Testing in GMM Models without Truncation

This paper proposes a new approach to testing in the generalized method of moments (GMM) framework. The new tests are constructed using heteroskedasticity autocorrelation (HAC) robust standard errors computed using nonparametric spectral density estimators without truncation. While such standard errors are not consistent, a new asymptotic theory shows that they lead to valid tests nonetheless. In an over-identified linear instrumental variables model, simulations suggest that the new tests and the associated limiting distribution theory provide a more accurate first order asymptotic null approximation than standard HAC robust tests. Finite sample power of the new tests is shown to be comparable to standard tests. Because use of a truncation lag equal to the sample requires no additional choices for practitioners, the new approach could potentially lead to a standard of practice (which does not currently exist) for the computation of HAC robust standard errors in GMM models.

A Fixed-b Perspective on the Phillips-Perron Unit Root Tests

We extend fixed-b asymptotic theory to the nonparametric Phillips-Perron (PP) unit root tests. We show that the fixed-b limits depend on nuisance parameters in a complicated way. These non-pivotal limits provide an alternative theoretical explanation for the well known finite sample problems of PP tests. We also show that the fixed-b limits depend on whether deterministic trends are removed using one-step or two-step approaches, contrasting the asymptotic equivalence of the one- and two-step approaches under a consistency approximation for the long run variance estimator. Based on these results we introduce modified PP tests that allow for fixed-b inference. The theoretical analysis is cast in the framework of near-integrated processes which allows to study the asymptotic behavior both under the unit root null hypothesis as well as for local alternatives. The performance of the original and modified tests is compared by means of local asymptotic power and a small simulation study.Nonparametric kernel estimator, long run variance, detrending, one-step, two-step

Integrated Modified OLS Estimation and Fixed-b Inference for Cointegrating Regressions

This paper is concerned with parameter estimation and inference in a cointegrating regression, where as usual endogenous regressors as well as serially correlated errors are considered. We propose a simple, new estimation method based on an augmented partial sum (integration) transformation of the regression model. The new estimator is labeled Integrated Modified Ordinary Least Squares (IM-OLS). IM-OLS is similar in spirit to the fully modified approach of Phillips and Hansen (1990) with the key difference that IM-OLS does not require estimation of long run variance matrices and avoids the need to choose tuning parameters (kernels, bandwidths, lags). Inference does require that a long run variance be scaled out, and we propose traditional and fixed-b methods for obtaining critical values for test statistics. The properties of IM-OLS are analyzed using asymptotic theory and finite sample simulations. IM-OLS performs well relative to other approaches in the literature.Bandwidth, cointegration, fixed-b asymptotics, Fully Modified OLS, IM-OLS, kernel

Powerful Trend Function Tests That Are Robust to Strong Serial Correlation with an Application to the Prebisch-Singer Hypothesis

In this paper we propose tests for hypotheses regarding the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data and they are robust to strong serial correlation. The data can contain a unit root and the tests still have the correct size asymptotically. The tests we analyze are standard heteroskedasticity autocorrelation (HAC) robust tests based on nonparametric kernel variance estimators. We analyze these tests using the ï¾…xed-b asymptotic framework recently proposed by Kiefer and Vogelsang (2002). This analysis allows us to analyze the power properties of the tests with regards to bandwidth and kernel choices. Our analysis shows that among popular kernels, there are speciï¾…c kernel and bandwidth choices that deliver tests with maximal power within a speciï¾…c class of tests. Based on the theoretical results, we propose a data dependent bandwidth rule that maximizes integrated power. Our recommended test is shown to have power that dominates a related test proposed by Vogelsang (1998). We apply the recommended test to the logarithm of a net barter terms of trade series and we ï¾…nd that this series has a statistically signiï¾…cant negative slope. This ï¾…nding is consistent with the well known Prebisch-Singer hypothesis.

Testing for Common Deterministic Trend Slopes

We propose tests for hypotheses on the parameters for deterministic trends. The model framework assumes a multivariate structure for trend-stationary time series variables. We derive the asymptotic theory and provide some relevant critical values. Monte Carlo simulations suggest which tests are more useful in practice than others. We apply our tests to examine if monthly temperatures in The Netherlands, measured from 1706 onwards, have a trend and if these trends are the same across months. We find that the January and March temperatures have the same upward trend, that the September temperature has decreased and that the temperatures in the other months do not have a trend. Hence, only winters in The Netherlands seem to get warmer.

Nonparametric Rank Tests for Non-stationary Panels

This study develops new rank tests for panels that include panel unit root tests as a special case. The tests are unusual in that they can accommodate very general forms of both serial and cross-sectional dependence, including cross-unit cointegration, without the need to specify the form of dependence or estimate nuisance parameters associated with the dependence. The tests retain high power in small samples, and in contrast to other tests that accommodate cross-sectional dependence, the limiting distributions are valid for panels with finite cross-sectional dimensions.Nonparametric rank tests, unit roots, cointegration, cross-sectional dependence

An integrated modified OLS RESET test for cointegrating regressions

We propose a RESET-type test for the null hypothesis of linearity of a cointegrating relationship with an asymptotic chi-squared null distribution. The test is based on an extension of the Integrated Modified OLS estimator of Vogelsang and Wagner (2014) from linear cointegrating relationships to multivariate cointegrating polynomial relationships. For the case of full design we furthermore provide fixed-b asymptotic theory for our RESET test. The theoretical results are complemented by a small simulation study

Multivariate trend comparisons between autocorrelated climate series with general trend regressors

Abstract Inference regarding trends in climatic data series, including comparisons across different data sets as well as univariate trend significance tests, is complicated by the presence of serial correlation and step-changes in the mean. We review recent developments in the estimation of heteroskedasticity and autocorrelation robust (HAC) covariance estimators as they have been applied to linear trend inference, with focus on the Vogelsang-Franses (2005) nonparametric approach, which provides a unified framework for trend covariance estimation robust to unknown forms of autocorrelation up to but not including unit roots, making it especially useful for climatic data applications. We extend the Vogelsang-Franses approach to allow general deterministic regressors including the case where a step-change in the mean occurs at a known date. Additional regressors change the critical values of the Vogelsang-Franses statistic. We derive an asymptotic approximation that can be used to simulate critical values. We also outline a simple bootstrap procedure that generates valid critical values and p-values. The motivation for extending the Vogelsang-Franses approach is an application that compares climate model generated and observational global temperature data in the tropical lowerand mid-troposphere from 1958 to 2010. Inclusion of a mean shift regressor to capture the Pacific Climate Shift of 1977 causes apparently significant observed trends to become statistically insignificant, and rejection of the equivalenc

Integrated Modified OLS Estimation and Fixed-b Inference for Cointegrating Multivariate Polynomial Regressions

This paper shows that the integrated modified OLS (IM-OLS) estimator developed for cointegrating linear regressions in Vogelsang and Wagner (2014a) can be straightforwardly extended to cointegrating multivariate polynomial regressions. These are regression models that include as explanatory variables deterministic variables, integrated processes and products of (non-negative) integer powers of these variables as regressors. The stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous. The IM-OLS estimator is tuningparameter free and does not require the estimation of any long-run variances. A scalar long-run variance, however, has to be estimated and scaled out when using IM-OLS for inference. In this respect, we consider both standard asymptotic inference as well as fixed-b inference. Fixed-b inference requires that the regression model is of full design. The results may be particularly interesting for specification testing of cointegrating relationships, with RESET-type specification tests following immediately. The simulation section also zooms in on RESET specification testing and illustrates that the performance of IM-OLS is qualitatively comparable to its performance in cointegrating linear regressions