Abstract
International trade economists made seminal contributions to general equilibrium theory, moving away from an emphasis on existence of equilibrium to algebraic formulations which enabled us to characterize key relationships between parameters and variables, such as that between tariffs and domestic factor prices and welfare. But the early analyses remained limited in value for policy evaluation: the analysis was local, it provided only qualitative results, it was limited to very small models, and strictly interior solutions had to be assumed. The contribution of this paper is pedagogic and methodological, providing a primer for those wishing to do or teach general-equilibrium counterfactuals on computable general-equilibrium (CGE) or structural econometric models. I show how the tools from early local comparative statics analyses can be generalized via the use of Shepard’s lemma, duality, complementarity and the Karush-Kuhn-Tucker theorem into a global, quantitative analysis of large changes in high-dimension models which also allows for regime changes and corner solutions. I then show how the resulting non-linear complementarity problem directly translates into a numerical model using GAMS (general algebraic modeling system). The paper concludes with two examples: (a) comparison of a tax versus a real trade/transactions cost, (b) comparison of a tax versus a quantitative restriction such as a quota or license.
Highlights
Simulation analysis of general equilibrium models used to be the territory of the field of applied general-equilibrium and members of this group were largely disjoint from international trade theorists and empiricists using the tool kit of econometrics
Many applied generalequilibrium (AGE) modelers might benefit from a clearer understanding of the theoretical foundations needed for a good model
I will show how this global analysis is rigorously built up from several key results from mathematics and economic theory. These generalizations are hugely important in the evaluation of large policy changes such as BREXIT, or economic shocks such as covid-19 where qualitative local analyses of small changes are of no practical value
Summary
Is fair to say that there was even some hostility among these groups. I regret not keeping some of the referees’ reports on my early papers using numerical simulation as a theory tool in models far too complex for traditional paper-andpencil analytical methods. A general-equilibrium model can be built up, embodying optimization by individual agents in the equations and inequalities of the model These early contributions were path breaking and remain important today. I will show how this global analysis is rigorously built up from several key results from mathematics and economic theory These generalizations are hugely important in the evaluation of large policy changes such as BREXIT, or economic shocks such as covid-19 where qualitative local analyses of small changes are of no practical value. I compare the effect of a tax and a quota, which are calibrated to be equivalent initially, but which lead to large differences when parameter changes are large Both of these situations are, I believe, quite common elements of AGE models used for policy analysis
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