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Working Paper 8709 AMENITIES AND THE RETURNS TO HUMAN CAPITAL by P a t r i c i a E. Beeson P a t r i c i a E. Beeson i s a v i s i t i n g economist a t the Federal Reserve Bank o f Cleveland and an a s s i s t a n t professor o f economics a t the U n i v e r s i t y o f Pittsburgh. Working Papers o f the Federal Reserve Bank o f Cleveland are p r e l i m i n a r y m a t e r i a l s c i r c u l a t e d t o s t i m u l a t e discussion and c r i t i c a l comment. The views s t a t e d h e r e i n a r e those o f the author and n o t n e c e s s a r i l y those o f the Federal Reserve Bank o f Cleveland o r o f t h e Board o f Governors o f the Federal Reserve System. November 1 987 I. Introduction The determinants of interregional wage differentials is a topic that has drawn considerable attention among economists. Two theories have come to dominate as explanations of these differentials. The first assumes a national labor market and, therefore, views interregional differences in nominal wages as compensation for differences in rents and other prices or nonpecuniary attributes. According to the second theory, labor market conditions may vary regionally, and interarea wage differentials result from structural differences across these local labor markets. Attempts to discriminate between these two hypotheses have involved estimating reduced form wage equations. The belief that factor mobility will result in the equalization of characteristic prices across regions has led researchers to interpret shifts of the wage equation in response to amenity and price differences as compensation for regional differences in amenities. Differences in the return to human capital (that is, changes in the slope of the wage equation) such as those found by Hanushek (1973), Sahling and Smith (19831, Krumm (1984>,Jackson (1985), and Farber and Newman (1985), on the other hand, have been interpreted as reflecting structural differences in regional labor markets--an interpretation some find difficult to accept given the persistence of these differences despite the geographic mobility of the U.S. labor force. This paper shows, theoretically, that regional differences in the returns to human capital do not necessarily imply structural differences in regional labor markets. Regional differences in the returns to human capital, like regional differences in the level of wages, could be reflecting compensation for regional differences in amenities. These compensating differences in the return to human capital depend on the income elasticity of the marginal evaluation of amenities relative to the income elasticity of demand f o r l a n d and o t h e r goods, and can e x i s t even when workers a r e m o b i l e and have i d e n t i c a l p r e f e r e n c e f u n c t i o n s . The e x t e n t t o which r e g i o n a l d i f f e r e n c e s i n t h e r e t u r n s t o human c a p i t a l r e f l e c t compensation f o r r e g i o n a l d i f f e r e n c e s i n human c a p i t a l i s then examined e m p i r i c a l l y . Regional d i f f e r e n c e s i n t h e r e t u r n t o e d u c a t i o n a r e found t o be e x p l a i n e d almost e n t i r e l y by r e g i o n a l d i f f e r e n c e s i n a m e n i t i e s . Furthermore, a s u b s t a n t i a l p o r t i o n o f r e g i o n a l d i f f e r e n c e s i n t h e r e t u r n s t o o c c u p a t i o n a r e a l s o f o u n d t o be r e l a t e d t o a m e n i t i e s . Together t h i s evidence s u p p o r t s t h e view o f a n a t i o n a l l a b o r market w i t h r e g i o n a l wage d i f f e r e n t i a l s r e p r e s e n t i n g compensation f o r r e g i o n a l d i f f e r e n c e s i n a m e n i t i e s . I n t h e f o l l o w i n g s e c t i o n , Roback' s (1983) general equi 1 ib r i u m model o f household and f i r m l o c a t i o n i s extended t o i n c o r p o r a t e d i f f e r e n c e s i n human capital. I n t h e c o n t e x t o f t h i s model, t h e r e l a t i o n s h i p between s i t e c h a r a c t e r i s t i c s and r e n t s , average wages, and t h e r e t u r n s t o human c a p i t a l i s examined. 11. The e m p i r i c a l r e s u l t s a r e presented and discussed i n S e c t i o n 111. T h e o r e t i c a l Model I n t h i s s e c t i o n , we develop a model t h a t shows t h e mechanism t h r o u g h which i n t e r a r e a d i f f e r e n c e s i n s i t e c h a r a c t e r i s t i c s a r e c a p i t a l i z e d i n t o wages. I n t h i s model, s i t e c h a r a c t e r i s t i c s a r e a l l o w e d t o a f f e c t b o t h t h e u t i l i t y o f households and t h e p r o d u c t i v i t y o f f i r m s . The i n t e r a c t i o n s of t h e s e two groups then determines t h e average wage and r e n t s i n an area. Rents a r e shown t o r e f l e c t t h e average v a l u e p e r u n i t o f l a n d of s i t e c h a r a c t e r i s t i c s t o b o t h f i r m s and households. The t o t a l payment made by an i n d i v i d u a l o r f i r m i n t h e f o r m o f l a n d t h e n i s t h e i r consumption of l a n d t i m e s t h e average value o f t h e amenity. Differences in the marginal evaluation of the site characteristics per unit of land for the average worker relative to firms are shown to be capitalized into the average wage change and therefore are reflected in a shift of the wage equation as related to amenities. It is then shown that, since differences in human capital imply differences in real income, the size of the wage premium will vary for workers with different amounts of human capital if the income elasticity of the marginal valuation of amenities differs from the income elasticity of demand for land and for all other goods. This, in turn, will lead to regional differences in the return to human capital reflected in the slope of the wage equation. THE MODEL Cities are assumed to differ in endowed site characteristics, s. ' Workers are assumed to have identical preference functions and to differ only in their endowments of human capital, which determines their real income. While skills vary across individuals, tastes do not. For simplicity, differences in leisure that result from differences in intercity commuting are ignored and it is assumed that individuals live in the city in which they work.' Workers produce and consume a composite commodity, x, sold in national markets and used as the numeraire. Workers and physical capital are assumed to be completely mobile across locations, at least at the margin. In each city with amenity level, s, workers maximize their utility, which is a function of their consumption of a composite commodity, x , land, h, and amenities, s, subject to an income constraint. In equi 1 ibrium, the utility of all workers with the same endowment of human capital must be the same at all locations. If this were not the case, workers would relocate and arbitrage away differences in utility. This yields n equilibrium conditions, one f o r each c l a s s o f worker. I n the form o f i n d i r e c t u t i l i t y functions, equilibrium requires, where, i indexes t h e workers by human c a p i t a l ; Vi i s t h e l e v e l o f u t i l i t y a t t a i n a b l e f o r workers i n c l a s s i; w i i s t h e nominal wage o f workers i n c l a s s i; r i s t h e r e n t a l r a t e o f l a n d , which i s t h e same f o r a l l workers i n a c i t y r e g a r d l e s s o f human c a p i t a l ; and s i s t h e amenity l e v e l i n t h e c i t y . D i f f e r e n t i a t i n g the i n d i r e c t u t i l i t y function f o r the representative worker i n each c l a s s w i t h r e s p e c t t o a m e n i t i e s and s e t t i n g t h e r e s u l t equal t o zero y i e l d s , Rearranging and u s i n g Roy's i d e n t i t y y i e l d s t h e f o l l o w i n g e q u i l i b r i u m r e l a t i o n s h i p s f o r workers i n each c l a s s , or dlogwi ds (4) = k i dlogr ds - fi Wi where h i i s consumption o f l a n d ; p e i s t h e monetized v a l u e of m a r g i n a l u t i 1i t y of t h e amenity; and k i = r h / w i i s t h e budget share o f land. According t o e q u a t i o n 3, wage d i f f e r e n t i a l s a c r o s s c i t i e s f o r each c l a s s o f worker r e p r e s e n t t h e d i f f e r e n c e between t h e i r m a r g i n a l e v a l u a t i o n o f t h e a m e n i t i e s , p e , and t h e i r payment f o r these a m e n i t i e s i n t h e f o r m o f l a n d rents, h i (drlds) . Firms i n each c i t y a r e assumed t o employ workers w i t h d i f f e r e n t amounts of human c a p i t a l ( N i ) , l a n d ( L P ) and p h y s i c a l c a p i t a l t o p r o d u c t t h e composite commodity, X, a c c o r d i n g t o a c o n s t a n t r e t u r n s t o s c a l e p r o d u c t i o n function. The p r o d u c t i v i t y o f f i r m s may a l s o be a f f e c t e d b y t h e s i t e c h a r a c t e r i s t i c s of a c i t y . Firms minimize u n i t c o s t t h a t , i n e q u i l i b r i u m , must be equal across l o c a t i o n s and equal t o the p r i c e o f x , assumed t o be 1. D i f f e r e n t i a t i n g the u n i t c o s t f u n c t i o n w i t h respect t o s i t e c h a r a c t e r i s t i c s gives the f o l l o w i n g e q u i l i b r i u m c o n d i t i o n f o r f i r m s : S u b s t i t u t i n g C,, = Ni/X and C , = L P /X, EQUILIBRIUM RENTS AND WAGES Given a l e v e l o f u t i l i t y a t t a i n a b l e f o r each category o f worker ( V i > , the n e q u i l i b r i u m c o n d i t i o n s f o r workers, equation ( 3 > , together w i t h t h e e q u i l i b r i u m c o n d i t i o n f o r f i r m s , equation (61, determine wages and r e n t s i n each c i t y . S o l v i n g these equations simultaneously f o r changes i n r e n t s across c i t i e s yields where p i s the average marginal e v a l u a t i o n o f t h e s i t e c h a r a c t e r i s t i c s t o workers; h i s the average l a n d per household; and L C i s the t o t a l amount o f land used i n housing. I n t e r u r b a n differences i n the r e n t per u n i t o f l a n d are then the weighted average o f the value o f the amenities r e l a t i v e t o l a n d used, f o r f i r m s (-CsX/LP>, and the value f o r households (N$/Lc>, where the weights a r e the p o r t i o n o f land i n each a c t i v i t y . Note t h a t the f u l l value o f r e g i o n a l d i f f e r e n c e s i n s i t e c h a r a c t e r i s t i c s are c a p i t a l i z e d i n t o aggregate l a n d values, Since t h e r e n t a l r a t e o f l a n d r e p r e s e n t s an average v a l u e o f t h e s i t e c h a r a c t e r i s t i c s , r e n t a l payments by i n d i v i d u a l workers and f i r m s w i l l be equal t o t h e v a l u e o f t h e s i t e c h a r a c t e r i s t i c s t o t h e i n d i v i d u a l workers and f i r m s o n l y if t h e v a l u e p e r u n i t of l a n d used i s equal i n a l l a c t i v i t i e s . If this i s n o t t h e case, any d i f f e r e n c e w i l l be c a p i t a l i z e d i n t o wages i n t h e l a b o r market. The e f f e c t o f s i t e c h a r a c t e r i s t i c s on wages can be seen by s u b s t i t u t i n g e q u a t i o n ( 7 ) i n t o t h e e q u i l i b r i u m c o n d i t i o n f o r workers, e q u a t i o n ( 4 ) . For each c l a s s o f workers, and I n e q u i l i b r i u m , wages f o r each c l a s s o f workers a d j u s t t o r e f l e c t t h e d i f f e r e n c e between t h e i r marginal e v a l u a t i o n o f t h e a m e n i t i e s p e r u n i t o f l a n d t h e y own, and t h e average v a l u e f o r t h e community as a whole. THE AVERAGE CHANGE I N WAGES The average change i n wages across c i t i e s r e f l e c t s t h e average d i f f e r e n c e between households and f i r m s i n t h e i r v a l u a t i o n -o f s i t e c h a r a c t e r i s t i c s r e l a t i v e t o land. (13) dlogw = k (-CsX + NE) ds rL From e q u a t i o n (12) one can see t h a t t h e average wage d i f f e r e n t i a l depends on t h e a l l o c a t i o n o f l a n d i n t h e c i t y , ( L P ) , t h e amenity v a l u e of the s i t e c h a r a c t e r i s t i c per u n i t o f l a n d i n housing, (NF/Lc), r e l a t i v e t o i t s p r o d u c t i o n value per u n i t of land i n production, (-CsX/LP), and t h e d i s t r i b u t i o n o f workers across s k i 11 classes, which determines and p. The r e l a t i o n s h i p between the average wage change and r e l a t i v e amenity and p r o d u c t i v i t y values has a simple i n t e r p r e t a t i o n . If a site characteristic i s valuable t o both f i r m s and households ( t h a t i s , Cs<O and p>O>, r e n t s w i l l increase by t h e weighted average o f t h e two. I f the value o f households p e r u n i t o f l a n d exceeds t h a t o f f i r m s , r e n t payments by f i r m s w i l l exceed the p r o d u c t i v i t y value o f the s i t e c h a r a c t e r i s t i c t o f i r m s , and r e n t payments by households w i l l be l e s s than the amenity value o f the s i t e c h a r a c t e r i s t i c t o households. Competition i n the l a b o r market w i l l then lead t o lower average wages, which compensate the f i r m s f o r t h e r e n t payment i n excess o f p r o d u c t i v i t y value and make the t o t a l payment ( r e n t s and foregone wages) by households equal t o t h e value o f the amenity. I n general, wages w i 11 decrease whenever t h e amenity value p e r u n i t o f land t o workers o f an urban a t t r i b u t e exceeds i t s p r o d u c t i v i t y value p e r u n i t o f land t o firms. increase. I f the p r o d u c t i v i t y value i s r e l a t i v e l y l a r g e r , wages w i l l Whether r e n t s increase o r decrease, on t h e o t h e r hand, depends on the n e t value o f the s i t e c h a r a c t e r i s t i c t o both f i r m s and households, r a t h e r than the r e l a t i v e values. I f the n e t value i s p o s i t i v e , r e n t s w i l l increase; i f negative, they w i l l d e c l i n e . CHANGES I N THE SLOPE OF THE WAGE GRADIENT Any systematic d i f f e r e n c e between the value per u n i t o f l a n d o f amenities across workers w i t h d i f f e r i n g endowments o f human c a p i t a l w i l l be c a p i t a l i z e d i n t o the r e l a t i v e wages. Since increases i n human c a p i t a l i n c r e a s e r e a l income, t h e v a l u e p e r u n i t o f l a n d o f a m e n i t i e s may v a r y s y s t e m a t i c a l l y across s k i l l groups i f t h e income e l a s t i c i t y o f t h e m a r g i n a l e v a l u a t i o n o f t h e amenity i s n o t equal t o t h a t f o r l a n d and o t h e r goods. D i f f e r e n t i a t i o n e q u a t i o n ( 4 ) w i t h r e s p e c t t o r e a l income, y , which i n c l u d e s t h e v a l u e of a m e n i t i e s as w e l l as money income, f o r l o c a t i o n f i x e d yields, where q,, amenity, i s t h e income e l a s t i c i t y o f t h e marginal e v a l u a t i o n o f t h e qh,y i s t h e income e l a s t i c i t y o f demand f o r housing and, ,q,, i s t h e income e l a s t i c i t y o f demand f o r money income, which r e f l e c t s t h e demand f o r market goods. I f e q u a t i o n (14) i s n e g a t i v e , t h e s l o p e o f t h e amenity-wage g r a d i e n t decreases w i t h increases i n human c a p i t a l . I n r e f e r e n c e t o a s t a n d a r d wage e q u a t i o n , a n e g a t i v e v a l u e f o r e q u a t i o n (14) i m p l i e s t h a t t h e r e t u r n s t o human c a p i t a l w i l l be lower i n high- amenity areas. S i m i l a r l y , i f e q u a t i o n (14) i s p o s i t i v e , t h e r e t u r n t o human c a p i t a l w i l l be i n c r e a s i n g i n a m e n i t i e s . The s i g n o f e q u a t i o n (14) depends i n p a r t on t h e income e l a s t i c i t y of t h e m a r g i n a l v a l u a t i o n o f a m e n i t i e s r e l a t i v e t o t h e income e l a s t i c i t y o f demand f o r land. T h i s r e l a t i o n s h i p can be c l e a r l y seen i f we assume t h e income e l a s t i c i t y o f demand for housing i s equal t o t h a t f o r a l l o t h e r goods. I n t h i s case e q u a t i o n (14) can be w r i t t e n as, T h i s makes sense s i n c e those who most v a l u e a m e n i t i e s r e l a t i v e t o h o u s i n g w i l l pay p r o p o r t i o n a t e l y more f o r t h e amenity i n t h e f o r m o f wages. S i n c e t h e y consume r e l a t i v e l y l e s s land, t h e y pay r e l a t i v e l y l e s s f o r t h e amenity i n the form o f land rents. r e l a t i v e d e c l i n e i n wages. The d i f f e r e n c e i s made up i n t h e form of a I f the income e l a s t i c i t y o f demand f o r housing i s not equal t o t h a t f o r a l l o t h e r goods, the s i g n o f equation (14) depends o f f a c t o r s o t h e r than these two e l a s t i c i t i e s . nw,,; I n p a r t i c u l a r , equation (14) w i l l be negative if q,,,,, ) Q ~ , ~ p ; ositive if qpe,y < Q W , ~ <nh,,; equal t o zero i f a l l e l a s t i c i t i e s are equal; and the s i g n w i l l be indeterminate, i f b o t h q,, and qh,y are g r e a t e r o r l e s s than .q ,, I n the l a t t e r case, the s i g n w i l l depend on the share o f r e a l income spent on land and the share spent on amenities, as w e l l as the r e l a t i v e e l a s t i c i t i e s . To summarize, the average value o f s i t e c h a r a c t e r i s t i c s i s c a p i t a l i z e d i n t o r e n t s per u n i t o f land. Each i n d i v i d u a l then 'pays' i n r e n t an amount equal t o t h e i r consumption o f land, times the average marginal v a l u a t i o n o f the s i t e c h a r a c t e r i s t i c . D i f f e r e n c e between the amount an i n d i v i a u a l pays i n t h e form o f r e n t s and t h e i r v a l u a t i o n o f the amenity w i l l then r e s u l t whenever t h e i r consumption o f land r e l a t i v e t o t h e i r marginal v a l u a t i o n o f the amenity d i f f e r s from t h e average. Since increases i n human c a p i t a l increase the r e a l income o f i n d i v i d u a l s , the consumption o f l a n d r e l a t i v e t o the marginal v a l u a t i o n o f t h e amenity w i l l vary s y s t e m a t i c a l l y w i t h human c a p i t a l i f the income e l a s t i c i t y of demand f o r land i s n o t equal t o the income e l a s t i c i t y o f the marginal v a l u a t i o n o f t h e amenity. I f workers i n a l l s k i l l classes a r e mobile, a t l e a s t a t t h e margin, competition among workers w i t h i n each s k i l l class f o r l o c a t i o n s where the value o f the amenity i s greater than the payment i n l a n d r e n t s w i l l r e s u l t i n the c a p i t a l i z a t i o n o f the d i f f e r e n c e i n t o wages. I f , f o r example, the income e l a s t i c i t y o f the marginal v a l u a t i o n o f t h e amenity i s g r e a t e r than t h a t f o r land, the marginal v a l u a t i o n of the amenity w i l l increase more r a p i d l y than land consumption (and;therefore, payments) as income/human c a p i t a l increases. land r e n t Competition among h i g h - s k i l l workers f o r l o c a t i o n s i n these high- amenity l o c a t i o n s w i l l d r i v e down t h e i r wages r e l a t i v e t o l o w - s k i l l e d workers, decreasing t h e r e t u r n s t o human c a p i t a l i n the form o f wages, and decreasing the slope o f t h e wage g r a d i e n t . S i m i l a r l y , i f the income e l a s t i c i t y o f the marginal v a l u a t i o n o f the amenity i s l e s s than t h a t of land, t h e r e t u r n s t o human c a p i t a l r e f l e c t e d i n t h e slope o f the wage g r a d i e n t w i l l increase w i t h amenities. 111. EMPIRICAL RESULTS I n t h i s section, t h e e x t e n t t o which r e g i o n a l d i f f e r e n c e s i n the r e t u r n t o c a p i t a l r e f l e c t compensation f o r i n t e r r e g i o n a l d i f f e r e n c e s i n amenities i s examined e m p i r i c a l l y . Before reviewing the e m p i r i c a l model and r e s u l t s , a few p o i n t s should be noted. F i r s t , the t h e o r y developed i n the previous s e c t i o n assumes t h a t t a s t e s do n o t vary w i t h i n s k i l l groups. To the extent t h a t they do, the r e s u l t s presented represent an average across workers i n each s k i l l group. 4 Furthermore, t a s t e s f o r c e r t a i n amenities may v a r y w i t h human c a p i t a l independent o f the e f f e c t s o f increases i n r e a l income described above. H i g h l y educated i n d i v i d u a l s may value education o r c u l t u r a l f a c i l i t i e s more h i g h l y than those w i t h l e s s education and, therefore, may be w i l l i n g t o pay more than i n d i v i d u a l s w i t h l e s s education f o r l o c a t i o n s where schools a r e b e t t e r o r where there a r e more c u l t u r a l f a c i l i t i e s , even i f t h e i r r e a l income were the same. I n the e s t i m a t i o n , no attempt i s made t o separate these two e f f e c t s . ' Note, however, t h a t t h i s w i l l n o t a f f e c t any conclusions regarding the e x t e n t t o which r e g i o n a l d i f f e r e n c e s i n the r e t u r n s t o c a p i t a l r e f l e c t compensation f o r d i f f e r e n c e s i n amenities. I t would simply change t h e i n t e r p r e t a t i o n o f why compensation v a r i e s across s k i l l groups. The f i n a l note concerns the l i s t o f amenities and t h e types o f human capital considered. No attempt is made to include a complete list of amenities, though some care was taken to choose characteristics that reflect different aspects of cities. Cultural and recreational facilities and the quality of schools are included along with more standard attributes, such as climate and density. As with the amenity variables, the human capital variables considered--education and occupation--are not intended to fully describe all worker attributes that reflect human capital. DATA The principal source for wage data is the Census Bureau's Current Population Survey Earnings file for 1980. The sample used is limited to individuals reporting earnings of more than $1 per hour and residing in one of the 44 Standard Metropoliatn Statistical Areas (SMSAs) identified in the survey. The sample was further limited to full time, civilian, nonagricultural workers employed for wage or salary and not self-employed. The mean values of the personal characteristics of workers included in the wage equation, along with the coefficients from a regression of these characteristics on the log of hourly earnings, are presented in Appendix A . The 1 ist includes most individual attributes thought to influence wages. These coefficient estimates remain fairly constant when region and amenity variables are included in the wage equation. The sources and definitions of the amenity characteristics are presented in Appendix B. AMENITIES AND THE RETURNS TO EDUCATION Table 1 addresses the question of the influence of urban attributes on the returns to education. The first column of table 1 , presents evidence of differential returns to education across regions, as well as regional differences in the average wage. Standard t-tests indicate significant d i f f e r e n c e s i n the r e t u r n s t o education across regions, r e f l e c t e d i n t h e region- education i n t e r a c t i o n terms, i n a d d i t i o n t o r e g i o n a l d i f f e r e n c e s i n t h e average wage, r e f l e c t e d i n the r e g i o n a l i n t e r c e p t s . Furthermore, an F - t e s t o f the j o i n t s i g n i f i c a n c e o f the t h r e e slope c o e f f i c i e n t s gives an F- value o f 34.8 where the c r i t i c a l F a t 1 percent s i g n i f i c a n c e i s 3.78. We expect t h a t the i n c l u s i o n o f amenities w i l l reduce t h e importance o f r e g i o n i n e x p l a i n i n g the r e t u r n s t o education as w e l l as reducing i t s importance i n e x p l a i n i n g the i n t e r c e p t of the wage equation. The second column o f t a b l e 1, presents the regression r e s u l t s when amenities are included i n the i n t e r c e p t and i n t e r a c t e d w i t h education. A comparsion o f columns 1 and 2 o f t a b l e 1 support the hypothesis t h a t r e g i o n a l d i f f e r e n c e s i n the r e t u r n t o education represent, a t l e a s t i n p a r t , compensation f o r r e g i o n a l d i f f e r e n c e s i n amenities. The c o e f f i c i e n t s c a p t u r i n g d i f f e r e n t i a l r e t u r n s t o education across regions f a l l d r a m a t i c a l l y , and t - t e s t s i n d i c a t e d t h a t , a f t e r c o n t r o l l i n g f o r amenities, t h e r e t u r n s t o education i n the Northeast and West are n o t s i g n i f i c a n t l y d i f f e r e n t from t h e r e t u r n s i n the North Central r e g i o n . While the r e t u r n s t o education i n t h e South remain s i g n i f i c a n t l y h i g h e r than i n the North Central even a f t e r amenities are taken i n t o account, t h e r o l e o f r e g i o n i s reduced s u b s t a n t i a l l y , as i s r e f l e c t e d i n a d e c l i n e i n the c o e f f i c i e n t from .01583 t o .0061. Given the l i m i t e d number o f amenity v a r i a b l e s included, the higher r e t u r n s t o education i n the South may w e l l be r e l a t e d t o some unmeasured s i t e characteristics. The j o i n t s i g n i f i c a n c e o f the r e g i o n a l terms when amenities are i n c l u d e d was c a l c u l a t e d by comparing columns 3 and 2 i n t a b l e 1. Column 3 contains t h e estimates o f a wage equation, which includes the amenities, b u t which o m i t s the r e g i o n a l v a r i a b l e s . The i n c l u s i o n o f r e g i o n a l v a r i a b l e s does n o t s u b s t a n t i a l l y a f f e c t the c o e f f i c i e n t s o r s i g n i f i c a n c e o f most o f the amenity variables. I n a d d i t i o n , an F - t e s t o f t h e j o i n t s i g n i f i c a n c e o f t h e amenity- education i n t e r a c t i o n terms when a m e n i t i e s a r e i n c l u d e d g i v e s an F- value o f 34.8 when a m e n i t i e s were o m i t t e d . The combined evidence p r e s e n t e d i n t a b l e 1 suggests t h a t r e g i o n a l d i f f e r e n c e s i n t h e r e t u r n s t o e d u c a t i o n l a r g e l y r e p r e s e n t compensation f o r r e g i o n a l d i f f e r e n c e s i n a m e n i t i e s . A d e c l i n e i n t h e importance o f r e g i o n i n e x p l a i n i n g t h e d i f f e r e n c e s i n t h e average wage once a m e n i t i e s a r e t a k e n i n t o account i s a l s o e v i d e n t i n t a b l e 1. When a m e n i t i e s a r e i n c l u d e d , t h e c o e f f i c i e n t s on t h e Northwest and South dummies, w h i l e s t i l l s i g n i f i c a n t , f a l l d r a m a t i c a l l y . The average wage i s s i g n i f i c a n t l y h i g h e r i n t h e West than i n t h e N o r t h C e n t r a l a f t e r c o n t r o l l i n g f o r r e g i o n a l d i f f e r e n c e s i n amenities. P r i o r t o the i n c l u s i o n o f amenities, t h e o p p o s i t e was t r u e . A t e s t o f t h e j o i n t s i g n i f i c a n c e o f a l l t h e r e g i o n a l terms when a m e n i t i e s a r e n o t i n c l u d e d , g i v e s an F- value o f 68.9. Once r e g i o n a l d i f f e r e n c e s i n a m e n i t i e s have been accounted for, t h e F- value i s reduced t o 14.7. A s i m i l a r cornparision o f t h e s i g n i f i c a n c e o f t h e amenity v a r i a b l e s when r e g i o n i s n o t i n c l u d e d , and when t h e r e g i o n a l terms a r e i n c l u d e d , g i v e s F- values of 63.6 and 43.0, respectively. O v e r a l l , t h e evidence seems p e r s u a s i v e t h a t r e g i o n a l d i f f e r e n c e s i n b o t h t h e l e v e l o f e a r n i n g s and t h e r e t u r n s t o education, t o a l a r g e e x t e n t , r e p r e s e n t compensation f o r r e g i o n a l d i f f e r e n c e s i n amenities. AMENITIES AND REGIONAL DIFFERENCES I N THE RETURN TO OCCUPATION Table 2 addresses t h e q u e s t i o n o f t h e r e l a t i o n s h i p between a m e n i t i e s and t h e r e t u r n s t o occupation. t o education. The f i n d i n g s a r e s i m i l a r t o those f o r t h e r e t u r n s Column 1 p r e s e n t s t h e c o e f f i c i e n t e s t i m a t e s on t h e r e g i o n a l v a r i a b l e s when no a m e n i t i e s a r e i n c l u d e d i n t h e r e g r e s s i o n . Evidence o f r e g i o n a l d i f f e r e n c e s i n t h e r e t u r n s t o o c c u p a t i o n a r e found i n a t e s t o f t h e j o i n t s i g n i f i c a n c e o f t h e 27 s l o p e c o e f f i c i e n t s , which g i v e s an F- value o f 9.3 where t h e c r i t i c a l v a l u e i s 1.7. (F-values a r e summarized i n t a b l e 3 ) . Column 2 i n t a b l e 2 p r e s e n t s t h e c o e f f i c i e n t e s t i m a t e s f o r t h e r e g i o n a l i n t e r c e p t s and t h e r e g i o n - o c c u p a t i o n i n t e r a c t i o n terms when a m e n i t i e s a r e b o t h i n c l u d e d i n t h e i n t e r c e p t and i n t e r a c t e d w i t h occupation. O f t h e 20 r e g i o n - o c c u p a t i o n c o e f f i c i e n t s t h a t were s i g n i f i c a n t i n t h e absence o f a m e n i t i e s , 13 a r e no l o n g e r s i g n i f i c a n t when r e g i o n a l d i f f e r e n c e s i n a m e n i t i e s a r e t a k e n i n t o account. f e l l f o r 10. Of these 13, t h e a b s o l u t e value of t h e c o e f f i c i e n t Of t h e seven r e g i o n - o c c u p a t i o n c o e f f i c i e n t s t h a t remained s i g n i f i c a n t , t h e a b s o l u t e v a l u e o f t h e c o e f f i c i e n t d e c l i n e d f o r f i v e , and i n c r e a s e d f o r two. I n two cases, Sales and P r i v a t e Household S e r v i c e s i n t h e West, c o e f f i c i e n t s t h a t were i n s i g n i f i c a n t i n t h e absence o f t h e amenity v a r i a b l e s became s i g n i f i c a n t when t h e y were i n c l u d e d . A t e s t o f t h e j o i n t s i g n i f i c a n c e o f t h e region- occupation i n t e r a c t i o n terms when r e g i o n a l d i f f e r e n c e s i n a m e n i t i e s a r e accounted for g i v e s an F- value o f 2.7, which i s a s u b s t a n t i a l d e c l i n e f r o m t h e F- value o f 9.3 when amenities are not included. As was t h e case w i t h t h e r e g i o n a l d i f f e r e n c e s i n t h e r e t u r n s t o e d u c a t i o n , t h e evidence suggests t h a t t o a l a r g e e x t e n t these r e g i o n a l d i f f e r e n c e s i n t h e r e t u r n t o o c c u p a t i o n r e p r e s e n t compensation f o r r e g i o n a l differences i n amenities. THE DEMAND FOR AMENITIES The f i n a l q u e s t i o n addressed concerns i n f e r e n c e s t h a t can be made c o n c e r n i n g t h e demand f o r a m e n i t i e s . I n t h e absence o f r e n t d a t a , we a r e u n a b l e t o determine whether t h e urban a t t r i b u t e s i n c l u d e d i n t h e r e g r e s s i o n s a r e viewed b y households as a m e n i t i e s o r d i s a m e n i t i e s . Using the i n f o r m a t i o n on a m e n i t i e s from t h e e s t i m a t i o n o f a m e n i t i e s and e d u c a t i o n ( t a b l e 21, we can say, however, t h a t , on average, c h a r a c t e r i s t i c s , such as D e n s i t y , f o r which t h e average worker receives compensation i n the form of h i g h e r wages, a r e valued more h i g h l y by f i r m s than by households. Similarly, characteristics such as C u l t u r e t h a t are associated w i t h lower wages, on average are valued more h i g h l y by households than by f i r m s . A negative c o r r e l a t i o n between the i n t e r c e p t and slope c o e f f i c i e n t s on t h e amenity v a r i a b l e s i s apparent i n t a b l e 1. t o education increase w i t h n e t amenities. Without exception, the r e t u r n s That i s t o say, t h e more h i g h l y educated workers pay r e l a t i v e l y less i n the form f o r forgone wages f o r a t t r i b u t e s t h a t , on average, lower wages, and they r e c e i v e r e l a t i v e l y l e s s f o r a t t r i b u t e s t h a t , on average, r e q u i r e wage compensation. This does n o t imply t h a t h i g h l y educated i n d i v i d u a l s value amenities l e s s than others, e i t h e r a b s o l u t e l y o r r e l a t i v e l y . amenities more. They may w e l l value Payments f o r amenities take the form o f r e n t s as w e l l as wages and, as noted i n s e c t i o n I1 o f t h i s paper, increases i n human c a p i t a l (such as edudation) t h a t increase r e a l income, may increase l a n d ownership, thereby i n c r k a s i ng r e n t payments. I f these r e n t payments i ncrease more r a p i d l y than the value o f amenities, the d i f f e r e n c e w i l l be r e f l e c t e d i n r e l a t i v e l y lower wages. This evidence i s then c o n s i s t e n t w i t h a p o s i t i v e s i g n on equation (14) and an income e l a s t i c i t y o f demand f o r l a n d t h a t exceeds t h e income e l a s t i c i t y o f t h e marginal e v a l u a t i o n o f amenities. IV. SUMMARY AND CONCLUSIONS This paper has shown t h a t i n t e r p r e t i n g r e g i o n a l d i f f e r e n c e s i n the r e t u r n s t o human c a p i t a l as evidence o f s t r u c t u r a l d i f f e r e n c e s i n r e g i o n a l l a b o r markets i s i n c o r r e c t . The theory demonstrated t h a t r e g i o n a l d i f f e r e n c e s i n the r e t u r n s t o human c a p i t a l may r e f l e c t compensation f o r r e g i o n a l d i f f e r e n c e s i n amenities and t h a t these d i f f e r e n c e s i n the r e t u r n s t o human c a p i t a l would e x i s t i n e q u i l i b r i u m due t o d i f f e r e n c e s between t h e income e l a s t i c i t y o f t h e marginal e v a l u a t i o n o f amenities and t h e income e l a s t i c i t y o f demand f o r housing and o t h e r goods. The e m p i r i c a l work on wages found t h a t well- documented r e g i o n a l d i f f e r e n c e s i n t h e r e t u r n s t o b o t h e d u c a t i o n and o c c u p a t i o n can be l a r g e l y e x p l a i n e d by amenities. One i n t e r e s t i n g q u e s t i o n f o r f u t u r e r e s e a r c h i s whether t h e e m p i r i c a l r e l a t i o n s h i p between amenities and t h e r e t u r n s t o human c a p i t a l i s due t o s y s t e m a t i c d i f f e r e n c e s i n p r e f e r e n c e s across e d u c a t i o n o r o c c u p a t i o n groups, o r whether t h e r e l a t i o n s h i p r e s u l t s f r o m t h e r e l a t i v e income e l a s t i c i t i e s o f demand as was suggested i n t h e t h e o r e t i c a l model. Another area f o r f u r t h e r r e s e a r c h i s t h e impact o f d i f f e r e n c e s i n a m e n i t i e s on t h e m i g r a t i o n p a t t e r n s o f d i f f e r e n t human c a p i t a l groups. Finally, t h i s work c o u l d be extended by a l l o w i n g f o r s u b s t i t u t i o n o f i n p u t s by f i r m s and b y c o n s i d e r i n g d i f f e r e n t types o f f i r m s as w e l l as workers. References B a r t i k , Timothy J . "The E s t i m a t i o n o f Demand Parameters i n Hedonic P r i c e Models," J.P.E. 95 ( F e b r u a r y , 19871, pp. 81-88. Epple, Dennis. "Hedonic P r i c e s and I m p l i c i t Markets: E s t i m a t i n g Demand and Supply F u n c t i o n s f o r D i f f e r e n t i a t e d P r o d u c t s . " J.P.E. 95 (February, 19871, pp. 59-80. Hanushek, E r i c . " Regional D i f f e r e n c e s i n t h e S t r u c t u r e o f E a r n i n g s . " Rev. Econ. and S t a t i s . 55 (May, 19731, pp. 204-213. Hoehn, John P.; B e r g e r , Mark C.; and Bloomquist, Glenn C. "A Hedonic Model o f I n t e r r e g i o n a l Wages, Rents and Amenity V a l u e s . " Working Paper. L e x i n g t o n , Kentucky; U n i v e r s i t y o f Kentucky, ( A p r i l , 19861. Jackson, L o r i e D. "The Changing N a t u r e o f Regional Wage D i f f e r e n t i a l s f r o m 1979 t o 1983." Economic Review, Federal Reserve Bank o f C l e v e l a n d , F i r s t Q u a r t e r (19861, pp. 12-23. Krumm, Ronald J . " Regional Wage D i f f e r e n t i a l s, Labor Supply Responses and Race." J. Reg. S c i . 24 (August, 19841, pp. 431-442. Roback, J e n n i f e r . "Wages, Rents, and t h e Q u a l i t y o f L i f e . " (December, 19821, pp. 1257-1278. J.P.E. 90 S a h l i n g , Leonard, and Sharon Smith. " Regional Wage D i f f e r e n t i a l s : Has t h e South R i s e n Again?" Rev. Econ. and S t a t i s . 65 (February, 19831, pp. 131-135. Endnotes 1. The a b i l i t y o f an area t o c r e a t e amenities i s n o t considered. 2. The question o f intra- urban l o c a t i o n can be addressed i n t h e framework developed here. Hoehn, e t . a l . (1986) i n c o r p o r a t e i n t r a - u r b a n l o c a t i o n i n a s i m i l a r model t h a t o n l y a l l o w s f o r one type o f worker. 3. Common ownership o f l a n d and c a p i t a l are assumed and the income f r o m these f a c t o r s i s assumed t o be d i s t r i b u t e d e q u a l l y among t h e workers. 4. See Roback (1983) f o r a discussion o f t h i s p o i n t . 5. Recent work by Epple (1986) and B a r t i k (1986) address t h e q u e s t i o n o f e s t i m a t i n g hedonic equations when t a s t e s vary. 6. One n o t a b l e exception i s union s t a t u s , which has been found t o be an i m p o r t a n t determinant o f wages, b u t was n o t r e p o r t e d i n 1980 CPS data. 7. . The 80 amenity- occupation i n t e r a c t i o n terms, which are o m i t t e d for b r e v i t y , are avai l a b l e from the author upon request. Table 1: Amenities and the Returns o f Education Intercept New England (NE) South ( S ) West (W) Education * NE Education * S Education * W Model 1 Model 2 1.1447** (.0191) -. 1665** ( .0203) -. 2541* * ( .0205) -. 1052** ( .0205> .0093** (.0015> .0158** (.0016> .0090* * ( .0015> .9918** .I7531 -. 0825* (.0416) - .0675* ( .0402 > . 1ooo* * ( .0377) .0028 ( .0032) .0061* ( .0030) - .0040 ( .0028) Model 3 ( Recreation (Rec) Density (Den) Schools (Sch) Heal t h (Heal 1 Cul t u r e (Cult) Crime (Crime) Population (Pop) Heating Degree Days (HDD) Education * Rec Education * Den Education * Sch Education * Heal Education * Cult Education * Crime Education * Pop Education * HDD -R ( .0063> ( .00351 .4235 .4302 .4296 Note: Regression includes personal c h a r a c t e r i s t i c s ; standard e r r o r s are i n parenthesis. See Appendix f o r variable d e f i n i t i o n s . **1 percent l e v e l o f s i g n i f i c a n c e *10 percent l e v e l o f s i g n i f i c a n c e . Source: Author. - -- - Table 2: Amenities and the Return t o Occupation Model 1 New England Intercept Managers Sales Cl er i cal Craftsmen Operatives Transport Nonfarm Labor Private Household Other Service South Intercept Managers Sales Cl eri cal Craftsmen Operatives Transport Nonfarm Labor Private Household Other Services Model 2 Table 2: Amenities and the Return to Occupation (Cant.) Model 1 - - - - - Model 2 - - West Intercept Managers Sales Cl eri cal Craftsmen Operatives Transport Nonfarm Labor Private Households Other Service E2 .4248 Note: .0390** ( -0098) -.0186 ( .0160> .0020 ( .0209> -.0085 ( .0136> - .0562** ( .0153> -. 1042** ( .0162> -.0144 ( .0256> -. 0455* ( .0253) .0998 ( .0752) -.0073 ( .0175) .4333 .0326* (.0175> - .0004 ( .0286) .0726* ( .0360) .0050 ( .0240) .0036 (.0272> .0436 ( .0296> .0444 ( .0432) .0539 ( .0416) -. 2593* ( .I4241 .0329 ( .0308) Both regressions include personal characteristics; amenities are included in model 2; standard errors are in parentheses. See Appendix for variable definitions. * * significant at 1 percent * significant at 10 percent Source: Author --- Table 3: F- values f o r Regional Returns t o Human C a p i t a l Without Amenities Education Regional i n t e r c e p t s Regional slopes Both 102.6 34.9 68.9 Occupation Regional i n t e r c e p t s Regional slopes Both Source: Author 102.6 9.3 18.7 With Amenities Appendix A: Regression o f Log o f Weekly Earnings on Personal C h a r a c t e r i s t i c s Mean Coefficient Intercept Education Experience Experience squaredl 100 White Ma1e Marr ied Househol d Head Private Occupation Managers Sales Clerical Craftsmen Operatives Transport Nonfarm Labor P r i v a t e Households O t h e r Service Note : Source: - Data a r e f r o m t h e 1980 C u r r e n t P o p u l a t i o n Survey; R2 = .4194, N = 57,172. The o m i t t e d o c c u p a t i o n i s P r o f e s s i o n a l . Standard e r r o r s a r e i n parentheses. A l l c o e f f i c i e n t s a r e s i g n i f i c a n t a t 1 p e r c e n t l e v e l except Managers, which i s s i g n i f i c a n t a t 5 p e r c e n t . Author. Appendix B: Notes on S i t e C h a r a c t e r i s t i c V a r i a b l e s 1. R e c r e a t i o n : Index o f q u a l i t y o f r e c r e a t i o n a l f a c i l i t i e s . R e c r e a t i o n score f r o m P l a c e s Rated Almanac, 1981. S c a l e b y 10,000. = .1713. 2. D e n s i t y : P o p u l a t i o n d e n s i t y o f SMSA. Source: Book. Scaled by 10,000. Mean = .1517. 3. Schools: Student- teacher r a t i o f o r l o c a l p u b l i c s c h o o l s . Rated Almanac, 1981. S c a l e d by 100. Mean = .1759. 4. Health: Mean C i t y and County D a t a Source: Places Measure o f q u a l i t y o f h e a l t h c a r e f a c i l i t i e s . Based on d a t a -. f r o m t h r e e or more medical schools or t e a c h i n g h o s p i t a l s , (one a d d i t i o n a l p o i n t f o r 5 or more), c a r d i a c r e h a b i l i t a t i o n c e n t e r , a c u t e s t r o k e c e n t e r , and comprehensive cancer c a r e c e n t e r . Scaled b y 10. Mean = .521. Places Rated Almanac, 1981, one p o i n t f o r each o f t h e f o l l o w i n g : -- 5. C u l t u r e : Measure o f q u a l i t y o f c u l t u r a l a c t i v i t i e s . Based on A r t s s c o r e i n -Places Rated Almanac, 1981. Scaled b y 100,000. Mean = .1370. 6. Crime: I n d e x o f s e r i o u s crimes p e r person. Book. Mean = .0637. 7. P o p u l a t i o n : M e t r o p o l i t a n a r e a p o p u l a t i o n . Source: 1980. Scaled by 10 m i l l i o n . Mean = .3563. 8. H e a t i n g Degree Days: Average number o f h e a t i n g degree days, 1950- 1980. Source: County and C i t y Data Book, 1981. Scaled b y 10,000. Mean = .4347. Source: County and C i t y D a t a Census o f P o p u l a t i o n ,
@FedFRASER