Information Structure and Statistical Information in Discrete Response Models
AbstractDiscrete response models are of high interest in economics and econometrics as they encompass treatment effects, social interaction and peer effect models, and discrete games. We study the impact of the structure of information sets of economic agents on the Fisher information of (strategic) interaction parameters in such models. While in complete information models the information sets of participating economic agents coincide, in incomplete information models each agent has a type, which we model as a payoff shock, that is not observed by other agents. We allow for the presence of a payoff component that is common knowledge to economic agents but is not observed by the econometrician (representing unobserved heterogeneity) and have the agents' payoffs in the incomplete information model approach their payoff in the complete information model as the heterogeneity term approaches 0. We find that in the complete information models, there is zero Fisher information for interaction parameters, implying that estimation and inference become nonstandard. In contrast, positive Fisher information can be attained in the incomplete information models with any non-zero variance of player types, and for those we can also find the semiparametric efficiency bound with unknown distribution of unobserved heterogeneity. The contrast in Fisher information is illustrated in two important cases: treatment effect models, which we model as a triangular system of equations, and static game models. In static game models we show this result is not due to equilibrium refinement with an increase in incomplete information, as our model has a fixed equilibrium selection mechanism. We find that the key factor in these models is the relative tail behavior of the unobserved component in the economic agents' payoffs and that of the observable covariates.
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Bibliographic InfoPaper provided by Duke University, Department of Economics in its series Working Papers with number 11-19.
Date of creation: 2011
Date of revision:
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Postal: Department of Economics Duke University 213 Social Sciences Building Box 90097 Durham, NC 27708-0097
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endogeneity; semiparametric efficiency; optimal convergence rate; strategic response;
Find related papers by JEL classification:
- C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-09 (All new papers)
- NEP-CTA-2011-10-09 (Contract Theory & Applications)
- NEP-ECM-2011-10-09 (Econometrics)
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