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(1) See Marglin (1963) and Harberger (1972) for an early discussion
of the timing issue in investment projects. The growing literature on
"real options" has rediscovered this principle (Pindyck 1991).
(2) Roback (1988) also discusses conditions where similar migration
outcomes occur.
(3) When the annual rate of interstate migration is very low, as it
is in the PSID, a discrete probit model of interstate migration based on
a comparison of indirect utility values at the origin and destination
has little explanatory power, unless variables that are jointly
determined with migration are used as regressors.
(4) The hazard function H(t) is obtained from the survival function
as H(t) = - dlnS(t)/dt, so there is a sign reversal of coefficients in
going between the survival and hazard functions. The Weibull
distribution is monotone (constant, increasing, or decreasing) in
duration, but employment duration is generally nonmonotonic concave in
duration (Lancaster 1990, p. 9: Gritz 1993). We permit this pattern in
resident duration by adopting a mixture distribution--a Weibull and a
gamma (Heckman and Singer 1985: Greene 2003, pp. 790-798). An
alternative distribution with this pattern is log-logistic (Kiefer 1988;
Lancaster 1990: Greene 2003, p. 794). All are distributions for a
nonnegative random variable.
(5) Heterogeneity arises when a population of resident spells has
potentially different distributions of duration after controlling for
the effects of observables. The gamma distribution is frequently used
for representing the distribution of v associated with unobserved
heterogeneity. Chamberlain (1985) and Heckman and Singer (1985) have
shown that failure to include individual heterogeneity, when it is
present, causes significant bias in the estimated coefficients of the
regressors in the hazard function. Han and Hausman (1990) have shown
that a parametric gamma distribution of unobserved heterogeneity leads
easily to estimable models and is not unduly restrictive.
(6) Individuals were selected into the panel in 1968 or added as
new adult males because they either grew into adult males or joined the
household of an original 1968 data panelist. Individuals who leave an
original PSID household are followed and reinterviewed for as long as
they can be located. Among 915 adult males in the PSID SRC sample in
1968, 56 (6.12%) died, 144 (15.74%) were lost, and 132 (14.4%) retired
during 1968-87. Individuals who refused to participate in the survey at
any time were deleted from the sample. Individuals who were classified
as "lost" consist of those who joined the army (30.5%), and
those who moved out from the United States and/or were really lost
(69.5%). We did not adjust for attrition or reweight.
(7) We do not define migration as moves across standard
metropolitan statistical areas (SMSAs), because the boundaries of SMSAs
change over time and, furthermore, they are not exhaustive in their area
coverage. Roback (1982, 1988), however, uses SMSA labor market unit.
(8) We acknowledge that U.S. states vary considerably in
geographical area (e.g., across states like Colorado, Washington,
California, New York, Florida, Texas) population and labor force size
(e.g., as between Rhode Island and California), and number of cities.
(9) Given that we take the male's age as fixed at the
beginning of a resident spell, the effect of the time dependence hazard
rate is both the result of the individual aging and of pure time
dependence. For making policy recommendations, this is the outcome that
we want.
(10) Marriages vary in length, but we see no a priori reason for
the decision on interstate migration to be made jointly with marital
status.
(11) An alternative would be to define unemployment as an indicator
of an individual being unemployed at the beginning of a spell, but this
seemed too narrow. Our study is not a study primarily about
unemployment/employment.
(12) The time trend also captures the impact of omitted variables
that are correlated with time. This will improve the properties of the
estimated coefficients in the wage equation (10).
(13) The author does include heating-degree days but not other
indicators of the climate.
(14) An alternative route for simplifying the interstate migration
problem is to assume that an equilibrium sorting process exists across k
states such that the distribution of wage rates across states is
perfectly correlated. Individuals would then be assumed to move to the
state where their real wage is highest, and the same random variable
(education) would determine an individual's potential earnings in
each region. Educational attainment is then a matching mechanism.
However, matching is likely to be on more than one attribute, which
makes this alternative quite unattractive.
(15) Note that we do not claim to know exactly where an interstate
migrant moves. We do this in an attempt to get free of the problem that
choice of a new location is endogenous.
(16) Since a male's actual earnings at the origin reflect
idiosyncratic factors and the predicted wage at a new location reflects
expected compensation, we have captured two types of important factors
that can be expected to affect a migration decision. For example, a male
who is experiencing a large negative idiosyncratic shock to his wage at
the origin will be more likely to migrate than other similar males. Our
empirical measure of [DELTA]W is a proxy for the true measure and
reduces potential endogeneity and selectivity problems, but we do not
claim to have captured the effects of all relevant factors.
(17) Since wage rates are expressed in constant purchasing power,
ignoring discounting is of little consequence over the study period.
(18) A copy of the methodology used for treating left-censored
spells is available from the authors upon request.
The authors are C.F. Curtiss Distinguished Professor of Agriculture
and Professor of Economics, Iowa State University, Ames, IA, and
Economist and Ph.D. graduate of Iowa State University working in
Washington DC, respectively.
Table 1. The Distribution of the Number of Interstate
Moves by Adult Working-Age Males,
Twenty-Year Period, Starting in 1968
(Cumulative)
Number
of Moves Frequency Percent Frequency Percent
0 722 78.9 722 78.9
1 97 10.6 819 89.5
2 59 6.4 878 96.0
3 23 2.5 901 98.5
4 9 1.0 910 99.5
5 3 0.3 913 99.8
6 2 0.2 915 100.0
Source: PSID files.
Table 2. Variable Names and Sample Means of Variables for the Male
Hazard Function of Interstate Migration
Sample Means
Symbol Variable Description
W([ht.sub.is]) The average real hourly wage over the resident
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