Final Report Summary - IDENTIFICATION (Identification, Estimation and Implementation of Structural Economic Models)
Structural models are widely used in the analysis of economic and financial problems. Examples of structural models include static and dynamic discrete choice models (Berry, Levinsohn, Pakes, 1995; Rust, 1987), consumer demand models (Lewbel and Pendakur, 2009), dynamic stochastic general equilibrium models (Fernandez-Villaverde and Rubio-Ramirez, 2007) and dynamic games (Bajari et al, 2007).
Some of the advantages of structural models are that they are consistent with underlying economic theory, the components entering the model have a meaningful economic interpretation, and they allow for counterfactual analysis.
These attractive features are contrasted by certain complications arising from the steadily increasing complexity of structural models used by applied researchers. The increased complexity makes the analysis and implementation of the models more difficult. In particular, for many models, the following questions related to their econometric analysis and implementation are still unresolved: First, which, if any, parts of the model can we identify from data available? Second, how can we estimate and draw inference about the identified components? Third, if a component is only partially identified, how do we draw inference about it? Fourth, how do we implement the proposed estimators and other inferential tools in practice?
This ERC grant allowed for the development and completion of a number of projects each aiming at addressing one or more of these four issues in particular structural models. All projects have a strong methodological component involving both the development of novel econometric and numerical techniques, and the analysis of these. In addition, some of the projects also involve practical implementation and/or empirical analysis where the proposed methods are taken to data.
The following goals/results were achieved:
1. Identification: Many structural models are routinely estimated by imposing a somewhat arbitrary parametric structure on the unknown components entering the model. This raises the following questions: First, is the chosen parametric model identified from data - i.e. is it possible to estimate and draw inference regarding the parameters of interest? Second, which of the parametric restrictions are really needed for identification and which are simply imposed for computational simplicity? One part of the project involved developing new identification results in some important structural models. These allow researchers to design parametric models that are well-identified, and potentially even allow them to estimate the components of interest non- or semiparametrically.
2. Non- and semiparametric estimation and inference: Given identified components, the research team developed novel non- and semiparametric estimators of these. The new methods allow researchers to obtain results that do not suffer from risks of misspecification. An asymptotic analysis of proposed estimators and tests were developed, and numerical results demonstrated their usefulness in practice.
3. Numerical techniques for the practical implementation of models and estimators: Even in parametric models, implementation of structural models is hampered by some components not being available in closed form. A leading example is the computation of value functions in dynamic decision models. This complication often restricts implementations to somewhat unrealistic models and/or leads to large numerical errors in the computed outcomes. The project developed new numerical techniques to allow implementation of more realistic models. The properties of the new (and existing) techniques were investigated both in theory and practice in order to understand how the additional numerical errors affect estimators and counterfactual analyses.
Some of the advantages of structural models are that they are consistent with underlying economic theory, the components entering the model have a meaningful economic interpretation, and they allow for counterfactual analysis.
These attractive features are contrasted by certain complications arising from the steadily increasing complexity of structural models used by applied researchers. The increased complexity makes the analysis and implementation of the models more difficult. In particular, for many models, the following questions related to their econometric analysis and implementation are still unresolved: First, which, if any, parts of the model can we identify from data available? Second, how can we estimate and draw inference about the identified components? Third, if a component is only partially identified, how do we draw inference about it? Fourth, how do we implement the proposed estimators and other inferential tools in practice?
This ERC grant allowed for the development and completion of a number of projects each aiming at addressing one or more of these four issues in particular structural models. All projects have a strong methodological component involving both the development of novel econometric and numerical techniques, and the analysis of these. In addition, some of the projects also involve practical implementation and/or empirical analysis where the proposed methods are taken to data.
The following goals/results were achieved:
1. Identification: Many structural models are routinely estimated by imposing a somewhat arbitrary parametric structure on the unknown components entering the model. This raises the following questions: First, is the chosen parametric model identified from data - i.e. is it possible to estimate and draw inference regarding the parameters of interest? Second, which of the parametric restrictions are really needed for identification and which are simply imposed for computational simplicity? One part of the project involved developing new identification results in some important structural models. These allow researchers to design parametric models that are well-identified, and potentially even allow them to estimate the components of interest non- or semiparametrically.
2. Non- and semiparametric estimation and inference: Given identified components, the research team developed novel non- and semiparametric estimators of these. The new methods allow researchers to obtain results that do not suffer from risks of misspecification. An asymptotic analysis of proposed estimators and tests were developed, and numerical results demonstrated their usefulness in practice.
3. Numerical techniques for the practical implementation of models and estimators: Even in parametric models, implementation of structural models is hampered by some components not being available in closed form. A leading example is the computation of value functions in dynamic decision models. This complication often restricts implementations to somewhat unrealistic models and/or leads to large numerical errors in the computed outcomes. The project developed new numerical techniques to allow implementation of more realistic models. The properties of the new (and existing) techniques were investigated both in theory and practice in order to understand how the additional numerical errors affect estimators and counterfactual analyses.