Mohitosh Kejriwal

Testing for Multiple Structural Changes in Cointegrated Regression Models

We consider testing for multiple structural changes in cointegrated systems and derive the limiting distribution of the sup-Wald test under mild conditions on the errors and regressors for a variety of testing problems. We show that even if the coefficients of the integrated regressors are held fixed but the intercept is allowed to change, the limit distributions are not the same as would prevail in a stationary framework. We also propose a sequential procedure that permits consistent estimation of the number of breaks present. We show via simulations that our tests maintain the correct size in finite samples and are much more powerful than the commonly used LM tests, which suffer from important problems of nonmonotonic power in the presence of serial correlation in the errors.

A Sequential Procedure to Determine the Number of Breaks in Trend with an Integrated or Stationary Noise Component

Perron and Yabu (2009a) consider the problem of testing for a break occurring at an unknown date in the trend function of a univariate time series when the noise component can be either stationary or integrated. This article extends their work by proposing a sequential test that allows one to test the null hypothesis of, say, l breaks versus the alternative hypothesis of (l + 1) breaks. The test enables consistent estimation of the number of breaks. In both stationary and integrated cases, it is shown that asymptotic critical values can be obtained from the relevant quantiles of the limit distribution of the test for a single break. Monte Carlo simulations suggest that the procedure works well in finite samples.

Cointegration with Structural Breaks: An Application to the Feldstein-Horioka Puzzle

This paper revisits the well known Feldstein-Horioka saving-investment correlation puzzle from a time series perspective using a sample of 21 OECD countries. We argue that the strong positive correlation between saving and investment as originally identified by Feldstein and Horioka (1980) arises due to the neglect of the nonstationary properties of the variables as well as the failure to account for potential instabilities in the long run relationship between them. Our methodology is based on instability tests recently proposed in Kejriwal and Perron (2006a) as well as the cointegration test in Arai and Kurozumi (2005) extended to allow for multiple breaks under the null hypothesis of cointegration. Our empirical results show that for all countries except Mexico and the U.K., the cointegrating relationship has changed over time; in most cases, the change being towards a lower saving-investment correlation regime. This is perfectly consistent with the recent evidence on international diversification and integration of world capital markets. Finally, we find that while the saving-investment link bears a close relationship with the degree of openness of the country, there seems to be very little evidence in favour of the commonly held view that the correlation varies with the size of the country.

DATA DEPENDENT RULES FOR SELECTION OF THE NUMBER OF LEADS AND LAGS IN THE DYNAMIC OLS COINTEGRATING REGRESSION

Saikkonen (1991) developed an asymptotic optimality theory for the estimation of cointegrated regressions. He proposed the dynamic OLS estimator obtained by augmenting the static cointegrating regression with leads and lags of the first differences of the I(1) regressors. However, the assumptions imposed preclude the use of information criteria such as the AIC and BIC to select the number of leads and lags. We show that his results remain valid under weaker conditions which permit the use of such data dependent rules. Simulations show that, relative to sequential general to specific testing procedures, the use of such information criteria can indeed produce estimates with smaller mean squared errors and confidence intervals with better coverage rates.

Wald Tests for Detecting Multiple Structural Changes in Persistence

This paper considers the problem of testing for multiple structural changes in the persistence of a univariate time series. We propose sup-Wald tests of the null hypothesis that the process has an autoregressive unit root against the alternative hypothesis that the process alternates between stationary and unit root regimes. Both non-trending and trending cases are analyzed. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. The computation of the test statistics as well as asymptotic critical values is facilitated by the dynamic programming algorithm proposed in Perron and Qu (2006) which allows the minimization of the sum of squared residuals under the alternative hypothesis while imposing within and cross regime restrictions on the parameters. Finally, we present Monte Carlo evidence to show that the proposed tests perform quite well in finite samples relative to those available in the literature.

Breaks, trends and unit roots in commodity prices: a robust investigation

Abstract This paper empirically examines the time series behavior of primary commodity prices relative to manufactures with reference to the nature of their underlying trends and the persistence of shocks driving the price processes. The direction and magnitude of the trends are assessed employing a set of econometric techniques that is robust to the nature of persistence in the commodity price shocks, thereby obviating the need for unit root pretesting. Specifically, the methods allow consistent estimation of the number and location of structural breaks in the trend function as well as facilitate the distinction between trend breaks and pure level shifts. Further, a new set of powerful unit root tests is applied to determine whether the underlying commodity price series can be characterized as difference or trend stationary processes. These tests treat breaks under the unit root null and the trend stationary alternative in a symmetric fashion thereby alleviating the procedures from spurious rejection problems and low power issues that plague most existing procedures. Relative to the extant literature, we find more evidence in favor of trend stationarity suggesting that real commodity price shocks are primarily of a transitory nature. We conclude with a discussion of the policy implications of our results.