NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

2002 Japan Conference: A Summary of the Papers


A Search for Multiple Equilibria in Urban Industrial Structure


Donald R. Davis and David E. Weinstein

Are events like the terrorist strike of September 11, 2001, likely to have a permanent impact on New York? Can enterprise zones, special tax breaks, and other urban policies permanently alter the location of economic activity? These are questions that lie at the center of urban, regional, and even international debates about economic policy.

Traditionally, economists tended to focus on inherent characteristics of locations as the explanation for the structure of production. Industrial policy might alter the location of industries while a subsidy was being offered, but traditional analysis held that if the policy intervention ceased, things would return to their initial conditions.

This simple view of the world has come under attack in recent years. Indeed, one of the central themes of modern economics is the phenomenon of multiple equilibria. In macroeconomics, this is viewed as a potential explanation of the business cycle (Cooper and John 1988); in development, this is the source of poverty traps (Murphy, Shleifer and Vishny 1989); in urban and regional economics, this is a potential account of differences in spatial density (Fujita, Krugman and Venables 1999); and in international economics, it is viewed as a potential explanation for the division of the world economy into an industrialized North and a non-industrialized South (Krugman and Venables 1995).

Theories of multiple equilibria carry within them an important temptation. If multiple equilibria are possible, it is tempting to intervene to select that equilibrium deemed most advantageous by the policymaker. If thresholds separate radically different equilibria, then the resolute policymaker can change the whole course of regional development or strongly affect the industrial composition of a region, even with limited and temporary interventions. Implicitly, such views are at the base of regional and urban development policies in Europe, the United States, and elsewhere.

While recent decades have seen a robust exploration of the theoretical conditions that might give rise to multiple equilibria, very little work has explored empirically the question of whether such multiple equilibria are a salient feature of real economies. Our paper explores precisely this question in the context of urban industrial structure.

One difficulty in exploring the question is the inability of the economist to conduct controlled experiments. In an ideal experiment, we would subject an economy to large, variable, exogenous, and temporary shocks. In this paper, we approximate this with a "natural experiment" that examines data on the Allied bombing of Japanese cities and industries during World War II. These shocks were clearly large: eliminating 90 percent of Japanese manufacturing. Moreover, there was considerable variation across cities because of the fact that many large cities, for example, Kyoto, were not bombed, while others, like Hiroshima, were devastated. Although the United States targeted the biggest cities that were within range, exogeneity is established by very low correlations between destruction and pre-war growth. Finally, there is little question that the shocks were temporary.

The central problem is to consider how we would determine whether the results of this bombing are consistent with a unique versus multiple equilibria. Our approach to this is very simple. First, consider the possibility that there is a unique and stable equilibrium. If we could partition time into two periods – the first the period of the shock and the second the period of the recovery -- then the unique equilibrium model makes a very simple prediction. Starting from equilibrium, whatever shock there is in period one will simply be undone in the second period. If we were to plot this on a graph where the axes were the periods of shock and recovery, then the data should lie on a line with slope minus unity through the origin.

Next, consider the possibility that, rather than a unique equilibrium there are indeed multiple equilibria. If we assume the initial equilibrium is locally stable, then for "small" shocks, the periods of shock and recovery look precisely as in the case of the globally unique stable equilibrium: whatever shock there is in period one will simply be undone in the second period. In the locally stable interval, we can again plot this in a graph where the axes are the periods of shock and recovery, and the data should again lie on a line with slope minus unity through the origin.

In the model of multiple equilibria, large shocks (positive or negative) shift the economy past thresholds and eventually toward a new equilibrium. If by chance the shock moved the economy past the threshold precisely to the level of the new equilibrium, then in the recovery period, there would be no further change. If the period one shock fell short or exceeded the new equilibrium value for the economy, then the recovery period would complete this deficit or undo the excess relative to the new equilibrium value. That is, in the space of two-period growth rates, we again would have a line with slope minus unity; however, on the horizontal axis it would pass through the new equilibrium. In effect, a system with multiple equilibria generates in this space a family of lines with slope minus unity, each of which passes through an equilibrium on the horizontal axis.

If we know on an a priori basis the points of thresholds, then this would provide a very simple empirical strategy: group the data by the magnitude of the initial shock delimited by these bifurcations and estimate a line through each, which should have a slope of minus unity but different intercepts. For a low equilibrium (large negative shocks), the intercept should be significantly below that for shocks in the initially stable region; for a high equilibrium, the estimated intercept should be significantly above that for shocks in the initially stable region.

This leaves one key problem to solve – how to identify the breaks. Here, we try to allow the data to pick the relevant thresholds. We can develop a sequence of partitions of the data and ask whether for any of the partitions we can find the above stated pattern of significantly different intercepts. If yes, then this will be evidence in favor of multiple equilibria; if no, then this would count as evidence instead of a unique equilibrium.

The results yield unambiguous support for a single equilibrium. We confirm on population, manufacturing, and detailed industrial data that economic activity in cities is highly robust to temporary shocks even of gargantuan size. These results are robust to allowing for a large number of possible equilibria or allowing the equilibria to only be relevant for shocks of a very narrow range.

Our results yield an important lesson for policy: the temptation to use limited and temporary interventions to select advantageous equilibria is a chimera. The fact that cities have a very strong tendency to return not only to the prior level of manufacturing activity but also to recover the specific industries that previously thrived there, even in the aftermath of overwhelming destruction, is very strong evidence that temporary interventions of economically relevant magnitude are extremely unlikely to alter the course of aggregate manufacturing or even to strongly affect industrial structure in a given locale. Small and temporary interventions to reap large and permanent changes in levels and composition of regional economic activity is an idea that – in the data – is utterly bankrupt.

 
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