Search

Probit models with endogenous regressors are commonly used models in economics and other social sciences. Yet, the robustness properties of parametric estimators in these models have not been formally studied. In this paper, we derive the influence functions of the endogenous probit model’s classical estimators (the maximum likelihood and the two-step estimator) and prove their non-robustness to small but harmful deviations from distributional assumptions. We propose a procedure to obtain a robust alternative estimator, prove its asymptotic normality and provide its asymptotic variance. A simple robust test for endogeneity is also constructed. We compare the performance of the robust and classical estimators in Monte Carlo simulations with different types of contamination scenarios. The use of our estimator is illustrated in several empirical applications.

The econometrics literature proposed several new causal machine learning methods (CML) in the past few years. These methods harness the strength of machine learning methods to flexibly model the relationship between the treatment, outcome and confounders, while providing valid inferential statements. Whereas numerous options are available now to the applied economics researcher, there is limited guidance on the most useful methodology for a particular applied setting. In this paper, we perform a comprehensive evaluation of the finite sample performance of recently introduced CML methods from the econometrics literature, under a wide range of data generating processes. We focus our analysis on data features that are relevant for causal inference such as varying degrees of: nonlinearity in the outcome and treatment equations, overlap, percentage of treated, alignment and heterogeneity in the treatment effect. We evaluate the methods that have received the most attention so far from the empirical economics literature: double machine learning, causal forest and the generic machine learning methods. Results on the bias, root mean squared error, coverage rates and interval lengths for the average treatment effect, group average treatment effects and individual treatment effects reveal information on the characteristics of the methods and the data features that affect their performance the most.

Chapter One, A Forecast Rationality Test that Allows for Loss Function Asymmetries, proposes a new forecast rationality test that allows for asymmetric preferences without assuming any particular functional form for the forecaster's loss function. The construction of the test is based on the simple idea that under rationality, asymmetric preferences imply that the conditional bias of the forecast error is zero. The null hypothesis of forecast rationality under asymmetric loss (i.e. no conditional bias) is tested by constructing a Bierens [1982, 1990] conditional moment type test.\ud \ud Chapter Two, Global Identification Failure in DSGE Models and its Impact on Forecasting, considers the identification problem in DSGE models and its transfer to other objects of interest such as point forecasts. The results document that when observationally equivalent parameter points belong to the same model structure, the implied point forecasts are the same under both correct specification and misspecification. However, when analyzing the identification problem permitting models with different structures (e.g. different policy rules that produce sets of data dynamics that are quantitatively similar), the paper shows that indistinguishable parameter estimates can lead to distinct predictions.\ud \ud Chapter Three, Identification Robust Predictive Ability Testing, considers the predictive accuracy evaluation of models that are strongly identified in some part of the parameter space but non-identified or weakly identified in another part of the parameter space. The paper shows that when comparing the predictive ability of models that might be affected by identification deficiencies, the null distribution of out-of-sample predictive ability tests is not well approximated by the standard normal distribution. As a result, employing a standard (strong) identification critical value might lead to misleading inference. We propose methods to make the out-of-sample predictive ability tests robust to identification loss.