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The Heckman two-step estimator (Heckit) for the selectivity model is widely applied in Economics and other social sciences. In this model a non-zero outcome variable is observed only if a latent variable is positive. The asymptotic covariance matrix for a two-step estimation procedure must account for the estimation error introduced in the first stage. We examine the finite sample size of tests based on alternative covariance matrix estimators. We do so by using Monte Carlo experiments to evaluate bootstrap generated critical values and critical values based on asymptotic theory.

Researchers in economics and other disciplines are often interested in the causal effect of a binary treatment on outcomes. Econometric methods used to estimate such effects are divided into one of two strands depending on whether they require unconfoundedness (i.e., independence of potential outcomes and treatment assignment conditional on a set of observable covariates). When this assumption holds, researchers now have a wide array of estimation techniques from which to choose. However, very little is known about their performance – both in absolute and relative terms – when measurement error is present. In this study, the performance of several estimators that require unconfoundedness, as well as some that do not, are evaluated in a Monte Carlo study. In all cases, the data-generating process is such that unconfoundedness holds with the ‘real’ data. However, measurement error is then introduced. Specifically, three types of measurement error are considered: (i) errors in treatment assignment, (ii) errors in the outcome, and (iii) errors in the vector of covariates. Recommendations for researchers are provided.

In the spirit of White’s (1982) paper, this paper examines the consequences of model misspecification using a panel data regression model. Maximum likelihood, random and fixed effects estimators are compared using Monte Carlo experiments under normality of the disturbances but with a possibly misspecified variance-covariance matrix. We show that the correct GLS (ML) procedure is always the best according to MSE performance, but the researcher does not have perfect foresight on the true form of the variance covariance matrix. In this case, we show that a pretest estimator is a viable alternative given that its performance is a close second to correct GLS (ML) whether the true specification is a two-way, a one-way error component model or a pooled regression model. Incorrect GLS, ML or fixed effects estimators may lead to a big loss in MSE.

This paper studies test of hypotheses for the slope parameter in a linear time trend panel data model with serially correlated error component disturbances. We propose a test statistic that uses a bias corrected estimator of the serial correlation parameter. The proposed test statistic which is based on the corresponding fixed effects feasible generalized least squares (FE-FGLS) estimator of the slope parameter has the standard normal limiting distribution which is valid whether the remainder error is I(0) or I(1). This performs well in Monte Carlo experiments and is recommended.

For kernel-based estimators, smoothness conditions ensure that the asymptotic rate at which the bias goes to zero is determined by the kernel order. In a finite sample, the leading term in the expansion of the bias may provide a poor approximation. We explore the relation between smoothness and bias and provide estimators for the degree of the smoothness and the bias. We demonstrate the existence of a linear combination of estimators whose trace of the asymptotic mean-squared error is reduced relative to the individual estimator at the optimal bandwidth. We examine the finite-sample performance of a combined estimator that minimizes the trace of the MSE of a linear combination of individual kernel estimators for a multimodal density. The combined estimator provides a robust alternative to individual estimators that protects against uncertainty about the degree of smoothness.

In this chapter we perform a Monte Carlo simulation study of the errors-in-variables model examined in Ramsey, Gallegati, Gallegati, and Semmler (2010) by using a wavelet multiresolution approximation approach. Differently from previous studies applying wavelets to errors-in-variables problem, we use a sequence of multiresolution approximations of the variable measured with error ranging from finer to coarser scales. Our results indicate that multiscale approximations to the variable observed with error based on the coarser scales provide an unbiased asymptotically efficient estimator that also possess good finite sample properties.

This chapter examines the effect of changes in the public debt–gross domestic product (GDP) ratio on long, 10 year, interest rates in a panel of 17 countries over the period 1870–2016 controlling for other variables, in particular the world interest rate. Over this long period, one can argue that most of the big changes in public debt were the product of factors largely exogenous to national interest rate determination, such as war, depression or financial crisis. The issue is of current relevance since the Covid-19 pandemic has caused large increases in the ratio of public debt to GDP in many countries. The estimates suggest that it is the change in debt, rather than the level of debt or the deficit that matters for long interest rates. World interest rates have long- and short-run effects on interest rates which are very well determined and close to one. Current inflation has a small but significant effect.

Heavy-tailed distributions present a tough setting for inference. They are also common in industrial applications, particularly with internet transaction datasets, and machine learners often analyze such data without considering the biases and risks associated with the misuse of standard tools. This chapter outlines a procedure for inference about the mean of a (possibly conditional) heavy-tailed distribution that combines nonparametric analysis for the bulk of the support with Bayesian parametric modeling – motivated from extreme value theory – for the heavy tail. The procedure is fast and massively scalable. The work should find application in settings wherever correct inference is important and reward tails are heavy; we illustrate the framework in causal inference for A/B experiments involving hundreds of millions of users of eBay.com.

This paper is concerned with estimation and inference for difference-in-difference regressions with errors that exhibit high serial dependence, including near unit roots, unit roots, and linear trends. We propose a couple of solutions based on a parametric formulation of the error covariance. First stage estimates of autoregressive structures are obtained by using the Han, Phillips, and Sul (2011, 2013) X-differencing transformation. The X-differencing method is simple to implement and is unbiased in large N settings. Compared to similar parametric methods, the approach is computationally simple and requires fewer restrictions on the permissible parameter space of the error process. Simulations suggest that our methods perform well in the finite sample across a wide range of panel dimensions and dependence structures.

Statistical inference (estimation and testing) for the stochastic volatility (SV) model Taylor (1982, 1986) is challenging, especially likelihood-based methods which are difficult to apply due to the presence of latent variables. The existing methods are either computationally costly and/or inefficient. In this paper, we propose computationally simple estimators for the SV model, which are at the same time highly efficient. The proposed class of estimators uses a small number of moment equations derived from an ARMA representation associated with the SV model, along with the possibility of using “winsorization” to improve stability and efficiency. We call these ARMA-SV estimators. Closed-form expressions for ARMA-SV estimators are obtained, and no numerical optimization procedure or choice of initial parameter values is required. The asymptotic distributional theory of the proposed estimators is studied. Due to their computational simplicity, the ARMA-SV estimators allow one to make reliable – even exact – simulation-based inference, through the application of Monte Carlo (MC) test or bootstrap methods. We compare them in a simulation experiment with a wide array of alternative estimation methods, in terms of bias, root mean square error and computation time. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that ARMA-SV estimators match (or exceed) alternative estimators in terms of precision, including the widely used Bayesian estimator. The proposed methods are applied to daily observations on the returns for three major stock prices (Coca-Cola, Walmart, Ford) and the S&P Composite Price Index (2000–2017). The results confirm the presence of stochastic volatility with strong persistence.