U.S. housing policies as place-making policies.

Glaeser, Edward L. ; Gottlieb. Joshua D.

As in the case of transportation policy, one could have a housing policy without any particular spatial objective. It is not necessary for the cabinet secretary who oversees housing to also supervise urban development. Indeed, the earliest federal forays into the housing market during the Great Depression, the Reconstruction Finance Corporation and the Federal Home Loan Bank Board, were not intended to reinvigorate any particular locale. More modern interventions, such as Section 8 vouchers and the low-income housing tax credit, are similarly aimed mainly at making housing cheaper, not at making places more economically vibrant.

Urban Renewal

Starting in the 1940s, there has been an increasing tendency to link housing policy and urban revitalization. In 1941 the National Association of Real Estate Brokers advanced a scheme whereby the government would use its powers of eminent domain to assemble urban parcels and then subsidize private development of that land. (58) The Harvard economist Alvin Hansen endorsed a similar scheme, and individual cities, such as New York, increasingly subsidized urban renewal efforts. After a great deal of legislative wrangling, in which "Mr. Republican," Senator Robert Taft of Ohio, strongly supported public housing against the opposition of his fellow Republican, Wisconsin Senator Joseph McCarthy, Congress passed the Housing Act of 1949. Title I of that act brought the federal government into the business of urban renewal.

The 1949 housing act authorized $1 billion in loans to cities for them to acquire blighted land and $100 million a year in outright grants for such purchases. In principle, the cities were to pay one-third of the purchase price, but the contribution could be made in the form of new public facilities. (59) The sites would then be given to private developers to build new housing or commercial buildings. The Housing Act of 1954 broadened the program to allow funds to be used for renovation and for Federal Housing Administration mortgages for renewal projects.

Several rationales have been given for urban renewal. The intellectual roots of the slum clearance movement go back to the Progressive Era, when reformers believed that the poor conditions and high densities of poor neighborhoods spread disease and fomented crime. A related, externality-based argument is that blighted areas create aesthetic externalities for neighbors. Amy Schwartz and coauthors find some evidence for this view: (60) neighboring housing prices seem to go up when dilapidated housing is replaced with a new housing project.

Another argument for urban renewal is that private developers may be unable to assemble sufficiently large land parcels for major projects because of the hold-up problem: any individual landowner's part of the area is indispensable to the project, so all of the former landowners will try to extract the project's entire surplus. Of course, this argument is really a justification for the use of eminent domain and provides no rationale for subsidizing private developers. A policy intended to solve hold-up problems would presumably have developers pay market rates for land assembled through the use of eminent domain.

In the 1950s and 1960s, urban renewal was increasingly also seen as a tool for revitalizing cities. There are two ways of understanding how subsidizing housing might, in principle, help declining cities. The number of people in an area is generally proportional to the number of homes there. (61) Subsidizing new housing is one way of increasing the population of an area to take advantage of agglomeration economies. A slightly different view is that better housing might attract residents with more human capital, who will then generate positive externalities in the workforce. In this case housing policy becomes a human capital policy, as discussed in the next section. However, there are also good reasons for skepticism about these arguments. A key distinguishing characteristic of declining cities is that they have an abundance of housing relative to demand. (62) Many of these cities have large numbers of vacant homes, making it hard to see how building more housing is likely to improve the situation. Moreover, in many cases subsidized housing destroyed large numbers of units, so the overall population of the area did not increase.

We are not aware of any comprehensive data that measure total federal spending on urban renewal in the 1950s and 1960s. Since aid to cities often came from many different sources, there is no unified data source for such funding. Using the limited data that John Staples assembled on urban renewal for twenty-one cities, (63) table 8 examines whether any correlation exists between that spending and urban success. The regression reported in the first column examines the correlation between urban renewal spending per capita and population growth across these twenty-one cities during the 1960s. The point estimate is positive but statistically insignificant and small. The second regression investigates the correlation between this spending and growth in income per capita. Again the coefficient is tiny and not statistically distinguishable from zero.

These results cannot say whether the benefits of urban renewal outweighed its costs, only that there was no statistically significant surge in those cities that received more urban renewal funding. As with the ARC, however, these interventions were modest relative to the population covered; they were also modest relative to the other forces driving urban change. Such small-scale interventions are unlikely to ever yield statistically robust results, making proper cost-benefit evaluation essentially impossible. At best, one can say only that urban renewal does not seem to have turned places around, but that is perhaps sufficient to reject the strongest claims of the early urban renewal advocates.

The Model Cities Program

During the twenty years that followed the 1949 housing act, the primary opposition to urban renewal did not come from economists questioning the value of spending to build new houses in places with low demand. The loudest cries came from community activists who protested the destruction of older neighborhoods. The writer and civil rights activist James Baldwin famously referred to urban renewal as "negro removal." By the mid-1960s there was a growing consensus that urban renewal created social, or at least political, costs that outweighed its benefits.

In response to these outcries, Congress in 1966 passed the Demonstration Cities and Metropolitan Development Act, which established the Model Cities Program as part of the War on Poverty. This program still aimed to improve urban areas through new housing and commercial development, but it embraced community participation and the rehabilitation of existing neighborhoods. In the first round of the program, 193 cities applied to HUD to be included. There was no uniform model city plan; rather, the cities themselves offered detailed plans for using Model Cities funds. HUD then selected seventy-five model cities using an "intricate selection process." (64) Political pressure led eventually to an expansion to include 150 cities, which meant a reduction in the funding available per city.

At its height, the program was supposed to spend more than $500 million a year. Administrative difficulties, however, often meant that actual funding was significantly less. The more holistic nature of the plans developed under Model Cities made them a bridge between the housing-based urban renewal projects of the 1950s and the Empowerment Zones of the 1990s, discussed above.

The Model Cities Program was thus another place-based program that offered aid to particular cities in the hopes of reviving their fortunes. It was essentially a transfer from taxpayers nationwide to the governments of particular places. The individual projects are so varied that it is impossible to say anything categorical about them. We will only attempt to see whether cities that were included in the program achieved greater economic success than cities that were left out. We consider only those cities that won funding in the more selective and potentially more generous first round. Since HUD did not engage in random assignment, this is not a natural experiment.

The third regression reported in table 8 shows the correlation between Model Cities status and population growth between 1970 and 2000. The coefficient is negative and insignificant. The fourth regression considers the relationship between Model Cities status and growth of income per capita, and again the coefficient is insignificant. In results not reported here, we also found an insignificant relationship with housing prices, and we found similar results when we focused only on the 1970s, when the program was active.

Urban renewal and Model Cities thus do not seem to be significantly related to urban success, but this finding can lead to two very different conclusions. One view is that these programs could have had important results if they had been better funded. A second view is that these programs were never going to achieve meaningful results. Many commentators, such as the political scientist Edward Banfield, have embraced the latter view, but our statistical results certainly cannot distinguish between the two interpretations. Perhaps the only thing we can say is that our statistics do not yield any positive evidence supporting the benefits of these federal attempts at place making.

Housing Supply and Urban Growth

Past place-making forays into the housing market have focused primarily on generating new building in places where private demand is low. The theoretical grounds for such policies seem weak, and empirically there is little evidence that they were successful. However, this does not imply that there is no role for the federal government in housing and urban development. Over the past forty years, many localities have become much more stringent in their restrictions on land use. (65) These restrictions may be having a major impact on where and how America grows. If localities determine local supply conditions in ways that may benefit their own voters, but that do not maximize national welfare, then there may be a role for national policy toward land use.

The first analytical step in making the case for national involvement in land use planning is to show that land use restrictions do influence urban growth. It is clear that housing supply is not constant across the United States. Figure 10 plots relative growth in the housing stock between 2000 and 2005, as measured by permits issued, against housing prices in 2005. If housing supply were equally elastic in all areas, then this graph should show an upward-sloping relationship: places with stronger housing demand should have higher prices and more building. However, the figure reveals that the most expensive places have little building, while the places with the most building are not particularly expensive. This pattern cannot be explained by heterogeneity in demand alone. It must be that housing supply is quite inelastic in some areas and elastic in others.

One possible explanation for this heterogeneity is the natural availability of land. Perhaps land is simply abundant in the area around Las Vegas, for example, and not on the San Francisco peninsula. But land availability does not seem to be driving the heterogeneity in new construction. Figure 11 shows the relationship between permits per square mile between 2000 and 2006 and existing houses per square mile in 2000: the places with the least available land built the most. This fact persists when one controls for demand by controlling for prices, or when one considers only those areas where prices are high enough to motivate new supply. The negative correlation between land availability and new construction can also be seen within some metropolitan areas, such as Boston. (66)

[FIGURE 10 OMITTED]

An alternative explanation for the heterogeneity in housing supply is land use regulations. Local communities have significant ability to impact the ease of new development through regulations ranging from minimum lot sizes to rules concerning subdivisions. These supply restrictions would naturally be expected to reduce construction from its equilibrium level without the restrictions, and consequently to increase prices. After all, what does a minimum lot size do if not limit the number of homes that can be constructed on a fixed amount of land? Is a local growth control that explicitly limits the number of new homes anything but a limit on the size of the community? Glaeser and Bryce Ward compare 187 towns in Greater Boston and show a strong connection between the amount of housing in a town and its rules restricting new development. (67) Lawrence Katz and Kenneth Rosen compare communities with and without growth controls in California and find higher prices in those areas with controls. (68)

[FIGURE 11 OMITTED]

Figure 12 shows that the Wharton Land Use Index, described earlier as a measure of the difficulty of new construction, is positively correlated with housing prices. The overall correlation between this index and new construction activity is slightly negative but statistically insignificant. In a regression of permits issued on the Wharton index and climate and education variables, we find that the Wharton index is negatively associated with new permitting (results not reported).

Land use restrictions may reduce development and increase prices, but this does not necessarily mean they are bad policy. Perhaps there are externalities, such as congestion, that justify price-increasing restrictions. One way of testing whether land use restrictions are welfare maximizing is to see whether they appear to maximize land values. A standard result in urban economics is that land value maximization leads to efficient outcomes. (69) Local communities that succeed in maximizing land values by restricting development are in effect shifting the costs to outsiders, at least if the community does not have monopoly power over some particular amenity or natural resource.

[FIGURE 12 OMITTED]

To see whether communities are maximizing land values, we need to examine the elasticity of prices with respect to density. If the cost of building a house is denoted C, and a community has a total land area of one, and a total of D homes are built, then the value of land in the community is D[P(D) - C], that is, the number of homes times the price of homes, less construction costs. This quantity will be maximized with respect to D when DP'(D) + P(D) - C = 0, or [P(D) - C]/P(D) = -DP'(D)/P(D).

According to this calculation, efficient land use restrictions should imply that the elasticity of housing prices with respect to density equals that share of housing prices that is not related to construction costs. Glaeser and Ward found elasticities of price with respect to density that were less than -0.15 across areas in Greater Boston. These estimates were made using both ordinary least squares and a variety of instruments, including zoning laws and forest acreage in 1885. On average, construction costs are less than 50 percent of home value in their sample, so building more housing would substantially increase land values. Although Greater Boston is hardly typical of the United States as a whole, these results do suggest that some areas experience far less development than they would if communities were actually maximizing land value. (70)

The spatial equilibrium model presented above suggests that land use restrictions could be desirable if they move people from areas with low to areas with high agglomeration economies, or if they move people away from areas with large negative externalities. There is scant evidence that this is happening.

There are certainly environmental and other externalities associated with new construction, but it is far from obvious that existing land use restrictions handle these externalities appropriately or even work in the right direction. If one regards carbon emissions as creating an externality that is currently underpriced, then building on the urban fringe in Texas, where land use restrictions are few, is not environmentally friendly. Yet this is exactly the outcome if coastal California and the East Coast suburbs restrict new building. Communities do not have the ability to stop development in the United States as a whole; they can only push it elsewhere. So if denser communities restrict development, they will push it to areas where there are fewer people. Glaeser and Kahn show that land use restrictions are most stringent in places with the lowest carbon emissions, suggesting that the impact of land use restrictions is to move development to areas that have higher environmental COSTS. (71)

[FIGURE 13 OMITTED]

Land use restrictions also seem to push people away from high-income areas, which have stronger agglomeration effects, at least if the marginal utility of income is constant across space. Figure 13 shows that human capital, as measured by college completion rates, has a weak positive association with the Wharton Land Use Index. As we will discuss later, skilled areas are much more productive than unskilled areas. By restricting development in the nation's most productive places, land use restrictions are pushing people toward less economically vibrant areas.

If local governments are undertaking land use policies that are undesirable from a national point of view, then federal policies that worked against such policies could be welfare enhancing. What would a federal policy that tried to encourage development in high-cost, high-wage areas look like? It seems implausible that the federal government could directly oversee land use controls in tiny local areas. An alternative approach would be to reward high-cost states for undertaking policies that encourage building in restrictive areas. Another approach would be to directly offer incentives to those communities in high-cost areas that build. (72)

Any attempt to handle local land use restrictions runs into the same problems faced by the Model Cities Program: the federal government is not well positioned to interact directly with small communities. Yet moving people into high-wage areas seems to be an easier spatial policy that would increase GDP. More people will not be able to move into those areas unless there is more building, and this cannot happen unless localities change their land use rules.

Some transportation policies can also be seen as a means of dealing with local land use policies. (73) Building more highways allows more housing to be built on the urban fringe, where restrictions are less binding. But although this may allow some metropolitan areas to grow, it does so in a more expensive and inefficient manner than if more construction were allowed in areas closer to core employment centers. Whatever may be the best way to move people around, a fundamental reason that it matters where they end up is what comes of their interactions. Since ideas are non-rival, it is natural to examine their spillovers, and more generally all the externalities that flow from human capital. We now turn to human capital spillovers.

Human Capital and Industrial Spillovers

Human capital spillovers result whenever people learn from other people around them. As our neighbors acquire more knowledge, a little bit of that wisdom rubs off on us. The existence of such spillovers is beyond debate; we are an enormously social species who spend much of our lives listening to and watching people around us, beginning with our parents. The relevant empirical question is not whether such spillovers exist, but rather how important they are and where they are most prevalent.

For more than a century, economists and other urbanists have suggested that these idea flows will be more prevalent in dense environments flush with face-to-face interactions. If people learn by communicating ideas to each other, urban proximity helps them transmit those ideas. Alfred Marshall wrote that in industrial clusters, "the mysteries of the trade are no mystery, but are as it were, in the air." (74) The urbanist Jane Jacobs was particularly associated with the hypothesis that urban areas foster creativity by speeding the flow of knowledge. Robert Lucas connected the flow of urban ideas with his new growth theory, which emphasizes the production and sharing of knowledge. (75) Just as urban density two centuries ago facilitated the flow of cargo onto clipper ships, so that same density today serves to facilitate the flow of ideas among people.

Faster idea flows in cities are one of the many types of agglomeration economies, and they suggest that cities where large numbers of skilled workers live are likely to be particularly successful. Any urban edge in facilitating communication should be more important for more skilled people, who have more to communicate and can benefit more from others' knowledge. This type of reasoning has led to a significant literature documenting that skilled places are more successful than unskilled ones.

Over the past fifteen years, a series of papers has established several propositions about the relationship of skills to urban success. First, holding individual skills constant, incomes are higher in cities with more skilled workers. (76) Second, skilled cities have faster population and income growth than less skilled places. (77) Third, skilled places seem to be growing because productivity is rising faster there. (78) Fourth, skilled people tend increasingly to move near other skilled people. (79) Finally, skilled industries are more likely to locate near the urban core, and less skilled industries on the urban periphery. (80)

The existence of human capital spillovers justifies subsidizing education and provides some guidance for local leaders trying to boost either incomes or population growth. Indeed, the remarkably strong (50 percent) correlation between urban growth and initial skill levels among cities in the Northeast and Midwest suggests that skills are by far the best antidote for Rustbelt decline. Local policies that either attract or produce skilled people seem likely to offer the best chance of improving the fortunes of a troubled urban area. Good public education, which both produces skilled graduates and attracts skilled parents, is surely the primary example of such a policy.

However, the existence of human capital spillovers does not provide any clear guidance for national place-making policies. A policy that moves a skilled person from one area to another helps the area that receives the skilled worker and hurts the area that loses her. A framework like the spatial equilibrium framework presented in this paper can help sort through the welfare implications of human capital spillovers. The framework allows for individual heterogeneity, but to keep things simple we now omit the nontraded goods sector. If there are K types of people, we assume that total urban output in the traded goods sector is [A.sub.i]F([[??].sup.k.sub.i]), where [[??].sup.k.sub.i] is the vector of labor in each of the different subsectors.

The wage spillover literature essentially postulates that the productivity parameter, [A.sub.i], is a function of the average skill level in the area, [[??].sub.i]. (81) This literature emphasizes that working around skilled people makes people more productive at a single point in time. The urban growth literature that shows a connection between initial skills and subsequent population and income growth postulates that the average skill level in the area also increases the growth rate of [A.sub.i]. This literature suggests that the growth rate of local productivity is higher when there are more skilled people, perhaps because skilled people come up with more new ideas.

Since the urban growth literature considers both population and income, it has generally specified a spatial equilibrium, although usually the equilibrium does not fully explain why some places have more skilled people than others. The wage literature often fails to specify the spatial equilibrium at all. To specify a complete model that will help us interpret the results and discuss appropriate public policy, we assume that the utility of people of each group in city i can be denoted [[theta].sub.i][[upsilon].sup.k.sub.i] [([N.sup.k.sub.i]).sup.[sigma]][W.sup.k.sub.i], where [[theta].sub.i] is a city-level amenity variable, [[upsilon].sup.k.sub.i], is the exogenous endowment of amenities in city i that appeal to people of type k, [N.sup.k.sub.i] is the endogenous number of people of type k in city i, and [W.sup.k.sub.i] is the endogenous wage of type k people in city i. Each type of worker has an exogenous productivity scaling factor [W.sub.k] and a reservation utility denoted [[U.bar].sub.k]. Amenities will essentially drive the distribution of labor, and this is the best case for empirical work.

Firms' production functions are typically characterized by a constant

elasticity of substitution across different groups, or [[??].sup.k.sub.i] [[summation].sub.k E[[([[??].sup.k.sub.i]).sup.p]].sup.[phi]/[rho]],

so that wages for individuals of type k in city i equal

[A.sub.i][phi][E.sub.k][([N.sup.k.sub.i]).sup.[rho]-1] [summation over (k)] [E.sub.k] [[([N.sup.k.sub.i]).sup.[rho]]].sup.[phi]/[rho]-1. The skill distribution in an area satisfies

[N.sup.k.sub.i] = [N.sup.l.sub.i] ([[upsilon].sup.k.sub.i] [E.sub.k] [[U.bar].sub.l]/[[upsilon].sup.l.sub.i] [E.sub.l]) [[U.bar].sub.k]; hence the distribution of skills across cities is determined only by amenity differences. We let [n.sup.k.sub.l] denote the ratio of type k individuals to type l individuals in area i. For any type m, population will

equal [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], so total population in the area equals

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and wages for type m individuals equal

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

which is a function of amenities and productivity as in equations 2 and 3. This type of spatial equilibrium model provides an interpretation for the city-level growth regressions, because if only amenities and productivity change, then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. If human capital changes the rate of productivity or amenity growth, it will impact the growth of population and wages.

Figure 14 shows the relationship between population growth from 1940 to 2000 and the percent of the city's over-25 population with a college degree in 1940 for those metropolitan areas that had more than 100,000 people in 1940. This type of result holds when we instrument for population growth using the presence of land grant colleges before 1940, (82) or using the skills implied by a city's occupation distribution in 1880. (83) If the skill level in 1940 caused either productivity or amenities to grow more quickly, then the model predicts that more-skilled places will see more population growth, assuming the other parameters are constant over time.

[FIGURE 14 OMITTED]

Two recent papers have used this type of framework to test whether the rise of the skilled city reflects rising amenities or rising productivity; (84) both papers conclude that it is the latter. The premium associated with working around skilled people has risen steadily over time. The connection between initial skills and productivity growth can be understood as a reflection of the greater tendency of skilled people to innovate, or of the growing importance of working around skilled people. If people become skilled by being around skilled people, then the rising wage premium associated with working in skilled cities is yet another example of the rising returns to skill in the economy as a whole.

[FIGURE 15 OMITTED]

The assumption that skills are unrelated to changes in other parameters seems belied by the fact that skilled places are becoming more skilled. Figure 15 shows the relationship between the percent of the over-25 population with college degrees in 1980 and the growth in that share between 1980 and 2000. The correlation between these two variables is 58 percent. As the share of the population with college degrees in 1980 increases by 10 percent, the growth in the same variable over the next twenty years increases by 3 percentage points. This fact, documented by Christopher Berry and Glaeser, (85) might also reflect an increasing tendency of skilled entrepreneurs to innovate in ways that employ other skilled people.

To address contemporaneous human capital spillovers, we assume that productivity is a function of the current spillover level, [[??].sub.i], where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where [S.sub.k] might or might not equal [E.sub.k].

If A([[??].sub.i]) = [a.sub.i][[??].sub.[epsilon].sub.i], then the equation becomes

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [Q.sup.m.sub.W] is constant across areas. The [n.sup.k.sub.i] term denotes the ratio of type k individuals to type 1 individuals in area i, which captures the skill distribution within the city. Typically, some form of nonlinear least squares procedure would be needed to estimate this equation. If [phi] = [rho], then ordinary least squares can be used. In that case wages equal

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. To use least squares we would need to assume that [v.sup.m.sub.i] is constant for some group or set of groups across space, and that all of the variation in the skill distribution is coming from amenities that impact the location of the omitted groups. In that case we would need to run the regression only for the groups whose amenity levels do not change.

This formulation suggests the difficulty of using wage regressions to estimate spillovers. Even when we assume that there is no heterogeneity in the relative productivity levels of different skill groups across space, herculean assumptions are needed to justify least squares estimation. When different groups have different productivity levels, estimation becomes even more difficult.

James Rauch's 1993 paper was the first to set out to estimate human capital externalities using within-country data. He documented that, holding individual skills constant, wages were higher in cities that had a higher concentration of skilled people. He showed that rents were also higher in those areas, which presumably maintains the spatial equilibrium. Although it is possible that high wages in high-skilled areas reflect unobserved individual skill characteristics, Rauch's finding remains an important part of understanding wage patterns across urban areas.

Regression 9-1 in table 9 reproduces a version of the Rauch result using area-level human capital and wages from the 2000 Census. Individual skills and industries are held constant. As before, we look only at fully employed men between 25 and 55 years old. As the share of the adult population with college degrees increases by 10 percent, wages increase by 7.8 percent. Figure 16 shows the relationship across metropolitan areas between the average wage residual from this equation and the share of the population with a college degree.

The same two major problems that trouble the interpretation of the correlation between income and city size also bedevil interpretation of the correlation between area-level human capital and productivity. First, omitted area-level productivity variables may be positively correlated with area-level human capital, if skilled people move to areas that are more productive. Second, omitted individual-level human capital may be positively correlated with area-level human capital. The fact that real wages increase with human capital much less than nominal wages do should make one slightly less concerned about the second problem.

Two recent papers have tried to address the problem that unobserved ability may be correlated with area-level human capital. Daron Acemoglu and Joshua Angrist use changes in laws that mandate a minimum age of leaving school to estimate the social returns to schooling. (86) They find little evidence for human capital externalities using this method, but it seems unlikely that raising the skills of the people at the bottom of the skill distribution would generate the human capital externalities that lie at the heart of new growth theory. Enrico Moretti uses land grant colleges as an instrument for area education and looks at longitudinal data to correct for individual fixed effects, (87) He finds much stronger evidence supporting human capital externalities.

However, the model makes it difficult to interpret either approach unless these instruments are understood to be changes in the skill-specific amenities. Historical human capital levels will be valid instruments only when they have no direct effect on any of the productivity parameters. In the context of the model, this means that they must work through amenities. Moreover, just as in the case of agglomeration economies, the case for spatial policies that change the distribution of population depends on nonlinearities in human capital spillovers. Using the above framework, where we assume that utility is U([Y.sup.k.sub.i], [[theta].sup.k.sub.i]) and the production function is A([[??].sub.i]) F([[??].sup.k.sub.i]):

[FIGURE 16 OMITTED]

Proposition 4: (a) A competitive equilibrium, where net unearned income is constant across space, can be a social optimum if and only if both [U.sub.Y] ([Y.sup.k.sub.i], [[theta].sup.k.sub.i]) and

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are constant across space for every group k.

(b) Relative to a competitive equilibrium where U([Y.sup.k.sub.i], [[theta].sup.k.sub.i]) is constant across space, welfare can be improved by moving type k people from area j to area i if and only if

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

This proposition parallels Proposition 2. Just as in that case, the marginal utility of income, in this case within groups, must be constant across space in a social optimum. Moreover, the spillover effect from the group also needs to be constant across space. If this condition does not hold, then welfare can be improved by moving type k individuals to an area where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is higher. Our assumption that productivity depends on average skill levels yields the unambiguous result that if type k individuals are present in numbers below the average in area j and above the average in area i, they should be moved from j to i, raising the average ability of both places. This implication would not survive a more general skill spillover function that does not depend solely on average skills.

Just as in the case of Proposition 2, this proposition suggests that a federal spatial policy would be beneficial only if there are nonlinear effects. Moving skilled people from one area to another is advantageous only if the impact of skills differs across areas. We do not know of an instrumental variables strategy that can effectively estimate the degree of nonlinearity in the relationship between area-level human capital and wages. The imprecise relationship between instruments, such as historical levels of human capital, and human capital today makes it enormously difficult to reliably estimate the degree of nonlinearity. As a result, we restrict ourselves here to ordinary least squares estimates. We recognize that these estimates are plagued with the two problems facing most attempts to estimate human capital spillovers: the potential correlation between area-level human capital and unobserved individual-level skills, and the endogeneity of area-level human capital.

To illustrate the ordinary least squares relationships, regression 9-2 in table 9 finds that the impact of area skills on wages is slightly higher for more skilled than for less skilled places. The difference between the effects is only weakly significant, and there are many issues with interpreting this coefficient. However, it does cast doubt on the view that policy should be trying to move more skilled people into less skilled areas.

In principle, spillovers might come from different industries rather than different levels of human capital. This would justify government policies that create clusters of either industry or human capital. The U.S. government has never actively embraced such efforts, although certainly many states and localities, such as North Carolina's Research Triangle, have tried to build areas around particular activities. Many state economic development policies have sought to target particular industries in particular locales in the hope that the magic of agglomeration economies would make those places thrive. Outside the United States, countries have explicitly tried to build industrial areas or to induce human capital to migrate to particular regions.

Regressions 9-3 and 9-4 in table 9 address the skill level of industries rather than workers. The idea behind these regressions is that spillovers are created by working in cities surrounded by skilled, successful industries rather than working in less skilled industrial clusters. We use the national Census microdata to estimate average skills at the industry level and then use metropolitan area-level data to calculate the average skill level of the industries in the area. We continue to control for industry fixed effects in these regressions. We find that as the average educational mix of an area's industries rises, average earnings in that area also rise. A 10 percent increase in the predicted share of the industry's employment with a college degree raises wages by 5.9 percent.

Regression 9-4 finds significant nonlinearities in this effect. Increasing the skill mix of the industry grouping is quite unimportant for areas with a low average industry-based skill mix. The effect gets much stronger for areas with a high predicted skill level. The variable's impact is extremely convex, which suggests that it might be beneficial to push skilled industries to locate with other skilled industries.

Since the existence of general human capital externalities is also suggested by the link between human capital and area population growth, we performed similar regressions for the average skill level of an area's industries. In table B1 in appendix B, we show that this average industrial skill level increases area population, as it should if it increases productivity, and population growth. Just as in the wage-level regressions, the impact of this variable is convex in both the population and the population growth regressions (table B2 in appendix B).

There are reasons to be skeptical about the skill clustering policies suggested by regressions 9-2 and 9-4. First, these regressions represent correlations, not identified causal estimates. Second, policies that induce skilled groups to cluster together would tend to increase segregation by skill, which would probably end up increasing inequality as well. (88)

Finally, in regressions 9-5 and 9-6 in table 9 we turn to the question of industrial concentration. Does it make sense for cities to try to specialize in a small number of industries? Are workers more productive in places that have concentrated in a few core areas of excellence? Regression 9-5 controls for individual characteristics, again including industry fixed effects, and looks at the impact of overall industrial concentration at the metropolitan-area level. We use a Herfindahl index based on three-digit industries to measure the degree of concentration. In this case we find that more-concentrated places have lower productivity. This result is in line with the finding by Glaeser and others that industrially concentrated areas grow more slowly. (89)

Regression 9-6 looks within broad sectors. We measure the degree of concentration based on three-digit industries for each sector within each metropolitan area. This allows us to control for both metropolitan-area and industry fixed effects. In this case the workers in less concentrated one-industry groups earn more, but this is comparing them with other workers in the same metropolitan area. One concern with this type of regression is that if workers can readily move across industries within a metropolitan area, then productivity differences should be eliminated within that area.

Regression 9-6 confirms within broad sectors the result from regression 9-5. Having a wide range of industries helps the entire metropolitan area, and more diversity within a given sector in a given metropolitan area increases wages in that sector. Although neither regression is based on anything like a natural experiment, the consistency of the results supports the value of industrial diversity for an area's aggregate welfare.

These results suggest that concentrations of skilled workers and skilled industries may increase local productivity. Yet we worry about the equity consequences of a policy that would encourage such concentrations, especially since skilled people already tend to move disproportionately into skilled areas. The results on industrial concentration are certainly only suggestive, but they cast doubt on the view that cities are best off creating specialized industrial clusters.

The strongest results in this section support the view that skilled workers and skilled industries generate positive effects. At the national level, however, there is little evidence to support the view that any gains would be realized by moving these industries into less developed areas. If anything, the results point in the opposite direction. On the other hand, for local leaders the existence of human capital externalities suggests that attracting skilled workers and skilled industries may be the most promising avenue for improving the success of their region.

Conclusion

Urban economists generally believe that the world exhibits spatial equilibrium, agglomeration economies, and human capital spillovers. The concept of spatial equilibrium suggests that policies that aid poor places are not necessarily redistributive and will have indirect consequences, for example pushing up housing costs and inducing poor people to move to poor areas. Agglomeration economies and human capital spillovers are both positive externalities, whose existence raises the possibility that national spatial policies could increase welfare. However, for these externalities to create a justification for any particular spatial policy, these externalities must be stronger in some places than in others. Even if we accept the existence of agglomeration economies, those economies make the case for subsidizing particular places only if they are nonlinear. Empirically, we cannot be confident that these effects are either convex or concave. Economics is still battling over whether such spillovers exist at all, and we are certainly not able to document compelling nonlinear effects.

This does not mean that urban economics yields no implications for public policy. At the local level, human capital spillovers suggest policies for leaders who are trying to maximize either income or wages. If such spillovers are important, then increasing the skill level of a city, by either attracting or training more skilled people, will raise wages and population. At the national level, investment in infrastructure should be based on the tangible benefits of that infrastructure for consumers, not on the ability of that infrastructure to change location patterns. Indeed, the current tendency to subsidize transportation disproportionately in low-income, low-density states seems to run counter to what little is known about where agglomeration effects are more important.

Urban economics also yields suggestions for housing policy. Support for building new structures in declining areas merely subsidizes construction where it is least desired. After all, places that are in decline are defined in part by already having an excess of buildings relative to demand. A federal policy that enabled more building in those high-income areas that currently restrict new construction through land use controls seems more likely to increase welfare.