A Search for Multiple Equilibria in Urban Industrial Structure

Theories featuring multiple equilibria are now widespread across many fields of economics. Yet little empirical work has asked if such multiple equilibria are salient features of real economies. We examine this in the context of the Allied bombing of Japanese cities and industries in WWII. We develop a new empirical test for multiple equilibria and apply it to data for 114 Japanese cities in eight manufacturing industries. The data provide no support for the existence of multiple equilibria. In the aftermath even of immense shocks, a city typically recovers not only its population and its share of aggregate manufacturing, but even the specific industries it had before. Donald R. Davis Columbia University Department of Economics 1038 Intl. Affairs Building 420 West 118th St. New York, NY 10027 and NBER drd28@columbia.edu David E. Weinstein Columbia University Department of Economics 420 W. 118th Street MC 3308 New York, NY 10027 and NBER dew35@columbia.edu A Search for Multiple Equilibria in Urban Industrial Structure I. Multiple Equilibria in Theory and Data The concept of multiple equilibria is a hallmark of modern economics, one whose influence crosses broad swathes of the profession. In macroeconomics, it is offered as an underpinning for the business cycle (Russell Cooper and Andrew John 1988). In development economics it rationalizes a theory of the “big push” (Kevin M. Murphy, Andrei Shleifer, Robert W. Vishny 1988). In urban and regional economics, it provides a foundation for understanding variation in the density of economic activity across cities and regions (Paul R. Krugman 1991). In the field of international economics, it has even been offered as a candidate explanation for the division of the global economy into an industrial North and a non-industrial South, as well as the possible future collapse of such a world regime (Krugman and Anthony J.Venables 1995). The theoretical literature has now firmly established the analytic foundations for the existence of multiple equilibria. However theory has far outpaced empirics. The most important empirical question arising from this intellectual current has almost not been touched: Are multiple equilibria a salient feature of real economies? This is inherently a difficult question. At any moment in time, one observes only the actual equilibrium, not alternative equilibria that exist only potentially. If the researcher observes a change over time, it is difficult to know if this change reflects a shift between equilibria due to temporary shocks or a change in fundamentals 1 A simple indication of the flood of work in these areas is that the Journal of Economic Literature has featured three surveys of segments of this literature in recent years (see Matsuyama 1995, Anas, Arnott and Small 1998, and Neary 2001). Recent major monographs in economic geography include Masahisa Fujita, Paul R. Krugman and Anthony Venables (1998), Fujita and Jacques Thisse (2002), and Richard Baldwin, et al. (2003). 2 Cooper (2002) discusses issues of estimation and identification in the presence of multiple equilibria as well as surveying a selection from the small number of papers that seek to test empirically for multiple equilibria in specific economic contexts. We view these as welcome contributions to understanding a difficult problem, but also believe that are perhaps not yet well understood by the researcher. If a cross section reveals heterogeneity that seems hard to explain by the observed variation in fundamentals, it is hard to know if this may be taken to confirm theories of multiple equilibria or if it suggests only that our empirical identification of fundamentals falls short. Testing for multiple equilibria is also difficult for other reasons. The theory of multiple equilibria relies on the existence of thresholds that separate distinct equilibria. In any real context, it is difficult to identify such thresholds or the location of unobserved equilibria. In addition, a researcher may look for exogenous shocks, but these need to be of sufficient magnitude to shift the economy to the other side of the relevant threshold and they need to be clearly temporary so that we can see that we fail to return to the status quo ante. A researcher is rarely so blessed. Donald R. Davis and David E. Weinstein (2002) initiated work that addresses the practical salience of multiple equilibria in the context of city sizes. The experiment considered was the Allied bombing of Japanese cities during World War II. This disturbance was exogenous, temporary and one of the most powerful shocks to relative city sizes in the history of the world. Hence it is an ideal laboratory for identifying multiple equilibria. That paper examined city population data and, in the context of the present paper, may be viewed as having answered two questions. Do the data reject a null that city population shares have a unique stable equilibrium? Do the data support a stated condition that would be sufficient to establish multiple equilibria in city population shares? In both cases, our answer was “no” – we could not reject a unique stable equilibrium nor could we establish the sufficient condition for multiple equilibria in city population shares. much remains to be done. Andrea Moro (2003) considers multiple equilibria in a statistical discrimination labor model.