WHY DON'T STATE INCOMES CONVERGE? EFFECTIVE WORKER PAY DOES NOT DIFFER AMONG STATES JULIAN SIMON INTRODUCTION Income differentials among the states in the United States have long been troubling. Policy makers are distressed by the inequality. And economists are affronted by the continued dise- quilibrium.1 This paper finds that the observed differentials do not represent different pay for the same work, but instead (in addi- tion to differences in occupational composition) represent dif- ferent pay for different qualities of work. Workers tend to receive the same pay for the same amount of production in high- income and low-income states. Apparent pay differentials in given jobs seem most likely to stem from differences in the quality of schooling. The argument runs as follows: Natives of the United States with given amounts of education earn lower incomes in states with lower mean incomes; this result is shown with a conventional earnings equation with state average income as a variable. But this effect does not hold for a group of persons who were not raised in the states in which they are now working--immigrants from abroad--among whom the observed state income effect is much smaller than for natives, and perhaps non-existent. There seems no plausible reason why immigrants would select states in such fashion as to produce this result if there really are real-wage differences among the states. Therefore it would seem reasonable that if immigrants receive the same wage for the same work in all places, natives also receive the same wage for the same work in all places. Corroborating evidence of other sorts is offered in the Discussion section. And other possible explanations of the apparent differential are examined there. Absence of a complementarity effect between workers of different skill levels is also found. The state effect is positive for native workers with both more and less education, whereas complementarity suggests that the effect should be positive for workers with less education but negative for workers with more education. An implication of the analysis is that external effects of human capital in the market place are not large. If such an effect were to operate, the incomes of immigrants in the various states would be seen to be affected by the average stock of human capital in those states, as represented by the mean incomes of those states. But this is not observed. CONCEPTUAL FRAMEWORK: THE VARIABLES TO BE STUDIED The money earnings of a worker are in theory determined by two elements, the marginal physical product of the worker, and the price of the product in the place where the worker sells his/her wares. The possible difference in prices is too important not to be mentioned here. But auxiliary evidence, as well as some findings in this paper--referred to in the Discussion section--suggest an absence of a relevant pattern of price differences within the United States, and hence the matter can be left aside. It is not unreasonable to assume that a given marginal physical product receives the same return in all states, and therefore that earnings may be assumed proportional to to the individual's output. An individual worker's output may be viewed as a function of many factors: genetic elements which possibly affect intelligence and drive, parental nurturing, quantity of schooling, quality of schooling, quantity of experience on the job, physical capital complement, human capital complement, human capital in the environment from whom one may learn on and off the job, health, environmental factors such as temperature that may affect performance, and still others. Because of this paper's interest in the quality of the educational inputs to a person's productive capacity, this study tries to compare individuals with the same amounts of formal education, and hence the purpose of the variables for schooling and experience is to hold these factors constant rather than to throw light on the magnitudes of the effects. And a proxy for physical environment--temperature-- is used to adjust for differential effects upon people in different locations. Many other factors such as genetics are not considered, hopefully without harm to the analysis. The effects of quality of schooling, quality of the surrounding human capital at home and school, and the amount and quality of parental nurturing, are theoretically obvious. Data are lacking to infer the separate effects of these elements, and hence they will be considered together here as a single factor called "developmental quality." For completeness, the topic of externalities in learning is discussed in an appendix which may be omitted in publication. ESTIMATION The Size of the Effect for Persons Born in the U.S. The first task is to establish that the apparent differentials which we are investigating actually exist. Therefore, the first regression estimates the effect of a state's average income upon the earnings of individual workers, holding their quantities of education constant in a standard earning function. Such a model is LME = f(PPE, SCHL, EXP, EXP2, TEMP) where LME = log male earnings for an individual worker PPE = mean per-person earnings for the state population as a whole, as a proxy for the mean "effective" educational level, which in turn is a proxy for human capital per person. Assuming away other factors of production (as is probably reasonable, even physical capital), this is a good economic measure of the average quality of schooling for the labor force. SCHL = number of years of school for the individual EXP = length of work experience for the individual. TEMP = average temperature in the state, included to ensure that state income does not pick up variance due to temperature because of correlation between them; it is possible that the correlation between temperature and income (or economic development) is partly due to temperature affecting income, as many writers have speculated. The earnings function used is conventional except for the inclusion of the state's temperature and mean income. Demographic characteristics are not included in the income function, partly because the numbers of cases for each language and country of origin would be small in each state, and because the sex ratio could be expected to be the same in each state. The absence of such demographic characteristics would only cause difficulty if they are systematically related to location in a way that is linked to income, and I have no reason to believe that this is likely. The 1976 Survey of Income and Education conducted by the U.S. Bureau of the Census on about 150,000 households provides data on the earnings of individuals in various states, along with other necessary information such as the immigrant's date of entry into the United States. Consider the following regression results (extracted, as are other results, from Table 1, except as noted ) for native employed males age 24-64: Effect of Residence State on Earnings of Natives Regres- State Other Variables sion # Group Earnings Education In Regression 2 Natives, t = .000 t = .000 Experience, weighted b = .00007 b = .084 residence, beta = .07 beta = .34 marital status, elasticity=.39 temperature Source: Table 1, column 2, except elasticity from log-log regres- sion. State per-person earnings (PPE) clearly has a substantial effect, statistically and economically.2 The elasticity of .39 (taken from a regression like 2 but using the log of PPE) seems very large. To put this effect in perspective, the beta coefficient for the state effect (.07) is almost a fifth of the beta for the native individu- al's own years of schooling (.34). That is, the state effect appar- ently explains almost a fifth as much of the variance in natives' earnings as does the individual effect.3,4 Table 1 Does the Effect Arise During Development or While Working? There are two main possible causes of lower productivity per worker with given amounts of education and experience -- poorer education in the past, or lesser quality of cooperating human capital in the present. (Physical capital may safely be disregarded for reasons given below). This section discriminates between these possibilities by examining the pattern of earnings data for a group for which differences in education are not a factor--immigrants from abroad, who did not grow up in the area.5 Regression 6 shows a much smaller effect for PPE in a sample of immigrants, when controlling for their time in the United States, than for natives (see regression 2), and the coefficient is not statistically significant. page 1/article9 stateinc/July 22, 1992 Effect of Residence State on Earnings of Immigrants and Natives Regres- State Other Variables sion # Group Earnings Education In Regression 6 Immigrants, b = .00002 b = .07 Experience, weighted beta = .01 beta = .38 residence, t = .38 marital status, temperature, (and for immi- grants, date of immigration). 2 Natives, b = .00007 b = .08 " weighted beta = .07 beta = .34 t = .000 Given that the current environment is the same for natives and for immigrants, this finding suggests that the difference in productivity among natives in various states arises during the educational period in the past, rather than being due to differ- ences in the human capital with which workers cooperate on the job. This is the major finding of the paper. To put the matter in different words, the data suggest that the observed lower income for natives of given education levels in low-income states, compared to natives in high-income states, is due to their lower skills as a result of their having been educated in a state where the effective education per year of formal schooling is less. Less effective education is due to lower average human capital (including lower income of teachers). This force does not apply to immigrants, and hence it accounts for the difference in pattern between immigrants and natives. The result that apparent unexplained differences in income are due, not to current market conditions in different places but rather to differences in learning during development (holding quantity of income constant), is similar to the finding by Behr- man and Birdsall (1984) that apparent differences between geo- graphic regions in Brazil, and between urban and rural areas, are largely explained by the quality of education. Though the data indicate a learning effect during the devel- opmental period, they also contain some suggestion of an on-the- job effect as well. This may be seen in the strongly-significant PPE coefficient for the unweighted regression for immigrants (a beta of .09 in regression 7, Table 1), though the weighted- regression coefficient (regression 6) is weaker. This is also consistent with the clear absence of effect among the most recent immigrants (regressions 8 and 9), who have had the least exposure to the human-capital environment surrounding them and whose less- than-perfect English may have slowed their assimilation to the people around them.6 The reader may wish to view the results for natives alone in the perspective of international comparisons. Consider a given person working in a country with 1/20 the per-person money income of the U.S., say India. If the elasticity is .20, then one would expect the person's earnings in India to be 1/4 of what they are in the U.S.7 This does not seem to be out of joint with casual observation, and with the fact that the difference in mean educa- tion is very different in the U.S. and India and therefore must account for most of the difference in average incomes -- a ratio 1 to 20, not holding education constant. The fact that the state income coefficient is positive for U.S. natives but less so for immigrants suggests that some mecha- nism operates during the developmental period to affect later productivity. But at least two mechanisms could be responsible: the quality of schooling, and the quality and quantity of nurtur- ing. This suggests an attempt to distinguish between them. Expenditures on schooling were therefore substituted for per person income, on the assumption that the former would be a better proxy than the latter for educational quality. And 1950 data were used because workers in 1976 were in school in earlier years.8 Expenditures on education do indeed show an influence. But the effect, as measured by the sizes of the t ratios and of the betas, is not as large as the effect of per person income; and the effect of expenditures disappears when both variables are included in the regression. The same is true of expenditures on education in 1976, median state education in 1950 and 1976, and state per person income in 1950. The explanation of these re- sults is the high collinearity between state per person incomes in 1976 and the other variables, as may be seen in the correla- tion matrix in the appendix. The attempt to discriminate between schooling and nurturing therefore must be considered unsuccess- ful.9 (Results are available upon request.) Distinguishing Between Learning and Complementarity The next step is to distinguish between a learning effect and complementarity in production. If there is complementarity, individual high-skill persons should have lower earnings in states where there are relatively many persons in that high-skill group, and the opposite for low-skill groups. A learning effect suggests the same outcome as does the complementarity model for the low-skill groups, but a different outcome for the high-skill groups (i.e., learning implies higher earnings for high-skill persons in states where there is high average income and human capital, because high-skill immigrants would learn more from their colleagues there than they would if they lived in states where colleagues have less skill on average). Hence an examina- tion of the effects of state income on high-education and low- education groups separately. Regressions 4 and 5 show the results for native males with education of 12 years or less, and 13 years or more, respectively, and the basic regression specification. Complementarity versus Learning Regres- State Other Variables sion # Group Earnings Education In Regression 4 Natives, b = .0001 b = .09 Experience, < 12 yrs. t = .01 residence, schooling, marital status, weighted temperature, (and for immi- grants, date of immigration). 5 Natives, b = .0001 b = .09 " > 13 yrs t = .000 schooling, weighted 10 Immigrants, b = -.00001 b = .05 " < 12 yrs. t = .72 schooling, weighted 11 Immigrants, b = .0001 b = .10 " > 13 yrs. t = .04 schooling, weighted The coefficient for state income for the lower-education natives is positive as expected, due either to complementarity or to learning. The coefficient for the higher-education natives is also positive, which suggests a learning effect rather than complementarity. Furthermore, because there must be some complementarity effect, the PPE coefficient for the high-skill group should be biased downward. Therefore, since that coefficient is positive, it would seem to provide a lower bound to the effect, and vice versa for the low- skill group. Results for immigrants split into high and low education groups (regressions 10 and 11 above) with respect to state income effect (PPE) do not accord with expectations if a complementarity effect were to be operating. The state income coefficient for the higher-education group is considerably stronger than that for the lower-education group, both among natives and among immigrants. This is consistent with education increasing a person's capacity to learn from his or her environment (as it certainly ought to). The difference in the education coefficient between the education groups is interesting, but will not be pursued here. DISCUSSION Differences in Schooling Quality Versus Informal Learning The source of the learning during development may be in or out of school. Behrman and Birdsall (1984) emphasize the effect of in- school education quality in Brazil. Consistent with that idea is the stronger coefficient for PPE with more schooling compared to less schooling (regression 5 versus regression 4). But going in the other direction is the fact that the schooling coefficient is much the same in regressions that do and do not contain an argument for state income (results not shown here). Supporting evidence for the main conclusion of this paper is that the size of gross migrations back and forth between various pairs of states are not very different from each other, but both are large relative to the difference between them (i.e., net migration). If there were real wage differentials, one would expect migration to reduce the differentials. But the mean difference between the outcome distributions in pairs of states must be small relative to the variances of the distributions, because the net migration is small relative to the gross migration, though it is in the expected direction (Sjaastad, 1960, 1962). Additional evidence that supports the conclusion is that the total labor costs that enter into retailing of goods must be the same, because the prices of standardized goods are not systemati- cally different in states with different incomes (Love, 1982). That is, efficiency labor must be the same across states. Other Possible Explanations of the Observed Phenomenon The next issue is whether there are plausible explanations for the observed state-income coefficient other than differences in marginal output (holding constant the years of education). Differences in the Cost of Living. Certainly there are always temporary disequilibria in earnings. But there seems no obvious reason why there should be long-standing disequilibria associated with long-standing differences in living costs from place to place, and therefore the neo-classical model would not seem to be inappropriate. That is, even if workers are attracted to an area because of living costs as well as because of wages, in the long run the labor market should be no tighter in one place than in another. Employers might be able to take advantage of temporary differences in labor-market tightness in the short run. But unless there is some geographic difference in bargaining power or other structural condition that allows employers in some places to permanently hold wages below marginal output, the cost of living should not matter. Data that jibe with this theoretical analysis with respect to the cost of living will be adduced in the next section. Differences in Prices Among States for Identical Goods and Services. Surprising to many, data suggest that the cost of living is not related to income. Consider those classes of goods that, in comparison-shopping by the Bureau of Labor Statistics for the Consumer Price Index, can reasonably be considered identical when sold in various markets--for example, pipe tobacco, bath towels, floor wax, clothes dryers. Love (1982) and Simon and Love (1990) studied the elasticities of prices of various types of goods with respect to the mean wages (as a measure of income) in various cities. Excluding those services for which it is almost impossible to hold constant the quality of those products in a cross-city comparison, the average elasticity of the other categories is not even positive. Excluding women's apparel and men's clothing on the grounds of difficulty of holding style and quality constant even pushes the comparison strongly negative, suggesting that there is not a positive relationship between mean income of the city (and state) and the amount paid for quality-adjusted labor in retailing, at least. So even if one does not accept the theoretical argument given in the section above, these data suggest that the cost of living is not higher in higher-income places. Therefore both the empirical evidence and the theoretical argument concur in suggesting that the cost of living is not an important explanatory factor. Differences in Capital Used by Workers. Lower worker skill may lead to lower quality physical capital being used in a given place. This might at first seem to constitute two-way causation. But an investment decision to use relatively-low-technology equipment could have only two relevant causes: a) relatively-low worker skill because of relatively low formal education, which does not affect the analysis here; or b) low worker skill because of low-quality education or a low amount of human capital in the surrounding work environment, both of which constitute the phe- nomenon which the analysis here focuses upon. That is, the type of capital is endogenous, an intermediate variable rather than an independent variable which is a separate competing cause of lower wages for equal worker skill, and hence lower capital per worker in low-pay states does not call into question the conclusion arrived at here. Selective Migration. General migration toward high-income states is not inconsistent with the conclusion arrived at here, but in any case is not observed according to the low ratio of net to gross migration. Selective migration of higher-skill workers within homogeneous education groups also is not inconsistent with the conclusion arrived at here that pay is in accordance with skill and productivity.10 Persisting Disequilibrium. Perhaps the argument offered in this paper will seem more plausible if it is turned around. Is it not likely, if quality adjusted wages really are (and have been for a long time) lower in low-income states, that producers would exploit this advantage by moving their operations to the areas of lower labor cost? The only reasonable explanation for business not moving to exploit such a potential advantage is fixity of capital, together with other frictions that resist immediate response. But interstate income differences have existed from the most distant relevant economic past, with plenty of time for all appropriate adjustments to take place if these differences really indicate adjusted wage differences. Therefore, the fact that differences in per person income have not disappeared, though they have narrowed somewhat in proportional terms, suggests that differences in adjusted wages are not associated with differences in per person income. Length of Time in Job. Mincer (in conversation) suggested that the length of time working on the current job, if not allowed for explicitly, might account for some of the results observed here. Number of years residing in the current state of residence, which should be at least a partial proxy for that variable, is included in the regressions shown in regressions 12 and 13. Some positive effect is seen for natives. But the coefficient for immigrants has the wrong sign, which throws doubt upon the meaningfulness of the result for natives. More important, however, is that the other results discussed in the paper are not affected by the inclusion of this variable.11 SUMMARY Though much of the mean income differences among states is due to different compositions of persons with various amounts of education, the earnings also differ among people with the same amount of education and experience; persons in higher-income states earn more. The causes could operate during the process of growing up, or in the current environment. The results of comparing natives' and immigrants' earnings suggest that this effect is mainly due to influences during development rather than during adulthood, because immigrants show a smaller state-income effect (or none). Differences in the quality of education, and in parental nurturing, are possible explanations. Children may receive lower- quality education in poorer states. Children with poorer parents may receive less income-increasing education at home. Or both may be operative. Other possible explanations for the observed positive re- gression coefficient for state income were examined and found not persuasive; these include the costs of living, prices of output, selective migration, and capital endowment. The main result also is empirically distinguished from complementarity of different skill levels in production. The result for immigrants also implies that the average quality of human capital of the state within which a person works does not have an observable effect upon the person's earnings, at least within the first ten years in the state, suggesting that informal learning externalities are not a major influence. This paper may be viewed as following in the footsteps of the human-capital studies of Schultz (1960), Mincer (1963), and Becker (1967), in attempting to throw light on the determinants of a person's earning capacity. Stateinc 89-166 7-22-2 page 2/article9 stateinc/July 22, 1992 REFERENCES Gary Becker, Human Capital (New York: National Bureau of Economic Research--Columbia, 1964). Jere R. Behrman and Nancy Birdsall, "The Quality of Schooling: Quantity Alone Is Misleading," American Economic Review, 73, Dec. 1983, 928-947. Birdsall, Nancy and Jere R. Behrman, "Does Geographical Aggregation Cause Overestimates of the Returns to Schooling?" Oxford Bulletin of Economics and Statistics, 46, February, 1984. Barry R. Chiswick, "The Effects of Americanization on the Earnings of Foreign-Born Men," Journal of Political Economy, Vol. 86, No. 5 (October 1978), pp. 897-921. Douglas Love, "City Population Size and Item Prices", in Julian L. Simon and Peter H. Lindert (eds), Research in Population Economics, vol. 4 (Greenwich, CT: JAI Press, (1982)), pp. 83-92. Jacob Mincer, "Market Prices, Opportunity Costs, and Income Effects," in C. Christ (ed.), Measurement in Economics (Palo Alto: Stanford, 1963). Jacob Mincer, Schooling, Experience, and Earnings (New York: National Bureau of Economic Research, 1974). Theodore W. Schultz, "The Formation of Human Capital by Education," Journal of Political Economy. Vol. 68 (December 1960). Julian L. Simon and Douglas O. Love," City Size, Prices, and Efficiency for Individual Goods and Services," The Annals of Regional Science, 1990, Vol. 24, pp. 163-175. Larry A. Sjaastad, "The Costs and Returns of Human Migration," The Journal of Political Economy. October 1962, pp. 80-93. Larry A. Sjaastad, "The Relationship Between Migration and Income in the United States," Papers and Proceedings of the Regional Science Association, Vol. 6, 1960, pp. 37-64. Burton A. Weisbrod, "Education and Investment in Human Capital," The Journal or Political Economy. LXX, Oct. 1962, 106-123. Stateinc 89-166 7-22-2 page 3/article9 stateinc/July 22, 1992 Appendix 1 VARIABLES, STATISTICS, AND CORRELATIONS (for Natives including Puerto Ricans; data for Immigrants avail- able upon request) VARIABLE MEAN STANDARD DEV CASES Log male earnings (LME) 9.2 .8 5428 Experience (Exp) 24.9 12.5 5428 Exp2 783.0 669.9 5428 State temperature (TEMP) 55.9 6.6 5428 SMSA .9 .2 5428 AGE 42.2 11.3 5428 Schooling (SCHL) 12.2 3.2 5428 Not married (NOTMSP) .1 .3 5428 State per-person earnings 1976 (PPE) 5865.0 714.3 5428 State per-person earnings 1950 (PPE) 1457.0 305.3 5428 State education expendi- tures, 1950 (STEDX50) 178.0 51.7 5428 STEDX76 1364.9 247.3 5428 State mean education 1976 (STAED76) 12.4 .1 5428 STAED50 9.5 1.0 5428 page 4/article9 stateinc/July 22, 1992 ACKNOWLEDGEMENTS I appreciate valuable comments by Jere Behrman and Jacob Mincer, and excellent typing by Becky Smith and Helen Demarest. page 5/article9 stateinc/July 22, 1992 FOOTNOTES 1Sjaastad may serve as a classic example: Economists and others are generally dissatisfied with the past performance of migration in narrowing geographic income differentials . . . How can these large income differences persist in the face of such massive movements? (1962, p. 80) and The labor market, with respect to migration, has often been declared ineffective, and the evidence produced by this study to date indicates that the market is probably not up to the task that has been imposed upon it. That is, it seems a spatial misallocation of labor is not eliminated within a tolerable length of time. (1960, p. 53). 2A regression including state temperature but not state income shows much the same coefficients for all other variables as does regression 1, and much the same coefficient for temperature as does regression 2; therefore the results are not shown. 3A relatively small number of specifications are shown here. This is because much experience has been acquired with variations of the model in regression 1 in the course of work by Mincer (1974), Chiswick (1978), and others. 4These arise from regressions which weight each observation to allow for its probability of inclusion into the Bureau of the Census sample. (The purpose of the weighting was to ensure that in each state a sufficiently large number of poor persons were included.) There is some controversy as to whether it is more appropriate to use weighted or unweighted observations in the regression, and to my knowledge, the matter has not been settled by formal analysis. The reasons for putting more emphasis on the weighted regressions (while also presenting results for the unweighted regressions) are as follows: 1) The state effects shown by the weighted regressions are smaller than those of the unweighted regressions (an elasticity of .39 and a beta of .065, compared to .65 and .12 respectively for the unweighted regressions; see column 3.) This makes the presentation of the weighted estimate less dramatic, and therefore a more modest scientific claim. However, for completeness it seems important to present the larger unweighted estimates, too. 2) More important, on the basis of this reasoning the weighted regression seems more appropriate to the writer: If the data really are not completely linear--and no set of data ever will be completely linear- -then the relative number of observations at either end of the distribution will affect the coefficient. If the sampling scheme affects the distribution in that fashion, it therefore affects the coefficient. And the very purpose of a stratified sample is just that, to affect the distribution of observations with respect to the variable of stratification, which in this case is the key variable -- income. Therefore, it seems reasonable to attempt to reproduce the population distribution by applying the weighting scheme in the version of the sample that is used in our statistical manipulations. Replicating the work with the 1980 and 1990 U.S. Census samples would be useful in answering remaining questions about the weighting scheme. And replicating with data for other countries would test the generality of the findings. 5This matter could be pursued further by separating those who migrated domestically into the state from those who were born there. But this will require a better body of data than is now available. The fact that domestic migrants are lumped with natives operates to bias downwards the observed state income effect, of course. 6Domestic migration might conceivably account for some part of a positive coefficient for all immigrants. And migration must be less for more recent immigrants, which would be consistent with the absence of a PPE effect among them. But in general, selective migration would seem an unlikely force to be operating in this context. And a years-in-state variable does not have a significant coefficient (column 12), and a comparable regression for natives even has the wrong sign (column 13). 7This is a rough calculation for illustrative purposes only. It assumes that human capital is all-important and ignores physical capital. But because the amount of physical capital is a function of the amount of human capital in the intermediate and long run - the experiences of Germany and Japan after World War II - are dramatic evidence of this - the absence of physical capital from the calculation does not make it wildly wrong. 8Some sort of weighted average would be more appropriate, but there is high correlation in the state expenditure pattern from year to year. 9The variable for state expenditures on education in 1950 considered by itself has a significant effect on earnings, whereas state expenditures on education in 1976 does not, which makes sense and suggests that the effect is not just being exerted through the collinearity with per-person income. 10If a lower cost of living is associated with the lower wages, it would work against this migration taking place. Hence the presence of a low cost of living would tend to work against seeing what is actually observed here, rather than causing it. 11The code "0" was used both for no answer and for persons who were born in the state. The number of persons coded "0" was sufficiently small for immigrants however (less than half of one percent) so that it was deemed safe to substitute age for number of years in the state for all natives coded "0". page 6/article9 stateinc/July 22, 1992