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

Since Schultz' important paper on human capital (Schultz 1961), human migration has been an important topic of economic research. Much of the human capital literature on internal migration has emphasized expected net earnings benefits as the major factor driving human migration decisions, e.g., see Schwartz (1976), Schlottmann and Herzog (1981), Herzog and Schlottmann (1984), Sandefur (1985), Pissarides and Wadsworth (1989), and Detang-Dessendre and Molho (1999). A number of recent studies have also used aggregate data on migration, but aggregate data contain considerable migration against the economic gradient and are hard to interpret, for example, see articles by Deller et al. (2001), Huang, Orazem, and Wohlgemuth (2002), and Hunter, White, and Little (2003). Models underlying these studies assume that an individual moves in the first period in which he is made better off at a new destination than at the origin, but this approach ignores the timing decision, i.e., an individual should move when the payoff from migration is at a maximum rather than when it is first positive. Also, these studies ignore individual heterogeneity that can bias parameter estimates. Moreover, fixed costs and location-specific amenities are important to migration decisions, and they have received less attention (Greenwood 1997). Exceptions, however, are Mueser and Graves (1995), Deller et al. (2001), and Hunter, White, and Little (2003).

This article presents econometric estimates of the adult working-age male hazard function of interstate migration. The hazard function is the conceptually correct statement of the migration decision, i.e., it gives the probability that an individual moves at a given point in time, given that he has not yet moved. As such, it easily accommodates the migration timing decision. Furthermore, we include individual heterogeneity in the model to reduce omitted variables bias. The empirical hazard rate model is derived for an individual who has a finite-life and consumes leisure, purchased goods and local amenities, and incurs significant fixed costs of moving. The econometric hazard model of migration uses data on the length of an individual's resident spells, and the spells for this study are obtained from following a sample of adult males for a twenty-year period. These males were first interviewed in 1968, when they were nineteen to forty-five years of age, and hence, after twenty years of migration experience, the oldest males are sixty-five years of age. This is a relatively large amount of migration experience, given that we are primarily interested in the migration behavior of economically active males rather than males contemplating immediate retirement. The econometric results show a strong negative effect of men's real wage difference between origin and destination and of fixed costs associated with a move, and a positive effect of the local crime rate, a disamenity, on the hazard of interstate migration. Farmers and other self-employed men who own above-average location-specific assets have an unusually low hazard rate of interstate migration compared to wage earners.

The story unfolds in the following sections. First, a very brief summary of the economic problem is presented. Second, we present the econometric model and data, and third, we present the empirical results. The final section contains conclusions.

The Conceptual Model of Internal Migration

Males are born into a particular region, move with their parents until they are eighteen years of age, and then are assumed to make independent decisions about their residence for the remainder of their life. We assume an adult male receives utility from consuming his leisure time, purchased goods, and local amenities. Local amenities, representing location-specific culture, climate, topography (e.g., parks, access to the sea, mountains, plains), and environmental conditions (crime, pollution, congestion) are a type of local public good to an individual. An adult male chooses between staying at his current residence, the origin (o), or migrating to a new area or destination (d), and he is uncertain about future real wage and amenity outcomes at these locations. Let his expected indirect utility function for each year be [V.sub.j]([w.sub.jt], [x.sub.jt]), where [w.sub.j] is the expected real wage and [x.sub.j] is an indicator of the expected local amenities in location j,j = o, d (Greenwood 1997, pp. 668, 677). Let all expected relocation costs associated with moving from o to d in t, except for the foregone earnings, be represented by [c.sub.dt], and to simplify, assume that [c.sub.dt] is fixed and invariant with the distance moved. Also for simplicity, assume that local amenities and relocation costs can be measured in real wage units.

An adult male is assumed to choose a residence that gives him maximum utility. To further simplify, assume that he is risk neutral, that migration does not affect his length of remaining life, and ignore discounting. He then migrates when the summation of net real benefits is a maximum, provided that the summation is positive. (1) Let this maximum be:

(1) -[n.summation over (t=1)]([w.sub.ot] + [x.sub.ot] - [c.sub.d1] + [n.summation over (t=1])([w.sub.t] + [x.sub.dt]) [much greater than] 0

where n is his number of remaining years of life.

In equation (1), clearly [[summation].sup.n.sub.t=1]([w.sub.ot] + [x.sub.ot]) < [[summation].sup.n.sub.t=1]([w.sub.dt] + [x.sub.dt]) and [[summation].sup.n.sub.t=1]([x.sub.ot] - [x.sub.dt]) < [[summation].sup.n.sub.t=1]([w.sub.dt] - [w.sub.ot]). Hence, over n the summation of the difference in expected value of amenities between the origin and destination is less than the sum, over n, of the difference in expected real wage at the origin and destination. However, only if [[summation].sup.n.sub.t=1]([x.sub.ot] - (x.sub.dt]) = 0 can we say for certain that the expected real wage difference between the origin and destination will be positive. For example, if a destination gives an individual higher expected amenity value relative to the origin, it may be lifetime-utility-maximizing for him to migrate from o to d even, when the accumulated wage difference after migration is negative. (2)

Define D as an indicator variable taking a value of 1 if [NG.sub.t] = -[[summation].sup.n.sub.t'=t+1]([w.sub.ot] + [x.sub.ot]) - [c.sub.d1] + [[summation].sup.n.sub.t'=t+1]([w.sub.dt] + [x.sub.dt]) is a maximum (and positive) and 0 otherwise. Then the probability of an adult male migrating from o to d can be represented by the following probability statement:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The following comparative static results hold:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Hence, the probability of an adult male migrating from o to d is increasing in his destination wage [w.sub.d] and amenity [x.sub.d], and decreasing in his wage and amenity at the origin. It is also decreasing in the fixed cost of migration.

In a static environment, a strong economic incentive exists for a finite-life individual to migrate from o to d early, perhaps in the first period, or to stay at his current location. However, given that a move from o to d is completed, it is possible for additional moves to be optimal.

The Econometric Model and Data

At any point in time, each adult male is located at some residence location (o). Furthermore, as time in a particular place increases, he accumulates information on local conditions (knowledge of social networks, local culture, local businesses, local personal friends, and local amenities) that can be expected to strengthen his ties to a place and reduce mobility. However, if a change occurs in family composition such as a child leaves home, the local real wage declines, or if distant economic conditions improve, he may choose to move to a new location (d). Therefore, we expect the migration hazard, i.e., the probability that the resident spell ends at this time, to be a function of covariates (Greenwood 1997) and to be time dependent. Also, we can incorporate individual heterogeneity into the model. Because the migration hazard can accommodate these features, the hazard analysis of migration reveals a rich picture of interstate migration relative to a discrete choice model. (3)

The Hazard Model of Migration

Unlike discrete choice models of migration, the hazard rate model of migration treats the length of the resident spell as the dependent variable. For a given individual, define T as the duration or length of time that he has resided at a particular location, and t as a particular realization of T. T has an associated cumulative distribution function F(t) and probability density function f(t). An adult male's hazard of migration is represented as the limiting probability that a resident spell is completed at t + [DELTA], given that it has lasted until time t, or:

(6) H(t) = [lim.sub.h[right arrow]o][P.sub.r](t < T [less than or equal to] t + hIT > t)/h

= f(t)/[1 - F(t)] = f(t)/S(t)

where S(t) = [P.sub.r](T > t) is the individual's survival function for his current location. S(t) expresses the probability that a resident spell is of a length of at least t (Kiefer 1988; Lancaster 1990; Greene 2003, pp. 790-94).