The economics of place-making policies.

Glaeser, Edward L. ; Gottlieb. Joshua D.

ABSTRACT Should the national government undertake policies aimed at strengthening the economies of particular localities or regions? Agglomeration economies and human capital spillovers suggest that such policies could enhance welfare. However, the mere existence of agglomeration externalities does not indicate which places should be subsidized. Without a better understanding of nonlinearities in these externalities, any government spatial policy is as likely to reduce as to increase welfare. Transportation spending has historically done much to make or break particular places, but current transportation spending subsidizes low-income, low-density places where agglomeration effects are likely to be weakest. Most large-scale place-oriented policies have had little discernable impact. Some targeted policies such as Empowerment Zones seem to have an effect but are expensive relative to their achievements. The greatest promise for a national place-based policy lies in impeding the tendency of highly productive areas to restrict their own growth through restrictions on land use.

**********

Three empirical regularities are at the heart of urban economics. First, output appears to be subject to agglomeration economies, whereby people become more productive when they work in densely populated areas surrounded by other people. Second, there appear to be human capital spillovers, whereby concentrations of educated people increase both the level and the growth rate of productivity. Finally, the urban system appears to be roughly described by a spatial equilibrium, where high wages are offset by high prices, and high real wages by negative amenities. Do these three regularities provide insights for policymakers, at either the local or the national level?

The concept of spatial equilibrium, presented in the first section of this paper, generally throws cold water on interventions that direct resources toward particular geographic areas. If high prices and low amenities offset high wages in a spatial equilibrium, there is nothing particularly equitable about taking money from rich places and giving it to poor places. Subsidies to poor places will be offset by higher prices, and the primary real effect will be to move people into economically unproductive areas. The spatial equilibrium concept thus suggests that the case for national policy that favors specific places must depend more on efficiency--internalizing externalities--than on equity.

The second section of the paper formalizes this theory and discusses its implications for optimal spatial policy. The model allows for agglomeration economies, which imply that productivity rises with the population or the population density of an area. Two types of evidence support the existence of those externalities: the concentration of economic activity in dense clusters and the robust connection between density and productivity. In principle, omitted exogenous differences in local productivity could explain both facts, but there is little evidence that any such differences are large.

At the local policy level, agglomeration economies provide a further justification for local leaders to seek to maximize population growth. At the national policy level, the existence of agglomeration economies and congestion disamenities makes it unlikely that a centrally unencumbered spatial equilibrium will be socially optimal. However, the mere existence of agglomeration economies does not tell us which areas should be subsidized. The spatial equilibrium model suggests that resources should be pushed to areas that are more productive and where the elasticity of productivity with respect to agglomeration is higher. Empirically, however, economists have little idea where that is the case. Given the difficulty even of identifying the magnitude of agglomeration economies, it should not be surprising that we cannot convincingly estimate nonlinearities in those economies.

The spatial equilibrium model suggests that agglomeration economies are best identified through shocks to amenities or housing supply. For that reason, in the paper's third section we use the connection between climate and population growth to estimate the impact of population on productivity. We find little evidence to suggest that agglomeration economies are larger for smaller than for bigger cities, or for more compact than for less compact cities. We also find little evidence that the negative impact of population due to urban disamenities differs across types of cities. If anything, there seems to be a more positive link between population and amenities in more compact urban areas.

The fourth section discusses the historical record of place-making policies in the United States. From the Erie Canal to the Interstate Highway System, government-sponsored transportation infrastructure has long influenced the growth of particular places. We review the evidence showing a strong connection between access to railroads and growth in the nineteenth century, and between highways and urban growth in the twentieth century. (1) We argue that the place-making effects of transportation infrastructure do not imply that one should judge transportation spending on the basis of its ability to change the distribution of population across space. Since we lack confidence about which places should be subsidized, a simple model suggests that social welfare is maximized by choosing transport spending to maximize its direct benefits, not according to its ability to enhance one place or another. Current federal subsidies to transportation favor low-income, low-density states, which are unlikely to have particularly large agglomeration effects.

The Appalachian Regional Commission (ARC), created in the 1960s, is the largest example, in terms of total spending, of unambiguous American regional policy. Using transportation subsidies and other forms of spending, the U.S. government has tried to boost the fortunes of Appalachia. There is little robust evidence suggesting that this spending has been effective. Given that the program involved a modest amount of money spread over a vast geographic area, this is unsurprising. No regional policies that direct relatively small amounts of money at big places can be properly judged, since too many other forces influence these areas' outcomes.

The ability to measure impact is one of the appeals of highly targeted interventions, such as the Empowerment Zones established in the 1990s, that direct significant resources at small areas. Matias Busso and Patrick Kline find that Empowerment Zones did boost local employment, but at a high cost: the program spent more than $100,000 for each new job that can be attributed to an Empowerment Zone. (2) Moreover, just as the spatial equilibrium model suggests, housing prices rose in these zones, possibly more than offsetting any benefits to renters who were employed there before the policy.

The paper's fifth section turns to the national housing policies, such as urban renewal, that were seen as a tool for urban revitalization in the middle decades of the twentieth century. One rationale for these policies is that dilapidated housing creates negative externalities. The case against them is that declining areas already have an abundance of housing supply relative to demand, so that it makes little sense to build more housing. Empirically, we find little evidence that either urban renewal or the subsequent Model Cities Program had any discernable effects on urban prosperity.

Indeed, it might make more sense to focus on building in areas that are more, rather than less, productive. Given the huge wage gaps that exist across space, it may be better strategy to enable more people to move from Brownsville to Bridgeport than to try to turn Brownsville into a thriving, finance-based community. If the most productive areas of the country have restricted construction through extensive land use controls, and these controls are not justified on the basis of other externalities, then it may be welfare enhancing for the federal government to adopt policies that could reduce the barriers to building in these areas.

The sixth section of the paper turns to human capital spillovers, which occur when productivity is a function of other area residents' skills in the area. The existence of human capital spillovers suggests that local leaders trying to improve area incomes or increase area population should focus on policies that attract or train more skilled residents. Like agglomeration economies, human capital spillovers mean that a decentralized equilibrium is unlikely to be optimal. For example, some education subsidies are likely to enhance welfare. Determining the correct national policy toward places, however, requires not only identifying the average effect of human capital externalities or industrial spillovers, but also knowing where these effects are larger.

There is little clear evidence that human capital spillovers or industrial spillovers differ between smaller or larger, or more or less dense, cities. If anything, the impact of skilled workers and industries seems to be convex, suggesting possible returns from pushing skilled workers into already skilled areas. Of course, any tendency to artificially subsidize those areas with high human capital would seem inequitable. The recent tendency of skilled people to move to places where skills are already abundant seems to be progressing without government aid. If anything, these results bolster the case for working against land use restrictions that stymie growth in areas with high human capital.

The Spatial Equilibrium

The economic approach to urban policy begins with a model that has three equilibrium conditions. The urban model makes the standard assumption that firms are maximizing profits and hence hiring workers to the point where wages equal the marginal product of labor. The model also assumes that the construction sector is in equilibrium, which means that housing prices equal the cost of producing a house, including land and legal costs. Finally, and most important, the model assumes that migration is cheap enough to make consumers indifferent between locations. High wages in an area are offset by high prices; low real wages are offset by high amenities. For more than forty years this spatial equilibrium assumption has helped economists make sense of housing prices within cities and the distribution of prices and wages across cities. (3)

The assumption of low-cost migration between places implies only that expected lifetime utility levels should be constant across space. In practice, economists typically assume that enough migration occurs at every point in time to ensure that period-by-period utility flows are also constant across space. This assumption is standard, if extreme, and we will use it here. The indirect utility function for an individual in location i can be written as V [[W.sub.i], [P.sub.i.sup.j], [[theta].sub.i]([N.sub.i])], where [W.sub.i] refers to labor income in area i, [P.sub.i.sup.j] is a vector of prices of city-specific nontraded goods (especially housing), and [[theta].sub.i]([N.sub.i]) describes the quality of life in the area, which may be decreasing in population, N, because of congestion externalities. Traded goods prices and unearned income may also enter into welfare, but since these are constant over space, we suppress them. A variable [X.sub.i] that influences wages must have an offsetting impact on either prices or amenities that satisfies d[W.sub.i]/d[X.sub.i] + [summation over (j)] ([V.sub.P]/[V.sub.W] d[P.sub.i.sup.j]/d[X.sub.i]) + [V.sub.[theta]]/[V.sub.W] d[[theta].sub.i]/d[X.sub.i] = 0. If amenities are fixed, if the only nontraded good is housing, and if everyone consumes exactly one unit of housing, then d[W.sub.i]/d[X.sub.i] = d[P.sub.i.sup.j]/d[X.sub.i]. Any wage increase is exactly offset by a price increase.

The spatial equilibrium assumption has significant implications for urban policy. If individuals are more or less indifferent to location, then there is no natural redistributive reason to channel government support to poor places. The logic of the spatial equilibrium insists that the residents of those places are not particularly distressed, at least holding human capital constant, because low housing prices have already compensated them for low incomes. Moreover, the equilibrium's logic also suggests that governmental attempts to improve incomes in poor places will themselves create an equal and offsetting impact on housing prices. If the spatial equilibrium assumption holds, then property owners, not the truly disadvantaged, will be the main beneficiaries of aid to poor places.

How strong is the evidence supporting the spatial equilibrium assumption? The striking disparities in income and productivity across American regions might seem to be prima facie evidence against it. Table 1 presents some figures for the U.S. metropolitan areas with the highest and lowest values of several relevant characteristics. The top panel lists the top and bottom five metropolitan areas ranked by gross metropolitan product (GMP) per capita. These figures are produced by the Bureau of Economic Analysis; they are meant to be comparable to gross national product in that they attempt to measure an area's entire output. (The figures are based on the output of the people who work in the area, not of the people who live there.) By this measure Bridgeport, Connecticut (which includes Greenwich), Charlotte, North Carolina, and San Jose, California, are the most productive places in the United States, with GMP per capita in the range of $60,000 to $75,000 in 2005. The five least productive places all have GMP figures less than one-third of the low end of that range: GMP per capita in Brownsville, Texas, America's least productive metropolitan area, was about $16,000 in 2005. The relationship between income per capita and GMP, shown in figure 1, is very tight, with a correlation coefficient of 75 percent. (4)

The next panel of table 1 shows the disparity in family income between the five richest and the five poorest metropolitan areas. The five poorest areas have median family incomes less than half those in the five richest.

For these remarkable income differences to be compatible with the spatial equilibrium model, high prices or low amenities must offset higher incomes in the richest areas. The strongest piece of evidence supporting this view is that there are no legal or technological barriers preventing any American from moving from one metropolitan area to another, and indeed mobility across areas is enormous. Forty-six percent of Americans changed their place of residence between 1995 and 2000, half of them to a different metropolitan area. Critics of the spatial equilibrium assumption can argue, however, that moving costs--both financial and psychological--are often quite high. The existence of these costs leads us to examine other evidence on the existence of a spatial equilibrium.

[FIGURE 1 OMITTED]

One reason spatial income differences may not reflect differences in welfare for similarly skilled people is that people in different places do not have similar human capital endowments. The third panel of table 1 shows the differences across metropolitan areas in the share of the adult population with a college degree. Bethesda, Maryland, is one of the richest urban areas in the country, and more than half of its adults have college degrees. By contrast, fewer than one in ten adults in the least educated metropolitan areas have college degrees. The poorest metropolitan areas also have more non-native English speakers and more residents who speak English poorly or not at all. For example, more than three-quarters of the residents of McAllen, Texas, speak a language other than English at home.

One simple exercise is to compare the standard deviation of wages across metropolitan areas before and after controlling for observable individual-level human capital variables, such as years of schooling. The standard deviation of mean wages across metropolitan areas drops by 26 percent when we control for individual characteristics, suggesting that differences in human capital account for about half of the variance in metropolitan-area wage levels. (5) There are also important differences in unobserved human capital, which may themselves be a product of the differing experiences and role models across particular locales.

Even after accounting for differences in human capital, however, large differences in earnings remain across metropolitan areas. For the spatial equilibrium model to be correct, these differences must be offset by variation in the cost of living and amenities. The bottom panel of table 1 shows the disparities in housing prices across areas using Census data on housing prices. In the five most expensive areas, three of which are in California, the value of the median house was $309,000 or more in the 2000 census. According to National Association of Realtors (NAR) data on recent housing sales, the average sales prices for San Jose and San Francisco were $852,000 and $825,000, respectively, in the third quarter of 2007. Meanwhile prices below $60,000 are the norm in the five cheapest metropolitan areas. These places are again primarily in Texas, although Danville, Illinois, and Pine Bluff, Arkansas, are also among the least expensive areas. (6)

High incomes and high prices go together across metropolitan areas. Regressing the logarithm of income on the logarithm of housing prices across areas yields a coefficient of 0.33, which is reassuringly close to the share of housing in average expenditure. (7) Figure 2 shows a strong relationship (the correlation is 70 percent) between income per capita and house prices across metropolitan areas. For every extra dollar of income, prices increase by nearly ten dollars. This relationship means that higher housing costs exactly offset higher incomes if each extra dollar of housing cost is associated with l0 cents of annual expenses in interest payments, local taxes, and maintenance, net of any capital gains associated with living in the house. This figure does not seem unreasonable for many areas of the country.

Even though higher housing costs absorb much of the added income in high-wage places, they are only one of the costs of moving into a high-income area--many other goods are also more expensive. The American Chamber of Commerce Research Association (ACCRA) has assembled cost indices on a full range of commodities across metropolitan areas. Figure 3 shows the relationship between the logarithm of the ACCRA price index and the logarithm of income per capita, both as of 2000. The correlation between these variables is 54 percent, and as the ACCRA index goes up by 0.1 log point, personal income rises by 0.08 log point. Higher prices are offset by higher incomes, just as the spatial equilibrium model predicts.

[FIGURE 2 OMITTED]

Of course, there is still plenty of heterogeneity in real incomes across space. The spatial equilibrium model implies that lower real incomes must be offset by higher amenities. One of these is a pleasant climate. Figure 4 shows the relationship between average January temperature and real wages in 2000: warmer places pay less, just as the spatial equilibrium model suggests. A large literature shows that real incomes are lower where amenities are high. (8)

If it is much better to live in a high-income place, then one would expect population to be flowing toward richer areas. However, figure 5 shows a lack of any relationship across metropolitan areas between population growth from 1980 to 2000 and income per capita in 1980. People are not moving disproportionately to higher-income areas. The stability of the spatial equilibrium model is also supported by the relatively weak convergence of incomes across metropolitan areas in recent decades. If higher incomes in some areas represented some disequilibrium phenomenon, one would expect firms to abandon those areas and workers to gravitate toward them. Both forces would tend to make incomes converge. (9) But as we have documented elsewhere, the 1980s saw essentially no convergence, and in the 1990s convergence was much weaker than in the 1970s. (10)

[FIGURE 3 OMITTED]

One final piece of evidence comes from happiness surveys. We reject the view that responses to questions about happiness are a direct reflection of consumer welfare--we see no particular reason why utility maximization should be associated with any particular emotional state, even one as desirable as happiness. Still, a strong tendency of people who live in poor areas to report lower levels of happiness would be seen as a challenge to the spatial equilibrium approach. Using the General Social Survey between 1972 and 2006, we form self-reported happiness measures at the metropolitan-area level using the fraction of respondents who report being happy. (11) Figure 6 shows no relationship between self-reported happiness and income per capita--people do not seem any less happy in places that are poorer.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

These facts certainly do not prove that the spatial equilibrium assumption holds. Given that amenities are part of any region's appeal and that it is impossible to know how much people value those amenities, it is effectively impossible to prove that welfare levels are equalized across space. A better way to describe the evidence is to say that many empirical facts are compatible with the spatial equilibrium assumption, and few, if any, would cause us to reject the assumption. Of course, we accept that welfare might not be equalized in the short run. A negative shock to an area's productivity will lead to a reduction in income that is not immediately capitalized into housing costs. (12) Moreover, when such capitalization does occur, homeowners will face a real decline in wealth in response to the area's economic troubles. The spatial equilibrium assumption is best understood as a characterization of the medium and long runs, not year-to-year variation in regional well-being.

[FIGURE 6 OMITTED]

Economic Policy and Urban Theory

We will now fully specify a model to guide both our empirical work and our policy discussion. For our empirical work, we will assume that production and utility functions are Cobb-Douglas. But since these forms generate policy prescriptions that do not hold generically, we will have to move to a somewhat more general formulation when we discuss the implications for national policy.

We assume that individuals have Cobb-Douglas utility with a multiplicative amenity factor. We assume that they face a proportional tax rate of [t.sub.i], so that the indirect utility function can be written as [U.sub.i] = [[theta].sub.i[([N.sub.i])(1 [t.sub.i]) [W.sub.i][[PI].sub.j][([P.sup.j.sub.i]).sup.-[[beta].sub.j]. The spatial equilibrium assumption is that utility in each area is equal to a reservation utility [U.bar], which implies

(1) log([W.sub.i]) = log([U.bar]) - [[summation].sub.j][[beta].sub.j] log([P.sup.j.sub.i]) - log(1 - [t.sub.i]) - log[[[theta].sub.i]([N.sub.i])].

With a slight abuse of notation, we assume that [[theta].sub.i]([N.sub.i]) = [[theta].sub.i][N.sup.-[sigma].sub.i], to capture possible congestion externalities. On the production side, we restrict the model to two goods: one traded good that has a fixed price of one, and one nontraded good with an endogenously determined price of [P.sub.i]. The share of spending on the nontraded good is denoted [beta], so overall utility is [[theta].sub.i][N.sup.-[sigma].sub.i](1 - [t.sub.i])[W.sub.i] [P.sup.-[beta].sub.i].

The traded sector is characterized by free entry of firms that produce traded goods according to a constant-returns-to-scale production function [A.sub.i]([N.sub.i])[F.sub.i]([L.sub.i], [K.sub.T,i], [K.sub.N,i]). We let [A.sub.i]([N.sub.i]) = [a.sub.i][N.sup.[omega].sub.i], which is meant to capture the level of productivity in the area, which may be increasing in the total number of people working in the area. L represents labor, [K.sub.T] a vector of traded capital inputs, and [K.sub.N] a vector of nontraded capital inputs. A fixed supply of nontraded capital implies that a production function that displays constant returns to scale at the firm level will display diminishing returns at the area level--at least if agglomeration economies are not too strong. If the production function is written as [F.sub.i]([L.sub.i], [K.sub.T,i], [K.sub.N,i]) = [a.sub.i][N.sup.[omega].sub.i][K.sup.[alpha][gamma].sub.N,i] [K.sup.[alpha](1 - [gamma]).sub.T,i][L.sup.1[alpha].sub.i], and if nontraded capital in the area is fixed (denoted [[bar.K].sub.N,i]), then labor demand in the area can be written [Q.sub.w][([a.sub.i][N.sup.[omega].sub.i] [K.sup.[alpha][gamma].sub.N,i][W.sup.[alpha] - 1 [alpha] [gamma].sub.i]).sup.1/[alpha][gamma]], where [Q.sub.w] is constant across areas.

We assume a housing sector characterized by free entry of firms with access to a production technology [H.sub.i]G(L, [K.sub.T], [K.sub.N]). [H.sub.i] represents factors that impact the ability to deliver housing cheaply, and G(., ., .) is a constant-returns-to-scale production function. The housing production function is [H.sub.i][[bar.Z].sup.[mu][eta].sub.N,i] [K.sup.[mu](1 - [eta]).sub.T][L.sup.1 - [mu]], where [[bar.Z].sub.N,i] represents the nontraded input into housing (land), which we assume is different from the nontraded input into the traded goods sector. To account for the returns to nontraded capital inputs (land), we assume they go to rentiers who also live in the area. They have the same Cobb-Douglas utility functions as workers but do not work or noticeably affect aggregate population. Instead they are a wealthy but small portion of the population; because of their wealth they contribute to demand for the nontraded good, but because of their negligible number they do not add to area population. Thus, [N.sub.i] equals only the sum of labor used in the two sectors. The government also spends a share [beta] of its revenue on the nontraded good.

We now define our equilibrium concept:

Definition: In a competitive equilibrium, wages equal the marginal product of labor in both sectors, individuals optimally choose housing consumption, and utility levels are constant across space.

The spatial equilibrium condition, labor demand, and equilibrium in the housing sector produce solutions for population, wages, and prices:

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [[kappa].sub.N], [[kappa].sub.w], and [[kappa].sub.p] depend on the tax rate and constants, and [bar.[omega]] = ([sigma] + [beta][mu][eta])(1 - [alpha] + [alpha][gamma]) + ([alpha][gamma] - [omega])[1 - [beta](1 - [mu + [mu][eta])]. This system of equations will guide our discussion of the empirical work on agglomeration economies. These equations show that an exogenous increase in area-level productivity or amenities will impact population, wages, and prices. In urban research all three outcomes must be used to understand the impact of an intervention.

The most natural social welfare function is [[summation].sub.i][N.sub.i] [[theta].sub.i](1 -[t.sub.i])[W.sub.i][P.sup.[beta].sub.i], which equals the (fixed) total population times individual utility (which will be constant across people). We also include the welfare received by rentiers; if total rentier income is [Y.sub.i, and the size of this group is fixed exogenously, then the additive utility function that includes rentiers can be written as [[summation].sub.i][[theta].sub.i](1 - [t.sub.i])([N.sub.i][W.sub.i] + [Y.sub.i])[P.sup.-[beta].sub.i].

Our first policy question concerns the optimal local tax level to fund local amenities. We assume that local amenities are a function of local spending and population, so that [[theta].sub.i] = [g.sub.i]([t.sub.i] [W.sub.i][N.sub.i], [N.sub.i]). These amenities could include public safety, parks, and schools. Following Truman Bewley, (13) two assumptions are typical in the literature. Amenities may be a pure public good, meaning that there is no depreciation with population size and [theta] = [g.sub.i]([t.sub.i][W.sub.i][N.sub.i]), or a pure public service, which means that output is neutral with respect to population and [[theta].sub.i] = [g.sub.i]([t.sub.i] [W.sub.i]). We assume the latter so that amenities are a function of individual taxes. (14)

Proposition 1: The allocation of people across space in a decentralized equilibrium maximizes social welfare. If an individual's amenity level [[theta].sub.i] is a function of that individual's tax payments, then the area-specific tax that maximizes the sum of utility levels across areas is also the tax that maximizes utility within each area when holding population constant. A local government that seeks to maximize population will choose tax rates that maximize the sum of total utility levels, whereas a local government that seeks to maximize wages per capita will minimize social welfare. Housing prices should be maximized if agglomeration economies are sufficiently large or house production is sufficiently capital intensive, and minimized otherwise.

In this model, agglomeration economies do not change the optimal policies for local governments. Maximizing population was desirable even without agglomeration economies; the existence of such economies only provides another reason for its desirability. The result that population maximization is optimal is not general, however. In some cases local governments must decide between actions that improve the welfare of existing citizens and actions that attract more citizens. Restrictions on land use development are a pertinent example of a policy that reduces area population growth but may increase the quality of life for existing residents. When a conflict arises between attracting more people and caring for current residents, agglomeration economies will tend to strengthen the case for policies that attract new residents.

Despite the existence of externalities, our assumptions about functional forms imply that there are no welfare gains from reallocating people across space. (15) The key to this result is that our functional forms imply that the elasticity of welfare with respect to population is constant. To address spatial issues more generally, we will need a more general formulation for agglomeration economies.

This observation notwithstanding, Proposition 1 does not rule out a role for government. Indeed, by assumption the government provides the amenity level, so there is an inherent role for government spending. The proposition does imply, however, that decisionmaking about optimal spending can ignore population responses and simply maximize the welfare of the current population. A decentralized decisionmaking process, where individual areas choose tax and amenity levels to maximize the welfare of their citizens, will yield a Pareto optimal population distribution. This result depends on the functional form that guarantees a constant elasticity of well-being with respect to population.

The proposition also hints at some of the key results from urban public finance. When localities maximize population or property values, they will also be maximizing utility and choosing an optimal tax level. If they try to maximize income per capita, however, they will actually be minimizing social welfare. In other settings, of course, maximizing population does not yield socially beneficial results. For example, if one area suffers a negative externality from congestion and another area has no such congestion, it will not maximize social welfare for the congestion-prone area to try to maximize population. A distinguished literature, following Henry George, (16) shows that choosing policy to maximize local land values is usually the most reliable way to achieve a Pareto optimum. (17)

To derive more general results about the location of people across space, we move to a more general model and ignore the role of government in creating local public goods. We will also suppress the terms for capital and write output of nontraded goods in an area as [A.sub.i]([N.sub.i])[F.sub.i] ([N.sub.i] - [L.sub.i]), which represents total output of nontraded goods minus the costs of traded capital, assuming that traded capital is chosen optimally. Likewise, we write production of housing as [G.sub.i]([L.sub.i]), which again is meant to be net of traded capital. Utility is U[[Y.sub.i], [H.sub.i], [[theta].sub.i]([N.sub.i])], where [Y.sub.i] is net income, which may include rental income, minus housing costs. The next proposition then follows:

Proposition 2: (a) A competitive equilibrium where net unearned income is constant across space is a social optimum if and only if U[Yi,[[theta].sub.i] ([N.sub.i])] and [N.sub.i][[theta]'.sub.i]([N.sub.i])[U.sub.[theta],i] + [U.sub.Y][A'.sub.i]([N.sub.i])F([N.sub.i] - [L.sub.i]) are constant across space, where [U.sub.[theta],i] is the marginal utility of amenities in location i.

(b) If either all unearned income from an area goes to the residents of that area, or the marginal utility of income is constant across space, then moving individuals from area j to area i will increase total welfare relative to the competitive equilibrium if and only if

[[theta].sub.i]([N.sub.i])[U.sub.[theta],i] [N.sub.i][[theta]'.sub.i] ([N.sub.i])/[[theta].sub.i]([N.sub.i]) + [U.sub.Y,i] [N.sub.i][A'.sub.i] ([N.sub.i])/[A.sub.i]([N.sub.i]) [A.sub.i]([N.sub.i])[F.sub.i]([N.sub.i] [L.sub.i])/[N.sub.i] is greater than

[[theta].sub.j]([N.sub.j])[U.sub.[theta],j] [N.sub.j][[theta]'.sub.j] ([N.sub.j])/[[theta].sub.j]([N.sub.j]) + [U.sub.Y,j] [N.sub.j][A'.sub.j] ([N.sub.j])/[A.sub.j]([N.sub.j]) [A.sub.j]([N.sub.j])[F.sub.j]([N.sub.j] [L.sub.j])/[N.sub.j].

Part (a) of Proposition 2 reveals two reasons why a spatial equilibrium may not be a social optimum. First, a spatial equilibrium equates total utility levels across space, not marginal utilities of income. (18) Thus a planner could increase welfare by transferring money to areas where the marginal utility from traded-goods consumption is high, and holding population levels constant. (19) Since everyone is identical ex ante, there is no natural means of placing different social welfare weights on different individuals to eliminate the gains from redistribution that come from different marginal utilities of income.

The Cobb-Douglas utility functions discussed above imply that the marginal utility of income equals total utility (which is constant across space) divided by income. In this case redistributing income to poor places is attractive--if population can be held fixed--not because poorer places have lower welfare but because they have a higher marginal utility from spending. This result would disappear if poor places had amenities that were substitutes for rather than complements to cash. (20)

The second reason for government intervention arises if [N.sub.i] [[theta]'.sub.i]([N.sub.i])[U.sub.[theta],i] + [U.sub.Y][A'.sub.i]([N.sub.i]) F([N.sub.i] - [L.sub.i] is not constant across space. In the absence of congestion and agglomeration economies, the competitive equilibrium is a social optimum. Alternatively, if the sum of agglomeration plus congestion effects were (somewhat magically) the same everywhere, the decentralized equilibrium would be a social optimum. These unusual circumstances were satisfied under the functional forms described above, which reflect a constant elasticity of amenities and agglomeration with respect to population. Those conditions, and the assumption about the functional form of the utility function, ensured that welfare could not be improved by moving population around.

Another way to understand the benefits from subsidizing places is to consider moving people from one region to another, as discussed in part (b) of Proposition 2. Gains can accrue from reallocating people to an area if either the amenity elasticity is lower there or the agglomeration economies are higher. The condition on agglomeration economies multiplies the agglomeration elasticity [N.sub.i][N'.sub.i]([N.sub.i])/[A.sub.i] ([N.sub.i]) by [U.sub.Y,i] [A.sub.i]([N.sub.i])[F.sub.i](N.sub.i - [L.sub.i]/ [N.sub.i]; in words, it is the product of the marginal utility of income and output per capita in the nontraded sector. This second term implies that it is desirable to move people to richer areas if the marginal utility of income is constant across space. We will focus on the differences in agglomeration elasticities in the next section.

Agglomeration Economies

Two important facts support the existence of agglomeration economies: the spatial concentration of economic activity, and the tendency of densely populated areas to be richer and more productive. The majority of the world now lives in cities, and hundreds of millions of people crowd into a small set of particularly large megacities. Industries are also often spatially concentrated. (21) In principle, the concentration of people in cities and of industries in clusters could simply reflect exogenous differences in productivity. This view may well be accurate for the nineteenth century, when, for example, hundreds of thousands came to New York to enjoy the productive advantages created by its natural harbor. In the twenty-first century, however, it is hard to think of any comparable exogenous advantages that could explain massive urban agglomerations. Glenn Ellison and Glaeser find that a large battery of local characteristics can explain less than one-fifth of the concentration of manufacturing industries across space. (22) Since so much clustering occurs without an obvious exogenous cause, urban economists have tended to interpret it as the result of endogenous gains from co-location, which are referred to as agglomeration economies.

The belief in agglomeration economies is also bolstered by the robust correlations between income or productivity and urban density. Figure 7 shows the relationship between the logarithm of GMP per capita and the logarithm of metropolitan-area population. City size explains one-quarter of the variation in GMP per capita (that is, the correlation is 0.50), and the elasticity of productivity with respect to city size is 0.13.

[FIGURE 7 OMITTED]

Because GMP data have been available for only a few years, earlier researchers looked at either metropolitan-area income or state-level productivity measures. Antonio Ciccone and Robert Hall show the remarkably strong correlation between state productivity and the degree to which the population within a state is concentrated in a small number of dense counties. (23) Glaeser and David Mare show that the urban wage premium does not seem to reflect differential selection of more-skilled people into big cities. (24) They do find, however, that recent migrants to cities experience only a small portion of the urban wage premium immediately, instead reaping most of the gains through faster wage growth. The steep age-earnings profile in cities suggests that cities may speed the pace of human capital accumulation.

The great challenge facing research on the connection between city size and income is that this connection may reflect the tendency of people to move to already-productive areas, rather than any sort of agglomeration economy. Ciccone and Hall address this reverse causality issue by turning to historical variables, such as nineteenth-century population and railroad density. Pierre Philippe Combes, Gilles Duranton, and Laurent Gobillon pursue a similar exercise using French data. (25) Using these variables as instruments for density, these authors continue to find a strong connection between density and economic productivity. However, as we will discuss later, historical instruments of this kind do not naturally solve the identification problem in a spatial model such as the one described above.

Since the public policy implications of agglomeration economies depend on the size and nature of those economies, table 2 reproduces these standard approaches to measuring agglomeration using individual-level data from the 2000 Census. We run the regressions using only prime-working-age men (those between the ages of 25 and 55) to avoid capturing variation from differences in labor force participation, but similar results obtain when we include all employed adults. Regression 2-1 in table 2 shows the basic correlation between the logarithm of population in a metropolitan area and the logarithm of wages, holding individual-level controls constant. The measured elasticity is 0.041, meaning that as population doubles, income increases by a little more than 2.8 percent. If population is exogenously distributed, then the Cobb-Douglas functional forms above imply that the measured elasticity of wages with respect to area population equals [omega] + [alpha][gamma]/1 - [alpha] + [alpha][gamma]; thus if labor's share in output is two-thirds, then the agglomeration parameter [omega] equals 1.041 times [alpha][gamma], the share of nontraded capital in production, plus 0.027.

Regression 2-2 in table 2 examines whether the elasticity of wages with respect to population differs between big and small cities. It is specified as a piecewise linear regression with a break at the median population across our sample of metropolitan areas, thus allowing the impact of area population to be bigger or smaller for larger areas. The estimated elasticity is higher for smaller cities (0.076 versus 0.038), but the difference is not statistically significant.

Some agglomeration theories focus on area size, others on population density. Regression 2-3 includes both population and density as independent variables. The coefficients on the two variables are similar, at 0.023 and 0.029, respectively. Regression 2-4 is a piecewise linear regression for both density and population. Again the estimated coefficient on population is stronger for smaller cities. However, the estimated coefficient on density is stronger for areas with more people per acre, but the difference in the density coefficients is not statistically significant.

Regression 2-5 follows Ciccone and Hall and uses historical data--population of the metropolitan area in 1850--to instrument for current population. (26) We have data for only 210 metropolitan areas from this period, so our sample size shrinks. The estimated coefficient on population in this regression is actually higher than that in regression 2-1, which suggests that the population-income relationship does not reflect the impact of recent population movement to more productive areas.

The model clarifies what we need to assume for instrumental variables regressions such as this one to be interpreted as estimates of agglomeration economies. If historical population affects wages by raising productivity, perhaps because it is associated with investment in nontraded infrastructure, then the estimated coefficient will equal [alpha] - [micro][eta][beta]/1 - [beta](1 - [mu] + [micro][eta], which is also what ordinary least squares would estimate if cross-city variation came from heterogeneity in productivity. These parameters do not tell us anything about agglomeration economies, but instead provide us with information about decreasing returns in the housing sector. If, however, historical population acts through housing supply or amenities, then the estimated instrumental variables coefficient will equal [omega] - [alpha][gamma]/1 - [alpha] + [alpha][gamma] which can be transformed to get an estimate of agglomeration economies. This would also be the ordinary least squares coefficient if the exogenous spatial variation came entirely from amenities or housing supply.

Table 2 raises two challenges for economic policy. First, these simple correlations between income and area population may not be instructive about agglomeration economies, since they could result from omitted productivity. Second, even the ordinary least squares relationships fail to find a clear difference in agglomeration economies between bigger and smaller areas or between more and less dense areas. Since the rationale for agglomeration-based spatial interventions requires agglomeration elasticities to be different in different types of areas, we next look for this effect using more complex estimation techniques. But uncovering differences in elasticities that are not visible using ordinary least squares is a tall order.

Estimating Agglomeration

The urban model presented in equations 2 through 4 implies that agglomeration economies can be estimated if we have exogenous sources of variation that impact amenities or housing supply, but not productivity. If agglomeration economies exist, then the extra population brought in by amenities should raise productivity. The mean temperature of an area is certainly an amenity: people prefer milder climates. We therefore use climate data to see whether places that attract more people because of their climate also see an increase in wages.

January temperature and precipitation are both relatively reliable predictors of urban growth in postwar America. Regressing the change in population between 1970 and 2000 on these two variables yields the following equation:

(5) log ([population.sub.2000]/[population.sub.1970]) = 0.0603 +
 (0.0549)

 0.0166
(0.0012) temperature

 0.0068 precipitation
(0.0011)

The adjusted [R.sup.2] is 0.39 and there are 316 observations; standard errors are in parentheses. One interpretation of these correlations is that they reflect the interaction between climate and new technologies, such as air conditioning, that make warm places relatively more appealing. Glaeser and Kristina Tobio argue that warm areas tend also to have had more-permissive land use regulations. (27) An alternative approach might therefore be to use the Wharton Land Use Index, which measures the restrictiveness of the building environment, to capture variation related to housing supply. (28) In both cases identification hinges critically on these variables being orthogonal to changes in productivity at the local level, except insofar as the productivity changes are due to agglomeration economies. We cannot be sure that this is the case, but given the absence of other alternatives we will use variation in climate as our instrument.

Using the model above, we assume that our climate-based instruments predict changes in the housing supply and amenity variables, log[([H.sub.i] [[bar.Z].sup.[micro][eta].sub.N,i]).sup.[beta] + log([[theta].sub.i]), but not changes in the productivity variable log([a.sub.i][[bar.K].sup.[alpha][gamma].sub.N,i]). In this case the univariate regression of wage growth on population growth will estimate [omega] - [alpha][gamma]/1 - [alpha] + [alpha][gamma]. By examining the interaction of this treatment effect with other area-level characteristics, we can determine whether co appears to be higher in some places than in others. This procedure also requires [alpha] and [gamma] to be constant across space.

Taking the logarithm of our baseline wage equation (equation A1 in appendix A) yields the following relationship between the wage of person j and the size of metropolitan area i, where the person lives:

(6) log([W.sub.j]) = ([b.sub.0] + [b.sub.1][X.sub.i])log([N.sub.i,t]) + [sigma][Z.sub.j] + [[zeta].sub.i] + [[epsilon.sub.j].

The vector [Z.sub.j] represents individual characteristics, such as age and education, and [sigma] the vector of coefficients on Z at time t. Each metropolitan area has a fixed effect, [[zeta].sub.i], due to nontraded capital and MSA-specific noise, and the error term [[epsilon].sub.j] represents the effect of any unobservable individual characteristics as well as noise in setting the wage. Population size [N.sub.i.t] impacts the wage through the coefficient [b.sub.0] + [b.sub.1][X.sub.i] which equals [omega] - [alpha][gamma]/1 - [alpha] + [alpha][gamma]. The possibility that these coefficients might be different for different types of cities is captured by the term [b.sub.1][X.sub.i] which allows city-level characteristics, [X.sub.i], to impact the agglomeration economy. This procedure requires [b.sub.0] and [b.sub.1] to be constant across space. If we also assume them to be constant over time, then we can write

(7) log([W.sub.j]) = ([b.sub.0] + [b.sub.1][X.sub.i])log([N.sub.i,t + 1]) + ([sigma] + [tau])[Z.sub.j] + [[zeta].sub.i] + [[epsilon].sub.j],

where [tau] augments [sigma] because we allow the effect of individual characteristics to change over time. We can rewrite equation 7 to show an explicit dependence on population growth:

(7') [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In equation 7' the MSA-level fixed effect becomes [[mu].sub.i] = ([b.sub.0] + [b.sub.0] + [b.sub.1][X.sub.i]) log([N.sub.i,t]) + [[zeta].sub.i]. This is also the estimated MSA-level fixed effect in equation 6, so we can write

(6') log ([W.sub.j]) = [sigma][Z.sub.j] + [[mu].sub.i] + [[epsilon].sub.j].

We will estimate [b.sub.0] and [b.sub.1] by pooling equations 6' and 7' together for Census years 1990 and 2000. We can thus run

(8) log([W.sub.j]) = ([b.sub.0] + [b.sub.1][X.sub.j])log([N.sub.i,2000 / [N.sub.i,1990])[I.sub.2000] + [sigma][Z.sub.j] + [tau][Z.sub.j] [I.sub.2000] + [[mu].sub.i] + [[epsilon].sub.j],

where [I.sub.2000] is a dummy variable equal to one for observations in 2000.

We first estimate equation 8 as an ordinary least squares regression, omitting any interactions with population growth. Results are presented as regression 3-1 in table 3, and the sample again includes only prime-working-age men. The coefficient on population growth is strongly positive, indicating that expanding cities are also getting more productive. In regression 3-2 we attempt to identify the effect by using January temperature, July temperature, and precipitation as instruments for population growth between 1990 and 2000. If [b.sub.1] = 0, this should yield an unbiased estimate of [b.sub.0] = [omega] - [alpha][gamma]/1 - [alpha] [alpha][gamma]. The coefficient drops to 0.004, implying that a doubling in population is associated with a 0.3 percent increase in wages. But this coefficient does not mean that agglomeration economies are absent. The theory predicts that wages will only increase with population ([b.sub.0] > 0) if population is a larger input into production than fixed capital. If [b.sub.0] = 0, then [omega] = [alpha][gamma]; that is, extra population is just as valuable as extra fixed capital, and increasing prices absorb all of the gains from agglomeration.

We have little empirical guidance on the amount of nontraded capital in the production function. Eventually, all capital may be endogenous, but over the course of a decade or two, much capital is relatively fixed. The user cost of commercial real estate provides one possible source of information on the fraction of fixed capital in the economy's aggregate production function. If this real estate is worth the $5.3 trillion claimed by Standard and Poor's (2007), then assuming the same 10 percent user cost as for residential real estate gives a contribution of $530 billion to U.S. GDP, or about 4 percent. Assuming [alpha] to be one-third, fixed capital would thus represent [gamma] = 0.12, or 12 percent of all capital.

The coefficient of 0.004 estimated in regression 3-2 gives a point estimate indicating that agglomeration is only slightly more important than fixed capital, although the large standard errors make the true agglomeration effect hard to estimate. The 95 percent confidence interval on our estimate ranges from -0.19 to 0.2; with [alpha][gamma] = 0.04 (12 percent of one-third), the former implies that co = -0.09 and the latter yields co = 0.18. A higher value of y would push both of these estimates upward, and a lower value would reduce them.

The main implication of the model was that policy should subsidize places where the elasticity of productivity with respect to population is higher than elsewhere. One significant question is whether agglomeration economies are greater for larger or smaller cities, and table 2 suggested the latter. To test this hypothesis, regressions 3-3 through 3-5 interact the log of population in 2000 with various variables [X.sub.i] intended to capture larger, denser, and declining cities, respectively. We now instrument for population growth with the weather variables as well as the weather variables interacted with [X.sub.i].

We first explore whether adding people has more of an effect on the productivity of larger places. Regression 3-3 thus uses a dummy variable indicating whether an MSA's population was above the sample median in 1990 for [X.sub.i]. A positive coefficient 5 on the interaction between this dummy and population growth would imply that adding population is in fact more valuable for the productivity of larger places, but we find no significant evidence for any such interaction. The impact of population on productivity seems to be the same for both smaller and larger metropolitan areas.

Another possibility is that growing population has more of a positive effect in areas that are more geographically compact, with a dense urban core. To test this hypothesis, regression 3-4 uses a measure of centralization--the share of employment in the area that lies within five miles of the central business district--as the interaction variable. These data are based on zip code employment data described by Glaeser and Matthew Kahn. (29) The data would ideally come from before 1990 but are available only from 1998. In this regression the coefficient [delta] is small and statistically insignificant. We cannot conclude that density increases productivity more in faster-growing cities than in others.

Regression 3-5 examines whether agglomeration economies seem to be greater in places that were previously in relative decline. We let [X.sub.i] an indicator variable that takes a value of one if the area was in the bottom quartile of population growth (that is, had population growth of 7.08 percent or less) between 1970 and 1990. This regression shows that having been in relative decline reduces productivity, but this effect is dampened slightly for larger cities. This result suggests that population increases may be most advantageous in areas that have already been in decline.

This analysis does not offer a compelling answer as to where agglomeration economies are strongest. We look for differences based on size, compactness, and past decline and are unable to uncover convincing differences. If anything, the table suggests that agglomeration effects are stronger in smaller metropolitan areas, more centralized metropolitan areas, and metropolitan areas that have been in decline. However, all of these measured effects are statistically insignificant and not robust. Until further research yields more precise estimates, these results suggest the difficulty of establishing any clear gains to subsidizing one region or another.

Congestion Externalities

We now turn to the impact that metropolitan-area size has on amenities. We will first look at the connection between area population and three direct measures of urban disamenities: commute times, pollution, and crime. We will then consider real wages. In all of these cases we remain concerned that the disamenity is itself influencing urban population. However, since the costs of these disamenities are arguably minor relative to overall income, we are more comfortable looking at the ordinary least squares coefficients. Since the case for national spatial policies depends on different effects of population on amenities across different cities, our focus will be on whether the slope of population is different for cities that are larger or more centralized.

Regression 4-1 in table 4 examines the connection between average commute time and population. The basic elasticity is 0.12, meaning that as city size doubles, the average commute increases by 8.7 percent, or about two minutes. We also investigate whether this coefficient is larger for cities above the median population in our sample. The interaction is tiny in both economic and statistical terms. In fact, the interaction is sufficiently precisely estimated that we can reject the hypothesis that the elasticity of commute times with respect to population increases or decreases by any significant amount for larger cities.

Regression 4-2 in table 4 considers the interaction between area population and centralization, again using Glaeser and Kahn's data on the share of employment within five miles of the city center. (30) In this case we find a marginally significant interaction. Increasing population has a bigger effect on commute times in denser cities than in cities where the population is more dispersed.

Regression 4-3 looks at the atmospheric concentration of TSP-10 particulates, one of the key measures of air quality at the metropolitan-area level. (31) The elasticity of this variable with respect to city size is 0.142, which is statistically significant: bigger cities have slightly worse air. However, we do not find a larger slope for bigger cities. Regression 4-4 adds a variable interacting city size with centralization. We find that city population has a weaker effect on pollution in more centralized places, perhaps because people there are more likely to use public transportation.

Regression 4-5 focuses on crime, another disamenity generally associated with urban size. Glaeser and Bruce Sacerdote provide evidence that although some of this connection reflects the sorting of crime-prone individuals into urban areas, it partly also reflects the tendency of big cities to increase the supply of potential victims and make arrest and conviction more difficult. (32) This regression finds only a weak connection between murder and city size, although this has declined substantially over time. (33) Regression 4-6 finds no significant association between murder rates and centralization.

Regression 4-2 suggested that increasing population in centralized places has a more unfavorable impact on commute times, and regression 4-4 suggested that increasing population in centralized places has a small negative impact on pollution. The overall lesson for spatial policy is therefore unclear. We attempt to get around this by looking at real wages, which provide a measure of overall amenities. Since population is more likely to respond to the entire basket of amenities than to these individual disamenities, we are more concerned with problems of reverse causality in this regression.

Regression 4-7 investigates the elasticity of real wages with respect to area population. Neither the raw effect nor the interaction with population above the median is statistically significant. The failure to find a robust relationship confirms the spatial equilibrium assumption that agglomeration economies offer no free lunch: high nominal wages are offset by higher prices. The absence of a clear interaction means that there does not appear to be an amenity-based rationale for pushing population toward bigger or smaller cities.

Regression 4-8 finds a statistically significant negative interaction between area population and area centralization. Interpreted literally, this result implies that any negative effects of population on amenities are minimized in more centralized locales. In principle, this finding seems to suggest that pushing population toward more compact and less sprawling places might be welfare-enhancing.

Despite this finding, we have little confidence that either agglomeration or congestion externalities differ significantly across smaller or larger, or denser or less dense, cities. This does not reassure us that the current situation is a Pareto optimum, but it does suggest that it is not obvious which way government policy should deviate from the status quo. For us, this degree of ignorance suggests that explicit spatial policies are as likely to do harm as good.

U.S. Policies toward Places

In this section we turn to a brief empirical evaluation of three major types of policies related to urban growth. The first is transportation policy. America's most significant place-making policies have been improvements in transportation. Railroads in the nineteenth century and highways in the twentieth both had major impacts on the growth of different areas. Nonetheless, there is little evidence to suggest that the place-making capacities of transportation are actually working in a desirable ways As a result, transportation should be judged on its ability to reduce transport costs and not on its ability to remake the urban landscape. The second type of policy consists of large-scale interventions that had the direct goal of strengthening particular places. In the twentieth century, such interventions included urban renewal and the Appalachian Regional Commission. We find no clear effects of these policies, but this is unsurprising, because they involved small amounts of money relative to the sizes of the areas involved. The third type of policy is typified by the enterprise zones of the 1980s and 1990s, which provided much greater resources to much smaller areas. These policies do seem to have had an impact, but the costs per new job are extremely high.

Transportation and Place Making

American governments have been in the business of subsidizing transportation since the dawn of the Republic. Even before the Revolution, George Washington had contemplated a canal that would connect the Potomac River to the Ohio River valley and the western states. (34) After the Revolution, Washington's enormous prestige enabled him to get the support of the Maryland and Virginia legislatures to charter the Potomac Company. Washington served as its president. The states invested in the company, granted it a perpetual monopoly on water traffic along the Potomac, and gave it considerable powers to acquire land. Even with this support, the Potomac Canal was unable to fulfill its mission, and it collapsed in the mid-1820s. Construction along the route turned out to be enormously difficult, and the limited willingness of credit markets in 1800 to trust private companies with vast sums made it hard for any firm to raise sufficient finances to pay for such an expensive undertaking. The Potomac Company was not a complete failure, but it did not produce America's great waterway to the west.

That waterway would be created by an even more extensive governmental investment in transportation infrastructure. It seemed obvious to DeWitt Clinton, New York City's mayor during most of 1803-15, that connecting the country' s greatest seaport with the Great Lakes would yield enormous returns. (35) Clinton became one of the canal's greatest proponents, and when he was elected governor of New York State in 1817, he quickly began construction. To many contemporary observers, a New York canal looked no wiser than one in Virginia, and the idea was dubbed "Clinton's Folly." Yet with massive government spending and prodigious feats of engineering, Clinton managed to construct a canal that connected the Hudson River to Lake Erie.

The Erie Canal was an enormous success by any measure. Its toll revenues readily covered its costs, and, like the earlier success of the Bridgewater Canal in Manchester, England, it set off a national craze for canal building that changed the face of America. In 1816 it cost 30 cents to move a ton of goods a mile by wagon overland. At that price, moving goods fifteen miles overland cost the same as moving them across the Atlantic. The canal reduced the cost of transport by more than two-thirds, to less than 10 cents per ton-mile.

Urban economics certainly suggests that transportation infrastructure could have a major impact on urban growth. Some forms of transportation, like a port or a rail yard, significantly increase the productivity of adjacent land and therefore attract new businesses. Others, however, like the highway system, reduce the gains from clustering and hence disperse population. It is hard to accurately estimate the impact of the canals of the early nineteenth century on the economic development of different urban areas. It is occasionally claimed that the Erie Canal was critical to New York City's rise, but New York was already America's largest port before the canal, and Glaeser shows that it did not accelerate the city's growth. (36)

However, the growth of Syracuse, Rochester, Buffalo, and other cities of upstate New York was at least temporally connected with the canal. These cities are all close to the canal and grew as mercantile cities exploiting that proximity. Yet although individual histories certainly attest to the importance of canals in promoting urban growth, it is hard to tease out the impact of the Erie Canal statistically. For example, a regression of the logarithm of population growth for New York State counties between 1820 and 1840 on the logarithm of initial population and a dummy variable indicating whether the county contains or abuts the canal yields the following estimates:

(9) log([population.sub.1840]/[population.sub.1820])
= -3.4 - 0.08
 (0.7)-(0.12) * Erie Canal

+ 0.28
 (0.07) * log ([population.sub.1820])

The counties along the Erie Canal saw remarkable growth during this period, but there was remarkable growth everywhere--especially in those places that started at higher densities. The canal was surely important for the development of many places, but this regression raises questions about how to appropriately estimate its impact on regional growth.

By contrast, the growth of the railroads tends to be quite closely connected with different forms of local development. Michael Haines and Robert Margo show that areas that added rail transportation in the 1850s were much more likely to urbanize. (37) Although it would be hard to claim any sort of causality from such regressions, the correlations are striking.

Table 5 reports population growth regressions for the nineteenth-century United States using rail data from Lee Craig, Raymond Palmquist, and Thomas Weiss. (38) We construct a dummy variable indicating whether a county was accessible by rail in 1850 and then look at population growth both in the 1850s and for the rest of the century. Regression 5-1 looks at population growth in the 1850s and access to rail in 1850. We control for the logarithm of initial population, proximity to the ocean, and, as a proxy for human capital, the presence of Congregationalists in 1850. (39) There is a strong positive relationship between access to rail in 1850 and population growth in the ensuing decade: on average, those counties with access grew by more than 14 percent more than those without. Regression 5-2 looks at population growth over the entire 1850-1900 period and again finds a strong positive effect of rail access in 1850 on subsequent growth.

The Craig, Palmquist, and Weiss data also provide information on access to waterways in 1850, but for a smaller set of counties. We also find a significant effect for this variable for the 1850s: counties with access to water grew by 0.12 log point more, on average, than counties without access (results not reported).

It is easy to argue with these regressions. After all, rail yards were not randomly strewn throughout the United States, but rather were located in places considered to have the brightest economic future. Still, plenty of supporting evidence suggests that railroads were important for urban success. After all, civic boosters worked extremely hard to get rail lines to come through their towns. This would hardly have made sense if rail were not expected to have an impact. Moreover, case studies of most large American cities that grew rapidly in the nineteenth century, from Boston to Los Angeles, argue that rail played an important role in that growth.

In the nineteenth century, population growth accompanied rail access, and railroads seem to have particularly encouraged the growth of big cities. Initially, people and firms clustered around rail yards, as exemplified by Chicago's stockyards, to save transport costs. Later, intraurban railroads enabled cities to expand by facilitating commuting from "streetcar suburbs." (40) In the twentieth century, further declines in transportation costs accelerated the process of urban decentralization. Nathaniel Baum-Snow compellingly shows that suburbanization proceeded more rapidly in those cities that had more highway development. (41) He addresses the problems of reverse causality using an early highway plan developed for national security purposes.

Highway development also seems to have been strongly associated with the growth of metropolitan areas as a whole. Gilles Duranton and Matthew Turner show a striking connection between highways and urban growth in the United States over the last thirty years. (42) They use a number of different instruments, including the security-based highway plan used by Baum-Snow, to handle the issue of reverse causality. The raw correlations are impressive.

Regressions 5-3 and 5-4 in table 5 follow Duranton and Turner in reporting correlations between population and income growth, respectively, from 1960 to 1990 and highway mileage built during the same era. The first of these regressions shows the relationship between population growth and highway construction, controlling for initial population, proximity to the coast, and initial share of the population with a college degree. The elasticity of population growth with respect to new highway mileage is 0.11, and the coefficient has a t statistic of 4.3. Regression 5-4 reports the elasticity of growth in income per capita with respect to the same variables from 1960 to 1990. In this case the elasticity is 0.039 and the t statistic is again over 4. The extent to which we can be sure that highways were causing growth, rather than vice versa, depends on the validity of the instruments of Baum-Snow and Duranton and Turner, such as the initial highway plan based on national security needs. Yet it is certainly true that highways and growth move together quite closely.

[FIGURE 8 OMITTED]

More generally, the decline in transportation costs has been associated with a host of changes in urban form. Figure 8 documents the 90 percent reduction in the cost of moving a ton of goods one mile by rail, and figure 9 the parallel explosion of highway transport. These two developments mean that whereas it was enormously costly to move goods over space in 1900, transporting goods had become almost free 100 years later. Glaeser and Janet Kohlhase argue that this change has led to the rise of consumer cities, which are located in places where people want to live, rather than producer cities, which are located in places where firms have innate productive advantages due to waterways or coal mines. (43) That paper also argues that the decline of transportation costs helps explain the exodus of manufacturing from urban areas and the decline of manufacturing cities. Glaeser and Giacomo Ponzetto go a step further and argue that declining transport costs may have contributed to the decline of goods-producing cities like Detroit but boosted the growth of idea-producing cities like Boston and New York. (44) Their argument is that globalization has increased the returns to skill and that workers become skilled by locating around skilled people in cities that are rich in human capital.

[FIGURE 9 OMITTED]

Richard Green argues that airports have played the same role in promoting urban growth in the last fifteen years that railroads and highways did in the past. (45) His principal piece of evidence is that places that have more airline boardings per capita have grown faster. Although this fact could represent the positive impact of access to airports, it could also reflect consumer amenities: places that are attractive for people to visit should also be attractive places for people to live. (46) One way to check whether the connection between airplane boardings and growth reflects access or consumer amenities is to replace the number of boardings per capita with an indicator variable for whether a metropolitan area has a major airport. We constructed a dummy variable for having a major airport, with "major" defined as one of the fifty airports in the country with the most flights per day. Regressions 5-5 and 5-6 in table 5 show that having a major airport did have a positive but modest effect on population and income growth in the 1990s.

Although new transport technologies such as airports still seem to matter for urban growth, there is little evidence to suggest that investments in older technologies such as rail have any impact on urban success today. For example, Glaeser and Jesse Shapiro find that places with more public transit usage grew less in the 1990s than those with less usage. (47) This certainly casts some doubt on the view of public transportation advocates that new rail systems have the same potential to foster growth in the twenty-first century that they had in the nineteenth.

There is no question that new transportation infrastructure has been able to reduce the cost of moving people across space. This suggests that local leaders who lobby for new forms of transportation spending are not being foolish. However, it is less clear how transportation's ability to make places should influence the evaluation of national transportation projects. We turn to that issue next.

Place and the Evaluation of Transportation Investment

When discussing the benefits of transportation investments, it is typical for public officials to emphasize the ways in which a new highway or rail line could turn their area around economically. The previous discussion has suggested that these advocates have been right in some cases. Yet the ability of transportation to make or break cities does not necessarily change the rules by which transportation investment should be evaluated. Transportation infrastructure can be seen both as nontraded productive capital and as a consumer amenity that enters directly into the utility function. In that case:

Proposition 3: In a social optimum, the social benefits of transportation spending within an area,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

equal to the marginal cost of that spending. In a competitive equilibrium, where marginal utility of income is constant across space, the social benefit of transport spending in area i exceeds

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

This proposition implies that at the social optimum, transportation spending should be evaluated according to its direct effect on consumer welfare and firm productivity, not according to its place-making potential. This result reflects the fact that in a social optimum, population is directly optimized across space. In a competitive equilibrium there can be place-making benefits from transportation, but these benefits result only if the externalities are higher in particular locales. Unsurprisingly, the ability of transportation to move people across space has value only if moving people across space is desirable.

The previous section gave only a little guidance about where those externalities might be higher. There may be productivity gains from moving people to richer areas, and the negative externalities of population growth might be lower in places that are already denser, but these effects are weak. They do, however, provide a benchmark for thinking about current transportation spending. Should transportation be subsidized disproportionately in rich, dense areas?

Table 6 reports, for several different modes of transport, the correlations between transport spending per capita and measures of agglomeration--population size and population density--and income. Highways are the dominant recipient of federal aid to transportation. The table shows federal transfers for highways both with and without the gasoline tax payments that the states make to the national transportation trust fund. The results suggest that the United States subsidizes long-distance transportation in lower-density and lower-income places, which is exactly the opposite of the model's predictions. Transportation policy seems to be working against, rather than toward, taking advantage of agglomeration economies. Environmental externalities probably also push toward higher-density development that involves driving over shorter distances. (48)

Of course, if the direct benefits from transportation spending are greater in poorer, low-density areas, then current spending patterns make sense. Indeed, the major point of this section is that transportation needs to be evaluated according to its impact on travel costs, and nothing we have said suggests that the current distribution of highway spending fails to meet this criterion. However, if one includes the place-making effects of transportation when evaluating its benefits, then current spending does not appear to be targeting the high-income, high-density areas where the agglomeration effects are likely to be strongest.

Urban Renewal, the Appalachian Regional Commission, and Empowerment Zones

Americans have rarely embraced a wholesale regional policy dedicated toward reinvigorating declining regions. Despite regular calls from mayors and even promises from presidential candidates, only in a few instances has the U.S. government explicitly embraced policies meant to turn around declining areas. In this the United States stands in stark contrast to many European countries, which have regularly invested heavily in their poorer regions since before the formation of the European Union. For example, Italy has a long-standing policy of using tax incentives to encourage investment in its south. Such policies have been a particularly important activity for the European Union, which has regularly redistributed funds from wealthy areas to poor ones.

The supporters of place-based policies have generally argued for such policies on the basis of two related arguments. The first is purely egalitarian: place-based support for poor places may create more economic opportunity for poorer people. The second invokes some market failure that is causing a particular place to underperform. For example, it is sometimes alleged that the need for coordinated investments makes it impossible for private firms on their own to turn a declining area around. In the framework of the model, this can be understood as claiming that agglomeration economies are particularly strong for such places. Yet our empirical work in the previous section found little evidence to support that claim.

Against these arguments, economists argue that place-based policies are unlikely to be of material help to poor people. Place-based policies that aim to turn a declining region around are often thought to be futile, since the forces of urban change are quite powerful. Place-based policies that throw enough resources at a small enough community may indeed be able to improve the quality of that place, but it is not obvious that the poorer residents of that community will benefit. Some community-based policies may just lead employers to come to the area and hire new migrants. Others may make the community a more attractive place for outsiders to live and thus increase rental costs for longer-term residents. In general, the spatial equilibrium model leads economists to think that place-based improvements increase the value of property, which may be a good thing for local homeowners and landlords, but may not be so desirable for renters.

Finally, economists have voiced a basic skepticism about the desire to induce poor people to stay in poor areas. Place-based policies may boost a poor area, but they may also discourage poor people from leaving that area for areas where opportunities may be greater. The rationale for spending federal dollars to try to encourage less advantaged people to stay in economically weak places is itself extremely weak. For example, it is not clear why the federal government spent over $100 billion after Hurricane Katrina to bring people back to New Orleans, a city that was hardly a beacon of economic opportunity before the storm.

In U.S. history the major instances of regional policy have been the Appalachian Regional Commission (ARC), which targeted development of a large area in the eastern United States; the enterprise zones and Empowerment Zones of the 1980s and 1990s, which offered tax breaks to firms locating in poorer communities; and policies aimed at urban renewal. The last class of policies was primarily oriented toward housing and construction, and so we will consider them in the next section. We turn first to the ARC.

The Appalachian Experience

In 1963 Harry Caudill published Night Comes to the Cumberlands, which described the rural poverty of the Cumberland Plateau of eastern Kentucky. (49) Caudill's book brought national attention to Appalachia and suggested that the region's problems were the fault of northern coal investors who had taken the wealth out of the ground and then invested their returns elsewhere. Needless to say, this argument works better as rhetoric than as sound economic analysis--the policy implications of the spatial equilibrium model are not changed if rentiers live outside the regions where they receive their rents.

Even before Caudill's book, the governors of several Appalachian states had started a coordinated effort to obtain federal assistance, and President John Kennedy responded in 1963 by forming the Appalachian Regional Commission. The ARC was originally founded to seek legislation to provide assistance for the region. In 1965 Congress turned the ARC into a federal agency that would distribute funds among the Appalachian counties, to be used for a variety of local projects intended to enhance economic vitality. Transportation accounted for a particularly large share of this funding, so the ARC should be seen as a hybrid between a pure transportation program and a local economic development program.

The political definition of Appalachia was county-based, and the area covered by the ARC stretched from Mississippi to New York. The inclusion of so many states helped to create a legislative coalition for the policy, but it inevitably meant that funding per acre was modest. In the first thirty years after it was founded, the ARC disbursed $13 billion. (50) Today the ARC receives much less funding, about $90 million a year.

Did the billions spent on the ARC have a demonstrable effect on Appalachian success? Andrew Isserman and Terance Rephann address this question by comparing income and population growth for a matched sample of Appalachian and non-Appalachian counties. (51) They use a matching algorithm to connect counties that were in the Appalachian region with other areas. The study specifically excluded counties that were close to Appalachia as possible matches because of fears of contamination from the ARC. As a result, Allegheny County, Pennsylvania, was matched with Erie County, New York, which contains Buffalo, and Catoosa County, Georgia, was matched with Warren County, in southwestern Ohio. Comparing the growth experiences of the two samples, the authors find that income in the Appalachian counties grew by 5 percent more than in their comparison counties between 1969 and 1991, and income per capita 17 percent more. Their bottom line is quite remarkable: they find that $13 billion in Appalachian expenditure yielded $8.4 billion of income in one year alone. This appears to be a quite positive demonstration of the efficacy of regional policy.

Since Isserman and Rephann's methods are sufficiently different from those used in most economic analyses, we repeat their exercise using a more standard regression methodology. Our approach is to include all counties in any state that was partly included in the ARC, except those counties within 90 kilometers (56 miles) of the coast. We then use a dummy variable to identify those counties covered by the ARC. We are thus comparing Appalachian counties with reasonably comparable counties in the same region. We examine both income growth and population growth. We include only the initial values as controls, but the results are not sensitive to including other controls.

Table 7 presents our results. The first regression finds that between 1970 and 1980, being part of the ARC coverage area was associated with 0.037 log point faster population growth--evidence of a treatment effect on population during this first decade. Between 1970 and 2000, however (the second regression), the dummy variable for location in the ARC area has a coefficient of -0.002, which is small and statistically insignificant. The remaining two regressions report the relationship between inclusion in the ARC and growth in income per capita. We find an insignificant positive effect in the 1970s, which turns negative over the longer period. One possible interpretation of these results is that although the ARC was able to boost population growth slightly during the period in which it was best funded, the effect soon disappeared.

Given that Issermann and Rephann found quite different results, we do not claim to have proved that the ARC had no effect. Indeed, the standard errors on our coefficients are sufficiently large that we cannot rule out large positive effects of the program, at least relative to its modest cost. A more supportable conclusion is that it is unlikely that the effects of a $13 billion program spread over a giant swath of America over three decades can be accurately evaluated. Far too many things were affecting regional growth at the same time for a relatively modest government program to have had clear positive effects. Powerful economic forces are driving people to the Sunbelt and to coastal cities. Current spending on the ARC is no more than the cost of a few large Manhattan buildings. Could such a program really have changed the course of a region considerably larger than California? The ARC may or may not be cost effective, but there is little chance that its effectiveness will ever be evident in the data.

Enterprise and Empowerment Zones

We now turn to a much more targeted approach: enterprise zones. As Leslie Papke summarizes, enterprise zones were pioneered in the United Kingdom by Margaret Thatcher's government in 1981. (52) There were originally eleven such zones, but the number later increased to twenty-five. The British zones were particularly oriented toward industrial development. Firms that located in the zones were exempted from local property taxes and could deduct all spending on industrial buildings from corporate income tax. This tax relief was accompanied by significant public sector investment in the area.

Although plenty of economic activity occurred in the enterprise zones, evaluations of the zones were largely negative. Roger Tym suggests that most of the jobs in these zones did not represent new activity but simply a reallocation within the metropolitan area. (53) John Schwarz and Thomas Volgy estimate a cost per job created of $67,000 during the 1980s, which would be more than $125,000 in 2007 dollars. (54) Rodney Erickson and Paul Syms find a moderate increase in land prices within the enterprise zones. (55)

In the United States the enterprise zone experience begins with state enterprise zones in the 1980s. Papke reports that thirty-seven states had created such zones by the early 1990s. (56) Unlike the British zones, the American enterprise zones were particularly oriented toward revitalization of urban neighborhoods and were, in some sense, the descendants of the urban renewal projects described below. The zones were often quite small--the median zone had 4,500 residents--and they were quite poor.

Papke's own evaluation focused on the Indiana enterprise zone system, which exempted businesses in the zones from property taxes and taxes on income from inside the zone. There was also a tax credit for hiring workers who lived within the zone and an income tax credit for zone residents. Despite these considerable tax incentives, and despite an increase in business inventories within the zones, Papke finds that the zones actually lost population and income relative to nonzone areas. Certainly, this should not be interpreted as a true negative treatment effect of zones, but rather as evidence that the Indiana zones were relatively ineffective.

In the 1990s the federal government began its own system of areas called Empowerment Zones, administered by the Department of Housing and Urban Development (HUD). There were six original Empowerment Zones; two more were added later. Firms in the zones received employment tax credits and regulatory waivers. There were also block grants and spending on infrastructure. The overall cost of the program was slightly more than $3 billion. (57)

Busso and Kline undertake a particularly careful analysis of the federal zones' impact. They compare the zones with similar areas chosen from among communities that also applied to HUD to receive Empowerment Zone support. Busso and Kline use a propensity score method to match these communities appropriately and find strong positive results. Although the populations of the zones did not increase, the poverty rate fell by an average of 5 percentage points and the unemployment rate by an average of 4 percentage points in these communities relative to comparable outside areas. Housing prices increased by 0.22 log point and rents by 0.077 log point. There was no appreciable increase in earnings.

On one level these results seem much more promising than Papke's findings, but there are still reasons to be skeptical. First, the authors estimate that a program costing more than $3 billion created 27,000 jobs between 1995 and 2000. This comes to more than $100,000 per job in current dollars, which seems an expensive way to boost employment. The figure of 27,000 jobs refers to the employment increase in 2000. If 27,000 extra jobs were created in every year, then each job-year would have cost $20,000. The $3 billion figure includes substantial private money, however, so it is not clear whether this should be counted as an actual cost. The answer depends on whether this money reaped private returns and whether it was induced by other federal programs, such as the Community Reinvestment Act. Nevertheless, the true cost per year is probably below the $100,000 number.

For already-employed workers in Empowerment Zones who were renters, earnings did not increase, but rents did. Perhaps other amenities rose in the Empowerment Zones, but for this group the zones represent a pure financial loss.

Busso and Kline themselves suggest that the program generated a $1.1 billion increase in output and a $1.2 billion increase in the value of homes and rental properties. These two estimates should not be added, since the housing values are presumably capturing the value of having access to a more successful labor market. Indeed, one view is that the closeness of these figures reflects the fact that both are capturing the same gains. However, in the case of housing values these gains would omit benefits to previous residents who are not changing their behavior due to the program. Nevertheless, these gains do seem to be substantially less than the cost of the program.

Overall, the evidence on enterprise zones is hardly overwhelming. The British evidence shows positive effects, but the price per job created is extremely high. The Indiana evidence shows essentially no effects on key social outcomes. The evidence on federal Empowerment Zones shows significant employment gains from the programs, but the price per job is again extremely high. It is hard to see an empirical case for zone-based policy.

It is harder still to evaluate more amorphous government policies such as those embodied in the Community Reinvestment Act of 1977 (CRA). This act required financial institutions to invest in businesses in poor areas as well as rich areas and to make credit available to poorer people. It can be argued that economic efficiency would be better served by allowing banks to focus on lending to firms that are most likely to be most productive rather than firms that have a particular geographic locale. However, one could also argue that the CRA served equity purposes and had only a small negative effect on overall financial efficiency. Without more thorough evaluation--and it would be hard to imagine how to produce such an evaluation--it is difficult to come to any strong conclusions about the CRA.

An alternative way of understanding enterprise zones and certain other place-based policies is as a means of reducing taxes on nontraded business inputs such as real estate. Optimal taxation theory suggests that it makes sense to have lower tax rates in areas where these inputs are more elastic. Enterprise zones can be justified if the supply of the nontraded output is more elastic in depressed areas. However, we know of no evidence that this is the case.

Another interpretation of enterprise zones is as an indirect means of freeing local businesses from paying for social services for poor residents of their community. If one thinks of those social services as a national responsibility whose costs must be borne by someone, then making the residents of one community pay disproportionately for those services will be distortionary. These taxes will induce lower input demand in that area, which will lead to too little production there relative to the first-best outcome. A similar conclusion results if one taxes the rich in a community to pay for services to the poor in that community. Such a policy will lead the rich to live elsewhere, which is also a distortion relative to the first-best. Reducing the added governmental costs of locating near poor people may reduce the tax-created distortions that induce firms and people to leave poor places.

To sum up, the combination of theory and evidence leads us to be suspicious of local economic policies that are meant to increase production in a particular area, whether that area is depressed or booming. Empirically, these policies seem to be either extremely expensive or ineffective. Theoretically, the case for these policies depends either on extra agglomeration economies in depressed areas or on a particularly high elasticity of demand for inputs in those areas. These conditions may exist, or they may not. There is, however, a case for reconsidering policies that require local businesses and workers to pay for social services for the local poor in a way that essentially amounts to redistribution.