UNIT ROOTS, TREND BREAKS, AND TRANSITORY DYNAMICS: A MACROECONOMIC PERSPECTIVE

It is common to interpret rejections of the unit-root null hypothesis in favor of a trend stationary process with possible trend breaks as evidence that the data are better characterized as stationary about a broken trend. This interpretation is valid only if the model postulated under the alternative hypothesis is the only plausible alternative to the model postulated under the null. We argue that there are economically plausible models that are not well captured under either the null hypothesis or the alternative hypothesis of these tests. We show that applied researchers who ignore this possibility are likely to reject the unit-root null with high probability in favor of a trend stationary process with possible breaks. Our evidence shows that this potential pitfall is both economically relevant and quantitatively important. We explore the extent to which applied users may mitigate inferential errors by using finite-sample and bootstrap critical values.

[1]  G. Schwert,et al.  Tests for Unit Roots: a Monte Carlo Investigation , 1988 .

[2]  Francis X. Diebold,et al.  The Uncertain Unit Root in Real GNP: Comment , 1996 .

[3]  David H. Papell,et al.  Slowdowns and Meltdowns: Postwar Growth Evidence From 74 Countries , 1997, Review of Economics and Statistics.

[4]  Ellen R. McGrattan,et al.  Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem? , 1996 .

[5]  Lawrence J. Christiano,et al.  Searching for a Break in Gnp , 1988 .

[6]  David H. Papell,et al.  The Structure of Unemployment , 2000, Review of Economics and Statistics.

[7]  J. Stock,et al.  Recursive and Sequential Tests of the Unit-Root and Trend-Break Hypotheses: Theory and International Evidence , 1992 .

[8]  David H. Papell,et al.  The great wars, the great crash, and steady state growth: Some new evidence about an old stylized fact , 1995 .

[9]  Pierre Perron,et al.  A Test for Changes in a Polynomial Trend Functions for a Dynamioc Time Series , 1991 .

[10]  R. Lucas,et al.  Real Wages, Employment, and Inflation , 1969, Journal of Political Economy.

[11]  R. Lucas.  Expectations and the neutrality of money , 1972 .

[12]  Lucrezia Reichlin,et al.  Segmented trends and non-stationary time series , 1989 .

[13]  David H. Papell,et al.  IS THERE A UNIT ROOT IN THE INFLATION RATE? EVIDENCE FROM SEQUENTIAL BREAK AND PANEL DATA MODELS , 1997 .

[14]  A long-run view of the European monetary system , 1991 .

[15]  L. Ohanian.  The Macroeconomic Effects of War Finance in the United States , 1998 .

[16]  J. Stock.  Deciding between I(1) and I(0) , 1992 .

[17]  G. S. Maddala,et al.  Structural change and unit roots , 1996 .

[18]  Glenn D. Rudebusch.  Trends and Random Walks in Macroeconomic Time Series: A Re-examination , 1992 .

[19]  Paul Newbold,et al.  Testing for Unit Roots with Breaks: Evidence on the Great Crash and the Unit Root Hypothesis Reconsidered , 1997 .

[20]  Antonio Montañés.  Level shifts, unit roots and misspecification of the breaking date , 1997 .

[21]  P. Perron,et al.  Testing For A Unit Root In A Time Series With A Changing Mean , 1990 .

[22]  Steven Husted.  The Emerging U.S. Current Account Deficit in the 1980s: A Cointegration Analysis , 1992 .

[23]  Christina D. Romer.  The Prewar Business Cycle Reconsidered: New Estimates of Gross National Product, 1869-1908 , 1986, Journal of Political Economy.

[24]  Gerald A. Carlino,et al.  Are U.S. regional incomes converging?:A time series analysis , 1993 .

[25]  Pierre Perron,et al.  Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time , 1998 .

[26]  Timothy J. Vogelsang,et al.  Wald-Type Tests for Detecting Breaks in the Trend Function of a Dynamic Time Series , 1997, Econometric Theory.

[27]  Charles R. Nelson,et al.  The Uncertain Trend in U.S. GDP , 1997 .

[28]  B. Raj.  International Evidence on Persistence in Output in the Presence of an Episodic Change , 1992 .

[29]  D. Zelhorst,et al.  Does output have a unit root? New international evidence , 1993 .

[30]  P. Perron,et al.  Further Evidence on Breaking Trend Functions in Macroeconomic Variables. , 1997 .

[31]  Robin L. Lumsdaine,et al.  Unit roots, postwar slowdowns and long-run growth: Evidence from two structural breaks , 1998 .

[32]  Michael D. Bordo,et al.  Money, Sticky Wages, and the Great Depression , 1997 .

[33]  Apostolos Serletis,et al.  Random Walks, Breaking Trend Functions, and the Chaotic Structure of the Velocity of Money , 1995 .

[34]  The Trend Behavior of Alternative Income Inequality Measures in the United States from 1947-1990 and the Structural Break , 1994 .

[35]  Thomas B. Fomby,et al.  Shifting trends, segmented trends, and infrequent permanent shocks , 1991 .

[36]  Antonio Montañés,et al.  Testing for a Unit Root in Variables with a Double Change in the Mean , 1998 .

[37]  Testing for a Break in Output: New International Evidence , 1995 .

[38]  C. Nelson,et al.  Trends and random walks in macroeconmic time series: Some evidence and implications , 1982 .

[39]  Real exchange rates under the gold standard: can they be explained by the trend break model? , 1995 .

[40]  G. William Schwert,et al.  Effects of model specification on tests for unit roots in macroeconomic data , 1987 .

[41]  M. Chinn,et al.  DETERMINISTIC, STOCHASTIC, AND SEGMENTED TRENDS IN AGGREGATE OUTPUT: A CROSS-COUNTRY ANALYSIS , 1995 .

[42]  Paul Newbold,et al.  Unit roots and smooth transitions , 1998 .

[43]  Marcelo Reyes,et al.  EFFECT OF A SHIFT IN THE TREND FUNCTION ON DICKEY–FULLER UNIT ROOT TESTS , 1998 .

[44]  David H. Papell,et al.  Are U.S. regional incomes converging? Some further evidence , 1996 .

[45]  The behavior of U.S. tariff rates: Comment , 1994 .

[46]  Trend Breaks and the Unit-Root Hypothesis for Newly Industrializing and Newly Exporting Countries , 1995 .

[47]  Jörn-Steffen Pischke.  Measuring persistence in the presence of trend breaks: The case of US GNP , 1991 .

[48]  T. Vogelsang,et al.  A Note on the Asymptotic Distributions of Unit Root Tests in the Additive Outlier Model With Breaks , 1993 .

[49]  Rendigs Fels,et al.  A Monetary History of the United States, 1867-1960. , 1964 .

[50]  R. Barro.  Output Effects of Government Purchases , 1981, Journal of Political Economy.

[51]  Joon Y. Park,et al.  Testing for Unit Roots in Models with Structural Change , 1994, Econometric Theory.

[52]  P. Perron,et al.  Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions , 1992 .

[53]  D. Andrews,et al.  Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis , 1992 .

[54]  Martin D. D. Evans,et al.  Do expected shifts in inflation affect estimates of the long-run Fisher relation? , 1995 .

[55]  Philippe Jorion,et al.  Mean reversion in real exchange rates: evidence and implications for forecasting , 1996 .

[56]  Philip Hans Franses,et al.  The effects of additive outliers on tests for unit roots and cointegration , 1994 .

[57]  P. Perron,et al.  The Great Crash, The Oil Price Shock And The Unit Root Hypothesis , 1989 .

[58]  N. Duck.  UK Evidence on Breaking Trend Functions , 1992 .

[59]  Serena Ng,et al.  Unit Root Tests in ARMA Models with Data-Dependent Methods for the Selection of the Truncation Lag , 1995 .

[60]  Unit Roots and Infrequent Large Shocks: New International Evidence on Output Growth , 1995 .

[61]  Robin L. Lumsdaine,et al.  Multiple Trend Breaks and the Unit-Root Hypothesis , 1997, Review of Economics and Statistics.

[62]  P. Perron,et al.  Nonstationarity and Level Shifts With an Application to Purchasing Power Parity , 1992 .

[63]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .