James H. Stock

• Harvard University

The social cost of carbon dioxide (SC-CO2) measures the monetized value of the damages to society caused by an incremental metric tonne of CO2 emissions and is a key metric informing climate policy. Used by governments and other decision-makers in benefit-cost analysis for over a decade, SC-CO2 estimates draw on climate science, economics, demograp...

This paper describes a weekly economic index (WEI) developed to track the rapid economic developments associated with the onset of and policy response to the novel Coronavirus in the United States. The WEI is a weekly composite index of real economic activity, with eight of ten series available the Thursday after the end of the reference week. In a...

This paper describes a weekly economic index (WEI) developed to track the rapid economic developments associated with the onset of and policy response to the novel coronavirus in the United States. The WEI, with its ten component series, tracks the overall economy. Comparing the contributions of the WEI's components in the 2008 and 2020 recessions...

Heteroskedasticity‐ and autocorrelation‐robust (HAR) inference in time series regression typically involves kernel estimation of the long‐run variance. Conventional wisdom holds that, for a given kernel, the choice of truncation parameter trades off a test's null rejection rate and power, and that this tradeoff differs across kernels. We formalize...

We investigate the flattening Phillips relation by making two departures from standard specifications. First, we measure slack using real activity variables that are bandpass filtered or year‐over‐year changes in activity (these are similar), instead of gaps. Second, we study the components of inflation instead of the standard aggregates. We find t...

We develop a Bayesian latent factor model of the joint long-run evolution of GDP per capita for 113 countries over the 118 years from 1900 to 2017. We find considerable heterogeneity in rates of convergence, including rates for some countries that are so slow that they might not converge (or diverge) in century-long samples, and a sparse correlatio...

This paper studies Structural Vector Autoregressions in which a structural shock of interest (e.g., an oil supply shock) is identified using an external instrument. The external instrument is taken to be correlated with the target shock (the instrument is relevant) and to be uncorrelated with other shocks of the model (the instrument is exogenous)....

This paper describes a weekly economic index (WEI) developed to track the rapid economic developments associated with the onset of and policy response to the novel coronavirus in the United States. The WEI, with its ten component series, tracks the overall economy. Comparing the contributions of the WEI's components in the 2008 and 2020 recessions...

Heteroskedasticity‐ and autocorrelation‐robust (HAR) inference in time series regression typically involves kernel estimation of the long‐run variance. Conventional wisdom holds that, for a given kernel, the choice of truncation parameter trades off a test's null rejection rate and power, and that this tradeoff differs across kernels. We formalize...

The classic papers by Newey and West (1987) and Andrews (1991) spurred a large body of work on how to improve heteroscedasticity- and autocorrelation-robust (HAR) inference in time series regression. This literature finds that using a larger-than-usual truncation parameter to estimate the long-run variance, combined with Kiefer-Vogelsang (2002, 200...

External sources of as‐if randomness — that is, external instruments — can be used to identify the dynamic causal effects of macroeconomic shocks. One method is a one‐step instrumental variables regression (local projections – IV); a more efficient two‐step method involves a vector autoregression. We show that, under a restrictive instrument validi...

U.S. output has expanded only slowly since the recession trough in 2009, even though the unemployment rate has essentially returned to a precrisis, normal level. We use a growth-accounting decomposition to explore explanations for the output shortfall, giving full treatment to cyclical effects that, given the depth of the recession, should have imp...

This review tells the story of the past 20 years of time series econometrics through ten pictures. These pictures illustrate six broad areas of progress in time series econometrics: estimation of dynamic causal effects; estimation of dynamic structural models with optimizing agents (specifically, dynamic stochastic equilibrium models); methods for...

U.S. output has expanded only slowly since the recession trough in 2009, even though the unemployment rate has essentially returned to a precrisis, normal level. We use a growth-accounting decomposition to explore explanations for the output shortfall, giving full treatment to cyclical effects that, given the depth of the recession, should have imp...

This paper examines empirically whether the measurement of trend inflation can be improved by using disaggregated data on sectoral inflation to construct indexes akin to core inflation but with a time-varying distributed lags of weights, where the sectoral weight depends on the timevarying volatility and persistence of the sectoral inflation series...

This paper considers the estimation of approximate dynamic factor models when there is temporal instability in the factor loadings. We characterize the type and magnitude of instabilities under which the principal components estimator of the factors is consistent and find that these instabilities can be larger than earlier theoretical calculations...

By construction, the time series for radiative forcing that are used to run the 20c3m experiments, which are implemented by climate models, impart non-stationary movements (either stochastic or deterministic) to the simulated time series for global surface temperature. Here, we determine whether stochastic or deterministic trends are present in the...

This paper provides a simple shrinkage representation that describes the operational characteristics of various forecasting methods designed for a large number of orthogonal predictors (such as principal components). These methods include pretest methods, Bayesian model averaging, empirical Bayes, and bagging. We compare empirically forecasts from...

This paper examines the macroeconomic dynamics of the 2007-09 recession in the United States and the subsequent slow recovery. Using a dynamic factor model with 200 variables, we reach three main conclusions. First, although many of the events of the 2007-2009 collapse were unprecedented, their net effect was to produce macro shocks that were large...

This paper examines the macroeconomic dynamics of the 2007–09 recession in the United States and the subsequent slow recovery. Using a dynamic factor model with 200 variables, we reach three main conclusions. First, although many of the events of the 2007–09 collapse were unprecedented, their net effect was to produce macro shocks that were larger...

Given the widely noted increase in the warming effects of rising greenhouse gas concentrations, it has been unclear why global surface temperatures did not rise between 1998 and 2008. We find that this hiatus in warming coincides with a period of little increase in the sum of anthropogenic and natural forcings. Declining solar insolation as part of...

No abstract available.

We examine whether the U.S. rate of price inflation has become harder to forecast 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 m...

Dating business cycles entails ascertaining economy-wide turning points. Broadly speaking, there are two approaches in the literature. The first approach, which dates to Burns and Mitchell (1946), is to identify turning points individually in a large number of series, then to look for a common date that could be called an aggregate turning point. T...

In the United States, the rate of price inflation falls in recessions. Turning this observation into a useful inflation forecasting equation is difficult because of multiple sources of time variation in the inflation process, including changes in Fed policy and credibility. We propose a tightly parameterized model in which the deviation of inflatio...

We evaluate the claim by Gay etal. (Clim Change 94:333–349, 2009) that “surface temperature can be better described as a trend stationary process with a one-time permanent shock” than efforts by Kaufmann etal. (Clim Change 77:249–278, 2006) to model surface temperature as a time series that contains a stochastic trend that is imparted by the time s...

Angrist and Pischke highlight one aspect of the research that has positively transformed econometric practice and teaching. They emphasize the rise of experiments and quasi-experiments as credible sources of identification in microeconometric studies, which they usefully term "design-based research." But in so doing, they miss an important part of...

As Nelson and Startz [Nelson, C.R., Startz, R., 1990a. The distribution of the instrumental variable estimator and its t ratio when the instrument is a poor one. Journal of Business 63, S125-S140; Nelson, C.R., Startz, R., 1990b. Some further results on the exact small sample properties of the instrumental variables estimator. Econometrica 58, 967-...

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 2) as the number of entities n...

This paper presents and describes a newly available data set on monthly building permits for U.S. states from 1969-2007. These data are used to estimate regions of common housing construction activity. Building permits exhibit substantial comovement across states, and these comovements are modeled as being associated with a national factor, a regio...

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...

This paper establishes the asymptotic distributions of the likelihood ratio (LR), Anderson–Rubin (AR), and Lagrange multiplier (LM) test statistics under “many weak IV asymptotics.” These asymptotics are relevant when the number of IVs is large and the coefficients on the IVs are relatively small. The asymptotic results hold under the null and unde...

We compare the powers of five tests of the coefficient on a single endogenous regressor in instrumental variables regression. Following Moreira [2003, A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048], all tests are implemented using critical values that depend on a statistic which is sufficient under the null h...

We examine whether the U.S. rate of price inflation has become harder to forecast 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 m...

Historically, time series forecasts of economic variables have used only a handful of predictor variables, while forecasts based on a large number of predictors have been the province of judgmental forecasts and large structural econometric models. The past decade, however, has seen considerable progress in the development of time series forecastin...

We use recent advances in time series econometrics to estimate the relation among emissions of CO2 and CH4, the concentration of these gases, and global surface temperature. These models are estimated and specified to answer two questions; (1) does human activity affect global surface temperature and; (2) does global surface temperature affect the...

Comparing statistical estimates for the long-run temperature effect of doubled CO2 with those generated by climate models begs the question, is the long-run temperature effect of doubled CO2 that is estimated from the instrumental temperature record using statistical techniques consistent with the transient climate response, the equilibrium climate...

“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 multiperiod ahead value being forecasted. Which approach is better is an empirical matter: i...

This paper considers tests of the parameter on an endogenous variable in an instrumental variables regression model. The focus is on determining tests that have some optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consider tests that are similar and satisfy a natural r...

This paper reviews recent developments in methods for dealing with weak instruments (IVs) in IV regression models. The focus is more on tests and confidence intervals derived from tests than on estimators. The paper also presents new testing results under "many weak IV asymptotics," which are relevant when the number of IVs is large and the coeffic...

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 re...

This volume contains the papers presented in honor of the lifelong achievements of Thomas J. Rothenberg on the occasion of his retirement. The authors of the chapters include many of the leading econometricians of our day, and the chapters address topics of current research significance in econometric theory. The chapters cover four themes: identif...

This paper provides weak-instrument asymptotic representations of tests for instrument validity by Hahn and Hausman's (HH) [Hahn, J., Hausman, J., 2002. A new specification test for the validity of instrumental variables. Econometrica 70, 163–189.], and uses these representations to compute asymptotic power against weak or irrelevant instruments. T...

This paper provides a simple shrinkage representation that describes the operational characteristics of various forecasting methods that are applicable when there are a large number of orthogonal predictors (such as principal components). These methods include pretest methods, Bayesian model averaging, empirical Bayes, and bagging. We then compare...

‘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:...

This paper extends D. Staiger and J. H. Stock’s [Econometrica 65, 557–586 (1997; Zbl 0871.62101)] weak instrument asymptotic approximations to the case of many weak instruments by modeling the number of instruments as increasing slowly with the number of observations. It is shown that the resulting “many weak instrument” approximations can be calcu...

This paper uses forecast combination methods to forecast output growth in a seven-country quarterly economic data set covering 1959-1999, with up to 73 predictors per country. Although the forecasts based on individual predictors are unstable over time and across countries, and on average perform worse than an autoregressive benchmark, the combinat...

This paper considers tests of the parameter on endogenous variables in an instrumental variables regression model. The focus is on determining tests that have certain optimal power properties. We start by considering a model with normally distributed errors and known error covariance matrix. We consider tests that are similar and satisfy a natural...

Ever since the pioneering work of Jan Tinbergen, econometric modelers have been aware of the danger that their models can be unstable over time and across policy environments. Work over the past fifteen years has produced a set of statistical procedures for identifying and modeling structural instability. This essay summarizes some of those procedu...

More than 2 billion people rely on solid fuels and traditional stoves or open fires for cooking, lighting, and/or heating. Exposure to emissions caused by burning these fuels is believed to be responsible for a significant share of the global burden of disease. To achieve widespread health improvements, interventions that reduce exposures to indoor...

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, th...

1] We test hypotheses about the unknown sink for carbon by analyzing time series for the unknown carbon sink, carbon emissions, atmospheric concentrations, and surface temperature between 1860 and 1990. During this period, the time series for the unknown carbon sink is determined by annual changes in carbon emissions and summer land surface tempera...

This paper compares several time series methods for short-run forecasting of Euro-wide inflation and real activity using data from 1982 to 1997. Forecasts are constructed from univariate autoregressions, vector autoregressions, single equation models that include Euro-wide and US aggregates, and large-model methods in which forecasts are based on e...

Are asset prices useful predictors of inflation and real output growth? After reviewing the large literature on this topic, we undertake an empirical analysis of quarterly data for seven OECD countries spanning 1959-99. The literature review and the empirical analysis yield the same conclusions. Some asset prices predict inflation or output growth...

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. Data on test performance, school characteristics and student demographic backgrounds for California school districts, 1998-1999. 420 observations.

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. The number of state traffic fatalities, 1982-1988. 336 observations.

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. Data on 180 economics journals for the year 2000 with 180 observations.

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. Macroeconomic time series data for the United States and Japanese real GDP.

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. Data on the frozen orange juice component of processed foods and feeds group of the producer price index (PPI), collected by the U.S. Bureau of Labor Statistics. 642 observations.

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. webstar provides data on test scores, treatment groups, and student and teacher characteristics for four years (1985-86 to 1988-89) with 11598 observations. star_sw is a subset of the variables in webstar with 11598...

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. The Current Population survey (CPS) provides data on labor force characteristics of the population, 1992-1998. 11130 observations.

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. cig_ch10 provides annual per capita cigarette sales for 48 states in packs per fiscal year in 1985 and 1995, only. 96 observations. cig_85-90 provides annual per capita cigarette sales for 48 states in packs per fis...

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. hmda_aer is the mortgage applications made in 1990 in the greater Boston metropolitan area with 2925 observations. hmda_sw is the number of mortgage application made in 1990 in the greater Metropolitan area using a...

Instructional dataset, accompanying Introduction to Econometrics, James H. Stock and Mark W. Watson, Pearson Education, Inc. (c) 2003. District-wide averages for Mass. public elementary school districts in 1998 with 220 observations.

This article considers forecasting a single time series when there are many predictors (N) and time series observations (T). When the data follow an approximate factor model, the predictors can be summarized by a small number of indexes, which we estimate using principal components. Feasible forecasts are shown to be asymptotically efficient in the...

Weak instruments can produce biased IV estimators and hypothesis tests with large size distortions. But what, precisely, are weak instruments, and how does one detect them in practice? This paper proposes quantitative definitions of weak instruments based on the maximum IV estimator bias, or the maximum Wald test size distortion, when there are mul...

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 o...

This article studies forecasting a macroeconomic time series variable using a large number of predictors. The predictors are summarized using a small number of indexes constructed by principal component analysis. An approximate dynamic factor model serves as the statistical framework for the estimation of the indexes and construction of the forecas...

Weak instruments arise when the instruments in linear instrumental variables (IV) regression are weakly correlated with the included endogenous variables. In generalized method of moments (GMM), more generally, weak instruments correspond to weak identification of some or all of the unknown parameters. Weak identification leads to GMM statistics wi...

This paper critically reviews the use of vector autoregressions (VARs) for four tasks: data description, forecasting, structural inference, and policy analysis. The paper begins with a review of VAR analysis, highlighting the differences between reduced-form VARs, recursive VARs and structural VARs. A three variable VAR that includes the unemployme...

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 ac...

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 ac...

Often we are interested in the largest root of an autoregressive process. Available methods rely on inverting t-tests to obtain confidence intervals. However, for large autoregressive roots, t-tests do not approximate asymptotically uniformly most powerful tests and do not have optimality properties when inverted for confidence intervals. We exploi...

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...

This paper first reviews the large literature on the prediction of real economic activity and inflation using asset prices. We then undertake our own assessment of the practical value of the information in asset prices for short- to medium-term economic forecasting using data from seven developed economies,. This analysis of the literature and the...

This paper develops asymptotic distribution theory for GMM estimators and test statistics when some or all of the parameters are weakly identified. General results are obtained and are specialized to two important cases: linear instrumental variables regres- sion and Euler equations estimation of the CCAPM. Numerical results for the CCAPM demonstra...

The book is a collection of essays in honour of Clive Granger. The chapters are by some of the world'leading econometricians, all of whom have collaborated with or studied with (or both) Clive Granger. Central themes of Grangers work are reflected in the book with attention to tests for unit roots and cointegration, tests of misspecification, forec...

A panel of ex-ante forecasts of a single time series is modeled as a dynamic factor model, where the conditional expectation is the single unobserved factor. When applied to out-of-sample forecasting, this leads to combination forecasts that are based on methods other than OLS. These methods perform well in a Monte Carlo experiment. These methods a...

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 v...

This paper investigates forecasts of US in#ation 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. In#ation forecasts produced by the Phillips curve generally have been more accurate than forecasts based on other macroeco-nomic vari...

This paper examines monetary policy in Rudebusch and Svensson's (1999) two equation macroeconomic model when the policymaker recognizes that the model is an approximation and is uncertain about the quality of that approximation. It is argued that the minimax approach of robust control provides a general and tractable alternative to the conventional...

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. T...

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 me...

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...

This article considers inference about the variance of coefficients in time-varying parameter models with stationary regressors. The Gaussian maximum likelihood estimator (MLE) has a large point mass at 0. We thus develop asymptotically median unbiased estimators and asymptotically valid confidence intervals by inverting quantile functions of regre...

This paper develops methods for constructing asymptotically valid confidence intervals for the date of a single break in multivariate time series, including I(0), I(1), and deterministically trending regressors. Although the width of the asymptotic confidence interval does not decrease as the sample size increases, it is inversely related to the nu...

Robust tests and estimators based on nonnormal quasi-likelihood functions are developed for autoregressive models with near unit root. Asymptotic power functions and power envelopes are derived for point-optimal tests of a unit root when the likelihood is correctly specified. The shapes of these power functions are found to be sensitive to the exte...

This paper examines the precision of conventional estimates of the NAIRU and the role of the NAIRU and unemployment in forecasting inflation. The authors find that, although there is a clear empirical Phillips relation, the NAIRU is imprecisely estimated, forecasts of inflation are insensitive to the NAIRU, and there are other leading indicators of...

This paper develops asymptotic distribution theory for instrumental variables regression when the partial correlations between the instruments and the endogenous variables are weak, here modeled as local to zero. Asymptotic representation are provided for various statistics, including two-stage least squares and limited information maximum likeliho...

This paper develops asymptotic distribution theory for generalized method of moments (GMM) estimators and test statistics when some of the parameters are well identified, but others are poorly identified because of weak instruments. The asymptotic theory entails applying empirical process theory to obtain a limiting representation of the (concentra...