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

The wage equation (equation (10)) is fitted to all of the observations for the 915 adult males in the PSID, pooled over twenty years, starting in 1968. Results are reported in table 3. The performance of the fitted male wage equation is generally in agreement with results reported in other studies. A one-year increase in a male's schooling increases his real wage by about 7.5%. An increase in his experience has a positive effect on his real wage, but at a diminishing marginal rate. The maximum effect of EXP on a male's wage profile occurs at twenty-six years of experience (approximately forty-five years of age). All other measured variables held equal, white males earn 11% more than nonwhites. These results are consistent with those reported by Neal and Johnson (1996), but lower than those by Topel (1986).

Male real wage rates are shown to differ because of local cost-of-living and amenity differences. Both the real price of land (PLAND/[P.sub.y]) and congestion, as reflected in URBAN, have positive effects on the real male wage rate. The land-price effect on the male wage compares favorably to the findings of Kenny and Denslow (1980) and Tokle and Huffman (1991), but the effects of URBAN are greater in this study. Roback (1982) does not include a variable that is a good proxy for the cost of housing in her earnings equations, and this may color the interpretation and comparison of those results. However, Roback (1988) includes the local cost-of-living index in some of her wage equations.

Local amenities have significant effects on the male real wage. A one percentage point increase in a state's crime rate increases the male real wage by about 1.5% (significant at the 1% level), consistent with findings reported by Roback (1982). Roback (1988), however, did not find statistically significant effects of the crime rate in her wage equations, with one exception. The impacts of climatic amenities on the male wage are conditioned by the inclusion of regional dummy variables. However, a higher average January (or July) temperature for an area, holding the region constant, reduces the male real wage by 4 (17) percent per 10 degree increase, suggesting positive amenity value for higher values, other things equal. Roback (1982) includes weather variables in her earnings equations and finds that heating-degree days, snowfall, clear days, and cloudy days have statistically significant effects. She, however, largely excludes weather variables in her 1988 article (Roback 1988). (13)

State labor-market characteristics have a significant effect on male wage rates. A one percentage point increase in the anticipated job growth rate for the resident state (PJOBGR) increases the male real wage by 6.0%, and a one percentage point increase in the anticipated unemployment rate for the resident state (PURATE) increases the male real wage by 4.3%. This reflects the fact that over the long run, he must be compensated for taking the higher risk of being unemployed. The latter result is greater by a factor of three than those obtained by Topel (1986) and Tokle and Huffman (1991). The signs of the coefficients for unanticipated job growth (RSHOCK) and unemployment (RURATE), which cannot be factored into long-run decision making, are consistent with the results in Topel (1986) and Tokle and Huffman (1991).

Historically, the U.S. has had broad regional differences in real wage rates, and our results show that they persist over the twenty-year period of our data, even after controlling for land prices, urbanization, crime rates, and climate. Compared to the Northeastern region, the male real wage in the South is 8.9% lower and 13.7% lower in the West. However, the male real wage rate in the North Central region is not significantly different from that in the Northeast region. Consistent with other evidence, the results show a statistically significant negative trend in the male real wage rate of slightly less than 1% per year.

The Hazard of Interstate Migration

The empirical hazard function of adult male interstate migration is fitted to the data on resident spells over a twenty-year period starting in 1968, which is a large amount of information on migration experience. The male migration hazard model is fitted using the maximum likelihood estimation procedure (see Kiefer 1988; Lancaster 1990; Greene 2003). A male living in a particular state faces forty-seven potential destinations when considering an interstate move within the contiguous forty-eight states, and there are a total of 2,256 (= 48 x 47) different combinations of origins and destinations. To make progress empirically, we assume that state labor markets for male labor are approximately in equilibrium; then observations from the forty-eight state labor markets can be used to approximate the value of a male worker's attributes in the national market. (14) The predicted male wage from table 3 can then be used to provide the U.S. labor market's assessment of a potential male migrant's anticipated wage at a new destination, adjusted for local amenity values.

We combine the information on a male's actual real wage at his resident location and predicted real wage in the national labor market to define the empirical measure of [DELTA][W.sub.iy] = ln([W.sub.ioy]/[P.sub.y]) - E[ln([W.sub.idy]/[P.sub.y])], which is a proxy for the "true" differential between the current residence and a new location. (15) By construction, the male's real wage differential [DELTA]W is not correlated with any of the eighteen regressors entering the male market wage equation (10). The male real wage differential [DELTA]W partly represents luck, in the sense that it consists of random disturbances that explain why two adult males, living in the same state and having the same measured attributes, have different current wage rates. (16) It also reflects a return on current location-specific knowledge. We assume that a man who has a large positive wage differential is better off staying at his current location. This reduces his hazard of interstate migration and lengthens the resident spell at his current location. In contrast, when he has a large negative wage differential, his labor is most likely being undervalued at the origin relative to the national labor market. Hence, his hazard of interstate migration will be larger. We express the male wage differential [DELTA]W as an annual average value over a resident spell. (17)

Four sets of parameter estimates of the hazard function for interstate migration using resident spells of the PSID-males are reported in table 4. Column (1) presents estimates from a constant migration hazard rate function without individual heterogeneity, and column (2) presents estimates from the model after incorporating heterogeneity. Columns (3) and (4) present estimates of parameters for a time-dependent hazard function of migration with heterogeneity. The latter two sets of results differ only in the procedure used to close migration spells that are open on the left. (18)

The results in columns (3) and (4) show that the Weibull timing-parameter [sigma] is significantly different from one (t-value of 5.45); therefore, the data are not consistent with a constant hazard of migration over a resident spell. At the beginning of a spell, the hazard of migration is low, but it increases to reach a maximum at six years of residence; thereafter the hazard of migration declines. Furthermore, given that a male's age is defined to be at the beginning of a residence spell, the time dependency reflects two effects: aging and pure time dependency due to length of the spell.

Also, we reject the null hypothesis of no individual heterogeneity. The heterogeneity parameter [theta] is significantly different from zero in columns (2)-(4). Although the results in columns (3) and (4) are similar, we have a slight preference for the results in column (4), which use data on the largest number of resident spells. These results could not be easily obtained in a probit model of interstate migration.

The marginal impact of each of the regressors on the male hazard of interstate migration is computed and reported in table 5. Our results provide statistically strong evidence that the wage differential [DELTA]W is a statically important variable explaining interstate migration. A one percentage point increase in the expected wage differential decreases a male's hazard of interstate migration by 56%, which is quite large, and economically important.

The coefficients on a male's AGE and AGE-squared are significantly different from zero in the migration hazard equations for males. These age effects capture life cycle and finite-life effects at the beginning of a residence spell. The results imply that the marginal effect of AGE on the hazard of interstate migration is positive up to forty-two years of age, but then declines for each additional year of age. A male who has more schooling has a higher hazard for interstate migration; a one-year increase in a potential migrant's education increases his hazard of interstate migration by 6.6%, other things equal. These results support the findings of Detang-Dessendre and Molho (1999, 2000), but also confirm the results in other migration studies dating back to Schwartz (1976).