ࡱ>  g  bjbjVV  r<r<%@P`8 8 8 4l l l h !tl (#($$:^$^$^$9%9%9%  $؂L198 T9%9%TT18 8 ^$^$ja{a{a{T8 ^$8 ^$ a{T a{a{:}, ~^$p`s}0~ օsօ ~ ~օ8 ~9%A6* a{kB 'L9%9%9%11Uw 9%9%9%TTTTօ9%9%9%9%9%9%9%9%9% :  The Wealth of Cities: Agglomeration Economies and Spatial Equilibrium in the United States by Edward L. Glaeser Harvard University and NBER And Joshua D. Gottlieb Harvard University February 26, 2009 Abstract Empirical research on cities starts with a spatial equilibrium condition: workers and firms are assumed to be indifferent across space. This condition implies that research on cities is different from research on countries, and that work on places within countries needs to consider population, income and housing prices simultaneously. Housing supply elasticity will determine whether urban success shows up in more people or higher incomes. Urban economists generally accept the existence of agglomeration economies, which exist when productivity rises with density, but estimating the magnitude of those economies is difficult. Some manufacturing firms cluster to reduce the costs of moving goods, but this force no longer appears to be important in driving urban success. Instead, modern cities are far more dependent on the role that density can play in speeding the flow of ideas. Finally, urban economics has some insights to offer related topics such as growth theory, national income accounts, public economics and housing prices. I. Introduction Much economic research has focused on the wealth of nations. Many economists have tried to understand national business cycles and the higher incomes and faster income growth that occur in some countries. Yet the within-country differences in income and productivity are also quite striking. The average income per capita in 2007 in the San Francisco metropolitan area was above almost 60,000 dollars; the comparable figure for Brownsville, Texas, is under 20,000 dollars. Per capita gross metropolitan product (GMP) is more than three times higher in New York than in El Paso. The differences in population density across space within countries are even more striking. As of the last census, 68 percent of Americans occupied only 1.8 percent of the countrys land area. Facts of this sort motivate the central question of urban economics: Why do cities exist? To answer this question we also must also understand why dense areas are so much more productive. Urban economists approach this question by studying, among other things, within-country variation in incomes, population density and housing prices. This allows them to treat population densities appropriatelyas outcomes that are determined jointly with prices and wages. The fields central theoretical tool is the spatial equilibrium, which assumes that welfare is equalized across spaceat least for marginal migrants. The spatial equilibrium concept guides urban models of housing prices and industrial agglomeration as well as empirical work on city growth and the urban wage premium. In this paper, we review recent research on the economics of cities. We begin by presenting a version of the standard spatial equilibrium model that guides our interpretation of empirical work. The model has three core equilibrium conditions. Workers must be indifferent between locations, firms must be indifferent about hiring more workers and builders must be indifferent about supplying more housing. These three conditions provide the labor supply curve, housing supply curve and labor demand curve that collectively determine area population, wages and prices. Exogenous differences across space in productivity, amenities and the construction sector drive differences in density, incomes and home prices. We allow for the possibility of agglomeration economies, which exist when productivity rises with population. We first use this model to discuss the dramatic rise of Sunbelt cities. No variable can better predict city growth over the past 50 years than January temperature, yet it is unclear a priori why warm places have grown so dramatically. The spatial equilibrium model enables us to assess whether this growth reflects rising Sunbelt productivity, or an increased willingness to pay to enjoy warmth, or greater housing supply in the South. Over the past 50 years, Sunbelt productivity has increased, but in the past decade incomes have fallen in warmer areas. Housing prices have also stayed low and real wages have risen in the South. These facts, interpreted using the spatial equilibrium model, imply that the recent rise of cities like Atlanta, Dallas and Houston owes more to elastic housing supply than to amenities or productivity. The spatial equilibrium model is also needed to make sense of the dramatic connection between density and income within the U.S. (Ciccone and Hall, 1996). The standard regression of income on population makes little sense if population levels themselves endogenously increase with rising productivity. Natural factors or historical population levels are valid instruments for current population only if those instruments operate through shifts in housing supply or amenities that affect population for reasons unrelated to productivity. Despite the difficulties involved in estimating agglomeration economies, the dramatic concentration of people in high-income urban areas and the absence of obvious exogenous sources of productivity heterogeneity have lead most urban economists to believe that important agglomeration economies exist. In Section III of this paper, we review three core theories about agglomeration economies. Cities are ultimately nothing more than proximity, so the returns to urban concentration can be seen as reductions in transport costs. One set of theories about agglomeration economies emphasizes the gains that come from reduced costs of moving goods across space (Krugman, 1991a). A second set of theories emphasizes labor market pooling and the benefits of moving people across firms (Marshall, 1890). A third set argues that cities speed the flow of ideas, which creates human capital at the individual level and facilitates innovation (Jacobs, 1968). Some of these theories emphasize the benefits that come from co-location of diverse firms; others emphasize the gains from single-industry agglomerations. Empirical research on the sources of agglomeration economies uses information on both prices (the wages of workers) and quantities (the location of industry). For example, evidence on the co-location of industries shows that firms locate near industries that are suppliers or customers (Ellison, Glaeser, and Kerr, 2007; Kolko, 2000). The existence of human capital spillovers is suggested both by the positive correlation between individual wages and skills in the city, and by the connection between skills and city population growth. Despite the long history of research on these questions, the field has still not reached a consensus on the relative importance of different sources of agglomeration economies. There is some evidence supporting the continued importance of transport costs for goods. Gravity models suggest that firms are drawn to areas with robust local demand. Evidence on the co-location of industries provides further support for the importance of input-output linkages in determining industrial location, but these effects are often small. However, manufacturing firms and industries with high transport costs tend to avoid dense, urban areas. These facts cast doubt on the view that cities succeed by reducing the costs of moving goods. Labor market pooling and the gains from being able to move across firms remains an important idea, but no one has managed to make the case that cities rise or fall based on this force. A significant body of recent evidence points to the importance of skills and ideas in determining urban success. Cities with higher concentrations of skilled workers pay higher wages, and this tendency has been rising over time (Rauch, 1993). Skills predict urban growth, especially in the colder areas of the country (Glaeser, Scheinkman and Shleifer, 2005). Workers who come to cities dont receive the urban wage premium immediately, but instead experience faster wage growth rates, which suggests faster human capital accumulation in urban areas (Glaeser and Mare, 2001). After reviewing the empirical work on the economics of urban agglomerations, we turn to the insights from urban research that might be useful for other fields. For growth and development, the evidence from cities supports the view that human capital is a particularly important source of productivity and productivity growth. Urban intellectual interactions mean that innovations are highly correlated within cities and we should expect to see significant heterogeneity in the rate of technological change across space. As a result, it may make more sense to attribute events like the English industrial revolution to the random connection of a few people than to deep-seated national characteristics. The urban perspective emphasizes factor mobility and challenges researchers looking at sub-national data to analyze income, population and housing prices simultaneously. Running nave income change regressions, without also considering changes in employment and housing prices, misses the fact that labor is quite mobile across places within the U.S. Housing supply elasticity will determine how much an intervention affects urban prices and quantities. These insights are essential for public economists seeking to use state-by-state variation to assess different policies and for growth economists using within-country data. Urban economics also suggests that there are difficulties with using aggregate data to understand national inequality and income levels. Since higher-income people live disproportionately in high-income, high-cost areas, while lower-income people live disproportionately in low-cost areas, a failure to correct for local prices and amenities will overstate national income inequality. In particular, we have to be wary of using expenditure-weighted mean prices to correct for the income of the median household. Those price indices will tend to reflect the high housing prices in high-cost areas even though the median household is likely to live in a cheaper area and face a lower cost index. House prices represent the interaction of supply conditions and the individuals desires to live and work in certain locales. Factors such as income heterogeneity across space, amenities and land use restrictions will therefore drive housing prices. This approach is quite different from the macroeconomic perspective, which emphasizes national income and interest rates. The urban perspective on housing also differs from the standard finance perspective on housing, by emphasizing that individuals begin life short housing (Sinai and Souleles, 2003). Changes in house prices do not naturally represent an increase in national wealth since the increase in asset values has been offset by an increase in price of securing a basic necessity. Finally, the urban emphasis on mobility implies that local poverty is more likely to reflect something good that an area is providing for the poor than a failure in local labor markets. Poor people are attracted to big cities because they offer access to public transportation and inexpensive rental housing. Further attempts to improve the lives of poor people will tend to attract more poor people to places where other low-income people live. We now turn to the spatial equilibrium model that unifies urban economics. II. Metropolitan Heterogeneity and Spatial Equilibrium Just as macroeconomics explores both differences in growth rates and differences in GDP levels across countries, urban economists wonder why some cities are rich, some cities are growing, and others are doing neither. Why have some southern cities, such as Atlanta, and some former rustbelt areas like Boston seen dramatic increases in output per capita over the last 30 years, while others, like Detroit and Flint, have declined from great industrial centers to places known more for poverty than for production? How is it possible that the gap between poor and rich areas within a single country can be over 100 percent? Most importantly, why is there such a strong connection between city size and productivity, as shown in Figure 1? One response to these puzzles is that productivity differences represent temporary aberrations that will disappear as capital flees high cost areas and labor follows higher wages. Table 1 shows the correlation between initial income levels at the metropolitan area and ex post changes in both income and population for each decade since the 1960s. We have reported the coefficients and standard errors from regressing the change in the logarithm of income and the change in the logarithm of population against the initial income level. In every decade except the 1980s, there has been substantial income convergence. Convergence seems to have slowed down since 1980, but the tendency of incomes to grow faster in poorer places, emphasized by Barro and Sala-i-Martin (1991), continues to hold. (But measurement error in income can lead to a spurious finding of mean reversion, so these facts must be treated warily.) The second column shows the relationship between initial income in each decade and subsequent population growth. If people migrate to high income areas, then we would expect initially high incomes to predict population growth. There is a positive relationship between income and population growth in the 1960s, a negative correlation in the 1970s and no significant relationship since then. Incomes are converging, but this is not because people are moving to disproportionately to high wage areas. Does the phenomenon of income convergence suggest that current income differences are only temporary? Figure 2 shows the 0.77 correlation between the logarithm of income per capita in 1970 and income per capita in 2000. There has been some convergence since 1970, but over 30 years, rich places have stayed rich and poor places have stayed poor. This continuing income disparity has motivated urban economists to think about a spatial equilibrium where differences in per capita income and prices can persist for many decades. The Spatial Equilibrium The methods employed by urban and growth economists differ along one major dimension. Cross-national work rarely, if ever, assumes that welfare levels are equalized across space. After all, one goal of cross-country work is to understand how to make people in poorer countries better off. However, since the pioneering work of Mills (1967), Rosen (1979) and Roback (1982), cross-city work has almost always assumed that the free migration of workers creates a spatial equilibrium where utility levels are equalized. This assumption reflects the fact that over 40 percent of Americans change homes and around 20 percent of Americans change counties every five years. The high mobility of labor leads urban economists to assume a spatial equilibrium, where elevated New York incomes do not imply that New Yorkers are better off. Instead, welfare levels are equalized across space and high incomes are offset by negative urban attributes such as high prices or low amenities. By assuming that workers choose their locations, urban economists gain at least the possibility of explaining the large concentrations of people in urban area. We can only explain city sizes if our models allow people to move into cities. Following the standard models of urban economics, we assume people can move across places immediately and costlessly. In reality, of course, these adjustments take time and money. Blanchard and Katz (1992) quantify the process of these adjustments and find that regional shocks are largely absorbed by migration flows, and house prices take around five years to adjust. Glaeser and Gyourko (2005) argue that durable housing may cause urban responses to productivity shocks to be spread over decades. Hornbeck (2008) finds that large exogenous shocks to specific regionsspecifically due to soil erosion during the Dust Bowlwere mostly absorbed over long periods by largely-permanent migration. Saks and Wozniak (2007) find that migration flows respond strongly to business cycle variables, and do so differentially for workers in different stages of their careers, and Glaeser and Redlick (2008) find that education influences the size of migration flows. The slow migration response to local shocks does not imply that spatial equilibrium holds only over long periods. As long as house prices or rents can change quickly, the price adjustment suffices to maintain the spatial equilibrium. Glaeser et al. (1995) use a spatial equilibrium model where migration responds slowly to shocks but the spatial equilibrium is always maintained because of housing price flexibility. This leads us to ask if this is occurs in practice: Do housing costs actually move enough to equalize utility levels across space? If anything, Glaeser and Gyourko (2007) find that there is too much housing price volatility relative to volatility in local incomes. More generally, measurement difficulties mean that it is quite difficult to reject the hypothesis that welfare levels are equalized across space. The difficulties of assessing expected housing price appreciation makes it difficult to measure expected housing costs for homeowners. The fact that only a modest percentage of the population rents, and rental units are quite different from the standard stock, makes it difficult to avoid this problem by using rental prices. Researchers who use the spatial equilibrium assumption can either feel comfortable knowing that this assumption has never been rejected empirically or uncomfortable because data limitations make it impossible to test rigorously at high temporal frequencies. It is hard to see how urban economists could test the spatial equilibrium assumption with the same degree of empirical precision used by financial economists to evaluate the no arbitrage assumption in financial markets. American scholars often find it more natural to assume a spatial equilibrium than their European counterparts. After all, migration flows are much larger in the U.S. than in Europe, and Decressin (1993) finds that population flows in Europe respond much less to local labor market shocks. Hopefully, future work will better enable to us to determine whether Europe regions are better understand as separate economies or as places linked by the free migration of labor. There is also a tradition of using the spatial equilibrium model in developing countries. The Harris-Todaro (1970) model, where high wages in big cities are offset by high levels of unemployment is a classic example. The presence of migrants who bring the country into spatial equilibrium requires us to interpret many city characteristics as equilibrium outcomes rather than exogenous forces. In particular, a complete urban model has at least three key area-level dependent variables: wages, population levels and housing prices. These three variables are determined by three equilibrium conditions. First, workers must be indifferent across space. This ensures that real wages, corrected for local price and amenity levels, must be equalized across metropolitan areas. Second, firms must be in equilibrium, which means that wages equal the marginal productivity of labor. Third, the housing market must be in equilibrium, which requires housing prices to equal the costs of providing housing, at least in growing markets. The individuals location choice implies a spatial equilibrium where identical people have the same utility level across space. Following Alonsos (1964) pioneering book, a rich literature has examined the spatial equilibrium assumption within metropolitan areas. The most studied implication of that assumption was that prices would decline with commuting costs. DiPasquale and Wheaton (1996) provide the textbook treatment of this topic. Other authors have looked at the connection between housing costs and local amenities, such as good schools (e.g. Black, 1999) or disamenities, such as airports and crime (e.g. Thaler, 1978). The primary difference between the within-city spatial equilibrium work and the research that has applies the assumption across cities, is that within cities wages are typically treated as fixed. Across cities, wages differ and higher nominal wages are typically offset by higher housing costs. Higher real wages are offset by lower amenities. The spatial equilibrium yields some counterintuitive implications; for example, high real wages in an area imply that something else is bad about the place. Rochester, Minnesota, and Springfield, Illinois, are two American metropolitan areas with extremely high real wages. While correcting for national price levels almost always makes sense, there is considerable information in local incomes that is lost by correcting for local price levels. When we assume that firms behave competitively, the marginal product of labor will be reflected in nominal local wagesnot wages corrected for local prices. That information can be lost when we correct for local prices. In addition, if amenities are constant across space, then the spatial equilibrium model predicts that real wages will also be constant. Yet some places may have high wages, and high productivity levels, that are offset by high prices. Those high wages are informative because they help us to understand the correlates of local productivity. High prices will also be informative since they yield information about supply conditions in the local housing market. People and Prices Across Space We now turn to a benchmark model that draws on Rosen (1979) and Roback (1982) and can serve as the basis for empirical work on cities. Like growth economists, we begin with the production function , where  is a time-city specific productivity variable, F(.,.) is a constant returns to scale production function, K is capital and L is labor. The Cobb-Douglas production function,  is particularly natural for empirical work. This can either be thought of as an aggregate production function or a firm-level production function in a world with an elastic supply of firms. The factor inputs, K and L, can represent scalars or vectors. Given the importance that skilled workers seem to play in urban growth, it is particularly natural to divide the labor force into two types of labor, but here we will treat labor as homogeneous. We will divide capital into traded capital, denoted , that is bought at a nationwide, exogenous price of , and non-traded capital, denoted , that is city-specific and bought at local, endogenous price of . The stock of non-traded capital is fixed at . We assume that total capital K, is a geometric weighted average of the two types of capital so that total output is , where  denotes the share of non-traded capital. Non-traded capital offers diminishing returns at the city level, even when firms themselves face constant returns to scale. Firms first order condition for labor produces a city-level labor demand equation of , where  depends on constant terms, including the price of traded capital. At the city level, higher wages reflect higher productivity, more non-traded capital or fewer workers. In the economics of growth following Solow (1956), the production function is then connected to savings and investment decisions. Occasionally, the labor force itself is connected to fertility decisions (Barro and Becker, 1989). In urban models, these more dynamic considerations are generally swept under the rug. Non-traded capital is fixed and traded capital is perfectly elastically supplied at the fixed price. More sophisticated investment decisions could be brought into urban economics, and probably should be, but these issues have generally been treated as second-order. The utility levels of workers are assumed to equal , where  is the consumption of traded goods,  refers to non-traded goods (especially housing) and  represents local amenities. As in Roback (1982), this can be reduced to an indirect utility function  where  is income in place i at time t and  is the price of non-traded goods. In a static model, the spatial equilibrium assumption means that utility levels are equal across space. In a dynamic model, the spatial equilibrium assumption generally means only the lifetime utility levels will be equalized across space, but if migration is sufficiently cheap, it also implies that utility flows are equalized across space. Holding amenities constant, this yields the prediction that , where the ratio  equals the demand for the non-traded good. High income levels are offset by high prices. Again, the Cobb-Douglas utility function is a natural way to empirically use the spatial equilibrium assumption. Under this assumption, utility can be written as , which will equal  times a constant. The spatial equilibrium assumption requires this to equal , the reservation utility within the country. This formulation suggests that . Figure 3 shows the relationship between the logarithm of median home prices and the logarithm of median household income across space. The coefficient is 0.34, which is quite close to the average share of expenditure on housing, or . The final critical production sector concerns the making of non-traded goods, or homes. If we are interested in a truly static model, as in Roback (1982), it is natural to follow her assumption that non-traded goods are produced like traded goods with labor, traded capital and non-traded capital. In this case, the production function might be , where  refers to productivity in this sector. We will assume that the traded capital here is the same as the traded capital in the traded goods sector, but that non-traded goods require their own, distinct form of non-traded capital (presumably land), denoted . If total production of the non-traded good equals , then total output for this good will equal a constant times . The total labor allocated to the production of non-traded goods is  times the total population of the city. These equations can then be used to solve for city size, city wages and the wages of non-traded goods:    The values of these coefficients (except for the essentially irrelevant constant terms) are given in the first column of Table 2. These equations give us the relationship between the endogenous outcomespopulation, and pricesand the exogenous variablesproductivity in the traded goods sector, productivity in the non-traded goods sector, and amenities. These three static equations tell us that if an exogenous variable, denoted , influences productivity in the traded and non-traded sectors as well as amenities, then the relationship between that variable and population, prices and wages can be used to infer the impact it has on productivity, amenities and housing supply. Let ,  and  be the marginal impact of this variable on traded-sector production, non-traded production, and amenities. If the coefficients from regressions of population, wages, and price on this variable  are ,  and , respectively, then linear combinations of these parameter estimates provide unbiased estimates of  ,  and . The relationship between the exogenous variable and consumer amenities can be estimated with a linear combination of the price and wage coefficient, specifically . This is the way to understand the Rosen-Roback contribution. Earlier work simply looked at prices to infer the impact of location-specific attributes, like crime, and utility. The Rosen-Roback correction requires also accounting for the impact that amenities may have on income. To use this equation, we need a parameter estimate for , such as 0.3, the average share of household spending on housing. An exogenous variable that impacts traded goods productivity will increase both city size and wages. Both variables must be used to infer the productivity impact of that increase. The impact of an exogenous variable on traded good productivity, , will equal the weighted sum of the coefficients on that variable in the population and wage equations; specifically, . If non-traded capital is a particularly small part of the production process, then wages are most important for measuring the impact of a variable on productivity. In that case, even tiny increases in productivity can create large increases in the overall size of production, and as a result a citys size provides little information about productivity levels. Again, we need parameter values to implement this equation. Labors share in total output may be two-thirds, so we can assume =1/3. One estimate of the share of non-traded capital in production, , might be 0.1. Increases in housing sector productivity will increase population and lower both wages and prices. To identify the impact of a variable on housing sector or non-traded goods productivity, we must combine the variables connection with population, income and housing prices: . The parameter  reflects the share of non-traded capital (e.g. land) in the production of housing. Glaeser, Gyourko and Saks (2005) estimate that approximately thirty percent of housing costs are associated with land and permitting across the U.S. Gyourko and Saiz (2006) estimate that 57 percent of construction costs are associated with labor costs. This suggests values of 0.4 for labor costs and 0.3 for traded capital. The same equations are the workhorses of dynamic work on urban change. First-differencing equations (1) through (3) gives us: (1)  (2)  (3)  Letting ,  and , and denoting the estimated coefficients from population change, income change and non-traded goods price changes regressions by , and  respectively, then , and . As such, essentially the same formulas that are used to transform static regression coefficients into underlying parameters can be used to transform coefficients from growth regressions into parameters of interest. One issue with this transformation, however, is the use of housing prices to capture the prices of non-traded goods. In the model, these prices  should be interpreted as the flow cost of non-traded services like housing. These might be appropriately identified as rental costs, but as Glaeser and Gyourko (2007) emphasize, renters are so unlike owners that rental properties often fail to give a good sense of what the flow cost of housing is within a metropolitan area. As such, we need to consider the relationship between the stock price of housing and the flow price of housing. To move from flow costs to the stock price of housing, we must use a dynamic equation of the form , where  represents the actual price of a house,  represents maintenance and tax costs that are approximately proportional to the house price, r represents the interest rate and  is the expected price of housing next period. Solving this equation forward implies that . If the future price of housing is expected to grow at a constant rate so that , then , and . Assuming a constant expected growth rate allows us to use the prices of homes as our proxy for the user cost of housing. If the constant growth rate assumption were violated, or if rates of return changed over time, then this assumption would be problematic. An Example: Does the Rise of Sunbelt Cities Represent Amenities or Production? To illustrate the use of the spatial equilibrium model to understand urban change, we will use it to make sense of the growth of the Sunbelt, which is among the most striking, studied and debated trends in regional economics over the last 50 years. Over the past six years, Americas fastest growing metropolitan areas are Atlanta, Dallas, Houston and Phoenix. January temperature is currently positively correlated with both metropolitan area population and the growth of metropolitan area population. Cheshire and Margini (2006) find similar results within, but not across, European nations. If we look across metropolitan areas, the relationship between January temperature and size is: (4) Log(Population 2000) = 12.2 + 0.017*Average January Temperature (0.2) (0.005) There are 315 observations, and standard errors are in parentheses. More attention has been paid to the connection between growth and temperature across areas. In the 1990s, this relationship was: (4) Log(Population 2000/Population in 1990)=0.016 + 0.003*Average January Temperature (0.14) (.0004) There are again 315 observations and the R-squared is 0.162. This growth relationship is shown in Figure 4. The rise of the Sunbelt provides us with an opportunity to illustrate how the spatial equilibrium model can differentiate between different theories of Sunbelt success. Some authors, such as Barro and Sala-i-Martin (1991) and Caselli and Coleman (2001) have emphasized capital accumulation and structural transformation in the South. These are changes that can be interpreted as increases in the productivity variables, particularly non-traded capital. Other authors, such as Besley, Persson and Sturm (2005), Olson (1983), and Cobb (1982), also point to productivity growth but suggest that this growth resulted from improvements in Southern political institutions. An alternative literature (Borts and Stein, 1965, Meuser and Graves, 1995) has pointed to consumption amenities in the South. One version of this literature emphasizes technological changes, such as air conditioning, that were complements to warmth. A second version suggests that rising incomes in the country as a whole would lead people to sacrifice productivity to live in more pleasant areas. Still a third view is that the rise of the Sunbelts population reflects local policies that support new construction of housing (Glaeser and Tobio, 2007). To differentiate between these hypotheses, we can use the connection between January temperature, wage growth and price growth. We begin with cross-sectional wage regressions using microdata from the 2000 Census and then move to the growth regressions that are our primary focus. In our income regressions, shown in Table 3, we include only prime-age males (between 25 and 55) and we control for education and age. In our housing price regressions, we include a battery of housing characteristics as controls. Regression (1) shows that there is a significant negative association between January temperature and incomes. Combining the coefficients from the population regression above with the coefficient from the wage regression (-0.19), yields an overall estimate of the impact of January temperature on productivity of -0.14, suggesting that warmer places within the U.S. are still less productive (by 0.14% per degree of January temperature). This may reflect the legacy of older capital investments, or it may mean that colder places with significant population levels have omitted productivity variables that justify living in the cold. Combining the wage coefficient with the coefficient in the price regression, column (2) in Table 3, yields an amenity estimate of 0.59, meaning that people will sacrifice 0.59% of real wages per degree Fahrenheit. This result is supported by the third regression showing the impact on real wages, or in the model. In this case, we estimate a coefficient on January temperature of -0.52, which gives us another estimate of the amenity value of this variable. This exercise follows the Rosen-Roback static literature on quality of life variables, where papers such as Gyourko and Tracy (1989) use real incomes to infer the utility value of different local attributes. Combining population, price and income data also suggests that there is less housing supply in places with warm Januaries, which may reflect the abundance of older housing in declining, colder metropolitan areas (Glaeser and Gyourko, 2005). We look at the connection between January temperature and growth in the 1990s by interacting January temperature with a dummy variable that equals one for observations in 2000. We also include metropolitan area dummies and either individual or housing characteristics in the wage and housing price regressions, respectively. The overall coefficient on wages, shown in column (4), is weakly negative (-0.001). The connection between housing price growth and January temperature is significantly negative (-0.43), which suggests that amenities are actually falling in warmer places over this time period. The positive interaction between January temperature in real wage growth in regression (6) suggests a similar interpretation. A more detailed look at the data suggests that the January temperature effect on real wages combines a long-run secular rise in real wages in the South and desert regions with a cyclical decline in housing prices in California between 1990 and 2000 (Glaeser and Tobio, 2007). Combining the coefficients from all three regressions suggests that over the 1990s, January temperature was associated with neither rising productivity nor rising amenity values. Stagnant wages and declining housing prices both suggest that amenity values were not increasing. Instead, the rise of Sunbelt cities in the 1990s seems to be related to abundant housing supply, which reflects the combination of abundant land, freeways and pro-growth permitting. Over the longer run, Sunbelt status is positively associated with both productivity growth and abundant housing supply, but not with rising amenity values (Glaeser and Tobio, 2007). The urban growth literature has paid far too little attention to the differences in housing supply that are critical to understanding the growth of metropolitan areas like Houston and Atlantaplaces with high growth levels, moderate prices and moderate incomes. At the city level, the number of homes and the number of people are essentially the same thing so that differences in housing supply elasticity across space can have a large impact on how cities respond to positive shocks. Figure 5 shows the relationship between city growth from 2000 to 2007 and house prices in 2000. While many places saw high prices along with expansion, the pattern clearly fails to hold for about 40 of the most expensive cities. These places had virtually no population growth but still had the highest house prices in the country. Simultaneously, the 20 or so places with the largest population growth had moderate prices. Since the places that expanded the most are not expensive and the places that are expensive did not expand, housing supply must differ across areas. III. Agglomeration Economies and the Existence of Cities The central question of why cities exist ties together almost all of urban economics. Most of the field that follows von Thunen (1825) and Marshall (1890) can be understood as an attempt to make sense of the remarkable clustering of human activity in a small number of urban areas. The spatial equilibrium model again provides the grounding for thinking about the reasons for urban concentration, which again might reflect consumer amenities, housing supply or productivity advantages. Moreover, cities might form because some places have innate advantages in these areas-- New York Citys harbor increases productivity and San Diegos climate is pleasantor because clusters of people endogenously increase amenities, housing supply or productivity. There are certainly cases where cities have formed for consumption rather than production reasons. The early history of Los Angeles, for example is replete with examples of people, such as prosperous Midwestern retirees, who came there to enjoy the climate. Urban amenities, such as a thriving restaurant or theater scene, can occur endogenous with an influx of population. However, the spatial equilibrium model allows us to easily reject the view that consumer amenities are the primary force driving urban concentration in the U.S. If cities were driven by amenities, then real wages should be lower in big urban areas, and this is not the case. The real wage premium associated with living in big cities has declined over time (Glaeser and Gottlieb, 2006) which suggests that cities have become relatively more pleasant places to live, perhaps because of the decline in crime (Schwartz, Susin and Voicu, 2003). Yet even today, however, people require a mild wage premium to locate in big urban areas. It is even more implausible to think that big cities exist because these areas have an innate advantage in supplying housing or because density makes it easier to build. Data on construction costs show that it costs considerably more to build vertically than horizontally (Gyourko and Saiz, 2006). Across metropolitan areas, housing prices rise substantially with city size, so the spatial equilibrium approach suggests that housing supply is more expensive in those places. There are particular places, such as the growing Sunbelt metropolises or the declining cities of the Midwest, where abundant housing supply boosts population, but this is not generally true for urban areas. We are left with the view that cities exist because they are areas with high levels of productivity, which might occur because people come to places that are innately more productive or because density itself enhances productivity because of agglomeration economies. The strong correlation between urban size and productivity, shown in Figure 1, supports this view. Does that link reflect agglomeration economies, where size creates productivity, or heterogeneous local productivity levels which then cause agglomeration? Many cities have undoubtedly benefited significantly from innate productivity advantages, particularly waterways. The rise of New York City is intimately connected with the strengths of its spectacular natural harbor (Albion, 1938). Every one of the 20 largest American cities in 1900 was on a major waterway, reflecting the enormous cost savings associated with moving goods over water. Pittsburgh and its iron industry owes much to nearby coal mines. Chicagos stockyards benefited from proximity to the rich, black soil of Iowa (Cronon, 1990). Davis and Weinstein (2001) examine the continuing importance of natural advantage by looking at population growth among Japanese cities that were devastated during World War II. Despite significant population losses during the war, bombed cities almost all returned to their pre-war growth paths. If agglomeration economies were very important, then these cities might have been derailed from their long run growth paths. Since significant losses in population during the war did not materially impact the growth in these areas, agglomeration economies might not be all that important relative to underlying fundamentals. However, it is quite possible that the natural advantages of these places were actually man-made improvements, such as transportation networks that either survived the war or were rebuilt. As such, it is hard to interpret these results as strong evidence for true innate advantage. The substantial decline in shipping costs over the 20th century makes it hard to believe that innate productivity advantages remain terribly significant. The cost of moving a ton by rail has declined in real terms by more than 90 percent since the late 19th century and the rise in trucking has been even more dramatic (Glaeser and Kohlhase, 2004). As a result, access to the Great Lakes, other water systems and raw materials like coal and corn, has become less valuable over the 20th century. The growth of cities without access to major waterways has accompanied this decline. A century-long county growth regression yields: (5) Log(Population 2000/Population in 1900) = 0.62 + 0.00122* Distance to River (0.03) (0.00016) In this case, we use counties rather than metropolitan areas, since selection into the sample of metropolitan areas is itself an indicator of substantial success over this longer time period. There are 2,804 observations and the R-squared is 0.02. We define distance to a river using rivers identified by Fogel (1964) as navigable in 1890, from the Rappaport and Sachs (2003) data. The regression shows that places farther from rivers have grown more quickly, but the actual explanatory power of this variable is quite weakpossibly because water-related natural advantages might still matter for production or consumption. Surely, there are surely some innate advantages associated with particular areas. Moreover, many places are more productive because of decades, if not centuries, of investments in productive infrastructure. Most of the U.S. literature has implicitly assumed that political forces have only a modest impact on local productivity. This assumption is probably more palatable in the U.S. than it is in many other places, particularly developing countries. Ades and Glaeser (1995), for example, argue that outside of stable democracies there is a large return to firms in being close to the corridors of power. Those returns then attract people and firms, and help explain why capital cities are so much larger in unstable or dictatorial nations. While the bulk of the literature on cross-city income differences has focused on agglomeration economies, the empirical quest to accurately measure such economies has proven to be quite difficult, as the next section illustrates. Agglomeration in Productivity Agglomeration economies are, at their root, advantages that come from reducing transportation costs. After all, urban density is just the absence of physical space between people and firms. Agglomeration economies can exist because of reduced transportation costs for goods: input suppliers and customers save on those costs if they locate near one another. Agglomeration economies can exist because of reduced transportation costs for people: labor markets may be more efficient in urban areas and service providers may find it easier to cater to their customers. Finally, agglomeration economies can exist because of easier transmission of ideas: cities may thrive because they facilitate the flow of knowledge across people and enterprises. The most natural adjustment to the model is to assume that productivity is also a function of city size: , where  is a parameter and  is current population. This adjustment is a reduced-form method of incorporating the agglomeration economies that are explicitly derived in the models of the New Economic Geography (NEG) that follow Krugman (1991a). In those models, transportation costs are explicitly modeled, and as a result some places are more productive than others. Here, we just assume that a simple function captures those agglomerating forces. There is no conflict between the spatial equilibrium models that follow Rosen and Roback and the New Economic Geography models that follow Krugman, which also assume a spatial equilibrium. In a sense, the NEG models are just more complete in there derivation of productivity differences. With this adjustment, equations (1), (2), and (3), and equations (1), (2) and (3) continue to hold, but the parameters in those equations need to be interpreted somewhat differently. The second column of Table 2 gives the value of these equations' parameters when there are these agglomeration economies. As long as , the system will continue to be stable. Since rising productivity attracts more people which further increases productivity, agglomeration economies act as a multiplier that increases the relationship between exogenous productivity-enhancing factors and population, wages and housing prices. Agglomeration economies strengthen the positive relationship between amenities and housing supply and population for the same reason. The negative impact that amenities and housing supply have on prices and wages can be increased, muted or reversed by agglomeration economies. If >, for example, then rising housing supply and rising amenities actually increase wages and housing prices, because higher population levels increase productivity through agglomeration economies. One can begin to make such measurements by regressing either income or productivity on city size or density. Ciccone and Hall (1996), for example, show a strikingly powerful connection between density and productivity across states. Combes, Duranton, Gobillon and Roux (2009) perform similar regressions using French data. As Figure 1 shows, bigger metropolitan areas, which are also denser, are more productive. Regressions of this type, however, run counter to the whole spirit of the spatial equilibrium approach, which requires us to treat area population as an endogenous variable. Since migration lies at the very heart of the urban model, even those urban economists who believe in agglomeration economies most fervently find it hard to treat city size as an independent variable. Ciccone and Hall (1996) and Combes et al. (2009) are well aware of this endogeneity problem and they use an instrumental variables strategy. But to make sense of an instrumental variables approach to agglomeration economies, we must specify a full spatial model that incorporates those economies. The modified coefficients for equations (1), (2) and (3) tell us how to interpret instrumental variables estimates. We cannot interpret any empirical relationship between population and income unless we know whether the source of variation across communities is productivity, amenities or housing supply. If we were sure that productivity were constant across space, so that the variation was coming from housing supply or amenities, then the ordinary least squares coefficient estimated from regressing the log of income on the log of population would equal . That is the same coefficient that would be estimated in an instrumental variables regression using instruments that capture housing supply or amenities but not productivity. Alternatively, if an exogenous productivity shock is used to instrument for population in a regression of income on population, the procedure will estimate , or . The instrumental variable estimate will never yield an unbiased estimate of , the true treatment effect of population on productivity. If heterogeneous productivity provides the source of cross-area variation, then this parameter does not even enter into the estimated coefficient. If amenities and housing supply generate cross-area heterogeneity, then the agglomeration effect does enter into the estimated coefficient, but it is scaled down by , the share of production associated with non-traded capital, which creates congestion in the production process. The effect is also scaled up by , the share of production associated with labor plus non-traded capital. Table 4 shows relatively standard ways of estimating agglomeration economies. In the first regression, we show the 0.04 elasticity of income with respect to city size. The second regression uses the population of the agglomeration in 1880 as an instrument for population today. This procedure mimics Ciccone and Halls use of long-standing historical variables to instrument for city population. But how do we interpret historical population levels in light of the model? If historical population is correlated with the productivity level of the area it will not give us an estimate of the agglomeration effect. Ciccone and Hall (1996) suggest that the U.S. economy has changed so much that it is unlikely that the variables relevant for productivity in the mid-19th century still matter today. This may well be the case, but there is still the possibility that older areas have more non-traded physical capital or intangible assets that have been built up over time. If those factors make the region more productive, then the instrumental variables estimates will not tell us about agglomeration economies. Keeping these concerns in mind, we find that this procedure produces an elasticity estimate of 0.08. Regression (3) shows the alternative approach of using weather variables. This mimics Rosenthal and Strange (2003) and Combes et al. (2009) who use geological variables to instrument for current density levels. We use January and July temperature, precipitation, longitude and latitude as instruments. In this case, the estimated elasticity is 0.04, which is the same as the ordinary least squares estimate. If  equals 0.1 and  equals 0.76, and if these instruments reflect amenities or housing supply, then the estimated coefficient suggests a value of 0.13 for . We are not particularly confident that these, or any current instruments, are orthogonal to productivity, so any interpretation is hopeful at best. In regressions (4)-(6), we look at housing prices and city sizes. Regression (4) shows that housing prices are higher in big cities, but this ordinary least squares coefficient is difficult to interpret. If we use productivity variables to instrument for city size, the instrumental variables estimate should equal . If we use amenity variables to instrument for city size, the coefficient should equal . If housing supply variables are used to instrument for city size, then the estimated coefficient should be . Again, the nature of the exogenous source of variation is critical in interpreting the coefficients. City size is positively associated with housing prices in all three specifications, but the coefficient is by far the highest in regression (6), which may reflect the fact that the geography variables are most highly correlated with amenity variables and less highly correlated with housing supply. The remaining regressions in Table 4 look at real wages. In regressions (7)-(9) we find that real wages are not significantly associated with larger city size in OLS or using historical population as an instrument. In the amenity-driven IV specification, however, there is a significant negative effect of population on real wages. This suggests that amenities may be higher in bigger cities today than they have been in the past. The existence of industrial clusters also seems to suggest that agglomeration economies are important (Krugman, 1991b). There is a long tradition of examining such clusters to better understand agglomeration economies (Hoover, 1948, Fuchs, 1957). However, the same basic identification problem that plagues efforts to infer agglomeration economies by looking at city size-city income relationships also troubles research on industrial concentration. If natural advantage is heterogeneous across space, then we should expect to see industries clustering in particular locales even without agglomeration economies (Ellison and Glaeser, 1997). In principle, if industries are sufficiently footloose, then even a tiny edge in a particular locale can produce extreme industrial concentration. This tendency will be even greater if the industry is concentrated in a small number of manufacturing plants. One way to address the fact that industrial concentration can easily reflect both omitted natural advantages and agglomeration economies is to try to correct for observables sources of natural advantage. Ellison and Glaeser (1999) do that and find that controlling for an extreme large number of natural advantage variables reduces the average level of geographic concentration by twenty percent. The share of industries with extremely high levels of geographic concentration declines from 12.8 percent to 11.1 when controlling for a rich set of location characteristics. We cannot be sure that omitted variables are not significantly more important than the observed variables, but the relatively modest ability of observed variables to explain geographic clustering suggests that this clustering may reflect agglomeration economies of different forms. While estimating agglomeration economies is difficult, there remains a robust consensus among urban economists that such economies exist. The concentration of industries, the concentration of people in cities, and the higher urban incomes and productivity levels all point to the existence of these benefits from city size. Yet they do not tell us exactly why they exist, the question to which we now turn. People cluster in cities to be close to something. At their heart, agglomeration economies are simply reductions in transport costs for goods, people and ideas. We start by discussing transport costs for goods, and then discuss the role of cities as labor markets and places of idea transmissions. Transport Costs and Agglomeration Smith (1776), von Thunen (1825) and Marshall (1890) all discuss the role that cities can play in reducing transport costs. However Krugman (1991a) is appropriately given credit for crafting an internally consistent model where spatial concentration reflects the desire to cut shipping costs. In Krugmans initial formulation, the benefits of agglomeration come from reducing the costs of moving goods across space. That paper and the ensuing literature, some of which is described in Fujita, Krugman and Venables (1999), remind us that fixed costs as well as transport costs are needed to explain agglomeration. Without some scale economies, firms could divide into arbitrarily small sub-components and spread themselves throughout the hinterland. Fixed costs ensure that businesses will only have a moderate number of facilities and then transport costs push those facilities close to their suppliers and customers. Urban history is replete with examples of industries locating in cities to reduce transport costs. As Zipf (1949) noted, transport costs can cause industries to locate at the point where inputs are first produced, at the point of final consumption, or at a central spot in between. In Pittsburgh, a city formed around coal, a basic input into steel production. Meatpacking located in Chicago because cows and pigs came through that city as they traveled from the agrarian west to eastern markets. The vast stockyards exploited economies of scale. As scale economies declined, the stockyards left Chicago and moved upstream into the agricultural hinterland. In this case, the transport cost advantages came from Chicagos role as the hub of a major transportation network, not from selling to the citys residents. By contrast, New Yorks dominant industries in the 19th centurysugar refining, garment manufacturing and printing and publishingall sold much to New Yorkers. These industries certainly took advantage of inputs coming through the citys harbor (raw sugar, textiles and pirated English novels), and they also were big exporters. Yet in this case, the access to local demand also helped drive their urban locations. A number of papers seem to show the importance of market demand or supply for productivity or industrial location. Hanson (2005) connects employment and wages with the demand in neighboring areas, or market potential. He estimates a variant of the Krugman (1991a) model and finds support for strong input-output linkages. One problem with this estimation is the endogeneity of demand in neighboring areas. Head and Mayer (2004) address this issue by looking at the location of Japanese affiliates in Europe, and find that location choices are quite correlated with pre-existing market demand. Davis and Weinstein (2005) look at Japanese data and find that productivity rises with both market demand and input supply, though they have an endogeneity problem because the location of production may induce consumers to locate in a particular area. Cross-industry co-location patterns provide another source of evidence on the importance of input-output linkages. Ellison, Glaeser and Kerr (2007) find a moderate tendency of manufacturing firms to locate near industries that are either their suppliers or purchasers. The endogeneity problem here is that industries end up buying from other sectors that are geographically close. The authors address this problem by looking at purchasing patterns in the U.K. and in areas where industries are not co-located. Transport costs undoubtedly remain important for many industries. Figure 6 shows the connection across industries between average shipment length against the logarithm of value per ton, which measures how heavy the goods are per unit of value. Those goods that weight the most are shipped the shortest distances, which confirms the view that transport costs still matter, at least for shipping patterns. However, it isnt clear that high transport costs increase either geographic concentration or urbanization. If we correlate the Ellison and Glaeser (1997) geographic concentration index with the log of value per ton across industries, there is no significant correlation. If we correlate the log of value per ton with the share of the industrys employment in metropolitan areas, we find a significant positive relationship, shown in Figure 7. High transport cost industries locate away from urban areas. This fact pushes us away from the view that cities exist to reduce transport costs for hard-to-ship products. The fact that manufacturing firms generally locate outside of big cities further suggests that cities have lost their historic comparative advantage at moving goods cheaply. Cities today are much more likely to specialize in business services, and Kolko (2000) finds that business service firms are much more likely to locate near sectors that are abundant in potential customers or input suppliers. Indeed, it is natural to think that transport costs are more important for service firms where output typically involves face-to-face contact. Reducing the transport cost of purchasing inputs may still be an important element in urban economies, but the important inputs are now management consultants rather than iron ores. The one missing element in applying a theory designed to explain the concentration of manufacturing to business services is an understanding of the fixed costs in service industries. In the case of manufacturing there are scale economies in large plants, like the stockyards and sugar refineries, that are lost if production is spread through the hinterland. What is the equivalent force that applies to business services? One hypothesis is that the benefits of specialization create increasing returns in business services. In a large city, with abundant clients, it is possible to specialize in a narrow area, which will improve quality and reduce the need for general training (Becker and Murphy, 1992). Even Adam Smith (1776) wrote that division of labor is limited by the extent of the market. In large markets, business service providers can specialize more completely, reaping all of the associated benefits. Access to Workers and Dense Labor Markets The core idea of labor market-based agglomeration economies can be described as firms looking for workers and workers looking for firms. While this is surely true, without more elaboration the argument doesnt predict large agglomerationsjust that one firm and some workers will locate near one another. Alfred Marshall (1890) argued that larger agglomerations could result if there were shocks to firm demand or productivity. In that case, when multiple firms locate near one another, workers can move from firms that have experienced negative shocks to firms that have received positive shocks. If workers are risk averse, this increases average productivity through the process known as statistical returns to scale. Krugman (1991b) offers an elegant model of this concept. Similar gains to labor market agglomerations occur if there is uncertainty about match quality between worker and firm. If firms are in splendid isolation, then workers will be stuck with their first employer. If there are many firms locating near one another, there is opportunity for workers to hop from job to job in order to find the best match for their talents and interests (Helsley and Strange, 1990). Strange, Hejazi and Tang (2006) provide a general model linking uncertainty and the gains from agglomeration that come from statistical returns to scale. Changes in preferences over the lifecycle, such as a desire to change work patterns for parenting, create advantages from agglomeration even without uncertainty. There are numerous cases in which dense agglomerations provide extremely well-functioning labor markets. For example, Wall Streets dense labor market concentration allows workers to hop from firm to firm. The Connecticut hedge fund industry took advantage of the already dense agglomeration of financial services workers in the New York area and located close to many of their suburban homes. Likewise, Silicon Valley provides plenty of opportunity for job-hopping engineers to move firms (Saxenian, 1994; Fallick, Fleischman and Rebitzer, 2006). The presence of so many alternative employers also may induce workers to take on riskier jobs because they know that there will be other employment opportunities if a venture goes bust. Yet there has been relatively little empirical work documenting the importance of labor market pooling. Diamond and Simon (1990) show that workers in more specialized cities, who face greater employment risk, are compensated for that risk with higher wages. Costa and Kahn (2000) argue that highly skilled couples locate in big cities because of the benefits of thick labor markets. Ellison, Glaeser and Kerr (2007) find that industries locate near other industries that use the same type of workers. Overman and Puga (2007) use U.K. data and find that industries with more idiosyncratic risk are more likely to cluster near one another. This evidence is suggestive, but more work is needed to establish this as a major force driving either industrial location or urbanization. The theory of labor market pooling suggests that the gains from co-location will be highest for firms that use the same types of workers but are subject to different labor market shocks. This type of argument suggests that in some cases, agglomeration economies may come from locating near firms that do similar things and sometimes the gains come from locating near a wider range of industries. Following Henderson (1988), agglomeration economies that operate within industries are often called localization economies while agglomeration economies that work across industries are referred to as urbanization economies. Most of the interest in these different categories has come from researchers focused on the knowledge-related agglomeration economies. Cities and Ideas Over the past 15 years, following the new growth economics of Romer (1986) and Lucas (1988), urban economists such as Glaeser, Kallal, Scheinkman and Shleifer (1992) and Rauch (1993) have increasingly focused on the role of location-specific ideas and human capital. Idea-based agglomeration economies result when ideas move imperfectly over space, as suggested by Marshall (1890), Jacobs (1968), Helsley and Strange (2004) and many others. The key piece of empirical evidence supporting this claim comes from Jaffe, Trajtenberg and Henderson (1993) who show that patents are more likely to cite previous patents that are geographically proximate. There are several ways in which cities become more productive as centers of idea transmission. Faster intellectual flows in cities make firms more productive at any given point in time. Up-to-date information is a direct input into some industries, including journalism and finance. The spread of ideas in cities may also increase the rate of technological change in those areas. Anecdotal support for this view is given by Saxenian (1994) who discusses the communication of new ideas across firms in Silicon Valley in social settings, like the Wagon Wheel restaurant. Audretsch and Feldmann (1996) show that commercial innovations are concentrated in urban areas. Duranton and Puga (1998) present a version of this hypothesis suggesting that cities are nurseries for new ideas. In their model, mature industries then flee cities for the lower production costs of non-urban locales. The Ford Motor Company is a good example of a firm that had its most innovative stages in central city Detroit, where it could easily acquire inputs for its prototypes. Ford then moved to suburban River Rouge to lower costs when its product, the Model T, was fully designed. Figure 8 shows that industries with faster employment growth rates between 1980 and 2000 have tended to locate disproportionately in metropolitan areas, which supports the nursery city view. Another way in which the urban transmission of ideas can increase productivity is by increasing human capital acquisition for workers. This view has its roots in Marshall (1890) who wrote that in dense clusters, the mysteries of the trade become no mystery but are, as it were, in the air. According to this view, the flow of ideas in cities enhances worker human capital. Workers learn skills directly from each other. Proximity also enables them to observe mistakes and successes and to adjust accordingly. All of the agglomeration theories that emphasize idea transmission suggest that cities and human capital are complements, because higher levels of skills will mean more knowledge to be transmitted. In the case of innovation, more skilled workers and firms are more likely to be innovators. In the case of urban human capital accumulation, a more skilled work force means that there are more potential teachers for young workers learning from their urban peers. There is no real distinction between idea-based agglomeration economies and what non-urban scholars often call human capital externalities. Three separate bodies of empirical evidence bear on the role of cities as disseminators of knowledge. One body of evidence looks at wage levels, particularly the connection between incomes and area-level human capital. A second examines the connection between city growth and skills. A third literature looks at the connection between city growth and other variables and attempts to sort out different ways in which localities can increase innovation. Rauch (1993) began the modern empirical literature looking at the connection between wages and average human capital in an area. Rauch found a significant positive relationshipone extra year of area-level schooling increased the logarithm of wages by 0.05. He also found that higher levels of schooling increased housing costs. The major problem with interpreting this work is that unobserved human capital or other productivity variables may be higher in areas with higher levels of observed human capital. Acemoglu and Angrist (2001) use state-level mandatory schooling laws to test for the existence of these externalities. These rules force some cohorts in particular states to get more education than others, and Acemoglu and Angrist use this variation to look for human capital externalities. They find little evidence for such externalities, which could mean that the Rauch results reflected endogeneity and omitted human capital quality. An alternative interpretation is that human capital externalities flow mostly from people at the top end of the human capital distribution rather than people at the bottom end of that distribution and the mandatory schooling laws affect the latter group. Moretti (2004a) may be the most significant recent work on this topic. He uses a number of different approaches, including the presence of federally-funded land grant colleges and other historical variables, and individual fixed effects to correct for individual-level heterogeneity. Moretti (2004b) looks at plant level production functions, and finds that productivity rises with area level human capital. This work supports Rauchs initial findings that these externalities are present. Glaeser and Mare (2001) take a slightly different approach to using wage data to understand the returns from learning in cities. They first try to rule out the possibility that the urban wage premium represents omitted human capital characteristics. They then show that migrants who come to cities do not receive the wage premium immediately. Instead, the age-earnings profile is steeper in big cities; i.e., migrants wages grow faster than they would have otherwise. Furthermore, this effect is stronger in areas where a worker's industry is more heavily clustered (Freedman, 2008). One interpretation of these findings is that cities speed the acquisition of human capital. The work on wages is paralleled by a research program that looks at the connection between initial levels of human capital in cities and population growth of those cities. Following the urban model, the value of having both approaches is that if human capital creates productivity-enhancing externalities, this should show up both in higher wages and in higher levels of population. Glaeser, Scheinkman and Shleifer (1995) find a significant connection between skills and growth across cities in post-war America. Simon and Nardinelli (2002) examine a longer time frame and find that cities with more skilled occupations in 1880 have grown more steadily since then. Simon and Nardinelli (1996) show similar results for the United Kingdom. Using a framework like that in Section II, these results were interpreted as suggesting that skills increase the rate of productivity growth at the local level. More recently, Glaeser and Saiz (2003) and Shapiro (2006) have tried to understand why skills predict urban growth. Both papers find that the connection between area-level skills and area-level wages is rising, implying a connection between skills and productivity growth. These results support the view that successful cities thrive because of their ability to connect smart people. The third body of research attempts to distinguish between hypotheses about how cities foment innovation. One view, associated with Marshall, Arrow and Romer, suggests that industrial concentrations of large firms will be more innovative. This view suggests localization externalities. A second view, associated with Jane Jacobs, argues that new ideas are formed by combining old ideas, and that urban diversity is the key to innovation. A third view, following Porter (1990) argues that links with consumers are vital for generating new ideas. A fourth view, from Chinitz (1961), argues that small firms are better for innovation, especially when they are not vertically integrated. Regressions using city growth or the founding of new firms have typically been used to try to distinguish between these different views. For example, Glaeser et al. (1992) found evidence against concentration and for diversity. Henderson, Kuncoro and Turner (1995) find more support for the value of industrial concentration. Glaeser et al. (1992) also find that growth is faster in sectors with smaller firms, but this may reflect mean reversion of firm growth rather than new idea creation. Henderson (2003) takes a somewhat different approach and links plant-level productivity measures with area level characteristics using the Longitudinal Research Database. He finds that plants are more productive when surrounded by other similar plants. This finding is similar to the result that productivity rises with density. While it provides some evidence for agglomeration economies, it suffers from the problem that location is endogenous and omitted productivity variables should create a correlation between area-level concentration and measured productivity. Overall, a large body of research is at least compatible with the hypothesis cities thrive because of their ability to spread knowledge. This view is also supported by the tendency of idea-oriented industries to cluster in urban centers (Glaeser and Kahn, 2001). Figure 9 shows the correlation between average human capital in an industry and the likelihood that industry will locate in an urban area. At least for now, cities appear to have a comparative advantage in more idea-intensive sectors. The great improvements in information technology over past 30 years have led some to argue that the informational functions of physical proximity will eventually become obsolete. Gaspar and Glaeser (1998) question this view and argue that the important question becomes whether face-to-face communication and electronic communication are substitutes or complements. Theoretically, the two types of communication could certainly be complements, as people may expect to use both types of connection when forming relationships. Empirically, the situation is also murky as people seem to use the phone more when they are physically close and likely to meet. The example of Silicon Valley, which is both a famous geographic cluster and a center for information technology, cast doubts on the view that proximity and information technology are strong substitutes. Glaeser and Ponzetto (2007) go further and argue that changes in information and transportation technologies have increased the returns to new ideas. If new ideas are best created in cities, where people can readily learn from one another, then technological changes that increase the returns to new ideas will only make cities more important, at least when those cities specialize in creating ideas. This theory can help explain why idea-oriented agglomerations, like those that specialize in financial services, have thrived over the last 30 years while goods-oriented agglomerations, like those that specialize in manufacturing, have faltered. Public Policy and Agglomeration Economies While the literature may have converged on the view that agglomeration exist, it is not clear what, if any, policy implications come from that view. Such agglomeration economies are externalities, and externalities often imply that the unfettered market will not produce a social optimum. The presence of agglomeration economies naturally leads to the possibility of multiple equilibria and therefore suggests that small changes to initial conditions can significantly affect subsequent urban growth (Krugman, 1991a). As such, a small push could create big benefits, but what form should such small pushes take? Some countries, but not the United States, have followed more aggressive regional policies. For example, the European Union has long directed resources towards more disadvantaged areas. In the U.S., regional policy has been limited to modest interventions in Appalachia, various attempts at urban renewal and Empowerment zones. All of these interventions were meant to strengthen troubled areas. However, while the existence of agglomeration economies suggests that the free market may get things wrong, this doesnt imply the appropriate form of government intervention. For example, assume that a country had two placesone poor and the other rich. The poor place is less populated, while the rich place is denser. Do agglomeration economies imply that the government should create subsidies that induce either people are firms to move from one place to another? No. If agglomeration economies exist, then moving people out of one area will reduce the productivity of that area and increase the productivity of the receiving place. One area gets more productive and the other gets less productive. The existence of agglomeration economies does not imply that the winning area will gain more than the losing area loses. As Glaeser and Gottlieb (2008) discuss, any firm conclusions depend on the functional form of agglomeration economies. Even if we have reached a consensus that agglomeration economies exist, we have not reached any consensus over their functional form. Glaeser and Gottlieb find little clear evidence on that shape of any agglomeration effects. The existence of human capital externalities, likewise, provides little guidance about whether more skilled workers should be pushed into already skilled areas or dispersed throughout the country. Again, the policy implication depends not only on the existence of spillovers, but on their functional form. If anything, the empirical results suggest that productivity increases with concentration of talent, but we are far from confident about that finding. If human capital spillovers are real, then this may suggest that subsidizing education might increase social welfare, but it does not suggest a regional policy that would push talent in one direction or another. The results of this literature may, perhaps, offer more guidance to local policy-makers interested in boosting local productivity. If agglomeration economies exist, then local productivity would increase if local leaders are able to attract more economic activity. However, since attempts to attract such activity are rarely costless, the mere existence of agglomeration economies does not imply any particular policy action. They certainly do not, on their own, make the case for local subsidies to encourage new businesses. Greenstone, Hornbeck and Moretti (2007) provide the best evidence on this question. The existence of human capital externalities does suggest that attracting skilled workers may increase local productivity and local growth. However, again, the existence of those externalities does not suggest which policies will attract skilled workers or whether such policies carry benefits that will offset their costs. Those results do suggest that there are costs associated with policies that repel highly skilled workers, such as progressive taxation at the local level. IV. The Implications of Urban Economics for Other Fields We now turn to the implications that urban economics has for other fields. Some of these insights reflect empirical findings in the field. Others follow from the core ingredients of urban theory. The Economics of Growth: Human Capital and Urbanization Much of the recent work on cities has been motivated by a desire to shed more light on the processes that also drive national economic growth. While within-country research requires somewhat different methods than cross-country methods, there are a number of findings from city-level research that seem quite relevant for cross-country researchers. The connections between area-level human capital and urban success supports the cross-county work showing a correlation between initial human capital and later GDP growth (e.g. Barro, 1991; Mankiw, Romer and Weil, 1993). There are, of course, papers (e.g., Hausmann, Pritchett and Rodrik, 2004) challenging the view that human capital increases growth rates. Others suggest that human capital is endogenous, caused by institutions and cannot be seen as a driving force of growth. The city-level evidence does not disprove these arguments, but it does support the view that education is an important determinant of area-level productivity and growth. Indeed, a comparison of individual, metropolitan area and national income regressions shows that the correlation between human capital and incomes gets stronger at higher levels of aggregation. This is compatible with the presence of human capital spillovers that create a social multiplier, which causes group coefficients to be larger than individual level coefficients. If education improves the quality of political outcomes, then this will create another channel whereby living around skilled people can enhance productivity. Within-country evidence also supports the view that there is a link between area-level skills and reduced corruption (Glaeser and Saks, 2006). The urban growth literature has other implications for broader growth theory. The evidence that growth at the city-industry level was negatively associated with initial scale and positively associated with small firm size casts some doubt on the view that large firms in big single industry clusters are particularly innovative. This contradicts some of the early growth models that emphasize a positive connection between innovation and either monopoly or initial scale. Following Barro and Sala-i-Martin (1991), cross-city work on income convergence can be helpful for understanding income convergence at the national level. The urban literature also should remind us of the enormously strong connection between urbanization and income across space. Figure 10 shows the nearly-perfect connection between the logarithm of per capita GDP and urbanization rates across countries. Without sub-national evidence it would be easy to believe that this correlation was spurious, reflecting only the tendency of some countries to both be richer and have less farming. However, the within-country evidence showing a strong positive connection between density and productivity (Ciccone and Hall, 1996, Combes et al., 2008) makes that view less tenable. Of course, this does not necessarily mean that countries should subsidize urbanization, but rather that the transition to dense, urban living seems to be part of the process of countries becoming richer over time. Idea Spillovers and Variation across Space in Innovation The literature on knowledge spillovers suggests that ideas move quickly from person to person within urban areas. These spillovers seem to be the source of intellectual change, as urban innovators riff off each others ideas. The role of cities in creating chains of innovations can be seen historically in events like the Florentine Renaissance, where the architect Brunelleschi developed linear perspective, which was then used in low relief sculpture by his friend Donatello, then in painting by Masaccio, and passed to his student Filippo Lippi and others. Urban intellectual connections create agglomeration economies and help us to understand why skilled cities are so successful, but they also remind us that many intellectual revolutions involve small numbers of connected inventors. The presence of social interactions, in any context, can create high levels of random variation across space (Glaeser, Sacerdote and Scheinkman, 1996). Intuitively, when individuals act independently random variation averages out quicklythe variance of city-level averages of independent individual level outcomes is 1/N times the variance of individual level outcomes. But when outcomes are not independent, and are instead connected through urban interactions, then the variation of group-level averages can be much higher. 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