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...Department Commerce 2000a), while the unemployment rate varied from 1.6% to more than 20% (U.S. Department of Labor 2000). The variation in median housing prices was even greater, from less than $10,000 to more than $640,000 in 2000 (U.S. Department of Commerce 2000b). Spatial disparities in economic development exist not only between rural and urban areas but within rural America as well. In some rural areas, dwindling rural economies have caused once-viable communities to become ghost towns. In other areas, urbanization has presented both challenges and opportunities for rural communities.
Why do spatial inequalities in economic development exist in the United States? Why are the spatial differences in wages and housing prices not bid away by households and firms in search of high income and low production costs? The answers to these issues are central to understanding many aspects of economic underdevelopment in rural America (Henderson, Shalizi, and Venables 2001). They are also important for developing policies to improve the economy and quality of life in rural communities.
These issues have been explored in the literature (see Henderson, Shalizi, and Venables 2001 for review). Previous studies, often conducted at the international and cross-country levels, have identified three major factors that affect economic development: (a) natural endowments (e.g., water availability, land quality, environmental amenities), (b) accumulated human and physical capital (e.g., educational level of labor force, infrastructure), and (c) economic geography (e.g., remoteness, proximity to input and output markets)) These theories, however, have rarely been tested in the context of rural development in the United States. In a seminal article, Roback (1982) develops an equilibrium model of firm and household location decisions to examine the role of wages and rents in allocating workers to locations with different level of amenities. She applies the model to explain wage differences in major U.S. cities and finds that amenities have a significant effect on wages and rents. Extending Roback's work, Blomquist, Berger, and Hoehn (1988) develop a quality of life index that incorporates the effects of amenities on wages and housing prices for 253 urban counties in the United States. Rappaport and Sachs (2002) analyze the effect of coastal proximity on the concentration of economic activity in the United States and find that the coastal concentration derives primarily from a productivity effect, but also, increasingly, from a "quality-of-life" effect. Partridge, Rose, and Alessandro (2007) assess whether agglomeration economies in the major Canadian metropolitan areas lead to population growth in or near these cities and find that disparities such as the concentration of Canadians along its southern border may explain migration patterns. Levernier, Partridge, and Rickman (2000) use U.S. county-level data to explore potential explanations for the observed regional variation in the rates of poverty. Factors considered include those that relate to both area economic performance and demographic composition. Deller et al. (2001) examine the effect of amenity and quality of life attributes on regional economic growth in the United States and find that predictable relationships exist between amenities, quality of life and local economic performance. Halstead and Deller (1997), Rudzitis (1999), and Gottlieb (1994) find that quality of life plays an increasingly important role in community economic growth in the United States. However, to our knowledge, few studies have measured the relative contributions of natural amenities, accumulated capital and economic geography to spatial variations in economic development in the United States. (2)
The location decisions of firms have been at the center of economic research (Giannias and Liargovas 2002). According to Fujita, Krugman, and Venables (1999), firms' location decisions are based on both input price considerations and proximity to markets. Firms want to locate close to input and output markets in order to reduce transportation costs. So, a location with a lot of manufacturing firms will have a high demand for intermediate goods, making it an attractive place for intermediate producers. This, in turn, makes the location attractive to firms that use intermediate goods. Thus, there is a positive feedback between the location decisions of upstream and downstream firms in the chain of economic activity, although crowding may offset some of the positive feedback (Henderson, Shalizi, and Venables 2001). Resource abundance and scale effects are also key determinants of firms' location and economic growth (Romer 1996). As a disproportionate share of manufacturing is attracted to a location, either the wage rate is bid up or labor is attracted to the location, both of which will tend to further increase this location's share of total expenditure. This cluster or agglomeration effect has been explored by Krugman (1991) and others.
The location decisions of households have also been intensively studied in the economic literature. According to the classic urban economics model, households choose residential locations that provide the best trade-off between land costs and commuting costs. High-income households live in suburbs if and only if the income elasticity of the demand for housing is larger than the income elasticity of commuting cost. However, Wheaton (1997) provides empirical evidence that questions the validity of this theory. In searching for alternative explanations, many economists have turned to factors excluded from the classic central city model, such as transportation modes and environmental amenities (Brueckner, Jacques-Francois, and Zenou 1999; Wu 2001, 2006; Wu and Plantinga 2003). However, these studies do not consider the location decisions of firms and thus, the sources of household income.
The objective of this article is to identify the causes of spatial disparities in economic development in the United States and to evaluate the relative contributions of natural amenities, accumulated human and physical capital, and economic geography to these disparities. To this end, a theoretical model is presented to analyze the interaction between the location decisions of firms and households. Understanding this interaction is important because it determines the spatial distribution of economic activity. For example, if a household requires a compensating wage differential to live in a low-amenity location, the firms in that location must have some productivity advantage that allows them to pay the higher wage. Based on the theoretical analysis, an empirical model is estimated to evaluate the relative contributions of natural amenities, accumulated capital, and economic geography to spatial variations in wage, employment, housing price, and land-development density across counties in the United States.
The Theoretical Model
This section presents a model to analyze the interaction between the location decisions of firms and households and its effect on spatial variations in economic development. The model, which is a more fully developed restatement of Roback (1982), assumes that locations differ by natural endowments, accumulated human and physical capital, and economic geography. Some of these factors directly affect households' utility, while others directly affect firms' productivity or transportation costs. Factors that directly affect households' utility and residential location decisions are referred to as amenities and are denoted by vector [epsilon]. Factors that directly affect firms' location decisions are referred to as capital and are denoted by vector [kappa]. Some factors (e.g., climate conditions) may affect both the location decisions of households and firms and thus may be elements of both [epsilon] and [kappa]. For notional simplicity, [epsilon] and [kappa] are treated as scalars below.
The Household's Location Decision
Households have preferences that are defined over residential space (h), a numeraire nonhousing good (z), and environmental amenities ([epsilon]). Each household supplies one unit of time and receives wage w in return. (3) At each location, a household solves the following utility maximization problem:
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where p is the housing price per unit of residential space, [gamma] is a factor converting housing prices into annual rental or mortgage payments (real interest rate), and [w.sub.0] is the nonlabor income. (4)[gamma] is assumed to be independent of location and will be suppressed in the model henceforth. The solution of (1) yields the demand functions for residential space and the nonhousing good:
(2) [h.sup.d] = h(w, p; [epsilon], [w.sub.0])
(3) [z.sup.d] = z(w, p; [epsilon], [w.sub.0]).
[FIGURE 1 OMITTED]
The indirect utility function V(w, p; [epsilon], [w.sub.0]) gives the maximum utility achievable given the wage, the housing price, the level of amenities, and the nonwage income.
Households choose residential locations to maximize utility V(w, p; [epsilon], [w.sub.0]) by considering the trade-offs between wage (w), housing price (p), and amenities ([epsilon]). Households are assumed to be completely mobile and migration is assumed to be costless. Equilibrium for households requires that wages and housing prices adjust to equalize utility in all locations: (5)
(4) V(w, p; [epsilon], [w.sub.0]) = [bar.V]
where [bar.V] the national utility level, exogenous to individual locations. Graphically, iso-utility curves are upward sloping in the (w, p)-plane as shown in Figure 1. This means that for a given level of amenities, locations that offer higher wages must have high housing prices to equalize utility in all locations.
The Firm's Location Decision
Firms choose production locations to minimize total cost by considering the tradeoff between input prices, accumulated human and physical capital, and transportation costs. So, at any given location, a firm chooses the best combination of labor (l), capital (k), and factory space (s) to minimize the total production cost:
(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where r is the unit cost of capital, Q(.) is the production function, [phi] is a factor that converts factory-space prices to annual rental payments, and y is the optimal output (which is determined by the production technologies and markets and is set before the location decision is made). (6) Because y, [phi], and r all are assumed to be independent of location, they are henceforth suppressed in the model. The solution to (5) gives the firm's demand for labor and factory space: (7)
(6) [l.sup.d] = [l.sup.d](w, p; [kappa])...
NOTE: All illustrations and photos
have been removed from this article.
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