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Abstract:
This paper investigate the nature and the presence of bubbles in financial markets.

Are bubbles consistent with rationality? If they are, do they, like Ponzi games, require the presence of new players forever? Do they imply impossible events in finite time, such as negative prices? Do they need to go on forever to be rational? Can they have real effects? These are some of the questions asked in the first three sections. The general conclusion is that bubbles, in many markets, are consistent with rationality, that phenomena such as runaway asset prices and market crashes are consistent with rational bubbles.

In the last two sections, we consider whether the presence of bubbles in a particular market can be detected statistically. The task is much easier if there are data on both prices and returns. In this case, as shown by Shiller and Singleton, the hypothesis of no bubble implies restrictions on their joint distribution and can be tested. In markets in which returns are difficult to observe, possibly because of a nonpecuniary component, such as gold, the task is more difficult. We consider the use of both "runs tests" and "tail tests" and conclude that they give circumstantial evidence at best.

Abstract:
During six weeks in late 1937, Wesley Mitchell, Arthur Burns, and their colleagues at the National Bureau of Economic Research developed a list of leading, coincident, and lagging indicators of economic activity in the United States as part of the NBER research program on business cycles. Since their development, these indicators, in particular the leading and coincident indexes constructed from these indicators, have played an important role in summarizing and forecasting the state of macroeconomic activity.

The paper reports the results of a project to revise the indexes of leading and coincident economic indicators using the tools of modern time series econometrics. This project addresses three central questions. The first is conceptual: is it possible to develop a formal probability model that gives rise to the indexes of leading and coincident variables? Such a model would provide a concrete mathematical framework within which alternative variables and indexes could be evaluated. Second, given this conceptual framework, what are the best variables to use as components of the leading index? Third, given these variables, what is the best way to combine them to produce useful and reliable indexes?

The results of this project are three experimental monthly indexes: an index of coincident economic indicators (CEI), an index of leading economic indicators (LEI), and a Recession Index. The experimental CEI closely tracks the coincident index currently produced by the Department of Commerce (DOC), although the methodology used to produce the two series differs substantially. The growth of the experimental CEI is also highly correlated with the growth of real GNP at business cycle frequencies. The proposed LEI is a forecast of the growth of the proposed CEI over the next six months constructed using a set of leading variables or indicators. The Recession Index, a new series, is the probability that the economy will be in a recession six months hence, given data available through the month of its construction.

This article is organized as follows. Section 2 contains a discussion of the indexes and a framework for their interpretation. Section 3 presents the experimental indexes, discusses their construction, and examines their within-sample performance. In Section 4, the indexes are considered from the perspective of macroeconomic theory, focusing in particular on several salient series that are not included in the proposed leading index. Section 5 concludes.

Abstract:
This paper examines the empirical relationship in the postwar United States between the aggregate business cycle and various aspects of the macroeconomy, such as production, interest rates, prices, productivity, sectoral employment, investment, income, and consumption. This is done by examining the strength of the relationship between the aggregate cycle and the cyclical components of individual time series, whether individual series lead or lag the cycle, and whether individual series are useful in predicting aggregate fluctuations. The paper also reviews some additional empirical regularities in the U.S. economy, including the Phillips curve and some long-run relationships, in particular long-run money demand, long-run properties of interest rates and the yield curve, and the long-run properties of the shares in output of consumption, investment and government spending.

Abstract:
This paper investigates forecasts of U.S. inflation at the 12-month horizon. The starting point is the conventional unemployment rate Phillips curve, which is examined in a simulated out of sample forecasting framework. Inflation forecasts produced by the Phillips curve generally have been more accurate than forecasts based on other macroeconomic variables, including interest rates, money and commodity prices. These forecasts can however be improved upon using a generalized Phillips curve based on measures of real aggregate activity other than unemployment, especially a new index of aggregate activity based on 61 real economic indicators.

Abstract:
This paper considers VAR models incorporating many time series that interact through a few dynamic factors. Several econometric issues are addressed including estimation of the number of dynamic factors and tests for the factor restrictions imposed on the VAR. Structural VAR identification based on timing restrictions, long run restrictions, and restrictions on factor loadings are discussed and practical computational methods suggested. Empirical analysis using U.S. data suggest several (7) dynamic factors, rejection of the exact dynamic factor model but support for an approximate factor model, and sensible results for a SVAR that identifies money policy shocks using timing restrictions.

Abstract:
'Iterated' multiperiod ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas 'direct' forecasts are made using a horizon-specific estimated model, where the dependent variable is the multi-period ahead value being forecasted. Which approach is better is an empirical matter: in theory, iterated forecasts are more efficient if correctly specified, but direct forecasts are more robust to model misspecification. This paper compares empirical iterated and direct forecasts from linear univariate and bivariate models by applying simulated out-of-sample methods to 171 US monthly macroeconomic time series spanning 1959-2002. The iterated forecasts typically outperform the direct forecasts, particularly if the models can select long lag specifications. The relative performance of the iterated forecasts improves with the forecast horizon.

Multistep forecasts, VAR forecasts, forecast comparisons

Abstract:
"Iterated" multiperiod ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas "direct" forecasts are made using a horizon-specific estimated model, where the dependent variable is the multi-period ahead value being forecasted. Which approach is better is an empirical matter: in theory, iterated forecasts are more efficient if correctly specified, but direct forecasts are more robust to model misspecification. This paper compares empirical iterated and direct forecasts from linear univariate and bivariate models by applying simulated out-of-sample methods to 171 U.S. monthly macroeconomic time series spanning 1959-2002. The iterated forecasts typically outperform the direct forecasts, particularly if the models can select long lag specifications. The relative performance of the iterated forecasts improves with the forecast horizon.

Multistep forecasts, VAR forecasts, forecast comparisons

Abstract:
From 1960-1983, the standard deviation of annual growth rates in real GDP in the United States was 2.7%. From 1984-2001, the corresponding standard deviation was 1.6%. This paper investigates this large drop in the cyclical volatility OF real economic.activity. The paper has two objectives. The first is to provide a comprehensive characterization of the decline in volatility using a large number of U.S. economic time series and a variety of methods designed to describe time-varying time series processes. In so doing, the paper reviews the literature on the moderation and attempts to resolve some of its disagreements and discrepancies. The second objective is to provide new evidence on the quantitative importance of various explanations for this 'great moderation.' Taken together, we estimate that the moderation in volatility is attributable to a combination of improved policy (20-30%), identifiable good luck in the form of productivity and commodity price shocks (20-30%), and other unknown forms of good luck that manifest themselves as smaller reduced-form forecast errors (40-60%).

Abstract:
This paper examines old and new evidence on the predictive performance of asset prices for inflation and real output growth. We first review the large literature on this topic, focusing on the past dozen years. We then undertake an empirical analysis of quarterly data on up to 38 candidate indicators (mainly asset prices) for seven OECD countries for a span of up to 41 years (1959 1999). The conclusions from the literature review and the empirical analysis are the same. Some asset prices predict either inflation or output growth in some countries in some periods. Which series predicts what, when and where is, however, itself difficult to predict: good forecasting performance by an indicator in one period seems to be unrelated to whether it is a useful predictor in a later period. Intriguingly, forecasts produced by combining these unstable individual forecasts appear to improve reliably upon univariate benchmarks.

Abstract:
This paper examines the forecasting performance of various leading economic indicators and composite indexes since 1988. in particular during the onset of the 1990 recession. The primary focus is on an experimental recession index (tile "XRI"). a composite index which provides probabilistic forecasts of whether the U.S. economy will be in a recession six months hence. After detailing its construction, the paper examines the out-of-sample performance of the XRI and a related forecast of overall economic growth. the experimental leading index (XLI). These indexes performed well from 1988 through the summer of 1990 - for example. in June 1990 the XLI model forecasted a .4% (annual rate) decline in the experimental coincident index from June through September. when in fact the decline was only slightly greater,.8%. However. the XLI failed to forecast the sharp declines of October and November 1990. After exploring several possible explanations. we conclude that one important source of the forecast error was the use of financial variables during a recession that was not associated with a particularly tight monetary policy. Financial indicators -- and the experimental index -- were not alone. however. in failing to forecast the 1990 recession, An examination of 45 economic indicators shows that almost all failed to forecast the 1990downturn. and the few that did provided unclear signals before the recessions of the 19705 and 1980s.

Abstract:
Forecasts of the rate of price inflation play a central role in the formulation of monetary policy, and forecasting inflation is a key job for economists at the Federal Reserve Board. This paper examines whether this job has become harder and, to the extent that it has, what changes in the inflation process have made it so. The main finding is that the univariate inflation process is well described by an unobserved component trend-cycle model with stochastic volatility or, equivalently, an integrated moving average process with time-varying parameters; this model explains a variety of recent univariate inflation forecasting puzzles. It appears currently to be difficult for multivariate forecasts to improve on forecasts made using this time-varying univariate model.

Abstract:
This paper considers forecasting a single time series using more predictors than there are time series observations. The approach is to construct a relatively few indexes, akin to diffusion indexes, which are weighted averages of the predictors, using an approximate dynamic factor model. Estimation is discussed for balanced and unbalanced panels. The estimated dynamic factors are (uniformly) consistent, even in the presence of time varying parameters and/or data contamination, and forecasts based on the estimated factors are efficient. In an application to forecasting U.S. inflation and industrial production using 224 monthly time series, these forecasts outperform various state-of-the-art benchmark models.

Abstract:
Previous authors have reached puzzlingly different conclusions about the usefulness of money for forecasting real output based on closely related regression-based tests. An examination of this and additional new evidence reveals that innovations in M1 have statistically significant marginal predictive value for industrial production, both in a bivariate model and in a multivariate setting including a price index and an interest rate. This conclusion follows from focusing on the trend properties of the data, both stochastic and deterministic, and from drawing inferences using asymptotic theory that explicitly addresses the implications of these trends for the distributions of the various test statistics.

Abstract:
Using quarterly macro data and annual state panel data, we examine various explanations of the low rate of price inflation, strong real wage growth, and low rate of unemployment in the U.S. economy during the late 1990s. Many of these explanations imply shifts in the coefficients of price and wage Phillips curves. We find, however, that once one accounts for the univariate trends in the unemployment rate and in the rate of productivity growth, these coefficients are stable. This suggests that many explanations, such as persistent beneficial supply shocks, changes in firms' pricing power, changes in price expectations arising from shifts in Fed policy, and changes in wage setting behavior miss the mark. Rather, we suggest that explanations of movements of wages, prices and unemployment over the 1990s, and indeed over the past forty years, must focus on understanding the univariate trends in the unemployment rate and in productivity growth and, perhaps, the relation between the two.

Abstract:
No abstract is available for this paper.

Abstract:
The conventional heteroskedasticity-robust (HR) variance matrix estimator for cross-sectional regression (with or without a degrees of freedom adjustment), applied to the fixed effects estimator for panel data with serially uncorrelated errors, is inconsistent if the number of time periods T is fixed (and greater than two) as the number of entities n increases. We provide a bias-adjusted HR estimator that is (nT)1/2 -consistent under any sequences (n, T) in which n and/or T increase to infinity. The conventional heteroskedasticity-robust (HR) variance matrix estimator for cross-sectional regression (with or without a degrees of freedom adjustment), applied to the fixed effects estimator for panel data with serially uncorrelated errors, is inconsistent if the number of time periods T is fixed (and greater than two) as the number of entities n increases. We provide a bias-adjusted HR estimator that is (nT)1/2 -consistent under any sequences (n, T) in which n and/or T increase to infinity.

Abstract:
Propositions about long run neutrality are at the heart of most macroeconomic models. Yet, since the 1970's when Lucas and Sargent presented powerful critiques of traditional neutrality tests, empirical researchers have made little progress on testing these propositions. In this paper we show that. in spite of the Lucas-Sargent critique. long run neutrality can be tested without specifying a complete model of economic activity. This is possible when the variables are integrated. In this case, permanent shifts in the historical data can be uncovered using VAR methods, and neutrality can be tested when there is a priori knowledge of one of the structural impact multipliers or one of the structural long run multipliers. In most circumstances such a priori knowledge is available. We use this framework to test four long run neutrality propositions: (i) the neutrality of money, (ii) the superneutrality of money. (iii) a vertical long run Phillips curve, and (iv) the Fisher effect. In each application, our a priori knowledge consists of a range of plausible values for the relevant impact and long run multipliers. We find that the U.S. postwar data are consistent with the neutrality of money and a vertical long run Phillips curve. but find evidence against the superneutrality of money and the long run Fisher relation. The sign of the estimated effect of money growth on output depends on the particular identifying assumption used. For a wide range of plausible identifying restrictions, nominal interest rates are found to move less than one-for-one with inflation in the long run.

Abstract:
Recent developments in macroeconomic theory emphasize that transient economic fluctuations can arise as responses to changes in long run factors -- in particular, technological improvements -- rather than short run factors. This contrasts with the view that short run fluctuations and shifts in long run trends are largely unrelated. We examine empirically the effect of shifts in stochastic trends that are common to several macroeconomic series. Using a linear time series model related to a VAR, we consider first a system with GNP, consumption and investment with a single common stochastic trend; we then examine this system augmented by money and prices and an additional stochastic trend. Our results suggest that movements in the "real" stochastic trend account for one-half to two-thirds of the variation in postwar U.S. GNP.

Abstract:
The volatility of economic activity in most G7 economies has moderated over the past forty years. Also, despite large increases in trade and openness, G7 business cycles have not become more synchronized. After documenting these twin facts, we interpret G7 output data using a structural VAR that separately identifies common international shocks, the domestic effects of spillovers from foreign idiosyncratic shocks, and the effects of domestic idiosyncratic shocks. This analysis suggests that, with the exception of Japan, the widespread reduction in volatility is in large part associated with a reduction in the magnitude of the common international shocks. Had the common international shocks in the 1980s and 1990s been as large as they were in the 1960s and 1970s, G7 business cycles would have been substantially more volatile and more highly synchronized than they actually were.

Abstract:
An experiment is performed to assess the prevalence of instability in univariate and bivariate macroeconomic time series relations and to ascertain whether various adaptive forecasting techniques successfully handle any such instability. Formal tests for instability and out-of-sample forecasts from sixteen different models are computed using a sample of 76 representative U.S. monthly postwar macroeconomic time series, constituting 5700 bivariate forecasting relations. The tests indicate widespread instability in univariate and bivariate autoregressive models. However, adaptive forecasting models, in particular time varying parameter models, have limited success in exploiting this instability to improve upon fixed-parameter or recursive autoregressive forecasts.

Abstract:
We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes formulation (both parametric and nonparametric) treats the coefficients as i.i.d. and estimates their prior. Asymptotically, when K is proportional to T the empirical Bayes estimator is shown to be: (i) optimal in Robbins' (1955, 1964) sense; (ii) the minimum risk equivariant estimator; and (iii) minimax in both the frequentist and Bayesian problems over a class of nonGaussian error distributions. Also, the asymptotic frequentist risk of the minimum risk equivariant estimator is shown to equal the Bayes risk of the (infeasible subjectivist) Bayes estimator in the Gaussian case, where the 'prior' is the weak limit of the empirical cdf of the true parameter values. Monte Carlo results are encouraging. The new estimators are used to forecast monthly postwar U.S. macroeconomic time series using the first 151 principal components from a large panel of predictors.

Abstract:
This paper examines two questions. The first is whether economic fluctuations-business cycles-are due to an accumulation of nall shocks or instead mostly to infrequent large shocks. The paper concludes that neither of these two extreme views accurately characterize fluctuations. The second question is whether fluctuations are due mostly to one source of shocks, for example monetary, or instead to many sources. The paper concludes that evidence strongly supports the hypothesis of many, about equally important, sources of shocks.To analyze the empirical evidence and to reach these conclusions, the paper uses two different statistical approaches. The first is estimation ofa structural model, using a set of just identifying restrictions. The secondis non-structural and may be described as a formalization of the Burns Mitchell techniques. Both approaches are somewhat novel and should be of independent interest.

Abstract:
A forecasting comparison is undertaken in which 49 univariate forecasting methods, plus various forecast pooling procedures, are used to forecast 215 U.S. monthly macroeconomic time series at three forecasting horizons over the period 1959 - 1996. All forecasts simulate real time implementation, that is, they are fully recursive. The forecasting methods are based on four classes of models: autoregressions (with and without unit root pretests), exponential smoothing, artificial neural networks, and smooth transition autoregressions. The best overall performance of a single method is achieved by autoregressions with unit root pretests, but this performance can be improved when it is combined with the forecasts from other methods.

Abstract:
This paper surveys the literature since 1993 on pseudo out-of-sample evaluation of inflation forecasts in the United States and conducts an extensive empirical analysis that recapitulates and clarifies this literature using a consistent data set and methodology. The literature review and empirical results are gloomy and indicate that Phillips curve forecasts (broadly interpreted as forecasts using an activity variable) are better than other multivariate forecasts, but their performance is episodic, sometimes better than and sometimes worse than a good (not naïve) univariate benchmark. We provide some preliminary evidence characterizing successful forecasting episodes.

Abstract:
This paper considers the estimation of the variance of coefficients in time varying parameter models with stationary regressors. The maximum likelihood estimator has large point mass at zero. We therefore develop asymptotically median unbiased estimators and confidence intervals by inverting median functions of regression-based parameter stability test statistics, computed under the constant-parameter null. These estimators have good asymptotic relative efficiencies for small to moderate amounts of parameter variability. We apply these results to an unobserved components model of trend growth in postwar U.S. GDP: the MLE implies that there has been no change in the trend rate, while the upper range of the median-unbiased point estimates imply that the annual trend growth rate has fallen by 0.7 percentage points over the postwar period.

Abstract:
This paper investigates the precision of conventional and unconventional estimates of the natural rate of unemployment (the 'NAIRU'). The main finding is that the NAIRU is imprecisely estimated: a typical 95% confidence interval for the NAIRU in 1990 is 5.1% to 7.7%. This imprecision obtains whether the natural rate is modeled as a constant, as a slowly changing function of time, as an unobserved random walk, or as a function of various labor market fundamentals; it obtains using other series for unemployment and inflation, including additional supply shift variables in the Phillips curve, using monthly or quarterly data, and using various measures for expected inflation. This imprecision suggests caution in using the NAIRU to guide monetary policy.

Abstract:
We develop a framework to assess how successfully standard times eries models explain low-frequency variability of a data series. The low-frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low-frequency trigonometric series. The properties of these weighted averages are then compared to the asymptotic implications of a number of common time series models. We apply the framework to twenty U.S. macroeconomic and financial time series using frequencies lower than the business cycle.

Abstract:
An MLE of the unknown parameters of co integrating vectors is presented for systems in which some variables exhibit higher orders of integration, in which there might be deterministic components, and in which the co integrating vector itself might involve variables of differing orders of integration. The estimator is simple to compute: it can be calculated by running GLS for standard regression equations with serially correlated errors. Alternatively, an asymptotically equivalent estimator can be computed using OLS. Usual Wald test statistics based on these MLE's (constructed using an autocorrelation robust covariance matrix in the case of the OLS estimator) have asymptotic x2 distributions.

Abstract:
The average length of business cycle contractions in the United States fell from 20.5 months in the prewar period to 10.7 months in the postwar period. Similarly, the average length of business cycle expansions rose from 25.3 months in the prewar period to 49.9 months in the postwar period. This paper investigates three explanations for this apparent duration stabilization. The first explanation is that shocks to the economy have been smaller in the postwar period. This implies that duration stabilization should be present in both aggregate and sectoral output data. The second explanation is that the composition of output has shifted from sectors that are very cyclical, like manufacturing, to sectors that are less cyclical, like services. This would lead to increased stability in aggregate output even in the absence of increased stability in the individual sectors. The third explanation is that the apparent stabilization is largely spurious, and is caused by differences in the way that prewar and postwar business cycle reference dates were chosen by the NBER. The evidence presented in this paper favors this third explanation.

Abstract:
This paper catalogs the business cycle properties of 163 monthly U.S. economic time series over the three decades from 1959 through 1988. Two general sets of summary statistics are reported. The first set measures the comovement of each individual time series with a reference series representing real economic activity. These statistics focus on comovements at business cycle horizons. The second set of statistics examines the predictive content of each of the series for aggregate activity, relative to different sets of conditioning (or predictive) variables. These statistics are constructed and presented in a way that facilitates comparisons across series and across conditioning sets. They also provide new lists of leading indicators based on predictive content for overall economic activity. Some of the results confirm previously recognized empirical regularities, while others provide new or different insights into the business cycle properties of various series.

Abstract:
This paper uses factor analytic methods to decompose industrial production (IP) into components arising from aggregate shocks and idiosyncratic sector-specific shocks. An approximate factor model finds that nearly all (90%) of the variability of quarterly growth rates in IP are associated with common factors. Because common factors may reflect sectoral shocks that have propagated by way of input-output linkages, we then use a multisector growth model to adjust for the effects of these linkages. In particular, we show that neoclassical multisector models, of the type first introduced by Long and Plosser (1983), produce an approximate factor model as a reduced form. A structural factor analysis then indicates that aggregate shocks continue to be the dominant source of variation in IP, but the importance of sectoral shocks more than doubles after the Great Moderation (to 30%). The increase in the relative importance of these shocks follows from a fall in the contribution of aggregate shocks to IP movements after 1984.

Abstract:
Many economic models imply that ratios, simple differences, or `spreads' of variables are I(0). In these models, cointegrating vectors are composed of 1's, 0's and -1's, and contain no unknown parameters. In this paper we develop tests for cointegration that can be applied when some of the cointegrating vectors are known under the null or under the alternative hypotheses. These tests are constructed in a vector error correction model (VECM) and are motivated as Wald tests in the version of this Gaussian model. When all of the cointegrating vectors are known under the alternative, the tests correspond to the standard Wald tests for the inclusion of error correction terms in the VAR. Modifications of this basic test are developed when a subset of the cointegrating vectors contains unknown parameters. The asymptotic null distribution of the statistics are derived, critical values are determined, and the local power properties of the test are studied. Finally, the test is applied to data on foreign exchange future and spot prices to test the stability of forward-spot premium.

Abstract:
Seasonal adjustment procedures attempt to estimate the sample realizations of an unobservable economic time series in the presence of both seasonal factors and irregular factors. In this paper we consider a factor which has not been considered explicitly in previous treatments of seasonal adjustment: measurement error. Because of the sample design used in the CPS, measurement error will not be a white noise process, but instead it will be characterized by serial correlation of a known form. We first consider what effect the serially correlated measurement error has on estimation of the non-seasonal component in seasonal adjustment models. We also consider the effect of measurement error on the widely used seasonal adjustment process X11. X11 which is the seasonal adjust procedure used by the BLS will implicitly reduce the effect of measurement error because of the averaging process used. However, this treatment will not be optimal in general. We therefore specify a seasonal adjustment model which takes explicit account of the measurement error. For examples on the unemployment rate, we find that X11 does almost as well as the optimal filter on some series but its efficiency is less than 10% for the teenage unemployment series. We also find that optimal treatment of the measurement error which accounts for the serial correlation can reduce the overall mean square error of the seasonally adjusted series below the variance of the measurement error which is often used as the benchmark for the sampling procedure.

Abstract:
This paper studies the problems of estimation and inference in the linear trend model: yt=à+þt+ut, where ut follows an autoregressive process with largest root þ, and þ is the parameter of interest. We contrast asymptotic results for the cases þþþ < 1 and þ=1, and argue that the most useful asymptotic approximations obtain from modeling þ as local-to-unity. Asymptotic distributions are derived for the OLS, first-difference, infeasible GLS and three feasible GLS estimators. These distributions depend on the local-to-unity parameter and a parameter that governs the variance of the initial error term, þ. The feasible Cochrane-Orcutt estimator has poor properties, and the feasible Prais-Winsten estimator is the preferred estimator unless the researcher has sharp a priori knowledge about þ and þ. The paper develops methods for constructing confidence intervals for þ that account for uncertainty in þ and þ. We use these results to estimate growth rates for real per capita GDP in 128 countries.

Abstract:
This paper uses a dynamic factor model for the quarterly changes in consumption goods' prices to separate them into three components: idiosyncratic relative-price changes, aggregate relative-price changes, and changes in the unit of account. The model identifies a measure of pure inflation: the common component in goods' inflation rates that has an equiproportional effect on all prices and is uncorrelated with relative price changes at all dates. The estimates of pure inflation and of the aggregate relative-price components allow us to re-examine three classic macro-correlations. First, we find that pure inflation accounts for 15-20% of the variability in overall inflation, so that most changes in inflation are associated with changes in goods'relative prices. Second, we find that the Phillips correlation between inflation and measures of real activity essentially disappears once we control for goods' relative-price changes. Third, we find that, at business-cycle frequencies, the correlation between inflation and money is close to zero, while the correlation with nominal interest rates is around 0.5, confirming previous findings on the link between monetary policy and inflation.

Dynamic Factor Models, Inflation, Phillips relation, Relative prices

Abstract:
This paper uses a dynamic factor model for the quarterly changes in consumption goods’ prices to separate them into three independent components: idiosyncratic relative-price changes, a low-dimensional index of aggregate relative-price changes, and an index of equiproportional changes in all inflation rates, that we label “pure� inflation. The paper estimates the model on U.S. data since 1959, and it presents a simple structural model that relates the three components of price changes to fundamental economic shocks. We use the estimates of the pure inflation and aggregate relative-price components to answer two questions. First, what share of the variability of inflation is associated with each component, and how are they related to conventional measures of monetary policy and relative-price shocks? We find that pure inflation accounts for 15-20% of the variability in inflation while our aggregate relative-price index accounts most of the rest. Conventional measures of relative prices are strongly but far from perfectly correlated with our relative-price index; pure inflation is only weakly correlated with money growth rates, but more strongly correlated with nominal interest rates. Second, what drives the Phillips correlation between inflation and measures of real activity? We find that the Phillips correlation essentially disappears once we control for goods’ relative-price changes. This supports modern theories of inflation dynamics based on price rigidities and many consumption goods.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1) model for the common stochastic trends, which may not accurately describe the data's persistence. This paper discusses efficient low-frequency inference about cointegrating vectors that is robust to this potential misspecification. A simple test motivated by the analysis in Wright (2000) is developed and shown to be approximately optimal in the case of a single cointegrating vector.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.