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Dennis Epple: This is an ambitious and exceedingly valuable paper, which makes several significant contributions. Mills provides readers with an overview of density controls in the United States and several other countries. This overview highlights the roles of local and federal governments in land use regulations. He offers a critical assessment of the effects of growth controls in various U.S. regions, and he discusses the objectives that motivate adoption of growth and density controls. Mills also comments on the current state of growth and density control research, and suggests issues for future study. Mills makes several important observations and raises key questions about research linking sprawl and fragmentation. In sum, he says there is a need for:

• models that capture employment and population suburbanization and their interaction;
• better understanding of factors governing entry (or lack of entry) of new municipalities;
• better understanding of how municipalities interact with each other (that is, extent and forms of competition among municipalities).

Mills also indicates the need for further research to answer questions such as what is the relative importance of various potential motives in determining popularity of density controls. Is the answer property-value maximization; improving education quality, safety, other local services; low congestion; or keeping out low-income and minority households? Another question he raises is why are land use controls so popular if housing prices are sufficient to induce population stratification. In his paper, Mills discusses the downzoning in a wealthy Chicago area resulting from residents' objections to buildings that would increase density. In reading this discussion, it occurred to me that data that my colleagues and I have assembled might provide some further evidence to supplement Mills's presentation.¹ In particular, I investigated lot size heterogeneity and trends in lot sizes among municipalities in the Pittsburgh, Pennsylvania, metropolitan area. A brief summary of this evidence follows.

The data presented here are for approximately 370,000 residential properties in Allegheny County, Pennsylvania, which includes Pittsburgh and the surrounding area. The county, which has a population of approximately 1.3 million, includes 130 municipalities (four cities, forty-two townships, and eighty-four boroughs). A virtue of this data set is that properties are included, whether rental or owner-occupied. Figure 1 shows percentiles of lot size for houses constructed over the past 120 years in the county, and figure 2 shows that lot sizes throughout this period are skewed, with the mean being well above the median for the entire period. Figure 3 shows predicted lot sizes from a regression of ln (lot size) on a fourth-order polynomial in age, a second-order polynomial in travel time, and an interaction of travel time and age.² It is evident from this figure that lot sizes increase with distance (travel time), and lot sizes have trended up over time at each distance.

It is also interesting to investigate the extent to which lot sizes vary within and across municipalities. Table 1 provides decompositions of variance. Consider, for illustration, the two results shown in bold in the table's top panel. When houses of all ages are considered, and properties within the city of Pittsburgh are included, the variance of the logarithm of lot areas within municipalities equals the variance across municipalities. The variance within municipalities is 63 percent when only houses built since 1995 are considered. When observations for the city of Pittsburgh are excluded, the corresponding within-municipality percentages of variance are higher. When the decompositions are done without using logarithms, the within-municipality percentages are

greater still. The table's second panel presents the corresponding decompositions for house values. Comparison across both panels reveals that...