Conditional inference for possibly unidentified structural equations

The possibility that a structural equation may not be identified casts doubt on the measures of estimator precision that are normally used. We argue that the observed identifiability test statistic is directly relevant to the precision with which the structural parameters can be estimated, and hence argue that inference in such models should be conditioned on the observed value of that statistic (or statistics). We examine in detail the effects of conditioning on the properties of the ordinary least squares (OLS) and two-stage least squares (TSLS) estimators for the coefficients of the endogenous variables in a single structural equation. We show that: (a) conditioning has very little impact on the properties of the OLS estimator, but a substantial impact on those of the TSLS estimator; (b) the conditional variance of the TSLS estimator can be very much larger than its unconditional variance (when the identifiability statistic is small), or very much smaller (when the identifiability statistic is large); and (c) conditional mean-square-error comparisons of the two estimators favour the OLS estimator when the sample evidence only weakly supports the identifiablity hypothesis, can favour TSLS slightly when that evidence is moderately favourable, but there is nothing to choose between the two estimators when the data strongly supports the identification hypothesis

A Conditional Approach to Panel Data Models with Common Shocks

This paper studies the effects of common shocks on the OLS estimators of the slopes’ parameters in linear panel data models. The shocks are assumed to affect both the errors and some of the explanatory variables. In contrast to existing approaches, which rely on using results on martingale difference sequences, our method relies on conditional strong laws of large numbers and conditional central limit theorems for conditionally-heterogeneous random variables

Data needs for integrated economic-epidemiological models of pandemic mitigation policies

The COVID-19 pandemic and the mitigation policies implemented in response to it have resulted in economic losses worldwide. Attempts to understand the relationship between economics and epidemiology has lead to a new generation of integrated mathematical models. The data needs for these models transcend those of the individual fields, especially where human interaction patterns are closely linked with economic activity. In this article, we reflect upon modelling efforts to date, discussing the data needs that they have identified, both for understanding the consequences of the pandemic and policy responses to it through analysis of historic data and for the further development of this new and exciting interdisciplinary field

Identification and Inference in a Simultaneous Equation Under Alternative Information Sets and Sampling Schemes

In simple static linear simultaneous equation models the empirical distributions ofIV and OLS are examined under alternative sampling schemes and compared with their first-order asymptotic approximations. It is demonstrated why in this context the limiting distribution of a consistent estimator is not a¤ected by conditioning on exogenous regressors, whereas that of an inconsistent estimator is. The asymptotic variance and the simulated actual variance of the inconsistent OLS estimator are shown to diminish by extending the set of exogenous variables kept fixed in sampling, whereas such an extension disrupts the distribution of consistent IV estimation and deteriorates the accuracy of its standard asymptotic approximation, not only when instruments are weak. Against this background the consequences for the identification of the parameters of interest are examined for a setting in which (in practice often incredible) assumptions regarding the zero correlation between instruments and disturbances are replaced by (generally more credible) interval assumptions on the correlation between endogenous regressors and disturbances. This leads to a feasible procedure for constructing purely OLS-based robust confidence intervals, which yield conservative coverage probabilities in finite samples, and often outperform IV-based intervals regarding their length

Conditional inference for possibly unidentified structural equations

The possibility that a structural equation may not be identified casts doubt on the measures of estimator precision that are normally used. We argue that the observed identifiability test statistic is directly relevant to the precision with which the structural parameters can be estimated, and hence argue that inference in such models should be conditioned on the observed value of that statistic (or statistics).We examine in detail the effects of conditioning on the properties of the ordinary least squares (OLS) and two-stage least squares (TSLS) estimators for the coefficients of the endogenous variables in a single structural equation. We show that: (a) conditioning has very little impact on the properties of the OLS estimator, but a substantial impact on those of the TSLS estimator; (b) the conditional variance of the TSLS estimator can be very much larger than its unconditional variance (when the identifiability statistic is small), or very much smaller (when the identifiability statistic is large); and (c) conditional mean-square-error comparisons of the two estimators favour the OLS estimator when the sample evidence only weakly supports the identifiablity hypothesis, can favour TSLS slightly when that evidence is moderately favourable, but there is nothing to choose between the two estimators when the data strongly supports the identification hypothesi