Christian J. Murray

The purchasing power parity persistence paradigm

Abstract Rogoff (Journal of Economic Literature 1996;34:647–668) describes the ‘remarkable consensus’ of 3–5 year half-lives of purchasing power parity deviations among studies using long-horizon data. These studies, however, focus on rejections of unit roots in real exchange rates and do not use appropriate techniques to measure persistence. Our half-life estimates explicitly account for serial correlation, sampling uncertainty and, most importantly, small sample bias. Calculating confidence intervals as well as point estimates for long-horizon and post-1973 data, we find that, even though most of the point estimates lie within the 3–5 year range, univariate methods provide virtually no information regarding the size of the half-lives.

The Structure of Unemployment

We test for a unit root in postwar unemployment rates for sixteen OECD countries. When a one-time structural break is incorporated, the unit root hypothesis can be rejected for most of the countries and the measured persistence of unemployment falls dramatically. We then test for multiple structural changes and find evidence of one or two breaks for those countries for which the unit root hypothesis could be rejected. Almost all of the breaks are positive, reflecting the sustained rise in European unemployment. The major exception is the United States, where long-term unemployment rose in the 1970s and fell in the 1980s.

State of the Art Unit Root Tests and Purchasing Power Parity

Although the question of whether Purchasing Power Parity (PPP) holds in the long run has been extensively studied, the answer is still controversial. Some of the strongest evidence is provided by Taylor (The Review of Economics and Statistics 84[[2002] 139-150), who concludes that long-run PPP held over the 20th century. We argue that this conclusion is quite sensitive to the use of sub-optimal lag selection in unit root tests. Using superior lag selection methods, we find that long-run PPP held for the real exchange rates of only 9 out of the 16 industrialized countries in Taylors sample with the U.S. dollar as the base currency.

Cyclical Properties of Baxter-King Filtered Time Series

This note demonstrates that the Baxter-King (1999) filter, and in general any bandpass filter, does not isolate the cycle in an unobserved-components model with a stochastic trend. The first difference of the trend passes through the filter, and as a result, the spectral properties of the filtered series depend on the trend in the unfiltered series. It is demonstrated that for postwar U.S. real GDP, the spectral properties of the BK-filtered series are primarily to due to the stochastic trend in output.

The uncertain trend in U.S. GDP

Several recent papers conclude that U.S. real GDP is trend stationary, implying that all shocks are transitory and long run path is deterministic. These inferences fail to take into account two problems: the distortion of test size in finite samples due to data-based model selection, and the fragility of unit root tests in the face of plausible departures from the maintained hypothesis of temporal homogeneity. Indeed, additive outliers that alter the level of output for only one period reliably trigger false rejections of the unit root hypothesis when it is true and signal the presence of permanent shifts in trend that did not occur. Trend stationarity is not supported by the more homogeneous post-war data and if imposed would imply business cycles of implausble duration and pattern - the economy was 8% below the trend line in 1994

Do Panels Help Solve the Purchasing Power Parity Puzzle

Although Rogoff described the “remarkable consensus” of 3- to 5-year half-lives of purchasing power parity (PPP) deviations among studies using long-horizon data, recent works using panel methods with post-1973 data report shorter half-lives of 2 to 2.5 years. But these studies do not use appropriate techniques to measure persistence. We extend median-unbiased estimation methods to the panel context, calculate both point estimates and confidence intervals, and provide strong evidence confirming Rogoffs original claim. Although panel regressions provide more information on the persistence of real exchange rate shocks than univariate regressions, they do not help solve the PPP puzzle.

Testing for unit roots in panels in the presence of structural change with an application to OECD unemployment

There has been extensive research on testing for unit roots in the presence of structural change and on testing for unit roots in panels. This chapter takes a small step towards combining the two research agendas.We propose a unit root test for non-trending data in the presence of a one-time change in the mean for a heterogeneous panel.The date of the break is determined endogenously.We perform simulations to investigate the power of the test,and apply the test to a data set of annual unemployment rates for 17 OECD countries from 1955 to 1990.

State-Space Modeling of the Relationship between Air Quality and Mortality

ABSTRACT A portion of a population is assumed to be at risk, with the mortality hazard varying with atmospheric conditions including total suspended particulates (TSP). This at-risk population is not observed and the hazard function is unknown; we wish to estimate these from mortality count and atmospheric variables. Consideration of population dynamics leads to a state-space representation, allowing the Kalman Filter (KF) to be used for estimation. A harvesting effect is thus implied; high mortality is followed by lower mortality until the population is replenished by new arrivals. The model is applied to daily data for Philadelphia, PA, 1973-1990. The estimated hazard function rises with the level of TSP and at extremes of temperature and also reflects a positive interaction between TSP and temperature. The estimated at-risk population averages about 480 and varies seasonally. We find that lags of TSP are statistically significant, but the presence of negative coefficients suggests their role may be partially statistical rather than biological. In the population dynamics framework, the natural metric for health damage from air pollution is its impact on life expectancy. The range of hazard rates over the sample period is 0.07 to 0.085, corresponding to life expectancies of 14.3 and 11.8 days, respectively.

The Great Depression and Output Persistence

The persistence of shocks to aggregate output has been the subject of continuing investigation since Nelson and Plosser (1982) suggested they are largely permanent. Recent literature reaches mixed conclusions, largely due to disagreement about how to treat the Great Depression. We estimate output persistence based on a parametric bootstrap of a Markov-switching model for GDP 1870Ð1994 in which the economy can switch in and out of a turbulent state. Our results suggest that real shocks persist indefinitely if we drop the maintained assumption of homoskedasticity in favor of a Markov-switching representation of the Great Depression.

Markov Switching and the Taylor Principle

Early research on the Taylor rule typically divided the data exogenously into pre-Volcker and Volcker-Greenspan subsamples.  We contribute to the recent trend of endogenizing changes in monetary policy by estimating a real-time forward-looking Taylor rule with endogenous Markov switching coefficients and variance. The response of the interest rate to inflation is regime dependent, with the pre and post-Volcker samples containing monetary regimes where the Fed did and did not follow the Taylor principle. While the Fed consistently adhered to the Taylor principle before 1973 and after 1984, it followed the Taylor principle from 1975-1979 and did not follow the Taylor principle from 1980-1984.  We also find that the Fed only responded to real economic activity during the states in which the Taylor principle held.  Our results are consistent with the idea that exogenously dividing postwar monetary policy into pre-Volcker and post-Volcker samples misleading. The greatest qualitative difference between our results and recent research employing time varying parameters is that we find that the Fed did not adhere to the Taylor Principle during most of Paul Volcker’s tenure, a finding which accords with the historical record of monetary policy.