The Effect of Linear Time Trends on Cointegration Testing in Single Equations

This paper surveys the asymptotic distributions of three widely used single equation cointegration tests. Particular attention is paid to the case where the regressors are integrated with drift, i.e. at least one of the regressors follows a linear trend. Even if the regressions are not detrended, the asymptotic critical values are affected by the presence of linear trends in the regressors. Not taking into account this effect leads to tests that are biased towards establishing cointegration too often. The correct limiting distribution theory of regressions without detrending in the presence of integrated regressors with drift is described. Appropriate critical values are readily available from the literature and are simple to use following the tables included here.

Inflation-Unemployment Tradeoff and Regional Labor Market Data

We estimate a linear and a piecewise linear Phillips curve model with regional labor market data for West German and Neue Länder. Employing regional observations allows us to country difference the data. This eliminates, under the assumption of homogeneous Länder, supply shocks and changes in the formation of expectations as possible identification failures. With seemingly unrelated regressions we find a flat Phillips curve in the Neue Länder. For the West German Länder a piecewise linear model with a higher inflation-unemployment tradeoff for the regime of low unemployment rates fits the data very well. The results hold true if we control for endogeneity of the unemployment rate. With a kinked but upward sloping aggregate supply curve there seems to be room for stabilization policies, at least in the range of aggregate demand shifts that our data covers.inflation-unemployment tradeoff, NAIRU, regional labor market data, seemingly unrelated regression

Unit root testing

The occurrence of unit roots in economic time series has far reaching consequences for univariate as well as multivariate econometric modelling. Therefore, unit root tests are nowadays the starting point of most empirical time series studies. The oldest and most widely used test is due to Dickey and Fuller (1979). Reviewing this test and variants thereof we focus on the importance of modelling the deterministic component. In particular, we survey the growing literature on tests accounting for structural shifts. Finally, further applied aspects are addressed how to get the size correct and obtain good power at the same time. --Dickey-Fuller,size and power,deterministic components,structural breaks

Autoregressive distributed lag models and cointegration

This paper considers cointegration analysis within an autoregressive distributed lag (ADL) framework. First, different reparameterizations and interpretations are reviewed. Then we show that the estimation of a cointegrating vector from an ADL specification is equivalent to that from an error-correction (EC) model. Therefore, asymptotic normality available in the ADL model under exogeneity carries over to the EC estimator. Next, we review cointegration tests based on EC regressions. Special attention is paid to the effect of linear time trends in case of regressions without detrending. Finally, the relevance of our asymptotic results in finite samples is investigated by means of computer experiments. In particular, it turns out that the conditional EC model is superior to the unconditional one. --Error-correction , asymptotically normal inference , cointegration testing

A Residual-Based LM Test for Fractional Cointegration

Nonstationary fractionally integrated time series may possibly be fractionally cointegrated. In this paper we propose a test for the null hypothesis of no cointegration. It builds on a static cointegration regression of the levels of the variables as a first step. In a second step, a univariate LM test is applied to the single equation regression residuals. However, it turns out that the application of the LM test to residuals without further modifications does not result in a limiting standard normal distribution, which contrasts with the situation when the LM test is applied to observed series. Therefore, we suggest a simple modification of the LM test that accounts for the residual effect. At the same time it corrects for eventual endogeneity of the cointegration regression. The proposed modification guarantees a limiting standard normal distribution of the test statistic. Our procedure is completely regression based and hence easy to perform. Monte Carlo experiments establish its validity for finite samples.Long memory, LM test, single equations

Nonsense regressions due to time-varying means

Regressions of two independent time senes are considered. The variables are covariance stationary but display time-varying although not trending means. Two prominent examples are mean shifts due to structural breaks and seasonally varying means. If the variation of the means is not taken into account, this induces nonsense correlation. The asymptotic treatment is supplemented by experimental evidence

Residual Log-Periodogram Inference for Long-Run-Relationships

We assume that some consistent estimator of an equilibrium relation between non-stationary series integrated of order d E (0:5; 1:5) is used to compute residuals ˆut = yt - xt (or differences there of). We propose to apply the semiparametric log-periodogram regression to the (differenced) residuals in order to estimate or test the degree of persistence ± of the equilibrium deviation ut. Provided converges fast enough, we describe simple semiparametric conditions around zero frequency that guarantee consistent estimation of ±. At the same time limiting normality is derived, which allows to construct approximate confidence intervals to test hypotheses on ±. This requires that d ¡ ± > 0:5 for superconsistent b¯, so the residuals can be good proxies of true cointegrating errors. Our assumptions allow for stationary deviations with long memory, 0 · ± < 0:5, as well as for non-stationary but transitory equilibrium errors, 0:5 < ± < 1. In particular, if xt contains several series we consider the joint estimation of d and ±. Wald statistics to test for parameter restrictions of the system have a limiting Â2 distribution. We also analyze the benefits of a pooled version of the estimate. The empirical applicability of our general cointegration test is investigated by means of Monte Carlo experiments and illustrated with a study of exchange rate dynamics

The Effect of Linear Time Trends on Cointegration Testing in Single Equations

This paper surveys the asymptotic distributions of three widely used single equation cointegration tests. Particular attention is paid to the case where the regressors are integrated with drift, i.e. at least one of the regressors follows a linear trend. Even if the regressions are not detrended, the asymptotic critical values are affected by the presence of linear trends in the regressors. Not taking into account this effect leads to tests that are biased towards establishing cointegration too often. The correct limiting distribution theory of regressions without detrending in the presence of integrated regressors with drift is described. Appropriate critical values are readily available from the literature and are simple to use following the tables included here

When More Is Less: Pitfalls of significance testing

The controversy about statistical significance vs. scientific relevance is more than 100 years old. But still nowadays null hypothesis significance testing is considered as gold standard in many empirical fields from economics and social sciences over psychology to medicine, and small $p$-values are often the key to publish in journals of high scientific reputation. I highlight, illustrate and discuss potential pitfalls of statistical significance testing on three occasions.Comment: 16 pages, 2 figure