General equilibrium theories of spatial agglomeration are closed models of agent location that explain the formation and growth of cities. There are several types of such theories: conventional Arrow-Debreu competitive equilibrium models and monopolistic competition models, as well as game theoretic models including search and matching setups. Three types of spatial agglomeration forces often come into play: trade, production, and knowledge transmission, under which cities are formed in equilibrium as marketplaces, factory towns, and idea laboratories, respectively. Agglomeration dynamics are linked to urban growth in the long run.
Marcus Berliant and Ping Wang
Land is everywhere: the substratum of our existence. In addition, land is intimately linked to the dual concept of location in human activity. Together, land and location are essential ingredients for the lives of individuals as well as for national economies. In the early 21st century, there exist two different approaches to incorporating land and location into a general equilibrium theory. Dating from the classic work of von Thünen (1826), a rich variety of land-location density models have been developed. In a density model, a continuum of agents is distributed over a continuous location space. Given that simple calculus can be used in the analysis, these density models continue to be the “workhorse” of urban economics and location theory. However, the behavioral meaning of each agent occupying an infinitesimal “density of land” has long been in question. Given this situation, a radically new approach, called the σ -field approach, was developed in the mid-1980s for modeling land in a general equilibrium framework. In this approach: (1) the totality of land, L , is specified as a subset of ℝ 2 , (2) all possible land parcels in L are given by the σ -field of Lebesgue measurable subsets of L , and (3) each of a finite number of agents is postulated to choose one such parcel. Starting with Berliant (1985), increasingly more sophisticated σ -field models of land have been developed. Given these two different approaches to modeling land within a general equilibrium framework, several attempts have thus far been proposed for bridging the gap between them. But while a systematic study of the relationship between density models and σ -field models remains to be completed, the clarification of this relationship could open a new horizon toward a general equilibrium theory of land.
The current discontent with the dominant macroeconomic theory paradigm, known as Dynamic Stochastic General Equilibrium (DSGE) models, calls for an appraisal of the methods and strategies employed in studying and modeling macroeconomic phenomena using aggregate time series data. The appraisal pertains to the effectiveness of these methods and strategies in accomplishing the primary objective of empirical modeling: to learn from data about phenomena of interest. The co-occurring developments in macroeconomics and econometrics since the 1930s provides the backdrop for the appraisal with the Keynes vs. Tinbergen controversy at center stage. The overall appraisal is that the DSGE paradigm gives rise to estimated structural models that are both statistically and substantively misspecified, yielding untrustworthy evidence that contribute very little, if anything, to real learning from data about macroeconomic phenomena. A primary contributor to the untrustworthiness of evidence is the traditional econometric perspective of viewing empirical modeling as curve-fitting (structural models), guided by impromptu error term assumptions, and evaluated on goodness-of-fit grounds. Regrettably, excellent fit is neither necessary nor sufficient for the reliability of inference and the trustworthiness of the ensuing evidence. Recommendations on how to improve the trustworthiness of empirical evidence revolve around a broader model-based (non-curve-fitting) modeling framework, that attributes cardinal roles to both theory and data without undermining the credibleness of either source of information. Two crucial distinctions hold the key to securing the trusworthiness of evidence. The first distinguishes between modeling (specification, misspeification testing, respecification, and inference), and the second between a substantive (structural) and a statistical model (the probabilistic assumptions imposed on the particular data). This enables one to establish statistical adequacy (the validity of these assumptions) before relating it to the structural model and posing questions of interest to the data. The greatest enemy of learning from data about macroeconomic phenomena is not the absence of an alternative and more coherent empirical modeling framework, but the illusion that foisting highly formal structural models on the data can give rise to such learning just because their construction and curve-fitting rely on seemingly sophisticated tools. Regrettably, applying sophisticated tools to a statistically and substantively misspecified DSGE model does nothing to restore the trustworthiness of the evidence stemming from it.