Federal Reserve Bank of New York Staff Reports Have Amenities Become Relatively More Important Than Firm Productivity Advantages in Metropolitan Areas? Richard Deitz Jaison R. Abel Staff Report no. 344 September 2008 This paper presents preliminary findings and is being distributed to economists and other interested readers solely to stimulate discussion and elicit comments. The views expressed in the paper are those of the authors and are not necessarily reflective of views at the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the authors. Have Amenities Become Relatively More Important Than Firm Productivity Advantages in Metropolitan Areas? Richard Deitz and Jaison R. Abel Federal Reserve Bank of New York Staff Reports, no. 344 September 2008 JEL classification: R23, R30 Abstract We analyze patterns of compensating differentials to determine whether a region’s bundle of site characteristics has a greater net effect on household location decisions relative to firm location decisions in U.S. metropolitan areas over time. We estimate skill-adjusted wages and attribute-adjusted rents using hedonic regressions for 238 metropolitan areas in 1990 and 2000. Within the framework of the standard Roback model, we classify each metropolitan area based on whether amenities or firm productivity advantages dominate and analyze the extent to which these classifications change between 1990 and 2000. We then decompose compensating differentials into amenity and firm productivity advantage components and examine how these components change. Empirical results suggest that while the relative importance of amenities appears to have increased slightly between 1990 and 2000, firm productivity advantages continued to dominate amenities in the vast majority of metropolitan areas during this decade. Key words: compensating differentials, quality of life, productivity Deitz: Federal Reserve Bank of New York. Abel: Federal Reserve Bank of New York. Address correspondence to Richard Deitz (e-mail: [email protected]). The views expressed in this paper are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York or the Federal Reserve System. I. INTRODUCTION The traditional view of cities emphasizes the importance of firm productivity advantages, such as access to natural resources or a transportation hub, as the foundation for urban growth and development. To the extent that household location decisions are considered endogenous, a key source of such productivity advantages—agglomeration arising from urban density—is considered a disamenity to households; for example, in the form of higher rents, longer commutes, or more crime. Thus, according to this view, cities primarily provide production advantages to firms and consumption disadvantages to households. Recently, however, researchers have argued that quality of life, including various urban amenities and climate, has become a leading determinant of household location decisions and an important driver of regional growth. For example, Glaeser, Kolko, and Saiz (2001), coin the term “Consumer City,” arguing that cities are increasingly oriented around consumption amenities rather than productivity advantages. In addition, they provide some evidence that high amenity cities have grown faster than low amenity cities since at least the 1980s. Following this line of argument, Glaeser and Gottlieb (2006) document the rising importance of urban amenities to the resurgence of large cities during the 1990s. In addition, Rappaport (2007) has shown that population growth in the U.S. has been more rapid in places with nice weather, a valuable location-specific consumption amenity. A common hypothesis offered to explain the increasing importance of quality of life to urban development patterns is that the demand for consumption amenities has increased as incomes and education levels have risen nationwide. If this is true, quality of 1 life should be increasingly important in driving differences in growth across locations over time. A natural question that arises out of these views of urban development is whether there has been a fundamental shift in the importance of amenities relative to firm productivity advantages in urban areas. That is, have amenities become a more dominant actor shaping the development of urban areas, or do firm productivity advantages dominate? We attempt to answer this question empirically. We estimate compensating differentials to examine the relative importance of amenities and firm productivity advantages for a large sample of U.S. metropolitan areas over time. Compensating differentials in wages and rents reflect differences in location characteristics that benefit households and firms. Site-specific amenities that increase the utility of households reduce wages and increase rents, while locational advantages in productivity that increase the profitability of firms bid up both wages and rents. While these two forces act simultaneously, within the context of the standard Roback model, we infer which effect is dominant over time. Further, by analyzing changes in the patterns of compensating differentials, we can examine whether amenities have become relatively more important than firm productivity advantages in U.S. metropolitan areas. Thus, while much of the compensating differentials literature has focused on a single point in time (see, e.g., Bloomquist, Berger, and Hoehn 1988; Beeson and Eberts 1989, and Gyourko and Tracy 1991, among others), our work also contributes to a relatively recent literature analyzing the extent and source of changes in compensating differentials over time (see, e.g., Gabriel, Mattey, and Wascher 2003; Gabriel and Rosenthal 2004; and Shapiro 2006). 2 Specifically, we estimate the standard Roback model and its parameters using census data from 1990 and 2000. For each census year, we utilize hedonic regressions to estimate skill-adjusted wages and attribute-adjusted rents for 238 metropolitan areas, and classify each metropolitan area based on whether amenities or firm productivity advantages dominate using a framework proposed by Beesen and Eberts (1987). In particular, based on the relative values of a metropolitan area’s wage and rent differentials vis-à-vis the national average, we classify the metropolitan areas into four groups: “High Productivity,” “Low Productivity,” “High Amenity,” and “Low Amenity.” We then analyze the extent to which these classifications change between 1990 and 2000. Finally, we decompose our estimated wage and rent compensating differentials into amenity and productivity components for each metropolitan area, and examine how these components change over time. We find that more metropolitan areas are classified as either “High Amenity” or “Low Amenity” locations in 2000 than in 1990, and further, that the share of both wage and rent compensating differentials attributable to amenities increased slightly over the period. Thus, our analysis suggests that the relative importance of amenities increased modestly between 1990 and 2000, although productivity effects continued to dominate the majority of metropolitan areas during this decade. II. CONCEPTUAL FRAMEWORK Our analysis builds from the well-established model of household and firm location developed by Roback (1982) and extended by Beeson and Eberts (1987, 1989). Identical households choose among locations, and each location is endowed with a bundle of site characteristics, referred to as amenities, that affect household utility.1 1 As our analysis examines differences in wages and rents between locations, we adopt the standard modeling assumptions and do not explicitly consider intracity location differences. 3 Utility is equalized among locations through differences in local wages (w) and rents (r). Mobile workers of identical skills and tastes are assumed to choose quantities of a composite good and residential land, given the bundle of site characteristics (s) that differ among locations. Labor is inelastically supplied and total income is derived only from wages. Expressed via an indirect utility function, where V is a constant level of utility 0 across locations: V(w,r;s) =V (1) 0 Similarly, firms choose among locations with site-specific attributes that affect costs, referred to as productivity advantages, and profits are equalized among locations through differences in wages and rents. Firms produce a single good in a national market, and capital is mobile across locations. Normalizing the price of the good to one and expressing as an indirect cost function gives: C(w,r;s) =1 (2) If s provides a positive amenity value in a city relative to other locations, Vs>0; and, if s provides a productivity advantage to firms relative to other cities, Cs<0. Equations (1) and (2) can be expressed graphically as a set of isoutility and isocost curves, as shown in Figure 1. Isoutility curves are upward sloping in w and r since higher wages must offset higher land prices to keep utility constant. Similarly, isocost curves are downward sloping since higher wages must be offset by lower land prices to maintain zero profit. Given standard assumptions of the model, equilibrium conditions in labor and land markets lead to combinations of w and r for each city relative 4 to the average city, (r*, w*). This, in turn, identifies differences in wages and rents between each city and the average, commonly referred to as compensating differentials. Applying the equilibrium condition and totally differentiating both functions yields estimates of the slopes of both curves as: (dw ds)C (dr ds)C =lh (3) and (dw ds)V (dr ds)V = −LP NP (4) where lh is the quantity of land consumed by households, LP is the quantity of land used in production by firms, and NP is the quantity of labor used in production. Land and labor market equilibrium requires NP = N, and that LP = L -Nlh , where N is the number of workers and L is the land area of the city. The total wage and rent differentials between a city and the average city, due to its site characteristics, is made up of two components: a productivity component through what can be thought of as a shift of the isocost curve, and an amenity component through what can be thought of as a shift in the isoutility curve. The magnitude of each shift, given the slopes of each curve, determines whether the net wage or rent differential will turn out to be positive or negative. These shifts are, in reality, expressions of the relative position of a given city compared to the average city. Thus, it is possible to decompose wage and rent compensating differentials into an amenity component and productivity advantage component by quantifying shifts in the isoutility curve and isocost curves. Such a decomposition is represented graphically in Figure 1 for wages, which illustrates a city, A,—shown at (r ,w )—whose bundle of site-specific attributes is A A 5 associated with a combination of high amenities and low productivity advantages relative to the average city—again, shown at (r*,w*). The full wage differential is (w -w*), where A (w’-w*) represents the difference in wages due to an amenity advantage and (w -w’) A represents the wage differential due to the city’s productivity disadvantage. In this case, the net result is a wage discount. A similar exercise can be performed in terms of rents, which in the example shown would result in a rent premium resulting from a larger amenity advantage (rent premium) relative to a productivity disadvantage (rent discount). Thus, in this example, the isoutility curve shift is greater than the isocost curve shift. More formally, equations (3) and (4) can be used to quantify the proportion of observed wage and rent compensating differentials due to a metropolitan area’s site- specific amenities and productivity advantages. Since land prices are very difficult to observe, but housing prices are more readily available, we assume that variations in unit housing prices across space reflect only variations in land prices. As such, k=rlh/w, where l k is the share of housing in the consumer’s budget. l Therefore, dw ds =(dw ds)C +(dw ds)V =lh(dr ds)C −(LP NP)(dr ds)V (5) Employing equations (3) and (4), and expressing in log form: (dlogw ds)V =[(LP NP)/(lh +(LP NP))]×(dlogw ds−k dlogr ds) (6) l Given the assumption about the relationship between land and housing price changes, equation (6) can be written as: (dlogw ds)V =[(rLP wNP)/(rL wN)]×(dlogw ds−k dlogp ds) (7) h h 6 where p is unit housing rents and k is the share of housing in the consumer’s budget. h h We use equations (3), (4), and (7) to estimate the share of wage and rent compensating differentials due to the shift in each of the isoutility and isocost curves. Within this framework, it is possible to determine which curve is the dominant actor for a given location simply by observing compensating differentials (Beeson and Eberts 1987). That is, it is possible to classify metropolitan areas based on whether they are dominated primarily by amenities or firm productivity advantages related to their bundle of site characteristics.2 Specifically, for any metropolitan area with both above- average wages and rents or below-average wages and rents, it must be that the shift in the isocost curve is greater than the shift in the isoutility curve. For this reason, metropolitan areas with patterns of wage and rent compensating differentials of this nature are classified as “High Productivity” and “Low Productivity,” respectively. Similarly, for any metropolitan area with above-average wages and below-average rents or below- average wages and above-average rents, it must be that the shift in the isoutility curve is greater than the shift in the isocost curve. As such, metropolitan areas with these patterns of wage and rent compensating differentials are classified as “Low Amenity” and “High Amenity,” respectively. Such a classification is depicted in Figure 2, which shows an example of two cities, A (as before) and B, both with above-average amenity value and below-average productivity value. The space on this diagram is divided into quadrants using the average city as the reference point. Locations that fall within the lower-left and upper-right quadrants are dominated by productivity effects, while locations that fall within the 2 Classification of this nature assumes linear isoutility and isocost curves around the neighborhood of inquiry and approximately equal slopes over the relevant range of each curve. 7 upper-left and lower-right quadrants are dominated by amenity effects. Thus, City A would be classified as “High Amenity” because the amenity advantage dominates the productivity disadvantage in this instance. That is, the shift in the isoutility curve is larger than the shift in the isocost curve. In contrast, City B would be classified as “Low Productivity” because the productivity disadvantage dominates the amenity advantage. Classification of this nature provides insight into the relative attractiveness of different locations to firms and households. III. ESTIMATION OF COMPENSATING DIFFERENTIALS The data used for our analysis are drawn from the 5 percent Public Use Microdata Sample published as part of the 1990 and 2000 U.S. Census of Populations. We use standard hedonic regression techniques to estimate wage and rent compensating differentials for 238 metropolitan areas in both 1990 and 2000. We estimate these compensating differentials as metropolitan area fixed effects in wage and rent equations that control for observable differences between workers and housing units in each year. Such an approach allows us to estimate the net value of all site-specific location characteristics. Our estimation approach and results for each set of equations are described in more detail below. A. Wage Equations Hedonic wage regressions are estimated separately for 1990 and 2000 so as to avoid unnecessary restrictions on the coefficients. The individuals included in our analysis of wage differentials had to meet the following criteria: the person was over 16 years of age, currently employed, reported positive wage income, worked in the previous year, and resided in one of the 238 metropolitan areas in our sample. Individuals in the 8