Subset hypotheses testing and instrument exclusion in the linear IV regression

This paper investigates the asymptotic size properties of robust subset tests when instruments are left out of the analysis. Recently, robust subset procedures have been developed for testing hypotheses which are specified on the subsets of the structural parameters or on the parameters associated with the included exogenous variables. It has been shown that they never over-reject the true parameter values even when nuisance parameters are not identified. However, their robustness to instrument exclusion has not been investigated. Instrument exclusion is an important problem in econometrics and there are at least two reasons to be concerned. Firstly, it is difficult in practice to assess whether an instrument has been omitted. For example, some components of the “identifying” instruments that are excluded from the structural equation may be quite uncertain or “left out” of the analysis. Secondly, in many instrumental variable (IV) applications, an infinite number of instruments are available for use in large sample estimation. This is particularly the case with most time series models. If a given variable, say Xt, is a legitimate instrument, so too are its lags Xt1; Xt2. Hence, instrument exclusion seems highly likely in most practical situations. After formulating a general asymptotic framework which allows one to study this issue in a convenient way, I consider two main setups: (1) the missing instruments are (possibly) relevant, and, (2) they are asymptotically weak. In both setups, I show that all subset procedures studied are in general consistent against instrument inclusion (hence asymptotically invalid for the subset hypothesis of interest). I characterize cases where consistency may not hold, but the asymptotic distribution is modified in a way that would lead to size distortions in large samples. I propose a “rule of thumb” which allows to practitioners to know whether a missing instrument is detrimental or not to subset procedures. I present a Monte Carlo experiment confirming that the subset procedures are unreliable when instruments are missing.REPEC,

On the validity of Durbin-Wu-Hausman tests for assessing partial exogeneity hypotheses with possibly weak instruments

We investigate the validity of the standard specification tests for assessing the exogeneity of subvectors in the linear IV regression. Our results show that ignoring the endogeneity of the regressors whose exogeneity is not being tested leads to invalid tests (level is not controlled). When the fitted values from the first stage regression of these regressors are used as instruments under the partial null hypothesis of interest, as suggested Hausman and Taylor (1980, 1981), some versions of these tests are invalid when identification is weak and the number of instruments is moderate. However, all tests are overly conservative and have no power when the number of instruments increases, even for moderate identification strength

Do contacts matter in the process of getting a job in Cameroon?

We question whether the use of social networks to exit unemployment matters in Cameroon. We develop a Weibull-type duration model which allows us to address this issue in a convenient way. Our investigations indicate that there is a strong evidence of endogeneity and sample selection biases. We then propose a three-step procedure to deal with both problems. Our results show that the use of social networks to exit unemployment is effective. Furthermore, we find that the hazard monotonically increases with time. Hence, unemployment exhibits a positive duration dependence. Moreover, we provide an analysis of factors that determine labor market participation and the use of social networks. We find that the density of the west native population in the center of Cameroon and religion are the only factors that determine the use of social networks. In contrast, characteristics such as age, sex, education, association’s membership, determine labor market participation.RePEc

Testing for partial exogeneity with weak identification

We consider the following problem. A structural equation of interest contains two sets of explanatory variables which economic theory predicts may be endogenous. The researcher is interesting in testing the exogeneity of only one of them. Standard exogeneity tests are in general unreliable from the view point of size control to assess such a problem. We develop four alternative tests to address this issue in a convenient way. We provide a characterization of their distributions under both the null hypothesis (level) and the alternative hypothesis (power), with or without identification. We show that the usual 2 critical values are still applicable even when identification is weak. So, all proposed tests can be described as robust to weak instruments. We also show that test consistency may still hold even if the overall identification fails, provided partial identification is satisfied. We present a Monte Carlo experiment which confirms our theory. We illustrate our theory with the widely considered returns to education example. The results underscore: (1) how the use of standard tests to assess partial exogeneity hypotheses may be misleading, and (2) the relevance of using our procedures when checking for partial exogeneity

On Bootstrap Validity for Specification Tests with Weak Instruments

This paper investigates the asymptotic validity of the bootstrap for Durbin-Wu-Hausman (DWH) specification tests when instrumental variables (IVs) may be arbitrary weak. It is shown that under strong identification, the bootstrap offers a better approximation than the usual asymptotic 2 distributions. However, the bootstrap provides only a first-order approximation when instruments are weak. These results show unlike theWald-statistic based on a k-class type estimator (Moreira et al., 2009), the bootstrap is valid even for the Wald-type of DWH statistics in the presence of weak instruments

Specification tests with weak and invalid instruments

We investigate the size of the Durbin-Wu-Hausman tests for exogeneity when instrumental variables violate the strict exogeneity assumption. We show that these tests are severely size distorted even for a small correlation between the structural error and instruments. We then propose a bootstrap procedure for correcting their size. The proposed bootstrap procedure does not require identification assumptions and is also valid even for moderate correlations between the structural error and instruments, so it can be described as robust to both weak and invalid instruments

Uniform Inference after Pretesting for Exogeneity

Pretesting for exogeneity has become a routine in many empirical applications involving instrumental variables (IVs) to decide whether the ordinary least squares (OLS) or the two-stage least squares (2SLS) method is appropriate. Guggenberger (2010) shows that the second-stage t-test– based on the outcome of a Durbin- Wu-Hausman type pretest for exogeneity in the first-stage– has extreme size distortion with asymptotic size equal to 1 when the standard asymptotic critical values are used. In this paper, we first show that the standard residual bootstrap procedures (with either independent or dependent draws of disturbances) are not viable solutions to such extreme size-distortion problem. Then, we propose a novel hybrid bootstrap approach, which combines the residual-based bootstrap along with an adjusted Bonferroni size-correction method. We establish uniform validity of this hybrid bootstrap in the sense that it yields a two-stage test with correct asymptotic size. Monte Carlo simulations confirm our theoretical findings. In particular, our proposed hybrid method achieves remarkable power gains over the 2SLS-based t-test, especially when IVs are not very strong

Uniform Inference after Pretesting for Exogeneity

Pretesting for exogeneity has become a routine in many empirical applications involving instrumental variables (IVs) to decide whether the ordinary least squares (OLS) or the two-stage least squares (2SLS) method is appropriate. Guggenberger (2010) shows that the second-stage t-test– based on the outcome of a Durbin- Wu-Hausman type pretest for exogeneity in the first-stage– has extreme size distortion with asymptotic size equal to 1 when the standard asymptotic critical values are used. In this paper, we first show that the standard residual bootstrap procedures (with either independent or dependent draws of disturbances) are not viable solutions to such extreme size-distortion problem. Then, we propose a novel hybrid bootstrap approach, which combines the residual-based bootstrap along with an adjusted Bonferroni size-correction method. We establish uniform validity of this hybrid bootstrap in the sense that it yields a two-stage test with correct asymptotic size. Monte Carlo simulations confirm our theoretical findings. In particular, our proposed hybrid method achieves remarkable power gains over the 2SLS-based t-test, especially when IVs are not very strong