Econometrics, Volume 7, Issue 4 (December 2019) – 9 articles

The usual t test, the t test based on heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators, and the heteroskedasticity and autocorrelation robust (HAR) test are three statistics that are widely used in applied econometric work. The use of these significance tests in trend regression is of particular interest given the potential for spurious relationships in trend formulations. Following a longstanding tradition in the spurious regression literature, this paper investigates the asymptotic and finite sample properties of these test statistics in several spurious regression contexts, including regression of stochastic trends on time polynomials and regressions among independent random walks. Concordant with existing theory (Phillips 1986, 1998; Sun 2004, 2014b) the usual t test and HAC standardized test fail to control size as the sample size $n\to \infty$ in these spurious formulations, whereas HAR tests converge to well-defined limit distributions in each case and therefore have the capacity to be consistent and control size. However, it is shown that when the number of trend regressors $K\to \infty ,$ all three statistics, including the HAR test, diverge and fail to control size as $n\to \infty$ . These findings are relevant to high-dimensional nonstationary time series regressions where machine learning methods may be employed. Full article

We propose an econometric procedure based mainly on the generalized random forests method. Not only does this process estimate the quantile treatment effect nonparametrically, but our procedure yields a measure of variable importance in terms of heterogeneity among control variables. We also apply the proposed procedure to reinvestigate the distributional effect of 401(k) participation on net financial assets, and the quantile earnings effect of participating in a job training program. Full article

This paper considers observation driven models with conditional mean and variance dynamics for non-negative valued time series. The motivation is to relax the restriction imposed on the higher order moment dynamics in standard multiplicative error models driven only by the conditional mean dynamics. The empirical fit of a zero inflated mixture distribution is assessed with trade duration data with a large fraction of zero observations. All authors have read and agreed to the published version of the manuscript. Full article

The serial dependence of categorical data is commonly described using Markovian models. Such models are very flexible, but they can suffer from a huge number of parameters if the state space or the model order becomes large. To address the problem of a large number of model parameters, the class of (new) discrete autoregressive moving-average (NDARMA) models has been proposed as a parsimonious alternative to Markov models. However, NDARMA models do not allow any negative model parameters, which might be a severe drawback in practical applications. In particular, this model class cannot capture any negative serial correlation. For the special case of binary data, we propose an extension of the NDARMA model class that allows for negative model parameters, and, hence, autocorrelations leading to the considerably larger and more flexible model class of generalized binary ARMA (gbARMA) processes. We provide stationary conditions, give the stationary solution, and derive stochastic properties of gbARMA processes. For the purely autoregressive case, classical Yule–Walker equations hold that facilitate parameter estimation of gbAR models. Yule–Walker type equations are also derived for gbARMA processes. Full article

Previous findings indicate that the inclusion of dynamic factors obtained from a large set of predictors can improve macroeconomic forecasts. In this paper, we explore three possible further developments: (i) using automatic criteria for choosing those factors which have the greatest predictive power; (ii) using only a small subset of preselected predictors for the calculation of the factors; and (iii) utilizing frequency-domain information for the estimation of the factor models. Reanalyzing a standard macroeconomic dataset of 143 U.S. time series and using the major measures of economic activity as dependent variables, we find that (i) is not helpful, whereas focusing on the low-frequency components of the factors and disregarding the high-frequency components can actually improve the forecasting performance for some variables. In the case of the gross domestic product, a combination of (ii) and (iii) yields the best results. Full article

This paper considers estimation and inference concerning the autoregressive coefficient ( $\rho$ ) in a panel autoregression for which the degree of persistence in the time dimension is unknown. Our main objective is to construct confidence intervals for $\rho$ that are asymptotically valid, having asymptotic coverage probability at least that of the nominal level uniformly over the parameter space. The starting point for our confidence procedure is the estimating equation of the Anderson–Hsiao (AH) IV procedure. It is well known that the AH IV estimation suffers from weak instrumentation when $\rho$ is near unity. But it is not so well known that AH IV estimation is still consistent when $\rho =1$ . In fact, the AH estimating equation is very well-centered and is an unbiased estimating equation in the sense of Durbin (1960), a feature that is especially useful in confidence interval construction. We show that a properly normalized statistic based on the AH estimating equation, which we call the $\mathbb{M}$ statistic, is uniformly convergent and can be inverted to obtain asymptotically valid interval estimates. To further improve the informativeness of our confidence procedure in the unit root and near unit root regions and to alleviate the problem that the AH procedure has greater variation in these regions, we use information from unit root pretesting to select among alternative confidence intervals. Two sequential tests are used to assess how close $\rho$ is to unity, and different intervals are applied depending on whether the test results indicate $\rho$ to be near or far away from unity. When $\rho$ is relatively close to unity, our procedure activates intervals whose width shrinks to zero at a faster rate than that of the confidence interval based on the $\mathbb{M}$ statistic. Only when both of our unit root tests reject the null hypothesis does our procedure turn to the $\mathbb{M}$ statistic interval, whose width has the optimal $N^{-1/2}{T}^{-1/2}$ rate of shrinkage when the underlying process is stable. Our asymptotic analysis shows this pretest-based confidence procedure to have coverage probability that is at least the nominal level in large samples uniformly over the parameter space. Simulations confirm that the proposed interval estimation methods perform well in finite samples and are easy to implement in practice. A supplement to the paper provides an extensive set of new results on the asymptotic behavior of panel IV estimators in weak instrument settings. Full article

This paper begins with the observation that the constrained maximisation central to model estimation and hypothesis testing may be interpreted as a kind of profit maximisation. The output of estimation is a model that maximises some measure of model fit, subject to costs that may be interpreted as the shadow price of constraints imposed on the model. The replication crisis may be regarded as a market failure in which the price of “significant” results is lower than would be socially optimal. Full article

For modeling count time series data, one class of models is generalized integer autoregressive of order p based on thinning operators. It is shown how numerical maximum likelihood estimation is possible by inverting the probability generating function of the conditional distribution of an observation given the past p observations. Two data examples are included and show that thinning operators based on compounding can substantially improve the model fit compared with the commonly used binomial thinning operator. Full article

This paper proposes a class of partial cointegrated models allowing for structural breaks in the deterministic terms. Moving-average representations of the models are given. It is then shown that, under the assumption of martingale difference innovations, the limit distributions of partial quasi-likelihood ratio tests for cointegrating rank have a close connection to those for standard full models. This connection facilitates a response surface analysis that is required to extract critical information about moments from large-scale simulation studies. An empirical illustration of the proposed methodology is also provided. Full article