Strucfural Change In Models Of Migration Omission Of Psychic Income

The question of the relative importance of various migration determi nants has heen raised in recent migration research. Some of the associ ated debate has resulted from the inevitable squabbling among the pro ponents of various disciplines over the variables of their own special interest — economic, sociologic, geographic, etc., but much of the debate has real substance and policy significance. From an economic perspective, if differential regional incomes and unemployment are less important migration determinants than individualistic and personal factors (like amenities and better quality of life), then migration does not have the important equilibrating quality so frequently attributed to it. Without migration to equalize factor prices, commodity trade and capital move ments become strained as equilibrating factors and the conclusions of the neoclassical regional growth model, Borts and Stein [1964], are less likely to he obtained. In that case, national output would he suhopti-mized by regional concentrations of labor, and regional policy would have to become aimed at finding viable means of properly redistributing pop ulation.^

The question of the relative importance of various migration determi nants has heen raised in recent migration research. Some of the associ ated debate has resulted from the inevitable squabbling among the pro ponents of various disciplines over the variables of their own special interest -economic, sociologic, geographic, etc., but much of the debate has real substance and policy significance. From an economic perspective, if differential regional incomes and unemployment are less important migration determinants than individualistic and personal factors (like amenities and better quality of life), then migration does not have the important equilibrating quality so frequently attributed to it. Without migration to equalize factor prices, commodity trade and capital move ments become strained as equilibrating factors and the conclusions of the neoclassical regional growth model, Borts and Stein [1964], are less likely to he obtained. In that case, national output would he suhoptimized by regional concentrations of labor, and regional policy would have to become aimed at finding viable means of properly redistributing pop ulation.Î nterest in assessing relative importance of the migration determinants is expressed in the interdisciplinary surveys of the literature on migra tion, like those of Shaw [1975] and Yap [1975]. Those two studies, in particular, are in marked contrast to one another. Yap reviews studies in the less developed countries, citing surveys which show economic factors to he the most frequent reason for migration. Yap argues, how ever, that (a) it is difficult to measure and analyze properly the noneconomic factors (urban services) which influence migration, (h) noneconomic factors seem to be less important than economic factors, and (c) there is httle evidence to indicate that the relative importance of these migration factors wUl change in the near future. Yap [1975], pp. 13, 20, and 35. Shaw similarly finds support that economic factors are strongly motivating reasons for migration, listed by 50 to 60 percent of the migrating population in response to surveys as the prime factor causing the move, Shaw [1975], p. 58. Yet, Shaw concludes from the evidence he presents: *Assistant Professor of Economics, The Pennsylvania State University. I am indebted to Mon roe Newman for helpful comments on an early draft of the paper and for funding for research to the Regional Analysis Center, The Pennsylvania State University.
It may be that as an economy progresses toward an urban-indus trialized state, the role of pecuniary considerations . . . decline in importance as a motive to migrate. Shaw [1975], p. 101.
Others, as well, have also evaluated the question of importance of migration determinants. Gallaway et al. [1967] conclude that non-eco nomic factors are the predominant explanations. Sauli [1972], Liu [1975], Long and Hansen [1976] and Fuguitt and Zuiches [1975] argue that non-economic personal preferences are increasingly significant explana tions of migration. Liu, as an example typical of the others, states: Recently more and more people have been commenting on the paradoxes of affluence. Discontent with the quality of life seems to have increased proportionally with technological advance and growth in material wealth. Liu [1975], p. 9.
In this case, people move to obtain non-economic quality of life just as they had moved to increase material wealth.
The belief that the importance of determinants will shift over time as growth and development occur is the central theme of the mobility tran sition hypothesis, presented by Zelinsky [1970] and [1974]. As individ uals' incomes increase in pace with the economic growth of their society, individuals migrate for non-economic reasons because increased incomes lower relative migration costs and make any given real increment to in come (which might he obtained by migrating toward high income re gions) seem less significant than it might have seemed when incomes were low. Other things constant, the non-economic factors become more important. Of a five-phase mobility transition, Zelinsky theorizes; (in Phase IV there) is the emergence of ' aomic motiva tions for both migrant and circulator; ... <V: ; s ; V), it seems hkely that non-economic considerations will : c,; larger. Zelin sky [1970], p. 35.
The mobility transition or "determinants-shif t'l-xplains the apparent contrast between Shaw and Yap. Yap waiting about migration in the LDC's deals with countries in which inco; r loveh. ar« insufficient to permit non-economic factors to predominate. > s ! < . ; wntiug more gen erally about migration in high income countries ; e non-economic determinants to be growing in importance hecau ; sho income levels of the developed countries facilitate the expression i Uneconomic moti vations.
This paper makes no attempt to deny the existence of "determinantsshift", hut it does offer an alternative based on the belief that econometric misspecification in the earlier work has made the shifting importance of determinants more apparent than real. Under this alternative, either the importance of migration determinants have not changed at all or they have changed, hut by less than has been alleged. Coelen, Groover and Heinz [1977] have demonstrated this case empirically, showing the ef fects of omitting demographic factors which describe migrant popula tions. The current paper extends this approach, postulating that some of the apparent decrease in marginal propensity to migrate to obtain higher income is due to the use of incompletely specified structural equa tions which leave out psychic costs and benefits (which have not ever been measurable) and, therefore, have been excluded from empirical work.
I. Incomplete Specification of Migration Models Greenwood [1969] has already shown that omitting variables in migra tion models causes bias. He specifically considered the deletion of mi grant stock which is an estimate of the flow of information from j, the destination, to i, the origin. In conventional cases, deletion of migrant stock overestimates coefficients of variables when they are themselves autocorrelated. Greenwood's work is important because of the large amount of cross-sectional migration research that is done. Without con sidering migrant stock explicitly, the estimates that would be obtained are subject to bias.
The current work focuses on a similar but more implicit point. The psychic benefits (and costs) of origin and destination locations should influence the amount of migration (net and gross) that will occur be tween any two places, other variables constant. The problem is that psychic income is not measurable and the variable is deleted from em pirical work with the result that uncertainty about the effect of psychic income abounds. In comparing migration studies on the same nation over time or among nations at the same time, variation of the impact of psychic income provides confusing information which is often mistaken as a shift in the structure of migration behavior.
Consider a study of net migration to place i from all places j, Mi= ( Mij -Mji), in which Mij is the gross flow from j to i. Assume that gross migration. Mi, to place i is affected by regional levels of real money (per capita) income, Ri, psychic (per capita) income, Bi, and a catch-all factor, Zi. The weighted average of the regional per capita incomes gives national average per capita income R,,. Psychic income is distributed with mean zero-'and with elements Bi, positive and negative in the i regions. We assume individuals migrate to relative total (psychic and money) income among regions such that one does not distinguish be tween the sources of his income. Then migration occurs according to: Because psychic income cannot be measured with convenience or accu racy/ we are often left to evaluate migration with knowledge only of Yi, the real income regional differential. Thus, the model we often fit is: Denote deviation values of the log of these variables from the mean of their logs by small case letters and we have the estimated coefficient, with TTp:y|z the coefficient of y in regressing p on y in presence of z.T he expectation of (a') is: This shows bias whenever TTp:,v|z 0. The coefficient is the expected value of the derivative, dPi/dYi|zi=Zi, the partial of p with respect to y in a regression including z. It is the major purpose of this paper to evaluate such bias under the paradigm that the importance of Bi declines over time with increases in Rn. This is equivalent to the belief that the psychic value of one's home stead becomes smaller and smaller as income, and the associated ease of migration (caused by higher incomes), rises. At a given point in time, we might, therefore, represent psychic income as: I =Kt:y In this case, psychic income varies over time with changes in R,, and the associated variation in the Ri around Rn. Substituting (6) into the definition of Pi from (2) and approximating TTp:y|z as the expectation of the derivative, dPi/dYi, we can show that: since both , v > 0. The bias in 3' is positive so that ignoring psychic income makes us overevaluate the propensity to migrate to higher in- The behavior of TTp:,!/, over time is of interest because it shows how our estimated coefficient, S', will vary from the true parameter, a. If Rn in creases, as typical, over tim.e, we expect regional income divergence in the LDC's and regional income convergence in the developed countries, Williamson [1965]. This implies differing behavior of dependent upon the parameters, especially v, such that ■' > q lDC's upon the parameters, especially v, such that ' = 0 in the LDC's as V = 1 because the variance of Ri/R" rises with income divergence.
It implies " = 0 in the developed countries as v = 1 because the variance of Ri/Rn falls with income convergence. The result is a con sistently biased estimate that may vary with the level of income and growth. One plausible case is shown in Figure 1 with v > 1. At point K, roughly equivalent to Rostow's middle stage of economic growth, Rostow [1965], the estimated coefficient ceases to increase with the level of in come and starts to decrease. We may be observing the latter portion of Figure 1 in developed countries and the earlier portion of Figure 1 in de veloping countries. This would cause us to believe that income determi nants of migration are becoming increasingly less important in the de veloped countries, and increasingly more important in the developing countries.
FOOTNOTES is plausible that if migration occurs in response to sociological variables rather than economic, migration increases social welfare at a national level because of non-marketed fac tors influencing welfare. It is unlikely, how ever, that this case can lead to economic effi ciency producing the most valued output with the given stock of productive factors.
-Psychic income is the implicit sum of prices times characteristics of non-marketed goods and while with different price vectors, national average psychic income may be positive or negative, we can choose a numeraire in the utility maximization case for psychic income prices which will guarantee zero national aver age psychic income. The condition does little consequent harm.
Much of the work of the Commission on the Third London Airport, e.g., A. A. Walters [1975], concentrates on consumers' surplus measurement in residential location. .
2z-2my -Syz 2mz -,, 2y2 -(Syz)2 normal equations and equation (4) is derived by substituting equation (2), expressed mi = api ayi -(-jzi + ui, assuming yt and zi to be independent.^T his depends upon the form of the function used in equation (6), which in the text is quite general, chosen so that regional psychic income rises with increases in relative regional income while it falls with increases in national average per capita income, ceteris paribus. Whether psychic income increases or decreases from year to year depends on the value of parameter V and the magnitude of the relative and na tional income changes.
This function is specific in the sense that it is one of a small class of functions which eases mathematical complexity. Any changes in Pi or Yi can be traced to changes in Ri and Ru (exogenous to the model). The impact of equation (6) in deriving dPi/dYi is that the latter is independent of the specific source of variation of dRi or dRn because of the form of equation (6). Most other functions would have caused dPi/dYi to vary depending on the changes in all of the individual regional incomes in the national distribution.
One referee suggested that psychic and mon ey incomes are substitutes in a given location and that is an alternative plausible proposi tion. In that case, Bi and Ri would vary inversely and might look like Bi/Ri M = T^(Ri/Rn)^ , ^ , V > 0; -pyp. Then, dPi/ dYi depends upon the source of variation and solution is more difficult, calling for simulation and yielding different solutions under different conditions. The basic point remains unchanged, however, bias occurs and fluctuates systemati cally over time. BIBLIOGRAPHY