Gibrat's law for cities: uniformly most powerful unbiased test of the Pareto against the lognormal

We address the general problem of testing a power law distribution versus a log-normal distribution in statistical data. This general problem is illustrated on the distribution of the 2000 US census of city sizes. We provide definitive results to close the debate between Eeckhout (2004, 2009) and Levy (2009) on the validity of Zipf's law, which is the special Pareto law with tail exponent 1, to describe the tail of the distribution of U.S. city sizes. Because the origin of the disagreement between Eeckhout and Levy stems from the limited power of their tests, we perform the {\em uniformly most powerful unbiased test} for the null hypothesis of the Pareto distribution against the lognormal. The $p$-value and Hill's estimator as a function of city size lower threshold confirm indubitably that the size distribution of the 1000 largest cities or so, which include more than half of the total U.S. population, is Pareto, but we rule out that the tail exponent, estimated to be $1.4 \pm 0.1$, is equal to 1. For larger ranks, the $p$-value becomes very small and Hill's estimator decays systematically with decreasing ranks, qualifying the lognormal distribution as the better model for the set of smaller cities. These two results reconcile the opposite views of Eeckhout (2004, 2009) and Levy (2009). We explain how Gibrat's law of proportional growth underpins both the Pareto and lognormal distributions and stress the key ingredient at the origin of their difference in standard stochastic growth models of cities \cite{Gabaix99,Eeckhout2004}.Comment: 7 pages + 2 figure

Foreclosure Externalities: Some New Evidence

In a recent set of influential papers, researchers have argued that residential mortgage foreclosures reduce the sale prices of nearby properties. We revisit this issue using a more robust identification strategy combined with new data that contain information on the location of properties secured by seriously delinquent mortgages and information on the condition of foreclosed properties. We find that while properties in virtually all stages of distress have statistically significant, negative effects on nearby home values, the magnitudes are economically small, peak before the distressed properties complete the foreclosure process, and go to zero about a year after the bank sells the property to a new homeowner. The estimates are very sensitive to the condition of the distressed property, with a positive correlation existing between house price growth and foreclosed properties identified as being in above average condition. We argue that the most plausible explanation for these results is an externality resulting from reduced investment by owners of distressed property. Our analysis shows that policies that slow the transition from delinquency to foreclosure likely exacerbate the negative effect of mortgage distress on house prices

Pollution and the Efficiency of Urban Growth

We analyze the efficiency of urbanization patterns in a dynamic model of endogenous urban growth with two sectors of production. Production exhibits increasing returns to scale on aggregate. Urban environmental pollution, as a force that discourages agglomeration, is caused by domestic production. We show that cities are too large and too few in number in equilibrium, compared to the efficient urbanization path, if economic growth implies increasing aggregate emissions. If, on the other hand, production becomes cleaner over time (`quality growth') the urbanization path approximates the efficient outcome after finite time

Civic Capital and the Size Distribution of Plants: Short-Run Dynamics and Long-Run Equilibrium

We characterize how the size distribution of plants, within narrowly defined industries, changed in Italy over a ten-year time span, and relate this to the stock of civic capital at the provincial level. Data on plant size come from the 1991 and 2001 Italian censuses. Civic capital turns out to have a positive effect on both the average and standard deviation of size. Looking at several precise points of the plant size distribution, we find that it shifts toward the right and becomes more dispersed where civic capital is high. The potential endogeneity of current civic capital is addressed by instrumenting it with historical variables. Our main conclusion is that the geographic variation in the stock of civic capital poses substantial constraints on plants' ability to expand. Understanding this is the key for the implementation of effective industrial policies

Learning, career paths, and the distribution of wages

© 2019 American Economic Association. We develop a theory of career paths and earnings where agents organize in production hierarchies. Agents climb these hierarchies as they learn stochastically from others. Earnings grow as agents acquire knowledge and occupy positions with more subordinates. We contrast these and other implications with US census data for the period 1990 to 2010, matching the Lorenz curve of earnings and the observed mean experience- earnings profiles. We show the increase in wage inequality over this period can be rationalized with a shift in the level of the complexity and profitability of technologies relative to the distribution of knowledge in the population

Evaluating the economic cost of coastal flooding

Sea level rise will cause spatial shifts in economic activity over the next 200 years. Using a spatially disaggregated, dynamic model of the world economy, this paper estimates the consequences of probabilistic projections of local sea level changes. Under an intermediate scenario of greenhouse gas emissions, permanent flooding is projected to reduce global real GDP by 0.19 percent in present value terms. By the year 2200, a projected 1.46 percent of the population will be displaced. Losses in coastal localities are much larger. When ignoring the dynamic response of investment and migration, the loss in real GDP in 2200 increases from 0.11 percent to 4.5 percent. (JEL E23, F01, Q54, Q56)Desmet and Rossi- Hansberg acknowledge the support and hospitality of PERC while doing part of this research. Kopp, Kulp, and Strauss were supported in part by US National Science Foundation grant ICER- 1663807 and by National Aeronautics and Space Administration grant 80NSSC17K0698. Nagy acknowledges financial support from the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Program for Centers of Excellence in R&D (SEV- 2015-0563) and the Juan de la Cierva Grant (FJCI- 2017- 34728); and from the Government of Catalonia, through CERCA and SGR Program (2017-SGR-1393). Oppenheimer acknowledges support from US National Science Foundation Award Number 1520683

Evaluating the economic cost of coastal flooding

Sea-level rise and ensuing permanent coastal inundation will cause spatial shifts in population and economic activity over the next 200 years. Using a highly spatially disaggregated, dynamic model of the world economy that accounts for the dynamics of migration, trade, and innovation, this paper estimates the consequences of probabilistic projections of local sea-level changes under different emissions scenarios. Under an intermediate greenhouse gas concentration trajectory, permanent flooding is projected to reduce global real GDP by an average of 0.19% in present value terms, with welfare declining by 0.24% as people move to places with less attractive amenities. By the year 2200 a projected 1.46% of world population will be displaced. Losses in many coastal localities are more than an order of magnitude larger, with some low-lying urban areas particularly hard hit. When ignoring the dynamic economic adaptation of investment and migration to flooding, the loss in real GDP in 2200 increases from 0.11% to 4.5%. This shows the importance of including dynamic adaptation in future loss models