Cointegration for the Applied Economist.

This book comprises six chapters and five papers on unit roots and cointegration. Chapter 1 contains some background material that may facilitate the understanding of unit roots and cointegration by the reader. Rao also summarizes the steps of conducting unit roots and cointegration tests. The book is designed to serve the non-technical applied economist and for use by the undergraduate or graduate student interested in this field. I generally agree that the book is pedagogically useful and can serve the intended purpose. However, one cannot avoid raising questions about the usefulness of the book concerning its timing and the subject matter it covers. There are quite a few books already in print in this field that are easily readable to the average applied economist or student. Examples include books by Walter Enders, Applied Econometric Time Series (John Wiley & sons. Inc.), Cuthbertson et. al., Applied Econometric Techniques (The University of Michigan Press), and to some extent books by James Hamilton, Time Series Analysis (Princeton Univ. Press), Banerjee et. al., Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data (Oxford University Press) etc. Moreover, even though some of the papers in the present book could be inaccessible to some readers, the same empirical applications of some of these papers are contained, in some form or another, in the textbooks just mentioned. Cases in point are the application of cointegration on the demand for money by Dicky, Jansen, and Thornton in Chapter 2 in this book, and Perron unit root tests [Chapter 4].

Chapter 2 presents the expository paper of Dickey, Jansen, and Thornton (1991) that appeared at the Federal Reserve Bank of St. Louis Review. This paper uses the three cointegration procedures, that of Engle-Granger, Johansen, and Stock-Watson. The authors explain the masons why and the methods of conducting unit root tests, and provide a general framework for conducting cointegration tests, the economic interpretation of cointegrating vectors, and discuss, in a step-by-step fashion, the salient features of these three alternative procedures to testing for cointegration. They use the demand for money in their application.

Chapter 3 presents the Holden-Perman paper titled "Unit Roots and Cointegration for the Economist," which is basically a non-technical review of unit roots and cointegration techniques. The authors explain in a step-by-step procedure: 1) the methods of identifying whether the series are stationary or non-stationary (with an excellent brief discussion about stationarity and non-stationarity using the AR(1) and AR(2) processes); 2) applying a schematic step-by-step unit root (without drift, with a non-zero drift, and about a non-linear time trend) techniques of the Dickey-Fuller (1979) tests, the Phillips-Perron (1988) tests (when the error terms are generated by a moving average process), and the Perron (1989) tests (tests when the series have structural breaks) procedures. They use the consumption, income, and wealth series of the United Kingdom in their applications and link the analysis with the famous work of Davidson, Hendry, Srba, and Yeo (1978); 3) apply cointegration and error correction procedures and show the relationships between the two; and 4) like Dickey, Jansen and Thornton, they provide the different approaches to cointegration.

The third article [Chapter 4] in the book is the one by Pierre Perron: "Trends, Unit Root and Structural Change in Macroeconomic Time Series." In this paper, the author treats the intercept and the trend variables as random integrated processes in his maintained hypothesis. This procedure has paramount implication for unit tests because "unit root tests are biased towards non-rejection of the unit root hypothesis if the data are characterized by stationary fluctuations around a trend function that exhibits a structural change." Using simulation results, Perron shows how unit root tests could fail to reject the null hypothesis when the data generating process are characterized by stationary fluctuations around a trend with one time change in the level and/or slope.

Chapter 5 presents the paper by Mehra which is the expanded and revised version that was published in the American Economic Review (1991). This paper deals with the long run stochastic trends in the productivity-adjusted wage growth and inflation. Some popular expectations augmented-Phillips curve model suggests that prices are set as markups over the productivity-adjusted labor costs and hence wages and prices are causally related. Mehra employs the Engle-Granger cointegration procedure and shows that, wages and prices, along with other relevant variables such as demand pressures and supply-side shocks, are indeed cointegrated. Employing two methods of Granger Causality, one being the error correction model and the other being the standard causality model, the author shows that wages and prices are causally related. Contrary to one's expectations, however, he finds only a one-way Granger-causality: from inflation to wage growth which is in accord with the original Phillips curve that "past inflation and past output gap help predict future wage growth".

In Chapter 6, Glenn Otto provides a systematic application of diagnostic testing using the demand for M1 in Canada. The author estimates linear, log-linear, and semi-log-linear models using OLS and obtains results consistent with economic theory. The diagnostic tests discussed include serial correlation, heteroscedasticity, weak exogeniety, functional form, and parameter stability. Then, the author uses the log-linear model in order to illustrate mis-specification.

The book also contains an excellent bibliography and the original data used by the authors of the papers so that readers can try to replicate the original results. If the non-technical applied economist and/or student is interested in getting a feel and the intuition behind unit roots and the cointegration procedures of Engle-Granger, Johansen and Stock-Watson rather than pushing computer buttons to obtain the desired results, this book can serve as a good companion.

Seid Y. Hassan Murray State University