A Conditional Likelihood Ratio Test for Structural Models

Abstract

This paper develops a general method for constructing exactly similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reduced-form covariance matrix. These tests are shown to be similar under weak-instrument asymptotics when the reduced-form covariance matrix is estimated and the errors are non-normal. The conditional test based on the likelihood ratio statistic is particularly simple and has good power properties. Like the score test, it is optimal under the usual local-to-null asymptotics, but it has better power when identification is weak.

Estimating the causal effect of alcohol consumption on well-being for a cross-section of 9 former Soviet Union countries

“…The OLS estimations help us assess whether estimated parameters between full and restricted samples change and act as a crude sample selection test, while Wald tests are also computed for the statistical difference of coefficients across the two samples. Further we estimate two (one for each well-being indicator) standard two stage least square (2SLS) IV estimations for which we also compute robust (to weak instruments) confidence intervals for the effect of alcohol consumption (Baum, et al, 2012;Moreira, 2003). Estimations are performed in Stata with userwritten routines, -ivreg2- (Baum, Schaffer, & Stillman, 2012) and -condivreg- (Moreira & Poi, 2003).…”

“…implying that the link between the endogenous variable and the chosen instrument is not as strong) by means of robust statistics for inference in the covariate of interest (Moreira, 2003).…”

What Drives Personal Consumption? The Role of Housing and Financial Wealth

“…Estimation of consumption sluggishness χ in (2) Moreira (2003). Robust p val denotes the p value testing χ = 0 with Moreira's CLR test (robust to weak instruments).R 2 1 is the adjusted R 2 from the first-stage regressions of Δ log C t−1 on instruments.…”

“…The intervals are calculated by inverting the conditional likelihood ratio statistic (CLR) of Moreira (2003). 20 If the instruments are weak, the confidence intervals are wide (even infinitely as in the case of Belgium), which reflects the fact that χ is not identified under weak instruments.…”

Long-lasting bank relationships and growth of firms

“…[Insert Table 5] As t-tests and Wald tests based on the LIML estimator are more robust to weak instruments than those based on the TSLS estimator, i.e., as the maximal size of distortion in significance level for tests is lower in regressions using the former estimator, in Table 4 we report results based on both LIML and TSLS, and p-values from the standard t-test and the conditional likelihood ratio (CLR) test proposed by Moreira (2003) 22 . Moreover, as hypothesis testing with weak instruments is especially well developed (and coded in Stata routines by Mikusheva and Poi (2006)) for models with independent identically distributed homoskedastic normal errors, unlike in OLS regressions, we assume that the error term in the structural equation (1) is conditionally homoskedastic 23 .…”