Recent Published Papers

Policy Rule Legislation in Practice


(with Alex Nikolsko-Rzhevskyy and Ruxandra Prodan)


The legislated policy rules proposed by the Federal Reserve Accountability and Transparency Act of 2014 and the Financial Regulatory Improvement Act of 2015 have the potential to transform the conduct of monetary policy. If enacted, the Fed would have the obligation to explicitly state a benchmark for how the federal funds rate would respond to variables such as inflation and the output gap that enter into different variants of Taylor rules. While the Fed would choose its own legislated policy rule, it would be required to explain deviations from the rule and/or changes to the rule. Suppose that policy rule legislation had been in place for the past 60 years. When would the Fed have been in compliance, and when would there have been deviations from or changes to the rule? The central result of the paper is that, among the class of rules we consider, there is no single legislated policy rule that would have avoided large deviations over extended periods of time. Rules that produce low deviations during most of the 1950s and early 1960s produce high deviations during the late 1960s and between 1975 and 1985. More recently, rules that produce low deviations during the first half of the 2000s produce high deviations during the first half of the 2010s, and vice versa. If the legislation was adopted and the Fed wanted to avoid deviations from and/or changes to the rule, this would increase the predictability of monetary policy. Based on historical and statistical research showing that economic performance is better in rules-based than in discretionary eras, we believe this would be a desirable outcome. Forthcoming in John Cochrane and John Taylor, eds., Central Bank Governance and Oversight Reform, Hoover Institution Press


Markov Switching and the Taylor Principle


(with Chris Murray and Alex Nikolsko-Rzhevskyy)


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. Macroeconomic Dynamics, 19, June 2015, 913-930


Deviations from Rules-Based Policy and their Effects


(with Alex Nikolsko-Rzhevskyy and Ruxandra Prodan)


Rules-based monetary policy evaluation has long been central to macroeconomics. Using the original Taylor rule, a modified Taylor rule with a higher output gap coefficient, and an estimated Taylor rule, we define rules-based and discretionary eras by smaller and larger policy rule deviations, the absolute value of the difference between the actual federal funds rate and the federal funds rate prescribed by the three rules. We use tests for multiple structural changes to identify the eras so that knowledge of subsequent economic outcomes cannot influence the choice of the dates. With the original Taylor rule, monetary policy in the U.S. is characterized by a rules-based era until 1974, a discretionary era from 1974 to 1985, a rules-based era from 1985 to 2000, and a discretionary era from 2001 to 2013. With the modified Taylor rule, the rules-based era extends further into the 1970s and there is an additional rules-based period starting in 2006. We calculate various loss functions and find that economic performance is uniformly better during rules-based eras than during discretionary eras, and that the original Taylor rule provides the largest loss during discretionary periods relative to loss during rules-based periods. Journal of Economic Dynamics and Control, 49, December 2014, 4-18


Long-Run Time Series Tests of Constant Steady-State Growth


(with Ruxandra Prodan)


We propose a new methodology to study the stability of steady-state growth. Long-run GDP per capita can be characterized by: (1) the linear trend hypothesis, where there are no long-run changes in GDP levels or growth rates, (2) the level shift hypothesis, where there are long-run level shifts, but not changes in growth rates, and (3) the growth shift hypothesis, where there are long-run changes in both GDP levels and growth rates. We formally test these hypotheses using time series techniques with over 135 years of data. The results are not favorable to the hypothesis of constant steady-state growth. While we find evidence supporting the linear trend hypothesis for the United States and Canada and the level shift hypothesis for three additional OECD countries, the growth shift hypothesis is supported for seven OECD and four Asian countries. The results are not driven by transition dynamics. Economic Modeling, 42, 2014, 464-474


Median-Unbiased Estimation of Structural Change Models: An Application to Long-Run Real Exchange Rates


(with Hatice Ozer Balli and Christian Murray)


Measuring deviations from Purchasing Power Parity has been the subject of extensive investigation. The most common practice in empirical research for measuring real exchange rate persistence is to estimate univariate autoregressive time series models and calculate the half-life, defined as the number of periods for a unit shock to a time series to decay by 50 percent. In the presence of structural change, there are two potential biases in the parameter estimates of autoregressive models: (1) a downward small sample median-bias and (2) an upward bias which occurs when structural change is present and ignored. We conduct a variety of Monte Carlo simulations and demonstrate that the existence of structural change causes a substantial increase in the small sample bias documented in Andrews (1993). We then propose an extension of median-unbiased estimation which explicitly accounts for structural change and apply these methods to estimate half-lives of several long-horizon real exchange rates analyzed by Lothian and Taylor (1996) and Taylor (2002). The upward bias from neglecting structural change dominates the downward median-bias for these real exchange rates. When structural change is present and accounted for, the median-unbiased half-lives toward a changing mean decrease and the confidence intervals tighten. Applied Economics, 46, 2014, 3300-3311


Taylor’s Rule versus Taylor Rules


(with Alex Nikolsko-Rzhevskyy)


Does the Taylor rule prescribe negative interest rates for 2009-2011? This question is important because negative prescribed interest rates provide a justification for quantitative easing once actual policy rates hit the zero lower bound. We answer the question by analyzing Fed policy following the recessions of the early-to-mid 1970s, the early 1990s, and the early 2000s in the context of both Taylor’s original rule and latter variants of Taylor rules. While Taylor’s original rule, which can be justified by historical experience during and following the recessions, does not produce negative prescribed interest rates for 2009-2011, variants of Taylor rules with larger output gap coefficients, which do produce negative interest rates, cannot be justified by the same historical experience. We conclude that the Taylor rule does not provide a rationale for quantitative easing. International Finance, 2013, 16:1, 71-93


Taylor Rule Exchange Rate Forecasting During the Financial Crisis


(with Tanya Molodtsova)


This paper evaluates out-of-sample exchange rate predictability of Taylor rule models, where the central bank sets the interest rate in response to inflation and either the output or the unemployment gap, for the euro/dollar exchange rate with real-time data before, during, and after the financial crisis of 2008-2009. While all Taylor rule specifications outperform the random walk with forecasts ending between 2007:Q1 and 2008:Q2, only the specification with both estimated coefficients and the unemployment gap consistently outperforms the random walk from 2007:Q1 through 2012:Q1. Several Taylor rule models that are augmented with credit spreads or financial condition indexes outperform the original Taylor rule models. The performance of the Taylor rule models is superior to the interest rate differentials, monetary, and purchasing power parity models. International Seminar on Macroeconomics 2012, Volume 9, July 2013



The (Un)Reliability of Real-Time Output Gap Estimates with Revised Data


(with Onur Ince)


This paper investigates the differences between real-time and ex-post output gap estimates using a newly-constructed international real-time data set over the period from 1973:Q1 to 2007:Q2. We extend the findings in Orphanides and van Norden (2002) for the United States that the use of ex-post information in calculating potential output, not the data revisions themselves, is the major cause of the difference between real-time and ex-post output gap estimates to nine additional OECD countries. The results are robust to the use of linear, quadratic, Hodrick-Prescott, and Baxter-King detrending methods. By using quasi real-time methods, reliable real-time output gap estimates can be constructed with revised data. Economic Modeling, 2013, 713-721



Median-Unbiased Estimation in DF-GLS Regressions and the PPP Puzzle


(with Claude Lopez and Chris Murray)


Using median-unbiased estimation based on Augmented-Dickey-Fuller (ADF) regressions, recent research has questioned the validity of Rogoff’s “remarkable consensus” of 3-5 year half-lives of deviations from PPP. The confidence intervals of these half-life estimates, however, are extremely wide, with lower bounds of about one year and upper bounds of infinity. We extend median-unbiased estimation to the DF-GLS regression of Elliott, Rothenberg, and Stock (1996). We find that combining median-unbiased estimation with this regression has the potential to tighten confidence intervals for the half-lives. Using long horizon real exchange rate data, we find that the typical lower bound of the confidence intervals for median-unbiased half-lives is just under 3 years. Thus, while previous confidence intervals for median-unbiased half-lives are consistent with virtually anything, our tighter confidence intervals are inconsistent with economic models with nominal rigidities as candidates for explaining the observed behavior of real exchange rates and move us away from solving the PPP puzzle. Applied Economics, February 2013, 455-464



Taylor Rules and the Great Inflation


(with Alex Nikolsko-Rzhevskyy)


Can U.S. monetary policy in the 1970s be described by a stabilizing Taylor rule when policy is evaluated with real-time inflation and output gap data? Using economic research on the full employment level of unemployment and the natural rate of unemployment published between 1970 and 1977 to construct real-time output gap measures for periods of peak unemployment, we find that the Federal Reserve did not follow a Taylor rule if appropriate measures are used. We estimate Taylor rules and find no evidence that monetary policy stabilized inflation, even allowing for changes in the inflation target. While monetary policy was stabilizing with respect to inflation forecasts, the forecasts systematically under-predicted inflation following the 1970s recessions and this does not constitute evidence of stabilizing policy. We also find that the Federal Reserve responded too strongly to negative output gaps. Journal of Macroeconomics, December 2012, 903-918



The Statistical Behavior of GDP after Financial Crises and Severe Recessions


(with Ruxandra Prodan)


Do severe recessions associated with financial crises cause permanent reductions in potential GDP, or does the economy return to its trend? If the economy eventually returns to its trend, does the return take longer than the return following recessions not associated with financial crises? We develop a statistical methodology that is appropriate for identifying and analyzing slumps, episodes that combine a contraction and an expansion, and end when the economy returns to its trend growth rate. We analyze the Great Depression of the 1930s for the U.S., severe and milder financial crises for advanced economics, severe financial crises for emerging markets, and postwar recessions for the U.S. and other advanced economies. The preponderance of evidence for episodes comparable with the current U.S. slump is that, while potential GDP is eventually restored, the slumps last an average of nine years. If this historical pattern holds, the Great Recession that started in 2007:4 will not ultimately affect potential GDP, but the Great Slump is not yet half over. The B.E. Journal of Macroeconomics, Special Issue: Long-Term Effects of the Great Recession, October 2012, Article 2, 1-29



Convergence of Euro Area Inflation Rates


(with Claude Lopez)


(Journal of International Money and Finance, 2012, 1440-1458)


We study the behavior of inflation rates among the 12 initial Euro countries in order to test whether and when the group convergence initially dictated by the Maastricht treaty and now by the ECB, occurs. We also assess the impact of events such as the advent of the Euro and the 2008 financial crisis. Due to the small size of the estimation sample, we propose a new procedure that increases the power of panel unit root tests when used to study group-wise convergence. Applying this new procedure to Euro area inflation, we find strong and lasting evidence of convergence among the inflation rates soon after the implementation of the Maastricht treaty and a dramatic decrease in the persistence of the differential after the occurrence of the single currency. After the 2008 crisis, Euro area inflation rates follow the ECB’s price stability benchmark, although Greece reports relatively higher inflation.



Taylor Rules and the Euro


(with Tanya Molodtsova and Alex Nikolsko-Rzhevskyy)


(Journal of Money, Credit, and Banking, March-April 2011, 535-552)


This paper uses real-time data to show that inflation and either the output gap or unemployment, the variables which normally enter central banks’ Taylor rules for interest-rate-setting, can provide evidence of out-of-sample predictability for the United States Dollar/Euro exchange rate from the inception of the Euro in 1999 to the end of 2007. The strongest evidence is found for specifications that constrain the coefficients on inflation and real economic activity to be the same for the U.S. and the Euro Area, do not incorporate interest rate smoothing, and do not include the real exchange rate in the forecasting regression. The results are robust to the inclusion of inflation and real economic activity forecasts instead of realized variables, and evidence of predictability is found with both one-quarter-ahead and longer horizon exchange rate forecasts.



Out-of-Sample Exchange Rate Predictability with Taylor Rule Fundamentals 


(with Tanya Molodtsova)


(Journal of International Economics, 77, April 2009, 167-180)


Click here for the data and explanation of variable names.

Figures that are discussed but not included in the text can be found here.


An extensive literature that studied the performance of empirical exchange rate models following Meese and Rogoff’s (1983a) seminal paper has not convincingly found evidence of out-of-sample exchange rate predictability. This paper extends the conventional set of models of exchange rate determination by investigating predictability of models that incorporate Taylor rule fundamentals. We find evidence of short-term predictability for 11 out of 12 currencies vis-à-vis the U.S. dollar over the post-Bretton Woods float, with the strongest evidence coming from specifications that incorporate heterogeneous coefficients and interest rate smoothing. The evidence of predictability is much stronger with Taylor rule models than with conventional interest rate, purchasing power parity, or monetary models. 



Taylor Rules with Real-Time Data: A Tale of Two Countries and One Exchange Rate


(with Tanya Molodtsova and Alex Nikolsko-Rzhevskyy)


(Journal of Monetary Economics, 55, October 2008, S63-S79)


Using real-time data that reflects information available to monetary authorities at the time they are formulating policy, we find that estimated Taylor rules based on revised and real-time data differ more for Germany than for the U.S., Taylor rules using real-time data suggest differences between U.S. and German monetary policies, and Taylor rules for the U.S. using inflation forecasts are nearly identical to those using lagged inflation rates. Evidence of out-of-sample predictability for the dollar/mark nominal exchange rate with forecasts based on Taylor rule fundamentals is only found with real-time data and does not increase if inflation forecasts are used.


Restricted Structural Change and the Unit Root Hypothesis


(with Ruxandra Prodan)

(Economic Inquiry, October 2007, 834-853)


In a classic paper, Nelson and Plosser (1982) could not reject the unit root hypothesis in favor of trend stationarity for 13 out of 14 long-term annual macro series. Subsequent studies, allowing for one or two structural changes, have found more rejections with a broken trend stationary alternative. Since these changes are defined to be permanent, the rejections do not provide evidence of trend stationarity. We propose new tests for a unit root in the presence of restricted structural change. Allowing for two offsetting structural changes, we reject the unit root null in favor of restricted trend stationarity at the 5% significance level for 6 out of 13 series.


Are Real GDP Levels Trend, Difference, or Regime-Wise Trend Stationary?  Evidence from Panel Data Tests Incorporating Structural Change


(with Natalie Hegwood)


(Southern Economic Journal, July 2007, 104-113)


Rapach (2002) could not reject the unit root null in favor of trend stationarity for four panels of international real GDP and real GDP per capita.  Using panel methods that incorporate structural change, we reject the unit root null in favor of the alternative of trend stationarity with a one-time change in either the slope or in both the slope and the intercept for three of the four panels, the exception being the panel with both the fewest countries and the shortest span of data.  We conclude that real GDP levels are best characterized as regime-wise trend stationary.

Convergence to Purchasing Power Parity at the Commencement of the Euro

(with Claude Lopez)

(Review of International Economics, February 2007, 1-16)

We investigate convergence towards Purchasing Power Parity (PPP) within the Euro Zone and between the Euro Zone and its main partners using panel data methods. We find strong rejections of the unit root hypothesis, and therefore evidence of PPP, in the Euro Zone for different numeraire currencies, as well as in the Euro Zone plus the United States with the dollar as the numeraire currency, starting between 1996 and 1999. The process of convergence towards PPP, however, begins earlier, following the currency crises of 1992 and 1993, adoption of the Maastricht Treaty, and official completion of the Single Market.


Purchasing Power Parity and Country Characteristics: Evidence from Panel Data Tests

(with Joseph Alba)

(Journal of Development Economics, January 2007, 240-251)

We examine long-run purchasing power parity (PPP) using panel data methods to test for unit roots in US dollar real exchange rates of 84 countries. We find stronger evidence of PPP in countries more open to trade, closer to the United States, with lower inflation and moderate nominal exchange rate volatility, and with similar economic growth rates as the United States. We also show that PPP holds for panels of European and Latin American countries, but not for African and Asian countries. Our findings demonstrate that country characteristics can explain help explain both adherence to and deviations from long-run PPP. 

Additional Evidence of Long Run Purchasing Power Parity with Restricted Structural Change


(with Ruxandra Prodan)


(Journal of Money, Credit, and Banking, August 2006, 1329-1349)

We investigate two alternative versions of Purchasing Power Parity (PPP): reversion to a constant mean in the spirit of Cassel and reversion to a constant trend in the spirit of Balassa and Samuelson, using long-span real exchange rate data for industrialized countries. We develop unit root tests that both account for structural change and maintain a long run mean or trend. With conventional tests, previous research finds evidence of some variant of PPP for 9 of the 16 countries. With the unit root tests in the presence of restricted structural change, we find evidence of some variant of PPP for 5 additional countries.

The Panel Purchasing Power Parity Puzzle

(Journal of Money, Credit, and Banking, March 2006, 447-467)

Does long-run purchasing power parity hold over the post-1973 floating exchange rate period?  Panel unit root tests provide evidence of PPP that increases with the number of observations.  The strengthening of the evidence, however, is highly cyclical.  When the dollar appreciates at the end of the sample, the evidence of PPP strengthens and, when it depreciates, the evidence weakens.  While these patterns cannot be explained by the specifications that are normally used to model real exchange rates, the strengthening, but not the cyclical pattern, can be explained by a specification that incorporates PPP restricted structural change.

Testing for Purchasing Power Parity Using Stationary Covariates


(with Jomana Amara)

(Applied Financial Economics, January 2006, 29-39)

We test for Purchasing Power Parity in post-Bretton-Woods real exchange rate data from twenty developed countries using univariate tests and covariate augmented versions of the Augmented Dickey-Fuller (CADF) and feasible point optimal (CPT) unit root tests. The covariates are a combination of stationary variables - inflation, monetary, income, and current account. We perform a cross method comparison of the results.  We find very strong evidence of PPP using the CPT test, rejecting the unit root null for 12 out of the 20 countries at the 5% significance level or better, and 6 more at the 10% level. We find much less evidence of PPP with the CADF and univariate tests.

Do Panels Help Solve the Purchasing Power Parity Puzzle?


(with Christian Murray)


(Journal of Business and Economic Statistics, October 2005, 410-415)

While Rogoff (1996) describes the “remarkable consensus” of 3 to 5 year half-lives of purchasing power parity deviations among studies using long-horizon data, recent papers using panel methods with post-1973 data report shorter half-lives of 2 to 2.5 years.  These studies, however, 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 Rogoff’s original claim.  While panel regressions provide more information on the persistence of real exchange shocks than univariate regressions, they do not help solve the purchasing power parity puzzle.

Panel Evidence of Purchasing Power Parity Using Intranational and International Data

(with Sarah Culver)

(International Macroeconomics: Recent Developments, Nova Science Publishers, 2006, 39-51)

We investigate purchasing power parity (PPP) with CPI data for Canadian and United States cities, as well as for European countries. Using panel methods to test for the presence of a unit root, we find much less evidence of PPP with relative prices between cities within the same nation than with real exchange rates between European countries. The rates of price convergence are slower for United States cities than for Canadian cities or for European countries. We conduct a power analysis of the tests, and show that the results are consistent with differences in panel sizes and speeds of adjustment. (June 1999)

The Purchasing Power Parity Puzzle is Worse than You Think


(with Christian Murray)


(Empirical Economics, October 2005, 783-790)

The “purchasing power parity puzzle” is the difficulty of reconciling very high short-term volatility of real exchange rates with very slow rates of mean reversion.  The strongest evidence of slow mean reversion comes from least squares estimates of first-order autoregressive models of the long-horizon dollar-sterling real exchange rate.  Using median-unbiased estimation methods, we show that these methods underestimate the half-lives of PPP deviations, and thus overestimate the speed of mean reversion. When the specification is amended to allow for serial correlation, the speed of mean reversion falls even further. This makes resolution of the purchasing power parity puzzle more problematic.

State of the Art Unit Root Tests and Purchasing Power Parity

(with Claude Lopez and Christian Murray)

(Journal of Money, Credit, and Banking, April 2005, 361-369)


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 (2002), who concludes that long-run PPP held over the twentieth 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 Taylor’s sample with the U.S. dollar as the base currency. 


The Uncertain Unit Root in U.S. Real GDP: Evidence with Restricted and Unrestricted Structural Change

(with Ruxandra Prodan)

(Journal of Money, Credit, and Banking, June 2004, 423-427)

Unit Roots, Postwar Slowdowns and Long-Run Growth: Evidence From Two Structural Breaks

(with Dan Ben-David and Robin Lumsdaine)

(Empirical Economics, February 2003, 303-319)

This paper provides evidence on the unit root hypothesis and long-term growth by allowing for two structural breaks. We reject the unit root hypothesis for three-quarters of the countries n approximately 50% more rejections than in models that allow for only one break. While about half of the countries exhibit slowdowns following their postwar breaks, the others have grown along paths that have become steeper over the past 120 years. The majority of the countries, including most of the slowdown countries, exhibit faster growth after their second breaks than during the decades preceding their first breaks. (Revised: October 2001)

Comment on Frydman and Goldberg, "Imperfect Knowledge Expectations, Uncertainty-Adjusted Uncovered Interest Rate Parity, and Exchange Rate Dynamics"

(P. Aghion, R. Frydman, J. Stiglitz and M. Woodford, eds, Knowledge, Information, and Expectations in Modern Macroeconomics: In Honor of Edmund S. Phelps, Princeton University Press, 2003, p. 183-187)

The Great Appreciation, the Great Depreciation, and the Purchasing Power Parity Hypothesis

(Journal of International Economics, May 2002, 51-82)

Although there has been much recent work on Purchasing Power Parity (PPP), neither univariate nor panel methods have produced strong rejections of unit roots in U.S. dollar real exchange rates for industrialized countries during the post-1973 period. We investigate the hypothesis that these non-rejections can be explained by one episode, the large appreciation and depreciation of the dollar in the 1980s, by developing unit root tests which account for this event and maintain long-run PPP. Using panel methods, we can strongly reject the unit root null for those countries that adhere to the typical pattern of the dollar’s rise and fall. 

The Purchasing Power Parity Persistence Paradigm

(with Christian J. Murray)

(Journal of International Economics, January 2002, 1-19)

Rogoff (1996) 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 evidence regarding the size of the half-lives.

The Choice of Numeraire Currency in Panel Tests of Purchasing Power Parity

(with Hristos Theodoridis)

(Journal of Money, Credit, and Banking, August 2001, 790-803)

We investigate the implications of the choice of numeraire currency on panel tests of Purchasing Power Parity under the current regime of flexible exchange rates by conducting panel unit root tests with twenty-one different base currencies. We show that the conditions necessary for numeraire irrelevancy are not supported empirically, and that the choice of numeraire currency can and does matter for PPP. The evidence of PPP is stronger for European than for non-European base currencies. Distance between the countries and volatility of the exchange rates are the most important determinants of the results.




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