2h22t 2h22tl t+
2
Nt+ 1 (InNt+l Y21nNt)2
= ()  exp{ t 1 d(lnNI )
t 2h t+1
t 2th 1tt+
44t
44t
Since
E[E(' =
t+1
exp(ap lnEt + a2 hllt)
E(naI ) = exp{(a1)pl2nnt + 1(al)2h22
1
E(Nt+I) = exp{l21nNt + h44t
(M1) = exp{Yn + h }
E(Mt+I) = expfYllnMt + tht
t+I I 33t}
In{EtQ 4
t t+1
2
=In8 alnt + ap lnt + a 2hlt
+ alnnt + (al)p21nnt + i(a) 2h22t
+ iNt Y2nNt + h44t
61
1n{E Q m} = n + aP lnEt + laa 2 h
+ alnfl + (ctl)p2lnflt + (Ca1)2 h22t
+ lriiM Y21' t + jh44t
Therefore
InE Q
t t+1
 lnEtQtil = ('2)'nNt + 44t
(lyl)lntt 1h33t
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BIOGRAPHICAL SKETCH
Wenhe Lu was born in Shanghai, China, January 2nd 1953. When the
Cultural Revolution was launched, he was a firstyear student in
Nanyang Middle School in Shanghai.
In May 1969 he volunteered to settle down as an educated youth in
Xigomen Village, Diujiugo Commune, Feng Zhen County, Inner Mongolia,
where he spent four and a half hard years both as a farmer and as a
young revolutionary.
After passing a primitive entranceexam, he was assigned to study
English for three years in Inner Mongolia Teacher's College in Huhehot,
Inner Mongolia, China. Then he was assigned as a teacher of English and
Physics to No. 2 Senior and Middle School in Feng Zhen County, Inner
Mongolia.
In July, 1978 he took and passed the nationwide entranceexam for
the Graduate School of the Academy of Sciences in Peking and studied
English and Education there until August 1980.
He came to the United States as a special student in the Department
of Economics, University of Pittsburgh and was awarded his M.A. in
Economics in August, 1982. Since then he has been a Ph.D. student in
the Department of Economics, University of Florida.
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.
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
Doctor of Philosophy.
Edward Zabel
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
Doctor of Philosophy.
Stephen R. Cosslett
Associate 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 dis ion for degree of
Doctor of Philosophy.
Robert D. Emerson
Associate 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.
August, 1986
Dean, Graduate School
