A general structure of limited-endogenous-variable models and their applications to the sectoral shifts hypotheses


Material Information

A general structure of limited-endogenous-variable models and their applications to the sectoral shifts hypotheses
Physical Description:
vii, 110 leaves : ; 28 cm.
Sonn, Yang-Hoon, 1958-
Publication Date:


Subjects / Keywords:
Economic forecasting   ( lcsh )
Employment forecasting   ( lcsh )
Macroeconomics   ( lcsh )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )


Thesis (Ph. D.)--University of Florida, 1989.
Includes bibliographical references (leaves 103-109).
Statement of Responsibility:
by Yang-Hoon Sonn.
General Note:
General Note:

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 001572377
notis - AHJ6200
oclc - 22853902
System ID:

Full Text







U''~~Y I CJ -

I dedicate this dissertation to those who have taught economics to me.


I am deeply indebted to Professor G.S. Maddala, Lawrence Kenny,

Prakash Loungani, and Robert Emerson, my dissertation committee, for

their encouragement, guidance, support and patience, all of which

contributed to successful completion of this dissertation. Special

thanks are due to Professor Loungani for his friendship and guidance

throughout my doctoral program. I thank Professor Sanford Berg at Public

Utility Research Center of University of Florida, for his financial

support. I am grateful to Professor Richard Rogerson at Stanford

University for his contribution to this dissertation. I appreciate my

college, Byeong Kim, for helpful discussions.

Thanks are not sufficient for the care and support of my parents.

Finally, I am indebted to my wife and son, Hyo-Jin for their

encouragement as I worked to complete this dissertation.




ACKNOWLEDGEMENTS................................................... iii

ABSTRACT ........................................................... vi


I INTRODUCTION.............................................. 1

Recent Developments in Macroeconomics...................... 2
A New View of Recessions................................ 2
The Use of Panel Data .................................. 4
Statement of Goals......................................... 5
Notes...................................................... 10


Introduction.. ........................... ................. 11
The Standard Tobit Model................................... 12
Heckman Model............................................ 13
Endogenous Switching Regression Model..................... 19
Notes...................................................... 22


Introduction.. ........................... ................. 24
Alternate Specifications of Sectoral Mobility.............. 26
Mobility and Unemployment:
Results for the Primary Specification.................. 31
General Patterns....................................... 31
Detailed Patterns..................................... 36
Alternate Specification of Mobility:
A Comparison with Murphy and Topel..................... 41
Intra-Industry Mobility, Occupational Mobility
and Unemployment......... .............................. 44
Intra-Industry Mobility and Unemployment............... 44
Occupational Mobility.................................. 45
Individual Characteristics and Unemployment............... 47
Conclusions............................................... 52
Notes...................................................... 54


Introduction.. ........................... ................. 70
Censored Regression Model................................... 73
Estimation of The Wage and
Reservation Wage Distributions.......................... 76
Cyclical Patterns in Job Search Behavior.................. 83
Conclusions............................................... 86
Notes...................................................... 87

V SUMMARY AND CONCLUSIONS ................................... 96

APPENDIX ........................................................... 101

BIBLIOGRAPHY....................................................... 103

BIOGRAPHICAL SKETCH................................................ 110

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



Yang-Hoon Sonn

December, 1989

Chairman: Dr. G. S. Maddala
Major Department: Economics

This dissertation consists of one brief survey of the econometric

methods in limited-endogenous-variable models and two applications of

these models to sectoral shifts hypotheses.

Lilien argues that a substantial fraction of the variance of

unemployment can be attributed to fluctuations of the natural rate

brought about by the slow adjustment of labor to shifts of employment

demand between sectors of the economy. A recent paper by Murphy and

Topel, which uses data from the March Current Population Survey,

concludes that Lilien's hypothesis is inconsistent with the facts. The

major finding of the first essay is that their conclusion is quite

premature. We use longitudinal data from the Michigan Panel Study of

Income Dynamics(PSID). Our main finding is that the sectoral shifts

hypothesis receives greater empirical support, if the definition of

switchers is extended to include workers who spend a year or more


Other issues discussed in this essay include the impact of

individual characteristics on weeks of unemployment using an endogenous

switching regression model. The results indicate that the contribution

of industry switchers is higher during recessions than during booms.

Hence, the sectoral shifts hypothesis receives support even after

correcting for selectivity bias and holding other individual

characteristics constant.

The question we address in the next essay is the following: why is

the duration of unemployment longer for switchers than for stayers. A

stationary job search model based on Heckman (1974) is constructed. The

hypothesis is that job switchers lose some sector-specific skills when

they are displaced from their jobs and hence they are offered a lower

wage than they were on their old jobs, leading them to experience longer

period of unemployment (job search). The empirical evidence from the

PSID turns out to support this hypothesis strongly. Another issue

discussed in this essay is the cyclical pattern of the impact of

sectoral shifts on offered wages and reservation wages. The pattern of

the effects of sectoral shifts on the difference between the wages of

switchers and stayers is found to be acyclical.


Explanation of unemployment has been a major task of

macroeconomics due to the dramatic increase in level and variability of

the measured unemployment rate since mid 1970s. Economists distinguish

conceptually among three types of unemployment--frictional, cyclical and

structural. Frictional unemployment is attributed to the process of

normal labor turnover. Cyclical unemployment is associated with declines

in aggregate demand. If real wages are sluggish in their response to

demand changes, the impact of a shock to aggregate demand is felt on

employment. Macroeconomists have focused largely on cyclical

unemployment. In theory, such unemployment can be alleviated through the

macroeconomic tools of monetary and fiscal policy.

Structural unemployment is caused by shifts in the composition of

labor demand across industries or regions in the economy. Such sectoral

shifts create a mismatch between labor demand and labor supply. Since

the reallocation of workers across sectors cannot be instantaneously

accomplished, these shifts cause unemployment in some sectors. The

extent of this unemployment depends on many factors such as the nature

of the compositional shift, the opportunities and costs of retraining

and whether or not the shift was anticipated. Structural unemployment

can be combated through 'micro' policies such as employment and training

programs, the provision of information about jobs in other sectors and

the provision of relocation allowances. The frictional-cum-structural

component is often referred to as the natural rate of unemployment.

Recent Developments in Macroeconomics

A New View of Recessions

It has been a standard practice in macroeconomics to assume that

the natural rate of unemployment behaves in a fairly predictable way,

and then to focus on the causes and consequences of cyclical

unemployment. For instance, in the work of Robert Barro (1981), the

natural rate is modeled as a simple time trend; the deviation of actual

unemployment from this trend is considered to be the 'cyclical'

component. Barro then considers the extent to which 'cyclical'

unemployment can be explained by shocks to aggregate demand.

However, as a result of innovative work by David Lilien (1982) and

others, a new view of recessions has begun to emerge. Lilien argued that

much of cyclical unemployment may largely be the result of the slow

adjustment of labor across sectors of the economy to intersectoral

shifts in labor demand. He noted that most of the shocks experienced by

the U.S. economy in the 1970s the curtailment of defense expenditures

due to the end of the Vietnam War, the oil price shocks, the increase in

import competition affected some sectors of the economy more than

others. While these shocks undoubtedly had an impact on aggregate

demand, their impact on the composition of demand was perhaps equally

important. Stated differently, Lilien suggested that much of what

macroeconomists thought of as cyclical unemployment was in fact better

thought of as structural unemployment. The appropriate cure, therefore,

was not aggregate demand policies but the micro level policies described

above. Lilien's view is commonly referred to as the sectoral shifts


Lilien's empirical evidence on the extent of structural

unemployment in the 1970s, though suggestive, was not entirely

convincing. Lilien used annual time series data on aggregate

unemployment and on employment growth rates in different industries. He

constructed an index, at, which measured the variance, or dispersion, of

employment growth across different industries in the economy. For

instance, if all industries grew at the same rate over a given year, a

for that year would be zero; dispersion in growth rates would lead to

positive values of a. Lilien then demonstrated that, during the 1970s,

years of high unemployment coincided with years in which a was high.

At first sight, it may seem that the positive correlation between

a and aggregate unemployment, U, supports the sectoral shifts

hypothesis. However, subsequent work by Abraham and Katz (1986), Davis

(1986) and Loungani (1986) demonstrated that the a-U correlation was

consistent with other hypotheses, including the aggregate demand

hypothesis. The basic point in these papers is that this correlation can

arise even in the absence of labor reallocation. All that is needed is

that aggregate demand shocks trigger temporary layoffs in each sector

and that the magnitude of these layoffs differs across sectors. Hence,

the correlation between unemployment and dispersion could not be

unequivocally used to support the sectoral shifts view.

The Use of Panel Data

All of the studies cited above share the feature that they rely on

aggregate time series data. However, Lilien's basic point is that much

of unemployment can be attributed to individuals switching industries as

a result of sectoral shifts in demand; the use of micro data seems to

offer the best way for evaluating the relative merits of the sectoral

shifts hypothesis and the aggregate demand hypothesis.'

In light of this, Loungani and Rogerson (1989) used micro data in

order to directly test the validity of Lilien's view. They used data

from the Michigan Panel Study of Income Dynamics, a longitudinal data

set which started in 1968 by interviewing heads of households. Each year

there are additions to the sample as children of the original families

form their own households; however, some families are also 'lost' each

year for a variety of reasons.2 Since 1968, annual interviews have been

conducted with the head of each household. A wealth of socioeconomic

information is collected during these interviews, such as the head's

labor force status and also information on job changes and unemployment

experienced during the year. Using this information, Loungani and

Rogerson were able to explicitly show how the pace of labor reallocation

was different during booms than during recessions; they were also able

to measure how much unemployment could be attributed to the process of

labor reallocation across industries.

Their broad conclusions were as follows:

(1) The reallocation of labor from the goods-producing industries to the

service-producing industries is higher during recessions than in a

'normal' year. In other words, recessions are marked by an acceleration

in the rate of structural change in the economy.

(2) The incidence of unemployment among industry switchers goes up in a

recession. (Many of these industry switches are, of course, involuntary

in the sense that the worker was laid-off and not recalled.)

(3) Industry switchers account for about 25% of the total weeks of

unemployment experienced by all workers during a boom; during a

recession this proportion increases to 40%.

To summarize, their research shows that structural unemployment -the

unemployment caused by industry switching is an important component of

total unemployment and it becomes even more important during recessions.

Statement of Goals

The broad goal of this dissertation is to use longitudinal data in

order to determine the extent of structural unemployment in the U.S.

since the 1970s. Investigations are conducted in two different ways.

First, we investigate the relationship between sectoral mobility and

unemployment to find a role for sectoral shifts in explaining part of

the cyclical fluctuations in unemployment. We use micro data to measure

the exact magnitude of cross flow of labor between sectors.

Second, we use the individual-based information to present the

procedure of job switching behavior of workers. Since we encounter the

problems of potentially biased estimates arising from the limited

dependent variables, switching simultaneous equations model built by

Heckman (1976) is emphasized as a method to estimate the models.

The specific goals are three-fold:

(1) to make a brief survey on the general structure of limited-

endogenous-variable models;

(2) to compare the unemployment experience of displaced workers (and

other job switchers) with those of job stayers and to estimate

individual-based unemployment function;

(3) to explain differences between the unemployment experience of job

switchers and job stayers in terms of a model of job search.

The rest of the dissertation contains three chapters of main studies and

conclusions. Brief outlines of chapters II to IV are given below.

The objective of chapter II is to provide a brief note on the

estimation method for the next two chapters. Investigating the procedure

of job switching using the micro data, we encounter limited dependent

variable problems as in the usual cross-sectional studies. The dependent

variable to be explained in the third chapter is weeks of unemployment

which has a problem of potentially biased estimates arising from the

selection that generates the sample. This feature requires the use of

the endogenous switching regression model.

The job search model in the fourth chapter is aimed at explaining

the wage and reservation wage distribution that the workers encounter

during sectoral shifts. The offered wage is limited for the working

sample only and the reservation wage is totally unobservable. The

Heckman (1974) type of censored regression model is used to solve these


For the next two essays, chapter II contains the standard tobit

model and two other generalizations of the tobit model which involve

more than one limited dependent variable. We discuss the separate

mechanism governing the censoring and the estimation method.

The first part of the chapter III tests whether the total weeks of

unemployment experienced by switchers differs significantly from the

two-year unemployment experience of stayers. [The terms switcher and

stayer are used extensively in the discussion. A precise definition of

these terms is given in second section. For present purposes, it is

sufficient to note that the PSID classifies individuals into 26 industry

groups. A switcher is a worker who changes industry groups between some

date t and a later date t+k. Many of these switches may be involuntary.

A stayer is a worker who does not change industries between t and t+k.]

There are several conclusions that can be drawn from the results.

First, abstracting from cyclical patterns, we discuss the differences

between switchers and stayers. The average duration of unemployment is

always higher for switchers than for stayers; the difference is more

pronounced if the first measure, expectation of the weeks unemployed, is

used. For instance, in the 1974-76 period, the average duration for

stayers is about 3 weeks compared to nearly 9 weeks for switchers. The

percentage of stayers experiencing zero weeks of unemployment is always

higher than the percentage of switchers experiencing zero weeks.

However, the percentage of workers experiencing very long spells is

lower for stayers than for switchers. For both switchers and stayers, a

small fraction of workers accounts for a large fraction of total weeks

of unemployment.

Next, let's turn to the cyclical pattern. The first conclusion is

that the gap between the average duration for switchers and the average


duration for stayers widens during recessions. Second, the percentage of

movers who experience zero weeks of unemployment goes down sharply

during recessions. (A similar pattern holds for stayers but it is far

less pronounced.) Third, the percentage of movers who experience long

spells goes up during a recession. For instance, only 0.5% of switchers

had more than 52 weeks of unemployment between 1977 and 1979 and they

accounted for 6.5% of the total weeks of unemployment experienced by

switchers; in the 1974-76 recession 3.5% of switchers had more than 52

weeks of unemployment and they accounted for 27% of the total.

These results appear to be in conflict with those of an

influential recent paper by Murphy and Topel (1987). They also look at

the relationship between mobility and unemployment and reach the

following conclusion (p. 26): "the contribution of industry changers to

total unemployment is virtually constant over the post-1970 period." In

this chapter we explain why their results differ from ours.

Other issues that are investigated in this chapter are the impact

of individual characteristics such as education and skill on weeks of

unemployment and the role of occupational mobility.

Chapter IV is based on a stationary job search model. Since many

of the variables in search models are difficult to observe, we need some

special treatment in estimation. In this chapter we develop a model for

estimating both the reservation wage and offered wage distribution from

incomplete data based on the well-cited model by Heckman (1974).

Information on the accepted wage offers is the incomplete data used to

estimate the wage offer distribution. Estimates of the reservation wage


can also be derived from these same data provided certain identification

conditions are satisfied.

This chapter attempts to explain why the average duration of

unemployment is higher for switchers than for stayers. The basic

hypothesis is that job switchers lose some sector-specific skills when

they are displaced from their jobs and hence they receive wage offers

that are lower than what they earned on their old jobs. However, their

reservation wage does not decline immediately by a similar amount

because it takes time to realize how much offered wage has fallen,

leading them to experience longer periods of unemployment (job search).

The empirical evidence from the PSID turns out to strongly support this


The second issue of chapter IV is the cyclical pattern of the

impact of sectoral shifts on wage and reservation wage. We examine those

effects of sectoral shifts involved in job search behavior under

different economic conditions in the labor market. The switchers are

offered a lower wage than stayers regardless of the level of

unemployment. The difference is larger in booms than in recessions. The

difference in the effects of sectoral shifts in wage and reservation

wage between stayers and switchers is found to be acyclical.

The final chapter contains the summary and conclusions of the

present study.


1. The problem of this discussion is that it is difficult to use time
series data on the dispersion index. In measuring this we cannot control
several other labor flows such as,
(1) changes in the rate of new entry into different industries;
(2) changes in the rate of outflow from different industries
due to, for example, retirement;
(3) movement into and out of the aggregate labor force.
Above all, the dispersion index used only picks up the net flow of labor
among industries, whereas the amount of unemployment may depend on the
gross flows of labor.

2. Becketti, Gould, Lillard and Welch (1989) recently studied the
dynamics of exit from and entry into the PSID sample and concluded that
"attrition has not substantially reduced the representativeness of the
PSID" (p. 2). Becketti et. al. went on to state : "Weighing the PSID
with the weights supplied by ISR [Institute for Social Research] goes a
long way towards making the PSID sample resemble the CPS [Current
Population Survey] sample ... For some variables, particularly income
and education, there is some reason to believe that the reports in the
PSID may be more accurate than those in the CPS. At any rate, the PSID
participants behave almost identically, conditional on their observed
characteristics, to participants in the CPS." (p. 27).



This section explores the generalization of the censored

regression models which have been developed since the pioneering work by

Tobin (1958). He proposed the problem of limited dependent variable when

the dependent variable is constrained to be non-negative. He argued that

the presence of many observations at zero produces biased estimates if

the standard least square method is used. In his model the censoring is

governed by the value of the dependent variable itself.

Econometricians have given attention to discrete or limited data not

only because of the rapid growth in the availability of micro data sets

but because of the growing awareness of the importance of discrete

choice models for the analysis of microeconomic problems. Many

generalizations of Tobin's model have been proposed since the early

1970s. A more interesting generalization is to consider a model which

involves more than one limited dependent variable. We restrict our

attention to two cases where there is a separate mechanism governing the

censoring. They are Heckman's labor supply model and endogenous

switching regression model.' The standard tobit model is described in

second section. In third section, we discuss the statistical model of

Heckman. Endogenous switching models will follow after that.

The Standard Tobit Model

Tobin's model for explaining a household's expenditure on a

durable good is defined as

y y if y > YO (2-1)

= YO otherwise

If we assume that yO is zero and the same for all the individual

households, we obtain the following statistical model:

Yi = XiB + ui (2-2)

Yi = yi if yi > 0

= 0 otherwise

where u. are errors that are independently and normally distributed,
with mean zero and a common variance a Suppose that the data on the

dependent variable are 0 for all censored cases.

The least squares estimation applied to only the sample which is

greater than zero is also biased.

E(y.i y> 0 ) E(X.B+u.I X.B+u.>O)

i Z(X B/a)
= X.B + / (2-3)
1 (xi8/o)


Since the last term, conditional expectation of u., is omitted from the

regression, this is clearly biased.

While the least square estimator, whether it is applied to all of

the sample or to part of the sample excluding censored is biased and

inconsistent, maximum likelihood estimation provides, consistent and

asymptotically normal estimators.2 The likelihood function for the tobit

model is

L= H l-F(X.i/o) H ao a (y.-X.B)/C (2-4)
y.i0 y.>0
1 1

The likelihood function is composed of the probability of the observed

event y.<0 and the density of the observed y..
1 1
We can use a two-step estimator suggested by Heckman (1976) in a

two equation generalization of the tobit model, which we shall study in

the next section. We get the maximum likelihood estimates of B/o using

the probit model for the dummy variable defined to be 1 if y.>0 and 0

otherwise. Using these, we get estimated values of 0 and D. Now we can

get consistent estimates of B and a by estimating (2-3) by OLS, using

estimated values of 0/4 as an explanatory variable.

Heckman Model

In the standard tobit model the censoring is governed by the value

of the dependent variable itself. Many generalizations of Tobin's model

have been proposed since the early 1970s. Heckman (1974) proposed a very

interesting model in which the censoring is governed by another external


variable. He developed this statistical procedure extending Tobin (1958)

to a simultaneous equations system. This procedure solves the problem

of potentially biased estimates arising from the selection process that

generated the sample.

Heckman proposed a unified summary of statistical models for

sample selection, truncation and limited dependent variables. He

developed a statistical model which defines the joint distribution of

the wage rate and the hours worked.

The equation for the offered wage rate is,

W. = X. + u. (2-5)

He assumes an individual is free to adjust his or her working hours to

reach an equilibrium at which the offered wage equals reservation wage,

Wr. He specifies Wr explicitly as a function of the hours worked, H,

and other variables. As an appropriate time unit for the empirical

analysis, a year is taken to be "current period." Both annual hours

worked and weeks employed are used.

W = -yH + Z.a + v. (2-6)
1 1 1 1

We assume that u. and v. are jointly normally distributed, with mean
1 1

zero, and correlated with each other. We assume that the ith individual

works if

Wr < W0 (2-7)
1 1

Then the wage W. and H. are determined by solving (2-5) and (2-6) after
1 1

setting W. = W. = W. We can define Heckman's model as
1 1

W. = X.B + u. (2-8)
1 1 1

W. = yH. + Z.a + v. (2-9)
1 1 1 1

This gives a recursive system of reduced form equations for observed

wages and working hours as (2-8) and

X.B Z.a u. v.
H. + (2-10)

The problem is we cannot obtain observations with which to estimate

equation (2-8) and (2-10) if condition (2-7) doesn't hold. Thus, the

disturbances of equation (2-8) and (2-10) have conditional distribution

on inequality (2-7). Since there are common regressors in inequality and

equations, the regressors will be correlated with the disturbances.

Thus, it is impossible to obtain unbiased or consistent estimates using

ordinary least squares to estimate these equations.

If H. < 0, the individual is not in the labor force. For the

observations for which H. S 0, we have

u. v. < X.B + Z.a (2-11)

2 2 2
because 7 is expected to be positive. Since var(u.-v.) =a =a +a -2 ,
1 1 U V UV

X.B + Z.a
Prob(H.<0) = 4


where 4(*) is the distribution function of the standard normal.

If H. > 0, the individual is in the labor force, and we observe H
and W. For these observations, the joint distribution of observed hours

and wages for the ith individual may be written as

d(W,HI Hi>0) Prob(H---


where d is the conditional distribution and n is the joint normal

density function.3 The likelihood function for this model is

L = Hn Prob(H.>0)
H.>0 Prob(H.>0)
1 1

H 4D

- X.B + Z.a


Sn n(W,H)


H- X.[ + Z.Q
H #

Heckman (1974) estimated this model by a maximum likelihood

estimation method. Later (Heckman,1976), he suggested a two-stage

estimation method to get the wage equation by evaluating E(u.i H.>0) in

(2-8). This estimation method is as follows. From (2-10)

X.B Z.a u. v.
H. = +

where, u and v

error terms of


are assumed to be joint normal with zero mean. Thus, the

the two equations have the following covariance


S- a
u uv


a a
u uv

2 2
a + a 2 a
u v uv

Under this covariance structure, we can get the new equations for (2-8)

and (2-10)' by evaluating the conditional distribution of the error


E(W.i H.>0) = X.B +

u uv

2 2 ]1/2 i
a + a 2
u v uv

2 2 1/2
X.B Z. [ 2 + a 2 a i2
S i u v uv
E(H.i H>0) = -+
7 7

where A.=
1 1 -






In (2-18), f and 4 are the density function and the distribution

function of the standard normal evaluated at (-X.B + Z.a) / a.
1 1
The two stage procedure for the equations (2-16) and (2-17) involves an

estimation of the probit function determining whether or not an

individual works and then an estimation of equation (2-16) and (2-17) by

OLS after substituting the Inverse Mill's Ratio, A..

Though this gives us consistent estimates of the parameters, they

are not efficient when the model is overidentified. Heckman proposed an

alternative weeks employed equation. The weeks employed equation may be

estimated from the following equation (2-19) using the predicted value

from wage function given by equation (2-16) as a regressor.

SE(W Hi >)-Zi a2 a
E(HiI Hi>0) = 2 v uv x (2-19)
1 2 2 1/2 i
\a + a -2 a
u v uv

The advantage of this procedure is that it permits estimation of a

unique value of l/7 when the model is overidentified.

Lee, Maddala, and Trost (1980) extend Heckman's simultaneous two-

step estimator for structural parameters. Note that W = Wr for the

employed sample. We can now write (2-6) as


S 1 [ a2 2 /22a 1
a +a uv
u v uv

where w. is the error v. corrected for its mean, and hence E(w.)-0.

However, we can not estimate equation (2-20) by OLS, because H is an

endogenous variable. We have to find an instrumental variable for the

subsample with H>0. After estimating the parameters in equation (2-17)

by Heckman's simultaneous two-step estimation method, we get the
estimated values H. We substitute these values of H in place of H in

equation (2-20) and estimate it by OLS. This will also produce

consistent estimates for structural parameters.4

Endogenous Switching Regression Model

Switching regression models in which the censoring is governed by

another external criterion function is one of the major generalizations

of the tobit model. In its simplest form, the behavior of the agents is

described by two regression equations, and external selectivity

criterion function determines which of these two equations is

applicable. The endogenous switching regression model is defined as


yli= Xli B+ Uli (2-21)

y2i= X2i 2+ u2i

3i= X 3iB 3+ u3i

yi y2i if Yli> 0

= Y3i if Yli 0

yli= 1 if Yli> 0

0 if yli 0 i-1,2,...N

where uli, u2i, and u3i are i.i.d. drawings from a trivariate normal

distribution, with mean vector zero and the following covariance matrix.

1 a12 a13

a12 a2 a23 (2-22)

a13 a23 a3

This model is called an endogenous switching regression model because

the observed dependent variable switches between two equations depending

on the outcome of a random variable yli which might be correlated with

Y2i and Y3i
The likelihood function is given by

r0 0
I *
L= II f3(yliy3i) dli f2(YiY2i) dYli (2-23)
SliO -oo li>0 -oo

where f3 is the joint density of yli and Y3i and f2 is the joint density

of yli and y2i'

Lee (1978) discussed a simple two stage estimation method by

adjusting the expectations of the error terms conditional on the

selectivity criterion. Note that the conditional distribution of u2i

given uli is a normal with mean a12 uli and variance a 2 f *
12' l
the conditional expectations of error u2i is:

E(u2il Yli>0) = E(u2ii Uli> -Xi B1)

= E(al2uli uli> -XliB1)

= -a12 (-XliBl) [Z(-XliB l) (2-24)


r i-1
E(u3I yli:O) = -a13 0(-XliB1) 1 D(-X li l) (2-25)

These are used in the two stage estimation procedure. The

consistent estimates of B2 and 83 are obtained by OLS including these

Inverse Mill's Ratios as explanatory variables after replacing B1 by its

estimated values from the probit maximum likelihood estimation. This

procedure also provides consistent estimates of a12 and a13.


1. The importance of these models is discussed in Amemiya(1985). His
review of the empirical literature in this field suggests that most of
the econometric applications of Tobit models fall into these categories.

2. Amemiya(1973) presented the proofs of these propositions.

3. This joint normal density function can be written as

n(W,H) = 1yj


2 w oo 2(1- p )
u v

S (Gl+G2+G3)
2(1- p2)


u v

H.- 1

G2 = -2


[I w- X B ] [

G3 = [ Wi_ XI.B]2





2 a
2 2
a a
u v

4. Wales and Woodland(1980) reported a Monte Carlo study on the two
stage estimation and maximum likelihood estimation. They investigated
different methods of estimating a labor supply model when a significant
proportion of the sample is not working.

G1 =




2 2
u a
u v


5. The typical application of this model is given by Lee(1978) who
studied the effect of union membership on the wage rate. The two regimes
in this model are determined by whether the individuals join the union
or not, and the dependent variables of two regimes represent the
observed wage rate. Note that union wages are censored for observations
on nonunion workers and nonunion wages are censored for union workers.



The link between mobility and unemployment is a key feature of

many theories of unemployment. Lucas and Prescott (1975) modelled the

steady state unemployment rate as arising from the need for the economy

to continually adjust the allocation of workers across production units.

Similarly, Hall (1970) emphasized that the unemployment rate could be

high even at full-employment because of the normal turnover that is

inevitable in an economy where some sectors are expanding and others are

contracting. Black (1982), Lilien (1982) and Davis (1987a) used this

basic structure to motivate the sectoral shifts hypothesis, which

emphasizes that changes in the amount of desired reallocation of labor

may give rise to cyclical fluctuations.

An attractive feature of these models is that they are explicit

about the relation of mobility to unemployment and hence lend themselves

to empirical analysis. Because data at the individual level provides the

best way of evaluating these theories, the recent paper by Murphy and

Topel (1987), which uses data from the March Current Population Survey

(CPS), is an invaluable source of information. Their paper provides a

wealth of information about unemployment during the period 1968-1985,

but pays particular attention to the contribution of industrial mobility

to unemployment over this period. Murphy and Topel compare the incidence

of unemployment among those who change industries ("switchers") and

those who do not ("stayers"). They conclude that the contribution of

switchers to the incidence of unemployment is virtually constant over

the post-1970 period. Their conclusion appears to have been widely

accepted as evidence against the sectoral shifts hypothesis [see, e.g.,

Blanchard and Fischer (1989, p.355) and Mankiw (1989, p.87)].

Our goal is to elaborate upon the work contained in Murphy and

Topel, using data from the Michigan Panel Study of Income Dynamics

(PSID) for the period 1974 to 1985. Unlike the CPS, the PSID follows

individuals for several years and hence offers greater flexibility in

defining and investigating alternate concepts of sectoral mobility. One

of our main findings is that Murphy and Topel's conclusion is sensitive

to alternate definitions of industry switching. If the definition of a

switcher is extended to include workers who spend a year or more

unemployed in the interim, the sectoral shifts hypothesis receives

greater empirical support. When this broader concept of sectoral

mobility is adopted, the contribution of industry switchers to total

weeks of unemployment is higher during recessions than during booms. In

addition to the cyclical importance of mobility, our results indicate

that roughly half of all unemployment is accounted for by individuals

who are switching industries and/or occupations.

Another of our main findings is that mobility-based models of

unemployment which focus entirely on the volume of mobility may be

missing an important feature of the data. We find that different types

of mobility have significantly different amounts of unemployment

associated with them. For example, a typical transition from the goods


producing sector to the service producing sector involves over 50% more

unemployment than a transition in the opposite direction.

Another feature which has been overlooked in much of the mobility

literature is the case of workers who are displaced from one sector and

seem to remain without a strong employment connection for an extended

period. Recent papers by Lilien (1988) and Rogerson (1989) have

considered this type of outcome. Our results indicate that although this

group is small in number, it is significant in a discussion of aggregate

unemployment. Hence, identification of the factors that cause some

workers to require an extended period to relocate seems important in

understanding unemployment.

Alternate Specifications of Sectoral Mobility

The goal of this chapter is to provide a detailed analysis of the

relationship between mobility and unemployment. Abstracting from details

for the moment, the nature of the exercise we wish to carry out is

straightforward. Pick two dates, tl and t2. For a given set of workers

we can observe their industry of employment at these two dates, thus

partitioning them into stayers and switchers. We can then analyze the

unemployment experienced by each group over the chosen interval.

Repeating this procedure for several intervals [t ,l t2'], where some of

the intervals correspond to expansions and others coincide with

recessions would allow us (i) to determine the correlation between

mobility and the cycle and (ii) to determine the correlation between the

unemployment associated with mobility and the cycle. Although this

procedure is straightforward in principle, there are a number of issues

which arise in the context of providing a more detailed specification.

In fact, one of the points that we wish to emphasize is that one's

interpretation of the "facts" depends crucially on the definition of

sectoral mobility that is adopted. Rather than adopting a particular

specification of mobility at this point, it is instructive to consider

various examples that are suggestive of some of the issues involved.

Consider the following three cases:

Case 1: A worker becomes unemployed during a recession, finds a job in a

different industry and stays there until retirement.

Case 2: A worker becomes unemployed during a recession, finds a job in a

different industry but returns to his or her industry shortly after the

recession and remains there until retirement.

Case 3: A worker becomes unemployed during a recession, finds a job in a

different industry, stays there for ten years and then changes to a job

in the original industry.

Case 1 appears to involve no ambiguity: this worker should clearly

be classified as a switcher. The proper treatment of case 2 is not so

clear because of the temporary nature of the transition. If one is

interested in mobility of a permanent nature, then it may be desirable

to exclude situations like case 2 from the category of switchers. Case 3

is of interest because it is intermediate between cases 1 and 2. The

point is simply that there are cases where movement out of an industry

may not truly be permanent but is, nevertheless, more appropriately

interpreted as permanent than temporary. From a practical point of view,

one needs to determine an (arbitrary) cutoff time to distinguish

temporary from permanent switching. It seems to us that a natural way to


do this is to pick a horizon which allows for the possibility of return

during the first stages of an expansion.

The following two cases are also of interest:

Case 4: A worker becomes unemployed during a recession, never works

again and eventually leaves the labor market.

Case 5: A worker becomes unemployed during a recession, remains

unemployed for five years and then accepts a job in the same industry as

his or her previous job.

Case 4 is of interest because although it does not involve mobility

between industries it appears to be a perfect example of an individual

who is displaced from an industry. From a semantical point of view, it

may be appropriate to interpret this as a switch to the home production

sector of the economy. In any case, it seems to us that any attempt to

identify unemployment arising from workers leaving one industry should

be concerned with instances of this type. Case 5 is essentially a

combination of cases 3 and 4. In case 3 the argument was that even

though a worker returns to a particular industry, if the absence is

sufficiently long one may want to regard the original transition as

permanent rather than temporary. By analogy, the same argument applied

to case 5 suggests that if a worker is unemployed for a sufficiently

long period, he may be regarded as having been permanently displaced at

the time of the initial separation.

To summarize the above discussion, it is of interest to

distinguish mobility of a temporary nature from that of a permanent

nature, and to consider the case of workers who leave one industry but

do not enter any other industry.

The discussion suggests that the data set used to study the link

between mobility and unemployment should be flexible enough to allow for

alternate specifications of sectoral mobility. The PSID seems well

suited for this purpose. The PSID interviews individuals in the spring

of each year, gathering information about their labor force status,

current occupation and industry if applicable, and weeks of unemployment

experienced by the individual during the last calendar year. Because the

PSID is a panel data set, this information can be used to create a work

history for an individual at yearly intervals. The Annual Demographic

File of the CPS, which Murphy and Topel used, interviews individuals in

March and collects information on current employment status, industry

and occupation if applicable, industry and occupation of longest job

held during the previous calendar year, and unemployment during the last

calendar year. However, because individuals are interviewed only once,

the available information on an individual pertains to at most a 15

month period.

The potential difficulty of this situation is that one cannot

determine whether or not individuals who report themselves as currently

unemployed are in the process of switching industries. The importance of

this issue is an empirical question, but our results indicate that it is

very important because individuals who experience a large amount of

unemployment while changing industries tend to be concentrated in this

group and although small in absolute numbers they are large in terms of

their contribution to unemployment.

Although this aspect favors the use of the PSID over the CPS in

analyzing unemployment and mobility, it would be misleading to ignore

some other differences between the two data sets. The CPS has the

advantage of being significantly larger (Murphy-Topel have ten times the

number of yearly observations we have in this paper), and the CPS

interview has a special question about mobility which acts as a check

against spurious mobility caused by misreporting of industry2.

Finally, some limitations of the PSID--but not unique to the PSID-

-are that there is essentially no information about what industries (if

any) an individual may have worked for between two consecutive

interviews and unemployment is measured over the calendar year rather

than the interval between successive interviews.

We are now in a position to provide the details for what we refer

to as the primary specification. The basic feature of this specification

is that it focuses on permanent switchers and that individuals who

simply leave a sector for a substantial period of time without

necessarily showing up elsewhere will also be counted as switchers.3 We

emphasize that while we call this our primary specification we will

present some results for other specifications in a later section.

We study three cyclical episodes of equal length: the recessionary

periods of 1974-76 and 1981-83 and the expansionary period of 1977-79.4

The first year of each episode is referred to as the base year. For each

episode, a sample is chosen consisting of workers who were heads of

their households and who were in the labor force at the time of the

three interviews conducted during that episode. We also require that the

individuals be employed at the time of the interview in the base year.

This produces sample sizes of 2150, 2518 and 2708 for the periods

beginning in 1974, 1977 and 1981, respectively.5

We partition each sample into stayers and switchers using the

following criterion. Let t correspond to one of the base years. In order

to be classified as a switcher in the episode with base year t an

individual must be employed in a different sector or unemployed in

period t+l and must not have returned to employment in the base year

sector as of period t+2. All other individuals are counted as stayers.

Industries are classified into 26 groups, twelve of which are goods

producing and 14 of which are service producing.6 With respect to the

earlier discussion, note that initially unemployed workers are excluded

and individuals who are unemployed at both t+l and t+2 are counted as

switchers. An individual who does not change sectors between t and t+l

but who changes between t+l and t+2 is classified as a stayer. Hence the

above definitions focus on separations that are initiated between t and

t+l. Once the workers have been partitioned into switchers and stayers

we compute weeks of unemployment for each group over the two year

duration of each episode. (Ideally, this would correspond to the total

weeks of unemployment between the interviews at date t and t+2 but

because the PSID measures unemployment between calendar years this is

not exactly the case.)

Mobility and Unemployment: Results for the Primary Specification

General Patterns

Table 3-1 provides some summary information about the unemployment

experiences of stayers and switchers during the three episodes. The

table shows the average weeks of unemployment per individual [E(w)], the

average weeks of unemployment per individual conditional on experiencing

unemployment [E(wI w>0] and the distribution of total weeks unemployed

across individuals. Although the weeks of unemployment do not

necessarily correspond to a single spell of unemployment we will

sometimes refer to E(wI w>O) as the duration of unemployment, for lack

of a better term. As noted earlier, this data covers unemployment over a

two year period.

Several patterns are easily recognized from table 3-1:

(i) Stayers experience less unemployment per individual than switchers

in each episode. For both groups the average is lowest in the expansion.

Moreover, the gap between the average unemployment of stayers and the

average unemployment of switchers increases during recessions (See row 1

in each episode.)

(ii) Among individuals who report some unemployment, it is still true

that the average duration of unemployment is smaller for stayers than

for switchers during all three episodes and for each group the average

is lowest during the expansionary episode. Also, note that once again

the absolute increase in duration over the course of the cycle is

significantly larger for switchers than it is for stayers. (See row 2 in

each episode.)

(iii) Stayers are much less likely to experience unemployment than are

switchers and for both groups the probability of experiencing

unemployment is lowest during the expansionary episode. Although the

higher incidence of unemployment among switchers was to be expected, it

is of some interest to note that in all three episodes a majority of

switchers do not experience any unemployment (See row 3.)

Economists have known for quite some time [see Clark and Summers

(1979) and Summers (1986)] that although high unemployment individuals

are few in number they account for a disproportionately large amount of

unemployment. Table 3-1 reveals that this is true for each of the two

groups separately. However, several additional patterns are present in

the table (see rows 5 and 6):

(iv) High unemployment individuals (those with w>27) are more

significant in accounting for unemployment among switchers than among


(v) The importance of the extremely high unemployment group (w>52) is

very sensitive cyclically in the switcher group; much less so in the

stayer group.

We shall return to the significance of these findings shortly.

Table 3-2 provides information on the fraction of individuals classified

as switchers and the fraction of unemployment accounted for by switchers

in each episode. Two observations are apparent:

(vi) Mobility is highest during the two recessionary periods.

(vii) The fraction of total unemployment accounted for by switchers is

highest during the two recessionary periods.

These two conclusions are apparently at odds with the results of Murphy-

Topel; a detailed discussion of this point is postponed until fourth

section when we consider alternate definitions of sectoral mobility.

Although the cyclical pattern in switchers share of unemployment

is easily ascertained, assessing the quantitative importance of this

effect is much less so. Average unemployment rates for the three samples


are 3.9%, 2.4% and 5.2% respectively. In passing from the second to the

third episode unemployment increases by 2.8% and unemployment accounted

for by switchers increases by 1.4%. Hence, one half of the increase in

unemployment is accounted for by the increase in unemployment due to

switchers. In moving from the second episode to the first episode the

corresponding number is 40%.

Although these numbers do not provide any information about

causation, they do suggest a significant role for unemployment

associated with sectoral reallocation in accounting for cyclical

unemployment movements during the period being studied here.

Changes in the share of unemployment accounted for by switchers

can really be thought of as the combined result of changes in three


(a) direct effect: changes in the number of switchers relative to


(b) incidence effect: changes in the incidence of unemployment among

switchers relative to stayers.

(c) duration effect: changes in the amount of unemployment per

individual experiencing unemployment for switchers relative to stayers.

Using "sw" subscripts to denote switchers, total weeks of

unemployment experienced by switchers are given by N .f .d where N
sw sw sw
denotes the total number of switchers, f denotes the fraction that

experience unemployment and d denotes the amount of unemployment

conditional on experiencing unemployment. Using "st" subscripts to

denote stayers, it follows that the share of total unemployment

accounted for by switchers during a given period is given by

Switchers share = +r (3-1)

N f d
sw sW sw
where r -
st st st

The following calculation evaluates the importance of each factor. Take

the values of Ns/Nst, f/fst, d /dt corresponding to the
s st sw st sw st
expansionary period, 1977-1979. For each of the recessionary periods

insert the actual value for one of the three ratios, leaving the other

two unchanged and evaluate expression (3-1). The results are reported in

table 3-3.

This table shows that in neither case is the incidence effect

important and that in 1974-76 only the direct effect is important. These

results are of substantial interest. Many discussions of the aggregate

importance of sectoral shifts implicitly or explicitly assume that it is

the volume of mobility (i.e., the direct effect) that is of central

importance. For example, the model of Lucas and Prescott (1974), which

was used by Lilien and others as the basis for the sectoral shifts

hypothesis, assumed that the time required to switch was fixed

exogenously. The above results also suggest an important role for the

duration effect in influencing the contribution of switchers to

aggregate unemployment. It is also of interest that the incidence effect

is nonexistent since the study of Murphy and Topel (1987) concentrated

on incidence of unemployment in their discussion on mobility, another

point that we shall return to in fourth section.

Detailed Patterns

There is more to be learned by studying the pattern of

reallocation in greater detail. What types of transitions lie behind the

statistics? What types of transitions involve the most unemployment? To

address questions such as these, the switchers in each sample are

classified into one of five categories: those who move from one goods

producing industry to another (Gi-G ), those who move from goods to

services (G-S), with (S.-S.) and (S-G) defined analogously, and finally

the category (E-U) which refers to those individuals who were employed

in the base year t but were unemployed at both t+l and t+2. Stayers are

classified into two categories: those who stay in a particular goods

producing industry (G.-G.) and those who stay in a particular service

producing industry (Si-Si).

Table 3-4 presents the percentage of total weeks of unemployment

accounted for by each group during each of the episodes. Several points

are worth noting. First, the category G.-G. is by far the most
1 1
significant in accounting for total weeks of unemployment.8 Second,

while the two opposing transitions G-S and S-G are both contributing

during all three episodes, the relative size of the G-S flow is

significantly larger during recessions. Third, it is easily seen that

the category E-U is critical in explaining why switchers account for an

increased fraction of unemployment during recessions. This important

finding is discussed in more detail in the next section in the context

of analyzing differences between results reported here and those

reported by Murphy and Topel.

Table 3-5, which provides information on average unemployment per

individual for each of the seven categories discussed above also reveals

some interesting patterns. In both of the recessionary periods it is the

switcher categories G.-G. and G-S which have the highest average

unemployment of all the categories ending in employment. This suggests

that these types of transitions have some distinguishing characteristics

that cause them to be associated with high unemployment. By contrast,

the category S.-S. is relatively important from an aggregate point of
1 1

view but the unemployment experienced at the individual level is not

very severe.

The last column of table 3-5 shows the average unemployment per

switcher for each of the four switching categories ending in employment,

when all three samples are combined. The variation across categories is

quite striking. The average for the transition G-S is over 50% larger

than those for either S.-S. or S-G. This further illustrates the earlier
1 J
statement that the amount of unemployment associated with a particular

switch depends on the nature of the switch being considered. Moreover it

highlights the earlier conclusion that concentrating on the volume of

mobility may be misleading. Given the numbers in table 3-5 it is clearly

possible for the volume of mobility to be constant at the same time that

the share of unemployment accounted for by mobility is increasing

because of a change in the composition of mobility types9.

Additional evidence is provided by table 3-6 which shows the

distribution of total unemployment by category for the three samples

combined. The categories G,-Gj and G-S are not only prone to higher

average unemployment but they are also the categories where the

distributions are most heavily weighted in favor of high duration (over

36 weeks) as opposed to short duration (under 24 weeks).

There are many factors that may be relevant in producing the

pattern of average unemployment across mobility types. Cross-industry

differences in sector specific or firm specific skills may be important

because workers may choose to hold out for a job in their initial

industry (or firm) for a longer period of time before deciding to

actually switch sectors. This is consistent with the theory suggested by

Murphy and Topel (1987) as well as with the finding of Katz and Meyer

(1988) that some of the individuals with the highest unemployment are

those who ex ante believe they are temporarily laid off but who ex post

are not recalled. Differences in savings or unemployment insurance

benefits that are correlated with industry may also be a factor, as a

simple search model would predict.

To elaborate further on the connection between high unemployment

individuals, switching and the cycle, table 3-7 presents evidence on the

share of total unemployment accounted for by switchers and stayers. The

message from the table is very straightforward. The share of

unemployment due to high unemployment individuals that is accounted for

by switchers is strongly countercyclical. During recessions it appears

that high unemployment individuals are disproportionately composed of

switchers. The importance of this observation is brought out by the fact

that if the over 52 week group is discarded then the cyclical pattern

for switchers' share of total unemployment depicted in table 3-2 will

disappear. This is one of the major findings we wish to emphasize: the

extent to which the data support the sectoral shifts theory of

unemployment fluctuations is due entirely to the fact that the small

number of individuals who tend to have very large amounts of

unemployment are disproportionately composed of switchers during


It is important to note that our findings do not bear on the issue

of causation: it is not clear if switching tends to cause high

unemployment, high unemployment tends to cause switching or if both are

caused by some third factor. While Lilien argued that it is sectoral

shifts--and the switching that they entail--that trigger the cycle, some

other models in this literature do not rely on his argument. For

instance, in the models by Rogerson (1986) and Davis (1986), recessions

--whatever their cause--are a good time to carry out switches that were

going to be made later any way. Hence, there is a correlation between

switching and the cycle, but one does not cause the other.

We would also like to discuss the relationship between our work

and the literature on displaced workers. While there is likely to be a

substantial overlap between the group we call switchers and the

individuals who are generally regarded as displaced, the differences in

definitions, data sets and time period studied are substantial enough to

prevent us from undertaking a detailed comparison. However, some

qualitative conclusions can be compared. A study by Parnes, Gagen and

King (1981) used data from the National Longitudinal Surveys (NLS) on a

sample of men who were between the ages of 45 and 59 in 1966. As with

the PSID, this NLS study was based on a long work history since the men

were surveyed eight times between 1966 and 1976. Parnes et al.

calculated some statistics on the duration of unemployment for workers

who were permanently separated from their jobs over this period. They

found that "on average, the duration of postdisplacement unemployment

was 12.2 weeks, but this varied considerably depending on labor market

conditions at the time of displacement--from 4.8 weeks for those

displaced in the buoyant economy of 1966 to 1969 to 22.5 weeks for those

whose job loss occurred in the relatively depressed period of 1971 to

1975 (p. 83)." They also found that in the 1971-75 period 21% of

displaced workers experienced very high unemployment (greater than 52

weeks) whereas the corresponding figure for 1966-69 was 0%.

Bednarzik (1983) used CPS data to study the relative contribution

of temporary layoffs and permanent separations to the incidence of

unemployment over the 1968-82 period. One of his primary conclusions was

that "what really set the most recent recession (i.e., 1981-82) apart

fom its predecessors was the larger number of permanent separations. In

the three downturns prior to the 1981 episode, the rise in unemployment

as a result of permanent separations was about 37 percent. In contrast,

more than half the rise in unemployment in the 1981-82 recession was a

result of workers being permanently separated from their jobs (p. 7)."

Flaim and Sehgal (1985) studied the duration of unemployment for workers

displaced during the 1979-83 period using data from the January 1984

Displaced Worker Survey of the CPS. They found that the median period

without work for a displaced worker was about 24 weeks. However, for

those who were unemployed at the time of the survey, the median period

without work was about 32 weeks and for those not in the labor force it

was nearly 57 weeks. (Recall that the average unemployment per

individual for our E-U group was about 52 weeks for the 1981-83


Alternate Specifications of Mobility: A Comparison with Murphy-Topel

As mentioned in the last section, some of our findings appear to

be at odds with related findings by Murphy-Topel. In particular, their

findings over the time period studied here were that

(MT-1) Industrial mobility is procyclical with a declining trend.

(MT-2) The aggregate incidence of unemployment associated with

mobility was essentially acyclical.

They suggested that these findings were very damaging to the sectoral

shifts hypothesis as a theory of unemployment fluctuations.

The analysis reported in this section suggests that there is no

real discrepancy between the results presented here and those of Murphy

and Topel. Rather the differences are largely accounted for by

differences in definitions and accounting rules used in summarizing the

data. Before demonstrating this, there are two issues concerning their

findings that we wish to discuss. First is that in view of the results

in third section, the cyclicality of mobility, although an important

element of the sectoral shifts story, need not be the major element. In

particular, changes in the duration of unemployment associated with

switching due to compositional changes in the pattern of switching may

also be an important factor. Second is that their result on incidence is

in fact exactly what our results in third section suggest, namely that

the incidence effect has played no role in the recessionary periods.

Recalling the discussion of second section, the data used by

Murphy-Topel is produced by interviewing individuals once, at which time

they provide information on current status and industry of longest job

held during the last calendar year. Individuals whose current industry

is different from the one reported for the previous year are counted as

switchers. This leaves the group which is currently unemployed as

unassigned since they have no current job. The procedure used by Murphy-

Topel was to divide this group evenly between stayers and switchers0.

This procedure differs from that followed by us because we assigned this

group into the switcher category, although note that our horizon is two

years instead of one year. Looking back to table 3-4 it is clear that

this difference in accounting rules is quite significant. If the 50-50

rule is used in table 3-4, then the share of unemployment accounted for

by switchers has the acyclical pattern of 31.4, 31.5 and 31.3 for the

three episodes in chronological order.

A natural question to ask, of course, is how do we distinguish

between the appropriateness of these two accounting procedures. With the

PSID it is possible to follow individuals for additional periods to find

out what eventually happens to them, suggesting that one way to decide

the issue is to simply extend the analysis through time. Because the

available data limits this extension to one additional year for the

1981-83 period, we consider one additional year for each episode. In

this additional year, some individuals report themselves as employed,

others report themselves as still unemployed, and a small number have

left the sample and hence no record is available". For individuals who

are employed in t+3, we can then compare their sector of employment in

t+3 with that at t to classify them as switcher or stayer. We then take

the weeks of unemployment during t and t+l (as before) and distribute

them accordingly. Some weeks remain unclassified. Table 3-8 summarizes

the information. Several important points emerge. First, a significant

fraction of the weeks remain unclassified when the analysis is extended

by one year. Second, in both of the recessionary periods, the weeks that

are accounted for are roughly on the order of two-thirds switchers and

one-third stayers. Third, during the expansionary episode almost all of

the classified weeks are in the stayer category. Hence, the 50-50 rule

is clearly inappropriate.

As noted in the previous discussion, there is a certain degree of

arbitrariness in using a two-year horizon to define switches. Using the

numbers in table 3-8, we can calculate the effect of moving from a two-

year criterion to a three-year criterion, i.e., the E-U-U individuals

who return to their period t industry in t+3 are counted as stayers. The

resulting figures for the fraction of unemployment accounted for by

switchers are 33.5, 31.6 and 37.0 for the three episodes in

chronological order. Although the numbers are slightly affected by the

change in definition, the cyclical pattern is the same as before2.

At the risk of belaboring the point, we present a somewhat extreme

case to illustrate the importance of specification. This specification

uses the same three base years as before, the same samples, but the

horizon is limited to one year and the rule for determining a switcher

is that the individual must be employed at both t and t+l, but in

different industries. Based on the evidence presented in this paper this

is clearly an inappropriate choice of specification; however, without

this evidence it might have appeared to be a reasonable specification if

one imagined the sectoral shifts hypothesis entailing a lot of sectoral

mobility with reasonably small duration. Table 3-9 presents the table,

which is analogous to Tables 1 and 2. The contrast between the results

in the two tables is striking. Stayers now have more unemployment

conditional on having some unemployment; the duration figures for

switchers are lower during recessions; long duration is more important

in explaining the unemployment of stayers than of switchers; there is no

cyclical pattern to the volume of switching; and the fraction of

unemployment accounted for switchers is highest during the expansionary

episode. All of these observations are opposite to those found in Tables

1 and 2. The reason for this is quite simple. To be counted as a

switcher in this table, a worker has to complete the switch between

successive interviews. As shown earlier, much switching requires a

relatively long period, especially during recessions. As a result, the

procedure generating table 3-9 inappropriately excludes many workers who

simply are taking longer in the process of switching.

Intra-Industry Mobility. Occupational Mobility and Unemployment

This section reports results concerning two additional aspects of

mobility. First, we examine the role of intraindustry mobility among

stayers, and second we consider the effect of considering occupational

mobility in addition to industry mobility.

Intra-Industry Mobility and Unemployment

According to the definitions used in this study, there are several

different ways in which an individual can be classified as a stayer: an

individual can remain with the same employer, can change employers

within an industry or can leave the industry temporarily and then return

to either the original or a different employer. Examining these

different groups provides some information about mobility of workers

across firms within an industry and the unemployment that it entails.

We first measure the fraction of workers who were with the same

employer in both the base year t and year t+2, although possibly not at

t+l. The remaining group of stayers is then treated as intra-industry

switchers, i.e, those who stayed within the same industry but switched

employers. Table 3-10 shows the volume and the contribution to

unemployment of (inter-industry) switchers, intra-industry switchers,

and individuals whose employer does not change.

In an accounting sense, each group makes a significant

contribution to total weeks of unemployment. Once again, however,

different types of transitions are associated with different amounts of

unemployment. Looking at the volume of mobility, it is clear that over a

two year horizon, the majority of individuals are still with the same

employer. However, the contribution of this group to unemployment is

much smaller than their share in the sample. Similarly, even though

intra-industry switchers always outnumber inter-industry switchers, the

latter group always accounts for a significantly larger share of

unemployment. Clearly, inter-industry switchers are subject to a greater

amount of unemployment on average than intra-industry switchers. This

finding is of some interest because it suggests that the notion of

changing industries is significant beyond the notion of simply changing

jobs in terms of the average unemployment experience associated with it.

Occupational Mobility

Oi (1987) has pointed out that Lilien and other authors in the

sectoral shifts literature implicitly assume that "shifts across sectors

(industries) result in more frictional unemployment than shifts of

comparable magnitude across occupations or among firms of differing

sizes." However, as Oi goes on to state, "labor can be specialized to a

sector (major industry), occupation, or firm ... Relocating unemployed

typists to jobs as machinists is likely to entail more unemployment than

moving unemployed factory workers (who may have been typists and

machinists) into positions as typists and machinists in Business Repairs

(i.e., in services)." These comments suggest that the impact of an

inter-industry shock on unemployment may depend partly on the amount of

occupational mobility it entails.

In this section of the paper, we present evidence on the

contribution of occupational mobility to total weeks of unemployment.

Since there is likely to be some overlap between industrial and

occupational mobility, we classify workers into cells indexed by (i,j),

where i is the worker's 2-digit industry and j is the worker's 1-digit

occupation. The definition of a switcher is now altered. A switcher is a

worker who exits permanently from the (i,j)th cell; this can be

accomplished by switching industry only, or occupation only, or by

changing both industry and occupation.

The results are presented in table 3-11. The first row contains

figures that were presented earlier in table 3-2; they show the

contribution of switchers to total weeks of unemployment when we look

only at industrial mobility. The next row shows the contribution of

switchers to total weeks when the definition of a switcher is altered as

discussed above. It can be seen that the incorporation of occupational

mobility substantially increases the contribution of switchers to

unemployment without altering the cyclical pattern. The results for the

last episode are particularly striking: 52% of unemployment in the 1981-

83 recession is attributable to workers who switched 2-digit industries

or 1-digit occupation or both.

Individual Characteristics and Unemployment

In this section we consider the question of what, if any, personal

characteristics are associated with mobility and weeks of unemployment

experienced. As a byproduct we will produce some results which provide

evidence that some of the differences between booms and recessions that

we have discussed earlier are statistically significant in a formal

sense. A related issue is whether or not the differences we have

detected between the three epsiodes is partly caused by "statistical

aggregation." Because the three samples vary in characteristics this is

theoretically possible. Table 3-12 shows how some of the characteristics

of the sample have changed over time.

Our basic strategy is to pool the individual data on total weeks

for the three samples; then we regress the individual's total weeks on

individual characteristics and on dummy variables which pick up the

effects of the business cycle (i.e., whether the individual moved during

a boom or a recession). We estimate a set of two equations:

I. = a + Z.B + D75.6 + D82 6 + e (3-2)
1 1 il 12

WM. = a + X .8 + D75. + D82. + e (3-3)
1 m mi m i 1 i 2 mi (33

The following notation is used. WMi is the total weeks of unemployment

of switcher i, and I. is a (0,1) variable indexing whether individual i

is a switcher or a stayer. D75 is a (0,1) dummy variable which takes on

the value 1 if the switcher belongs to the 1974-76 sample. D82 is a

(0,1) dummy variable which takes on the value 1 if the switcher belongs

to the 1981-83 sample. The X's and Z's are sets of individual

characteristics. They include a constant, the individual's age, sex

(FEMALE, 1 if female) and education (EDU)13. The variable TENRS takes the

value 1 if the individual has been in his current job less than 6

months, and is zero otherwise; the variable TENRL is 1 if the individual

has been in his current job more than 10 years. The variable DUR takes

the value 1 if the individual was in a durables goods industry in t. The

variable SKILL takes on the value 1 if the individual is either a

manager or a professional or a craftsman; these occupations are commonly

considered to be more skill-intensive than the other 1-digit occupations

[see Duncan and Hoffman (1979), Shaw (1984, 1989) and Shapiro and Hills

(1986, p.47)]. Finally, the variable FRQ denotes the number of job

switches the individual has made in the three year period prior to the

base year.

The estimation procedure for this system is described in Lee

(1978) and Maddala (1983, p. 223-28)." The total weeks equations cannot

be consistently estimated using ordinary least squares because

E(Ecmi I.=l) 0 0.

Hence, a two-step procedure is used in which the first step is to

estimate equation (3-2) by probit analysis. Then, in the second step,

the parameters of the total weeks equation for switchers are

consistently estimated from an OLS regression of WMi on Xmi and a

selectivity variable, A. The selectivity variable


where = a + Z.B + D75 6 + D826 ,
i i l i2'

F and f are the cumulative distribution function and the density

function, respectively, of a standard normal random variable.

The results from estimating this system are reported in table 3-

13. The coefficient estimates on the time dummies--the 6's and the 7's--

are of particular interest. The 6 estimates capture cyclical patterns in

the volume of mobility while the y's reflect cyclical patterns in the

duration of unemployment for a switcher. If the differences between

booms and recessions documented in previous sections of this paper are

statistically significant, the estimates of 6's and y's should be

positive and the estimates of 62 and 72 should be greater or equal to 61

and -y. (They could be greater if the 1981-82 recession was more

'severe' than the 1974-75 one.)

The first column gives the probit estimates; the dependent

variable is a (0,1) dummy that indicates whether the individual is a

switcher or a stayer. The estimates of 6's are positive, and 62 is

greater than 61 as we expected. This means that, once the individual

characteristics that influence mobility are held constant, the volume of

mobility is acyclic.

The effects of individual characteristics on mobility accord with

intuition. The probability of switching declines with age and education,

but the standard error on the estimate of education is quite large.

Females have a lower probability of switching. There is more switching

among individuals with short tenure (but the estimated coefficient is

not significantly different from zero) and less among those with very

long tenure. Individuals in the durables goods sector show a higher

incidence of switching while individuals in skill-intensive occupations

show a lower incidence. Finally, those who switched more often in the

past have a higher incidence of switching. This last result is similar

to that reported by Mincer and Jovanovic (1981).

The second column gives the results for the total weeks equation.

The dependent variable is the total number of weeks of unemployment

reported by a switcher over the two year period (i.e., 1974-76 or 1977-

79 or 1981-83). The variable NE takes the value 1 if the individual's

region in the base year is the northeast, and is zero otherwise. The

variable CITY takes the value 1 if the population of the largest city in

the individual's SMSA is greater than 50,000. Note that the variable FRQ


appears in the probit equation but not in the total weeks equation; such

an exclusion restriction is needed to identify the second equation.

The estimated coefficients on the dummy variables D75 and D82

strongly support the results of previous sections. The coefficient of

D75 is positive and significantly different from zero; the duration of

unemployment for a switcher increases during a recession. The

coefficient on D82 is also positive and greater than that on D75,

supporting the impression conveyed earlier that the 1981-82 recession

was more severe than the 1974-75 one.

The results also show that the total weeks of unemployment

experienced by a switcher decline with age, education, length of tenure

and proximity to a large city. Individuals in skilled occupations have

lower total weeks of unemployment. Being in the northeast or in a

durables goods industry increases total weeks, though only the former

effect is statistically significant. The estimated coefficient on the

selectivity variable, A, is not significantly different from zero. In

light of this result, we also estimate a single equation for total weeks

without the selectivity correction. The results, reported in column

(iii), are similar to those in column (ii).

For purposes of comparison, we also estimate a total weeks

equation for stayers [see column (v)]. The estimated coefficients of the

dummy variables D75 and D82 show the same cyclical pattern as in the

switchers' equation; however, consistent with the results of the earlier

section, the pattern is much less pronounced for stayers. Another

interesting difference between switcher and stayer unemployment is the

following. Skilled individuals are less likely to switch, but,

conditional on switching, skill decreases total weeks of unemployment.

On the other hand, conditional on staying, skill increases total weeks

of unemployment. This suggests that skilled individuals typically wait

around for re-employment, possibly because some part of their human

capital is industry-specific (or firm-specific). However, some part of

their capital is useful in other industries; hence, if they do decide to

look elsewhere for employment, their weeks of unemployment are lower

than for unskilled switchers.

In addition to these results we have tried several specifications

with interaction terms, in particular interactions involving individual

characteristics and the time dummies to ascertain whether any particular

characteristics had different impacts on unemployment across the three

episodes. Columns (iv) and (vi) present results for the case where

education and skill are interacted with the time dummies. An interesting

pattern that emerges for the 1981-83 period is that conditional upon

staying, skilled and less educated individuals suffered higher

unemployment. This is suggestive of less educated skilled workers being

laid-off and simply waiting to get their old jobs back, even though the

likelihood of this may have been small. This also suggests a selection

process involving mobility. Individuals whose skills are not conformable

with alternate opportunities don't switch industries resulting in long

spells of unemployment whereas those who do switch experience little



The goal of this chapter has been to elaborate on the work of

Murphy and Topel in the particular area of the relationship between

unemployment, mobility and the cycle. As was the case with their work,

our strategy was to present a summary of the facts that a theory in this

area needs to address rather than to test a particular version of any


Several interesting findings emerge from our analysis. First,

there does seem to be a significant role for mobility-based models of

unemployment, not only in accounting for steady state unemployment but

also in accounting for cyclical fluctuations in unemployment. Another of

our main findings is that although the volume of mobility is an

important factor in determining mobility-related unemployment, there is

a substantial role for the duration of unemployment associated with

mobility. In particular, the relatively small group of workers who spend

a very long time unemployed during recessions in the process of changing

industries is very important from the point of view of accounting for

total weeks of unemployment. In addition, different types of mobility

are associated with different unemployment experiences at the individual

level. A special case of interest is that of workers who become

unemployed during a recession but do not develop any stable job

attachment over the ensuing three year period. Some of our findings

based on studying individual characteristics and unemployment point in a

direction suggested by Murphy and Topel, viz., paying more attention to

models in which firm or industry specific human capital interacts with

an unemployed individual's job search strategy.


1. This chapter is from the co-authered paper with Prakash Loungani
(University of Florida) and Richard Rogerson (Stanford University). An
earlier version of this paper was presented at the NBER conference on
"Alternative Models of the Labor Market", February, 1989. We wish to
thank David Lilien and Kevin Murphy as well as other conference
participants, and workshop participants at the Federal Reserve Bank of
Chicago and the University of Florida. Financial support from the NSF is
gratefully acknowledged.

2. Mellow and Sider (1983) compared CPS respondents' description of
their jobs with those provided independently by their employers. They
found a high level of agreement in worker and employer responses to
industry affiliation 92% at the one-digit SIC level and 84% at the
three-digit level. While we do not know if similar numbers would hold
for our data set, note that the industry classification we use
corresponds roughly to a two-digit level. Also, a lot of our results
pertain to cyclical patterns in mobility; there seems no reason to
believe that there are systematic cyclical patterns in misreporting of

3. This is a natural classification for two reasons : first, a large
fraction of these individuals do eventually end up being employed in
another sector, and second, from the point of view of sectoral shifts,
we are interested in individuals who lose employment in a particular
sector, even if they are unable to locate employment elsewhere.

4. Though the PSID began collecting data on industry affiliation in
1971, we did not use the 1971-73 data since there appear to some coding
errors in 1972 and 1973.

5. Our goal in using these sample selection criterion was to focus on
individuals with a stable attachment to the labor force.

6. The industry classification used by the PSID is similar to a two-
digit SIC classification but there are a few minor differences. In
appendix, we report the industry list.

7. The only exception is the second year unemployment of switchers who
are able to accomplish the switch between t and t+l. Including such
spells does not significantly alter any of our results.

8. Note that the stayers share include short-term layoffs within sector
and they are procyclical.

9. Loungani and Rogerson (1989) also found that the volume of mobility
is only mildly countercylical. However, the outflow of workers from
goods to services accelerates during recessions, while the flow from
services to stable employment in durables accelerates during booms.

10. This is not explicitly stated in their paper but was communicated to
us by one of the authors.

11. As argued by Parnes and King (1977), it is most likely that
individuals leaving the sample are experiencing continued instability in
their employment situation.

12. Although we do not report them here, it is also the case that all of
the other quantitative findings from section III are only marginally
affected by this change in definition.

13. The information on education was collected only during the 1975
interview; hence, any additional education acquired by the individual
after 1975 is not reflected in the data. Borsch-Supan (1987) uses the
PSID data to discuss the influence of education on mobility in greater

14. See the fourth section of chapter II for detailed description of
this procedure.

15. We also tried some other specifications, however none of them
produced any statistically significant results. For example, interacting
durables with the time dummies resulted, as expected, in positive
coefficients on the interaction terms but they were not significant at
conventional levels; for instance, in the 1981-83 episode the t-
statistic was 1.5.

Table 3-1

Unemployment Experience of Switchers and Stayers


Row Average Weeks

1. E(w)
2. E(wlw>0)

Weeks Unemployed
3. 0
4. 1-26
5. 27-52
6. >52



% workers

% weeks



% workers


Row Average Weeks Stayers Switchers

1. E(w) 2.1 5.5
2. E(wlw>0) 11.1 15.5
Weeks Unemployed % workers % weeks % workers % weeks
3. 0 81.6 0.0 64.6 0.0
4. 1-26 16.7 65.3 28.0 48.5
5. 27-52 1.4 25.3 7.0 44.9
6. >52 0.3 9.5 0.5 6.5


Row Average Weeks Stayers Switchers

1. E(w) 3.8 12.9
2. E(wlw>0) 15.5 27.1

Weeks Unemployed % workers % weeks % workers % weeks
3. 0 75.6 0.0 52.4 0.0
4. 1-26 19.8 52.4 29.6 23.1
5. 27-52 3.9 37.3 9.9 30.6
6. >52 0.6 10.2 8.2 46.3

Source: Panel Study of Income Dynamics

% weeks


Table 3-2

Percentage of Switchers and their Share of Unemployment

1974-76 1977-79 1981-83

% of Switchers 17.1 15.4 17.2

Switchers Share 35.6 32.8 41.6

Source: Panel Study of Income Dynamics

Table 3-3

Decomposition of Switchers Share of Total Unemployment

units: %

1974-76 1981-83

Direct Effect only 35.4 35.6

Incidence Effect only 32.7 32.9

Duration Effect only 33.1 38.0

Source: Panel Study of Income Dynamics

Note: aIn 1977-79, switchers accounted for 32.6% of all unemployment

Table 3-4

Unemployment Shares by Mobility Type

Category 1974-76 1977-79 1981-83

Switcher Categories

G. G. 7.7 8.1 6.2

S. S. 6.3 8.5 8.3
l J
G S 10.2 4.8 4.2

S G 2.9 7.6 2.3

E U 8.5 3.6 20.6

Switchers Share 35.6 32.8 41.6

Stayer Categories

G. G. 43.6 41.1 40.4
1 1
S. S. 20.8 26.1 18.0
1 1

Stayers Share 64.4 67.2 58.4

Source: Panel Study of Income Dynamics

Table 3-5

Weeks of Unemployment Per Individual by Mobility Type

Category 1974-76 1977-79 1981-83 pooled sample

Switcher Categories

G. G. 6.68 5.77 11.84 7.83

S. S. 5.02 3.40 6.73 5.12
3 J

G S 11.01 6.35 7.52 8.60

S G 5.34 6.56 4.64 5.55

E U 31.35 23.30 51.56 43.22

Switchers 8.57 5.47 12.94 9.24

Stayer Categories

G. G. 5.33 3.05 6.95 5.07
1 1
S. S 1.74 1.36 1.87 1.66

Stayers 3.20 2.05 3.78 3.01

Source: Panel Study of Income Dynamics

Table 3-6

Distribution of Unemployment
By Duration and Mobility Type, Pooled Sample

Category Weeks Unemployed
0 to 24 36 and over

Switcher Categories

G. G. 31.8 52.3
l J

S. S. 45.7 29.2
i J

G S 27.9 36.3

S G 58.7 17.7

Stayer Categories

G. G. 48.4 50.2
i 1

S. S. 30.1 26.5
1 1

Source: Panel Study of Income Dynamics


Distribution Between Switchers and

Stayers Conditional on Duration

1974-76 1977-79 1981-83

More than 52 weeks

Switchers 54.4 25.0 76.2

Stayers 45.6 75.0 23.8

More than 36 weeks

Switchers 44.0 32.3 62.6

Stayers 56.0 67.7 37.4

Source: Panel Study of Income Dynamics

Table 3-8

Decomposition of Total Weeks of E-U Group

1974-76 1977-79 1981-83

Switchers 32.1 2.6 34.4

Stayers 19.0 31.5 19.0

Others 48.9 65.9 46.6

Source: Panel Study of Income Dynamics

Note: aOthers group consists of sample which is unemployed even at t+3
and which is not in the labor force at t+3. Unemployment shares
of the sample which is unemployed even at t+3 are 24.6, 41.7, and
35.1, but sample size is too small to be significant

Table 3-9

Effect of Alternative Specification on Tables 1 and 2

Row Average Weeks Stayers Switchers

1. E(w) 2.3 3.7
2. E(wlw>0) 11.5 10.9

Weeks Unemployed % workers % weeks % workers % weeks
3. 0 79.9 0.0 65.9 0.0
4. 1-26 17.9 63.1 31.1 74.8
5. 27-52 2.1 36.9 3.0 25.2


Row Average Weeks Stayers Switchers

1. E(w) 2.1 3.5
2. E(wlw>0) 13.1 11.8

Weeks Unemployed % workers % weeks % workers % weeks
3. 0 83.9 0.0 70.2 0.0
4. 1-26 13.9 62.4 26.0 65.0
5. 27-52 2.1 37.7 3.8 35.1


Row Average Weeks Stayers Switchers

1. E(w) 3.6 3.6
2. E(wlw>0) 16.7 10.7

Weeks Unemployed % workers % weeks % workers % weeks
3. 0 78.2 0.0 65.8 0.0
4. 1-26 17.5 48.2 31.4 75.6
5. 27-52 4.3 51.8 2.8 24.4

1974-76 1977-79 1981-83

X of Switchers 13.5 13.1 12.4
Switchers Share 20.0 20.1 12.4

Source: Panel Study of Income Dynamics

Table 3-10

Inter and Intra-Industry Mobility

% Total Sample % Total Unemployment

74-76 77-79 81-83 74-76 77-79 81-83

Switchers 17.1 15.4 17.2 35.6 32.8 41.6
Switchers 20.5 21.2 20.1 28.5 29.4 30.1

Same Employer 62.4 63.4 62.7 35.9 37.8 28.3

Source: Panel Study of Income Dynamics

Table 3-11

Contribution of Switchers to Total Weeks of Unemployment
Industrial and Occupational Mobility

1974-76 1977-79 1981-83

Industrial Mobility only
Switchers Share 35.6 32.8 41.6

Industrial and
Occupational Mobility
Switchers Share 46.3 44.3 51.7

Source: Panel Study of Income Dynamics

Table 3-12

Selected Characteristics of the Samples

units: %

Characteristics 1974-76 1977-79 1981-83

age < 25 16.3 16.0 12.6
female 19.7 19.5 21.0
tenure < 6 months 22.2 21.0 21.5
tenure > 10 years 24.4 18.2 18.5
durables industries 20.7 18.8 16.3
skilled occupations 50.7 51.4 52.6

Source: Panel Study of Income Dynamics

Table 3-13

Regression Results


Variable (i) (ii) (iii) (iv) (v) (vi)

-1.115** 18.84** 20.47** 15.61** 13.70** 11.03**
(0.122) (3.77) (3.15) (4.36) (0.99) (1.29)

-0.004* -0.11* -0.10* -0.10* -0.12** -0.11**
(0.002) (0.05) (0.05) (0.05) (0.02) (0.02)

-0.203** 2.44 2.67* 2.63 1.56** 1.49**
(0.049) (1.38) (1.35) (1.35) (0.41) (0.41)

-0.004 -0.99** -0.97** -0.65* -0.91** -0.61**
(0.007) (0.19) (0.19) (0.32) (0.06) (0.09)





0.034 5.95** 5.80** 5.67** 10.29** 10.19**
(0.044) (1.14) (1.12) (1.12) (0.41) (0.41)

-0.168** -2.83 -2.54 -2.34 -0.51 -0.51
(0.058) (1.75) (1.71) (1.72) (0.44) (0.44)

0.028 2.40 2.40 2.31 -0.38 -0.41
(0.049) (1.33) (1.33) (1.33) (0.42) (0.41)

0.011 -2.06 -2.09 -2.02 0.93** 0.94**
(0.041) (1.08) (1.08) (1.08) (0.35) (0.35)

0.127** 1.09 0.92 0.95 0.18 0.19
(0.045) (1.19) (1.17) (1.17) (0.42) (0.41)

-0.307** -3.45** -3.08** -0.52 3.85** 2.03**
(0.039) (1.17) (1.07) (1.87) (0.34) (0.57)















Table 3-13 -- Continued


Variable (i) (ii) (iii) (iv) (v) (vi)

SKILL82 -4.47 4.51**
(2.47) (0.77)

D75 0.009 2.77* 2.67* 7.03 1.04** 2.72
(0.046) (1.25) (1.24) (5.23) (0.39) (1.53)

D82 0.097** 8.30** 8.15** 18.62* 3.94** 10.63**
(0.043) (1.18) (1.17) (5.30) (0.37) (1.58)

FRQ 0.365**

A 1.51

-Log Likelihood -3057.4

R-square 0.102 0.102 0.105 0.175 0.182

Sample Size 7759 1220 1220 1220 6539 6539

Probit Regression

(ii) Total Weeks Equation for Switchers
with A (selectivity correction)
(iii) Total Weeks Equation for Switchers
without A
(iv) Total Weeks Equation for Switchers
with Interaction Terms
(v) Total Weeks Equation for Stayers
(vi) Total Weeks Equation for Stayers with

Interaction Terms

1% significance level
5% significance level

Notes: a(i)




This chapter is an extension of the work contained in the previous

chapter. One of the main findings of the previous chapter was that

switchers tend to experience longer periods of unemployment than

stayers. The question we address in this chapter is the following: why

is the duration of unemployment longer for switchers than for stayers?

Since it seems plausible that the difference can be explained in terms

of job search behavior in the labor market, we analyze the process of

job search in greater detail.

The theory of stationary job search predicts a simple stochastic

relationship between unemployment duration and the reservation wage.

According to the simple job search model, the decision problem which the

individual faces is that of wealth maximization with uncertain wage

offers generated by a known wage offer distribution. Denoting wage

offers by W0 and reservation wages by Wr, we can write the offer

distribution as F(W ). In this type of environment, the optimal policy

has the reservation property that all offers below some reservation

wage, Wr, are rejected and the first offer exceeding W is accepted. In

the simple job search model studied by McCall (1970), the reservation

wage which maximizes wealth is found as the solution to the following

necessary condition:

(1-F(Wr)) (g(W )-Wr) = m + Wr (4-1)

rW f(W) dW

where g(Wr) = fWr 0 f(W) dW

Sr f(W) dW0

and p is the rate of discount, and m is the direct costs of search per

unit time. This implies that a person who has been unemployed for some

time is likely to have a rather high reservation wage, given his or her

other characteristics, since no offer high enough to be acceptable has

yet been forthcoming.

Individuals who become unemployed and eventually find new jobs in

a different sector sacrifice their accumulated sector-specific skills.

Holding other variables constant, switchers have more original-sector-

specific skill and less general human capital than the workers in the

new sector. Thus, wage offers for them are likely to become lower

because they are proportional to their productivity in the new work

environment. In the job search context there is no reason to believe

that only lower wage offers will lead to longer unemployment--this

depends on the response of reservation wage to changes in the offered

wage. Switchers also realize they can not use their firm specific skills

in the new place, hence their asking wage is lower than stayers.

However, the reservation wage of these individuals may not adjust

immediately, because it may take time to realize how much offered wage

has fallen. Since switchers are less certain about wage distribution,

the variance of wage distribution for the switchers would be higher than

that for the stayers. This feature raises the expected wage gain for the

switchers from more search at a certain reservation wage level if it is

not too far below the mean. Consequently, the reservation wage of the

switchers would be higher than that of stayers from the above

equilibrium condition for the wealth maximization.

These statements suggest the following testable hypotheses:

(i) switchers are offered a lower mean wage in offered wage

distribution than that offered to stayers,

(ii) switchers have lower reservation wages than stayers, but

(iii) the difference between the mean of offered wage of switchers and

that of stayers is greater than the difference between the

reservation wage of switchers and that of stayers. In other words,

the difference between the mean of offered wage and the

reservation wage is greater for switchers than for stayers.

If we test these hypotheses both in periods of booms and recessions, we

could detect some cyclical patterns in search behavior.

The remainder of the chapter is organized as follows. The

methodology for model estimation is described in second section. The

empirical results are divided into two parts. In third section the

hypotheses stated above are first tested using a single cross section of

data. Cyclical patterns in search behavior are studied in fourth section

using panel data. The findings of this chapter are summarized in the

last section.

Censored Regression Model

In this section, we derive an estimable model to test the

hypotheses of the previous section. Individuals will face the following

wage offer distribution:

log Wo= X.B + 6 SW.+ u. (4-2)
1 i 1 1

where u. is a normal with mean zero and variance a SW is switching

sector dummy and the vector X. denotes other variables like individual

characteristics and labor market conditions which affect job search


The reservation wage equation is:

log Wr= -H.+ Z.a + 62SW.+ v. (4-3)
i 1 1 1

where v. is a normal with mean zero and variance a, H. is weeks
i V i

employed, and the vector Z. are again other variables. Note that the
2 2
error terms, u. and v. with variances a and a are jointly distributed
1 1 u v
as bivariate normal with covariance a Then, the three hypotheses

stated in the introduction can be written as

(i) 61 < 0, (4-4)

(ii) 62 < 0, and

(iii) |511 > 1621

In actual estimation of the model (4-2) and (4-3), we need to be

careful because the wage data are not observed for individuals who are

currently unemployed. Furthermore, the reservation wage is an

unobservable latent variable. We cannot exclude this censored sample n

only because the resulting estimates would become biased and

inconsistent but also because this currently unemployed sample is very

important in explaining the unemployment rate, which is one of the maj

purposes of our work.

On the principle of search behavior, we assume that the ith

individual accepts a job if and only if log W? is greater than Wr.
i i1

W W= X.B Z. + (6 1 2) SW. + u.- v. > 0
i i 1 i i i i


2 2
where (u.- v.) N(0, a + 2a )
1 1 u v uv

The problem is we cannot obtain observations if the above condition does

not hold.

From the derivation of the Heckman model in chapter II,

expectations of logarithm of the observed wage offers and weeks employed


a a
E( log WI H.>0) = X.B + 6 SW.+ uv A.

l 1 2 a
E( Hi. H.>0) = [ X.B Z.a + (61- 6 )SW.+ a A.1
1' I i I





where A.=
S 1 (- 1 2

X.i Z.a + (6 1- 6 )SW.
1 1 i

2 2 2 2a
a = a + a 2a

Heckman (1976) proposed two stage estimation of the offered wage

equation. It involves an estimation of the probit function determining

whether or not an individual works. After obtaining A. using the

estimated coefficients, we estimate the wage offer equation by OLS:

o 1 u uv
log W = X.B + 6 SW.+ u uv A.+ e. (4-8)
1 1 1 a 1 1

To get the structural parameters of the reservation wage equation,

we use the method by Lee, Maddala, and Trost (1980):

A a a
2 uv v
log W. = TH.+ Z.a + 6 SW.+ + w. (4-9)
1 1 1 1 -1 1(

where H is the estimated value of weeks employed equation. We have to

use this instead of H, since it is an endogenous variable in the model.

Estimation of the Wage and Reservation Wage Distributions

The data utilized in the empirical investigation were from the

Michigan Panel Study of Income Dynamics. As in the previous chapter,

only household heads are included in the sample since it is difficult to

get the demographic characteristics of those who are not heads. However,

one difference from the earlier work is that we include not only the

primary labor group but also the sample which is out of labor force

(retired, disabled, student, and housewife).'

The wage is a censored variable because it is available for the

currently employed sample only. The offered wage is computed--from the

PSID's question about the individual's hourly wage rate and salary--as

annual earnings divided by annual worked hours. The latent variable in

this model is the reservation wage which represents the marginal rate of

substitution between goods and leisure. Information on "actual weeks

employed last year" is used to measure "unemployment duration"; of

course, the two are negatively related.2

The PSID divides private, nonagricultural industries into 2-digit

groups before 1981 and 3-digit groups from 1981. In order to maintain

consistency, the 3-digit industries classification is mapped onto the 2-

digit classification for 1981-1984. This gives 26 sectors. Individuals

are classified as switchers or stayers over a two year horizon.3 For

those who are employed in both years, the classification is

straightforward: individuals who are employed in a different sector in

year two than in year one are switchers, and those who remain in the

same sector are stayers. For those who are not employed at the time of

the interview in any one of the two years, their "industry of previous


job" is treated as their sector for that year. Even if the individual is

unemployed in both years, this makes it possible to trace his switching

record. Finally, those who were not employed both years and do not

report their previous sectors are assumed to be stayers.4

Table 4-1 shows descriptive statistics for the variables we use in

this model. These are the offered wage rate(W), actual weeks employed

over the last one year(H), years of educational attainment(EDU), job

experience since 18 years of age(EXP), individual's AGE, and sex(FEMALE,

1 if female). The variable MARR and NOWH denote dummies for married and

nonwhite respectively. The variable MISSJOB is a (0,1) dummy formed

using the PSID question: "did you ever miss your job last year?". [The

phrase 'did you miss' is used in the sense of 'were you absent from'.]

The idea behind using this variable is that absences from the job may

indicate a lack of commitment to the job or may reflect some

characteristics of the individual (e.g., laziness). Note that this

variable is one for those who are employed but have missed their job

whereas it is zero for either those who were not employed or fully

employed. UC is local unemployment rate in at the county level. NE and

CITY denote the northeast regional dummy and city area dummy. The

switching variable mentioned above is denoted as SW.

The results from estimation of this model are reported in table 4-

2.5 The first column gives the probit estimates; the dependent variable

is I, a (0,1) dummy that indicates whether the weeks employed is zero or

positive.6 This equation is estimated to get the Inverse Mills Ratio.

[We will not discuss these coefficients because the coefficients in the

fourth column--where the dependent variable is weeks employed rather


than a (0,1) dummy--are of greater interest and from more information.]

The second column gives the estimated version of the offered wage

equation; the dependent variable here is offered hourly wage. The

results show that the wage is high for those who are better educated.

EXP2 is EXP squared. Even though it can be expected to be highly

correlated with EXP, it is included to detect nonlinearities in the

earnings function, as in Mincer (1974). As EXP goes up, wage increases,

but at a diminishing rate, hitting a peak point at 24 years of

experience. This reflects greater investment in on the job training by

young workers. The MISSJOB dummy has a significantly negative effect on

the wage. As suggested earlier, this may be picking up lack of

commitment or some similar individual characteristics. The coefficients

of NE and CITY reflect the fact that wages are generally high in the

northeast region and in cities. These are from the wage compensation for

the less desirable climate and higher living cost. These results reflect

the wage compensation for the climate and the living cost of cities.

Marital status dummy shows a positive and surprisingly high coefficient.

This is somewhat difficult to interpret; it might pick the effect of

omitted variables like spouse income or wealth of family.7

The coefficients that we are particularly interested in are those

that capture the impact of switching sectors. The offered wage of the

switchers is significantly less than that of stayers: the wage decrement

attributable to switching at the mean wage is 0.8 dollars.8 This result

constitutes strong evidence in favor of our first hypothesis that

switchers are offered a lower wage than stayers are.

The coefficient on A. is negative and significant. From the

estimable wage equation, this coefficient is

a auv
u uv (4-10)

S+ 2 a 1/2
u v uv

where u denotes offered wage and v denotes reservation wage equation,
therefore, a is greater than a Thus, we can say the error terms in
uv u
the wage equation and in the employment equation are negatively

correlated from the covariance structure of the error terms of two

equations. The correlation between the errors in the wage offer equation

and the reservation wage equation is positive.9

The structural parameters for reservation wage equation are

reported in the third column of table 4-2. Unit increases in schooling

raise the asking wage by 6%. Since it is almost the same as its role in

the offered wage equation, we can conclude that educational difference

does not affect the gap between asking and offered wages. The estimated

coefficient of weeks employed, y, is positive as we expected. This may

be used to measure the effect of exogenous wage change on the actual

weeks employed since H is an endogenous variable in this model. Since

an exogenous wage increase is equivalent to a shift in the intercept of

the market wage equation, the partial effect of this on weeks employed

becomes l/y. For this model, this partial effect is 76.9, implying that

5% of increase in hourly wages leads to roughly 3.8 additional weeks of

work. 1

While most of the independent variables included have positive

effects on the level of the reservation wage, FEMALE and NOWH (1, if

non-white) have negative ones. The positive coefficient of age shows the

potential wage effect on reservation wage very well. In this linear

model 40 year old workers ask 30% more than 20 year old workers, if

other things are the same. The sex dummy has negative and significant

effect. This implies that females ask 21% less than male workers. The

local unemployment rate has a positive (though insignificant) effect on

asking wage. This is somewhat difficult to interpret; there exists some

simultaneity between reservation wage and local unemployment rate. The

coefficients of NE and CITY show similar pattern with offered wage

equation. Marital status dummy picks the effect of omitted variables

like spouse income or wealth of family as mentioned before. Note that

the magnitudes of marriage effects on offered wage and asking wage are

quite different while they are almost the same in the other common

variables; this might be due to the fact that suffering of unemployment

is higher for married people.

Of particular interest is the impact of switching behavior on the

reservation wage. The reservation wage of the switchers is lower than

the reservation wage of the stayers. However, since the estimated

coefficient is small and not significantly different from zero, it is

reasonable to conclude that there is only modest evidence in favor of

the second hypothesis.

Comparing the coefficients of the switching dummies on the offered

wage (second column) and the reservation wage (third column), it is

clear that the third hypothesis is also accepted. The effect of


switching on offered wage is greater than that on reservation wage. In

other words, the difference between offered wage of switchers and

stayers is greater than that between reservation wage of switchers and

stayers. This lends support to our earlier contention about the reason

that switchers have longer duration than stayers do. People switch

retaining almost the same level of their reservation wage. However,

they are offered lower wage than stayers from the destination sector.

So, the difference between wage and reservation wage of switchers is

greater than that of stayers. This difference makes switchers have a

longer duration of search.

The coefficient on A. in this is large, negative and very

significant. From the estimable equation of the reservation wage this

coefficient is

uv (4-11)

a + a 2 a 1/2
u v uv

where u denotes offered wage and v denotes reservation wage equation,
therefore, a is greater than a. Thus, the error terms in the
v uv

reservation wage equation and in the employment equation are highly

negatively correlated, although the correlation between the errors in

the wage offer equation and the reservation wage equation are positively


The weeks employed equation, is reported in the fourth column of

table 4-2. Surprisingly, educational attainment has a negative effect,

although the magnitude is quite small. Note that educated individuals

are more likely to be employed (see the first column of the same table).

These results imply better educated are more likely to be employed, but

they work less hours." As experience increases, weeks employed increase

at diminishing rate. But neither one is significantly different from

zero. The secondary workers group, elderly and female workers, are less

likely to be employed. The local labor market environment, as measured

by the county unemployment rate, has a negative effect on individual's

weeks employed. Both the northeast regional and city dummies have a

weakly positive effect. Married individuals and whites are likely to

work a little more than others.

The coefficients of the variables in X that are not in Z are B./y,

and those in Z and not in X are a./7. However, the coefficients of the

common variables in X and Z are (B.-a.)/y. We have SW, NE, CITY, MARR,

and NOWH as common variables in both equations for wage and reservation

wage. The weeks employed of the switchers are less than that of stayers

by 2.1 weeks. Though we can not identify the coefficient 7 from this

system, we can test the hypotheses indirectly by the fact that 7 should

be positive. The negative sign of the coefficients of the switching

dummy supports the third hypothesis once again.

Note that we include not only the primary labor group but also the

sample which is out of labor force in the previous regression. The

assumption is that many of these individuals may decide to work when the

offered wage is greater than their reservation wage, which is out of the

range of wage distribution. This is based upon the assumption that those

individuals are searching jobs though inactively. However, it may be

plausible to assume that those who are not in the labor force are not

searching for a higher wage. If so, the job search framework applies

only to those in the labor force. To implement this alternative

assumption, we deleted those not in the labor force. We also include

FEMALE in the offered wage equation. Table 4-3 reports the regression

result. Most of the variables showed no difference from the previous

regression. However, we can find two notable differences. First, in the

previous regression the coefficient of married dummy shows big effect on

offered wage. This may be from the misspecication of the independent

variables. Since most of the female household head are single, inclusion

of the sex dummy in table 4-3 lowers the coefficient. Second, the

coefficient of selectivity correction varible becomes insignificant in

the offered wage equation. This is not so surprising, because we deleted

substantial amount of the censored sample which is not searching job


Cyclical Patterns in Job Search Behavior

This section explores the variations of the effect of job

switching on wage rates and weeks employed over the business cycle. The

strategy we use in this section is to estimate the model by pooling 10

pairs of years, from 1975 to 1984. The primary motivation is to see if

there exists any evidence of cyclical patterns in search behavior over

this period which includes two recessions and one boom.

Figure 1 and Figure 2 provide further information about the

average real wage rate for the sample. In order to abstract from changes

in the inflation rate over this period, the wage data is transformed to

real terms by dividing by the GNP deflator based on 1984. Plots of

average wage level for the whole sample and for the sub sample who

worked are in Figure 1 and Figure 2 respectively. They represent the

cyclical pattern of wages very well. In particular, the difference

between stayers and switchers is small in recessions and large in the


The results of these regressions are presented in table 4-4.

Since we pooled the data from 1975 to 1984 the estimation is based on a

fairly large data set, 28,688 observations. The annual unemployment

rate, U, from CITIBASE data set is used to indicate the state of the

business cycle over the sample period.

The equation in the first column is the probit regression which is

used to get the Inverse Mills' Ratio for the next three equations. The

second column gives the wage equation, and the third column gives the

reservation wage equation for this sample period. The coefficients that

are of interest here are those of SW (the switching dummy) and SW*U,

which is the interaction between SW and the unemployment rate. In both

equations, the SW coefficient is negative and the interaction term is

positive (all are significant at a 1% level). To get a sense of what

these numbers mean, suppose that the aggregate unemployment rate was

7.7%, which is its average value over this period. Then the estimates

imply that the overall impact of switching is to lower the hourly

offered wage by $0.71 (7.8% of wage) and the reservation wage by $0.48

(5.3% of wage). These estimates support the three hypotheses that were

formulated earlier.

The fourth column gives us very interesting results. Both the

switching dummy and the interaction term are negative. This implies that

switchers suffer a longer duration of unemployment than stayers at any

level of unemployment. Furthermore, the difference is more pronounced in

recessions: their additional unemployment is nearly 2 weeks when the

aggregate unemployment is 8%. These results are fairly consistent with

the results of chapter III.

Table 4-5 shows the estimated effect of switching on the hourly

wage rate and the reservation wage by the level of aggregate

unemployment rate (using the estimates in table 4-4). The first column

shows that switchers are offered a lower wage than stayers regardless of

the level of unemployment. Surprisingly, this disadvantage is larger in

booms than in recessions. This procyclical pattern of the disadvantage

for switchers supports the hypothesis that individuals are encouraged to

switch during recession because of the lower opportunity cost of job

switching in recessions than in booms.

The effects of switching on the reservation wage are also given in

column two. For any value of unemployment between 5% and 11% the impact

of switching is to lower the reservation wage. The dollar effect is

lower than that on offered wage, and it decreases faster as the

unemployment rate goes up. What is important is the difference between

the two effects, which is larger in recessions. This provides one

explanation for why switchers have a longer duration of unemployment

than stayers and why it is more pronounced in recessions.


In this chapter we have studied the effects of sectoral shifts on

wage, reservation wage, and unemployment involved in job search

behavior. Individuals who switch sectors tend to have a longer average

duration of unemployment than those who stay within the sector. In this

chapter we have presented evidence that this empirical fact can be

explained in terms of a simple job search story: individuals who switch

sectors suffer declines in the wage offered to them but their

reservation wage does not decline by a similar amount.

We have examined those effects of sectoral shifts involved in job

search behavior under different economic conditions in the labor market.

The switchers are offered a lower wage than stayers regardless of the

level of unemployment. The disadvantage is larger in booms than in

recessions. The sectoral switching is desirable during recession because

of the procyclical pattern of disadvantage in wages. The difference in

the effects of sectoral shifts in wage and reservation wage between

stayers and switchers is acyclical. This provides one of the primary

reasons that the difference in duration of unemployment is more

pronounced in recession.


1. The assumption is that many of these individuals may decide to work
when the offered wage is greater than reservation wage. They just do not
work because their reservation wages are higher than their offered
wages. One of the major contributions of Heckman(1974) model is inclusion
of the censored sample.

2. The appropriate measure of labor supply is a matter of debate. Note
that Heckman(1974) discussed an appropriate time unit for the
estimation. He used annual weeks and hours worked to quantify annual
labor supply. In this model annual weeks worked is a more appropriate
measure than hours worked not only because we are interested in the
duration of unemployment but also because individuals can adjust their
weeks worked much more freely than their hours per week.

3. This feature is different from that in the previous chapter, where
three year horizon was used. In this chapter, we study the cyclical
pattern of the effects of sectoral shifts on job search behavior by
introducing a new explanatory variable, aggregate unemployment rate,
which represents the economic environment of the labor market. Since we
need to have enough number of episodes to do this, we use two year
horizon in this chapter.

4. This is reasonable because most of them are new entrants to the
labor market.

5. The actual specification of the model to be estimated is following

Offered Wage Equation


Reservation Wage Equation


The estimable equations for offered wage, reservation wage, and weeks
employed are derived from these two equations.

6. The dependent variable is 1 in 66.2 % of the sample.

7. It might pick up the sex effect, because those heads who are married
are likely to be male. In light of this, we tried interaction term
between sex and marital status. However, it was not supported

8. This value is from following formula:

exp[ -0.088 + log E(W)] E(W)

The average percentage of the effect of switching at mean wage is -8.4%.
If they work fully one year, annual wage difference between stayers and
switchers would be $ 1,664. This amount is not insignificant for

9. It seems intuitively reasonable that there exist high positive
correlation between reservation wage and market wage. But we cannot find
a priori reason that this should be so. Suppose that there exist an
omitted variable which affects both the offered wage and the reservation
wage. Then the estimated covariance would be positively biased.
Therefore, a correct specification of the model should be assumed in

10. At this 5% increase of hourly wage means 0.049 increase in log W.

11. As the wealth effect dominates the substitution effect, people
demand more leisure. This result is consistent with the backward bending
property in the labor supply curve.

Table 4-1

Descriptive Statistics of the Variables
Interview Year 1984 -

Stayers Switchers Total

Variable Mean Std.Dev. Mean Std.Dev. Mean Std.Dev.

I 0.64 0.48 0.73 0.44 0.66 0.47
W 6.32 6.19 6.20 5.76 6.29 6.10
H 29.70 22.88 30.72 21.22 29.93 22.52
EDU 11.57 3.25 12.00 2.48 11.67 3.10
EXP 17.04 14.95 11.26 11.22 15.74 14.40
MISSJOB 0.11 0.31 0.32 0.47 0.16 0.36
AGE 46.61 18.28 36.95 13.28 44.43 17.74
FEMALE 0.33 0.47 0.27 0.45 0.32 0.47
UC 7.32 3.04 7.22 3.00 7.30 3.03
NE 0.18 0.38 0.16 0.36 0.17 0.38
CITY 0.58 0.49 0.63 0.48 0.59 0.49
MARR 0.56 0.50 0.58 0.49 0.57 0.50
NOWH 0.36 0.48 0.41 0.49 0.37 0.48
SW 0.00 1.00 0.23 0.42

n 2906 847 3753

Note: a = 1
= 0

if H>0

Table 4-2

Regression Results (1984 Sample)

Dependent Variables
o r
I log W log W H























-Log Likelihood 1365.16
R-Square 0.378 0.402 0.337
n 3,753 2,485 2,485 2,485
Notes: .Standard errors are in parentheses.
** 1% significance level.
5% significance level.

Table 4-3

Alternative Regression Results (1984 Sample)

Dependent Variables
o r
I log W log W H

























-Log Likelihood 580.24
R-Square 0.396 0.381 0.348
n 2,684 2,440 2,440 2,440
Notes: .Standard errors are in parentheses.
** 1% significance level.
5% significance level.






c o
f" ii

r- L
r '-

o w


enr cn

Nr r' 0 i D mO D l N D 0 C 0 0 t tL
S 0 10 0 10 10 0 ID 10 0 D nD I t to 0t





m '
\ a



LD bn

(7 m o D c o C co o I
/ 1 ( -

/ on H
n(~~~o \.r n (

\ / ~r- n <

rfa~~~ \,_ < *
-'~~^ ^_^ ^-^cn x

^ ^ ~ ~ ~ ~ ^ ^ ^ \

^""~' ^^ ^s ^^ lr
-- I ---- ) I ---- I -- 1 -- I I -- I T2^ -
C\! O O Ll ^ C) C C lD ^r r\J CD CD D
o cn n ai cn a m a CD ^ r^