### Why Most Published Results On Unit Root And Cointegration Are False

Algoma University

Algoma University

October 3, 2015

**Abstract: **

The method of cointegration analysis for modeling nonstationary economic time series variables has become a dominant paradigm in empirical economic research. Critics argue that a cointegration analysis produces results that are, at best, useless and, at worst, dangerous. In this research, we explain why and how the use of a cointegration analysis in economic research will likely lead to findings and subsequent recommendations for public policy that will be unsound, misleading and potentially harmful. We recommend that, except for pedagogical review of policy failure of a historical magnitude, this method not be used in any analysis that affects public policy.

### Why Most Published Results On Unit Root And Cointegration Are False – Introduction

Cointegration analysis for analyzing and modeling non-stationary economic time series variables, proposed by Engle and Granger (1987), has become a dominant paradigm in empirical economic research1 (Hendry 2004; Royal Swedish Academy of Science 2003). Critics, however, argue that a cointegration analysis produces results that are, at best, useless and, at worst, dangerous (Moosa 2011, pp. 114). In this research, we will explain why and how the use of a cointegration analysis in economic research will lead to spurious findings and why any recommendations for public policy will likely be unsound, misleading and potentially harmful.

In economics, when a historical perspective is overlooked in a descriptive research design, misleading conclusions may often follow.2 Here, by historical perspective, we refer to the understanding of a subject matter in light of its previous stages of intellectual development and successive advancement. We think, therefore, it is imperative to put our arguments against unit roots and cointegration analysis in a historical perspective. The recognition of a spurious regression problem in the late 1970s contributed decisively to the development of unit roots and cointegration (Granger and Newbold 1974; Hendry 1980, 1986; Granger 1981, 1986). A spurious regression problem arises when a regression analysis indicates a relationship between two or more unrelated time series variables because each variable has either a trend, or is nonstationary, or both. While working with economic time series data, researchers, attempting to account for spurious regression problem, began testing for nonstationarity before estimating regressions. If, on the basis of an appropriate unit root test, data were found to be nonstationary, researchers would routinely purge the nonstationarity by differencing and then estimating regression equations using only differenced data as solution to the spurious regression problem. The practice of purging the nonstationarity by differencing would also result in the loss of valuable information from economic theory about the long-run equilibrium properties of the data (Kennedy 2003). It was in this context that Granger proposed that if two nonstationary variables were I(1) process, the bivariate dynamic relation between the two nonstationary variables would be misspecified when both of the nonstationary variables were differenced. This class of models has since become a dominant paradigm in empirical economic research and is known in the literature as cointegrated process (Hamilton 1994; page 562).

**Test of Order of Integration and Data**

A time series is said to be strictly stationary if its marginal and all joint distribution are independent of time. For practical purpose, however, it is the weak stationarity or covariance-stationarity that is more useful. A time series is said to be weakly stationary or covariance-stationary if the first two moments — mean and autocovariances — of a series do not depend on time. A stationary time series that does not need differencing is said to be integrated of order zero and is denoted I(0). A nonstationary time series that becomes stationary after first differencing is said to be integrated of order one and is denoted I(1). In general, a time series that needs differencing d times to become I(0) is said to be integrated of order d and is denoted I(d) (Granger 1986, page 214). Since the number d equals the number of unit roots in the characteristic equation for the time series (Said and Dickey 1984, page 599) unit root tests are often used to determine the order of integration of a series. Thus, we describe below the unit root tests that we will use in our analysis.

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