Migration, fixed costs, and location-specific amenities: a hazard analysis for a panel of males.

We expect an adult male's hazard of migration to be time dependent and depends on a set of covariates, X. This is a so-called accelerated failure-time model (Greene 2003, p. 769). In addition, individual heterogeneity may exist because of (i) individual-specific unmeasured effects, e.g., intensity of psychological costs of moving, (ii) measurement error in X, or (iii) measurement error in the duration of a resident spell. Following others, for example, Heckman and Singer (1985), we impose the Weibull distribution on the density function for residency at a particular location (t), which permits constant, decreasing, or increasing time dependence of the hazard function for migration determined by the sign of [sigma]. If [sigma] is one, then the hazard of migration is not time dependent. We define [upsilon] to be individual-specific unmeasured heterogeneity, and assume [upsilon] is distributed gamma with unit mean and variance [theta]. It is incorporated as in Heckman and Singer (1985) or Greene (2003, pp. 797-798). Hence, a male's mixed resident-survivor function is

(7) S(t, X, [beta], [sigma], [theta]) = [{1 + [theta][[t exp(X[beta])].sup.1/[sigma]}.sup.-1/[theta].

His associated hazard function of migration is

(8) H(t, X, [beta], [sigma], [theta])

= [[S(t, X, [beta], [sigma], [theta])].sup.[theta]] (1/[sigma])[t.sup.(1/[sigma])-l][[exp(X[beta])].sup.1/[sigma]]. (4)

If [sigma] is not significantly different from zero, the hazard of migration is monotone in duration. An important feature of this specification is that the effect of heterogeneity is increasing in [theta], but as [theta] goes to zero, heterogeneity vanishes. (5)

Some variables in X for the ith individual, say [X.sub.ij], change over time and are jointly determined with duration. For example, an individual who has children and chooses a place to reside may make a joint decision. When this is the case, [X.sub.itj] is typically assigned its value at the beginning of the resident spell, say [X.sub.ij0], (Lancaster 1990; Greene 2003, pp. 790-800). Other variables are time varying but not endogenous to duration, e.g., marital status, and actual value during the spell can be included as a regressor.

The Data

Individuals in this study are working-age adult males of the Panel Study of Income Dynamics (PSID). We use the Survey Research Center (SRC) Sample, which was a probability sample of all U.S. households in the contiguous forty-eight states in 1968 and not the Survey of Economic Opportunity sample, which drew mainly from low-income households. Critical to this study, the PSID identifies the state of residence. These males were first surveyed for the PSID in 1968 when they were nineteen to forty-five years of age. Males were surveyed annually starting in the year after they completed school and were reinterviewed annually until they retired, died, or disappeared. We have data on twenty years of migration experience for 915 men where 193 of them had at least one move in the twenty-year period; 10.6% moved once, and the remaining 10.5% moved more than once (table 1).

From the full number of males, we derived a total of 865 resident spells having known starting dates, and 1,268 residence spells that have adjusted starting dates. The 1,268 open and "closed" spells are the total number of observations in our econometric hazard rate of interstate migration analysis. The adjustment closes the migration interval when it is open on the left, i.e., when we do not have data on the starting date. This provides a relatively large amount of information on resident-location decisions of working-age adult males and variation in length of resident spells. However, the oldest-aged males are sixty-five years, and some of them have retired or are contemplating retirement. (6) The PSID has major advantages over cross-sectional micro-data sets on migration, because we have twenty years of information on migration decisions, and for the most part we know the individual's attributes at the start of each resident spell. Data for these adult males are supplemented with data from other sources for their resident area.

For working-age males, internal migration over a long distance is generally associated with a change in employment, whereas short-distance migration is frequently associated with a change only in residence or housing. Since the latter is not of interest to us, we choose to define migration decisions for adult working-age males as interstate moves, which is the most frequently used area designation for migration studies in the U.S. States have fixed geographical boundaries over time and are exhaustive in their geographical coverage. Occupational licensing practices and union membership policies are set at the state level, and the state government is a major fiscal and jurisdictional authority. (7) Some important amenity benefits of states include the quality of local public goods, such as public schools and park areas, air and water quality, crime rate and "mildness" of the climate. Much of the important variation in topography is also captured at the state level. Other migration studies that have analyzed interstate migration include Sandefur (1985), Brinig and Buckley (1996), Clark, Knapp, and White (1996), and Pashigan (1979). (8)

For our study, an adult male is defined as a long-distance migrant if he moves across a state boundary. Although states differ in area, population, employment, and number of cities, we ignore these differences. Adult males and families may be affected marginally by the distance of a move to a new destination, but a major part of the cost is fixed. Costs of moving for an adult male with a family include: time spent weighing the decision to move, finding new places to shop, finding schools for kids, finding a church to attend, and finding and making new friends. They also include the cost of selling a house or ending a lease at the origin, finding a new house or apartment at a destination, and the cost of loading one's possessions at the origin, and unloading and putting them in order at the new destination.

Since destinations and their location-specific amenities are a choice, all potential working-age males face a similar common fixed amenity-effect of potential destinations. Hence, when they live in different places, the local amenity attributes that differ among them, and that is relevant to their decision to migrate is the amenity attributes of their current location (Huang, Orazem, and Wohlgemuth 2002).

The PSID identifies the state of residence of each adult male in the survey We focus on a twenty-year period, starting in 1968.

The Empirical Hazard Function of Migration

The systematic part of the hazard function of interstate migration is specified as:

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where i = 1, 2, ..., n, denotes sample males, s = 1, 2, ..., [C.sub.i], denotes the resident spells, W([ot.sub.is]) denotes the real wage for ith male at his current location or the origin o in time t during spell s, W([dt.sub.is]) denotes the real wage for the ith male at a new destination in spell s, AGE is the age of the ith male at the beginning of spell s, EDU([t.sub.is]) denotes the years of schooling completed by the ith male at the beginning of spell s, DSLFEMP([t.sub.is]) denotes an indicator for the ith male being self-employed or being a farmer at the beginning of spell s, UNION([t.sub.is]) denotes an indicator for the ith male being a labor union member at the beginning of spell s, UNEM([t.sub.is]) denotes the ith male's unemployed status in resident spell s, MARR([t.sub.is]) denotes the ith male's marital status in spell s, CHILD([t.sub.is]) denotes the ith male's number of children at the start of spell s, CRIME([t.sub.is]) denotes the crime rate at the origin for the ith male relative to the U.S. average in spell s, PARKS([t.sub.is]) denotes for the ith male the share of origin or of the resident state that is in state and federal parks relative to the U.S. average at the start of spell s, JAN([t.sub.is]) denotes for the ith male the thirty-year average January temperature at the origin or resident state relative to the U.S. average at the start of spell s, JULY([t.sub.is]) denotes for the ith male the thirty-year average July temperature at the origin or resident state relative to the U.S. average at the start of spell s, and DWHITE([t.sub.is]) denotes the ith male's race.

The set of covariates is largely defined as the beginning of a resident spell, especially for those variables that seem most likely to be jointly determined with the probability that a residence spell ends--EDU, DSLFEMP, UNION, and CHILD. (9) For other variables that are time varying, but that are not jointly determined with the probability of a spell ending, we use a summary of the variable over the resident spell, for example, MARR. (10) Also, we choose to incorporate the effect of unemployment on the probability of a resident spell ending as the average amount of time in the spell that the individual was unemployed. (11)