An Empirical Analysis of Income Expectafions and Intersfafe Migration

Income expectations have been examined at considerable length as a result of their central role in the "permanent income" hypothesis formulated initially by Friedman [10] and in the "life cycle" hypothesis formulated by Ando and Modighani [l]d Income expectations have also been investigated in terms of their impact on a number of other issues, including investment in human capi tal,^ the efficacy of economic stabilization policies, and migration/ This paper seeks to extend the latter body of literature by investigating how and td^ what extent certain income expectations proxies may influence human migration decisions in the United States. linear to An alternative is developed are offered in the

Section I provides the basic theoretical framework (model) of the paper, while Section II provides an empirical framework for the analysis of the rela tionship between labor migration and expected income changes. Section III uses multiple linear regression analysis to evaluate the framework in Section II. An alternative model is developed and tested in Section IV. Concluding remarks are offered in the final section of the paper.

I. Investment in Migration
The basic framework of the paper is one in which the individual chooses to migrate from one area to another if over time there are positive net benefits from such migration. In particular, we maintain that an individual residing in area 2 will choose to migrate to area j only if the discounted present value of the net benefits associated with the migration is positive. Thus, assuming that all of the various benefits and costs that can he associated with migration can be expressed in pecuniary terms,^ we argue that (1) Mij > 0 only if where Be , e=l,...,n, represents the value of all the benefits associated with migrafiorT from area to area j for year ^ C e , je=l,...,n, represents the value of aU the costs associated with migration from~area ^ to area_2 for year e, r is the appropriate rate of discount for the individual, and Mij denotes migration from area to area J.
*Emory University and Ohio University, respectively. Now, the analysis of the net benefits of migration (which clearly need not be positive) involves appraisal of all the benefits and of all the costs associated with migration. There may, of course, be many different sources of benefits and of costs from migration which may accrue over a given time period (year). The total gross value of the benefits accruing from migration in the eth year, B g , may thus be represented as X Be = e=l,...,n.
where Bek , k=l,...,x, is the value of the kth form of benefit accruing from migration in year e. Similarly, the total gross value of the costs accruing in the eth year, Ce , may be represented as It follows from (1), (2), and (3) that migration from area i to area j, Mij, is a function of B g^ and C gm such that The primary emphasis of this paper is on the impact of income expectations on migration. Accordingly, we note that the income increase expected from mi gration in year_e can be represented as one of the benefits accruing from mi gration in year _e=l,...,ri. More generally, the income increase expected from migration in any time period represents one of the benefits from migration ac cruing in that time period. It follows then from (4) that In this paper, it is assumed initially that the income increase expected in an area over a period of time depends upon the rate of the area's income growth over the previous time period. Thus, the income change expected for the ten year period 1960-1970 would depend in part upon the income growth rate over the prior ten year period: 1950-1960. The rate of income growth in area is measured hereby the percentage (6) ^1960 -^1950 = AYi Thus, AYi, as defined here, is treated as a proxy for expected future income changes for the following ten-year time period (1960)(1961)(1962)(1963)(1964)(1965)(1966)(1967)(1968)(1969)(1970) in area h Given the argument presented above, the next section of this paper addresses empirically the following question: Has migration in the United States over various time periods in fact been responsive to expected income changes, and if so, to what extent?

II. An Empirical Framework
To investigate empirically the impact of income expectations on migration, we first postulate the following migration model: where ^i is net migration into area i, Yi is current per capita personal income in area i, Yi is expected future income increases associated with migration to area h Q is the number of days per year when the tepiperature in area^ fell to 32°F arenheit or below, and K is the population per square mile in area iŴ e impose the following restrictions on the partial derivatives in (6): 9 Mi ^Mi < 0 a Ci, aPi The sign of d Mi/ d Yi follows from orthodox theory, while the sign of d Mi/ d Yi follows from (5) and (6) above and the discussion thereof. Namely, it is argued that, on average, migrants are attracted to those areas which exhibit the greatest income growth since in such areas incomes may well be expected over time to rise the most rapidly. The sign of d Mi/ d Ci follows from the fact that, on aver age, people prefer warmer or more moderate climates to colder climates. Finally, the sign of d Mi/6 Pi follows from the notion that as population density rises, so do congestion, risk of loss from crime, loss of privacy, pollution, etc.
The specific regression equation to be estimated is where a is a constant and u is a random error term.

III. Empirical Results
We use Stanley Lebergott's estimates of net migration by states, except for the 1960-70 decade, where we use Census estimates (Lebergott [16,[846][847] and Department of Commerce [6,15]. The net migration estimates are for in ternal migration only (excluding immigrants) except for the 1960's, where immi grants are included in the data. The state personal income per capita data used in our analysis are taken from two sources. We use Richard Easterlin's estimate for 1880, 1900, and 1920 (Easterlin [8,753]). For 1930For , 1940For , 1950For , 1960, and 1970, we use Department of Commerce estimates (Department of Commerce [7,13]; Department of Commerce [6,314]).'^ The population density and cli mate data were also obtained from Department of Commerce sources (Easterhn [8,349]; Department of Commerce [6,12,164]). To get state estimates of the number of days per year below freezing, we took the arithmetic mean of the average number of cold days for all the weather stations in each state for which data were reported in the 1971 Statistical Abstract of the United States [6,173].
As shown in Table 1, the results overall are gratifying. In six of nine in stances, the model explains a majority of the variation in net migration between the states. In 33 of 36 cases, the observed relationship between net migration and the independent variables is in the postulated direction; in 27 instances, the results are significant at the five percent level using a one-tailed test.
Most important, the empirical results support our hypothesis concerning the relationship between both Mi and Yi and AR and AYi. Our variable measuring ĥ as the expected positive sign and is statistically significant at the five percent level in every instance. Our proxy for expected income, AYi, has the expected posi tive sign in seven of nine instances. In addition, it is statistically significant in five cases at the five percent level, and in six cases at the ten percent level. Of the three cases where the results were not significantly positive at the 10 percent level, two were for early decades (1890)(1891)(1892)(1893)(1894)(1895)(1896)(1897)(1898)(1899)(1900)(1900)(1901)(1902)(1903)(1904)(1905)(1906)(1907)(1908)(1909)(1910) where the probabihty of error in the measurement of AYi is fairly substantial. The only other case where AYi did not work as expected was the decade of the 1940's -a period encom passing the massive disruptions associated with World War II.® This general strength of AYi is compatible with a number of recent studies, including Pack [20] and Cebula and Vedder [5].
The empirical results also support the hypothesis that migrants, ceteris paribus, prefer to avoid cold climates', and prefer less congested (densely populated)  AYi is for the same period as the migration *Significa£Vit at the ten percent level. areas. In the case of our measure of the results are statistically significant at the five percent level in seven instances; with respect to the results are sig nificant in six cases and have the expected sign in two of the three remaining instances.
IV. An Alternative Model The analysis ahove has two limitations which can quickly be attended to. First, the migration model was one of net migration rather than gross migration. Given the large volume of high quality data on interstate gross migration flows, it might he appropriate and indeed desirable to use such data to examine our expectations hypothesis. Accordingly, this paper will now examine the effects of expected income changes on gross immigration to states for the periods 1955-1960 and 1965-1970. Census data ( [24] and [25]) wiU he used. Second, the paper has thus far assumed that the income increase expected in an area over a time period of given length is dependent solely upon AYi, the rate of income increase in only the directly preceeding period of equal length. Obviously, expected income growth for a given time period might depend not only upon the rate of income growth in the preceeding period, but also may depend upon income growth rates in earlier periods. More specifically, the income increase expected in an area over, say, the (five year period) 1955-1960 period would perhaps depend not only upon the income growth rate for (the five year period) 1950-1955, given The impact of A xYi may well be greater than that of A 2Yi since it may be viewed as a more current and hence more relevant and dependable indicator of changes for the near future. In any event, the model here argues that ex-pected income changes for a given period are formed on the hasis of some form of weighted average of the appropriate values of A ;^Yi and A2Yi.
To examine the migration impact of our two expectations factors, A^Yi and A 2Yi, we examine the following migration model for 1955-1960 and 1965-1970: (15) Mgi=:Mgi (Yi, A^Yi, AaYi, Ci, Pi) where Mgi = the gross migration rate to state T he actual form of (15) to he estimated is where a is a constant and u is an error term.
The results of estimating (16) for the periods 1955-1960 and 1965-1970 are given in Table 11. The results, once again, are very gratifying: all of the variables had the hypothesized signs, and statistically significant (at the five percent level) coefficients were obtained in eight of the ten cases. Of particular interest is the fact that the term A i Yi did very well in both regressions while A 2Yi did quite well in the 1965-1970 regression. Overall, it would appear that A 2Yi may have per formed somewhat better than _A2Yi. In any event, it may be concluded that in come expectations, as measured by our proxies A i Yi and A oYi, seem to influ ence migration decisions in an important way.

V. Conclusion
Our model of labor migration maintains that the migration decision is basi cally an investment decision in which migration from one area to another occurs if the discounted present value of the expected future stream of net benefits® from such migration is positive. Within this framework, this paper has sought to ascertain the impact of income expectations on the interregional migration of labor. Our empirical findings indicate that income expectations, as measured in one set of cases by our proxy A Yi, and in another set by A i Yi and A 2Yi, for the most part have had a significant influence upon interstate migration in the United States. These findings are compatible with the results of other recent studies, including Bowles [4], Cebula and Vedder [5], GaUaway and Yedder [11], and Pack [20].
One possible implication of our analysis is that there may exist some form of "permanent income" or "life-cycle" hypothesis of migration. Just as consump tion of commodities may be partially explicable in terms of a permanent income or life-cycle hypothesis, so may consumption of (investment in) "migration" be explained. This notion would seem especially appealing if migration in fact can be treated as a commodity.