Modeling and Forecasting

Modeling Behavioral Responses to COVID19
Many models have been developed to forecast the spread of the COVID19 virus. We present one that is enhanced to allow individuals to alter their behavior in response to the virus. We show how adding this feature to the model both changes the resulting forecast and informs our understanding of the appropriate policy response. We find that when left to their own devices, individuals do curb their social activity in the face of risk, but not as much as a government planner would. The planner fully internalizes the effect of all individuals’ actions on others in society, while individuals do not. Further, our simulations suggest that government intervention may be particularly important in the middle and later stages of a pandemic. Read More

Applications of Markov Chain Approximation Methods to Optimal Control Problems in Economics
In this paper we explore some of the benefits of using the finitestate Markov chain approximation (MCA) method of Kushner and Dupuis (2001) to solve continuoustime optimal control problems. We first show that the implicit finitedifference scheme of Achdou et al. (2017) amounts to a limiting form of the MCA method for a certain choice of approximating chains and policy function iteration for the resulting system of equations. We then illustrate the benefits of departing from policy function iteration by showing that using variations of modified policy function iteration to solve income fluctuation problems in two and three dimensions can lead to an increase in the speed of convergence of more than an order of magnitude. We then show that the MCA method is also wellsuited to solving portfolio problems with highly correlated state variables, a setting that commonly occurs within general equilibrium models with financial frictions and for which it is difficult to construct monotone (and hence convergent) finitedifference schemes. Read More

Recessions and the Trend in the US Unemployment Rate
The unemployment rate in the United States falls slowly in expansions, and it may not reach its previous low point before the next recession begins. Based on this feature, I document that the frequent recessions prior to 1983 are associated with an upward trend in the unemployment rate. In contrast, the long expansions beginning in 1983 are associated with a downward trend. I then estimate a twovariable vector autoregression (VAR) that includes the unemployment rate and a recession indicator. Longhorizon forecasts from this VAR conditioned on no future recessions project that the unemployment rate will go to 3.6 percent after a long period with no recessions. Read More

Addressing COVID19 Outliers in BVARs with Stochastic Volatility
Incoming data in 2020 posed sizable challenges for the use of VARs in economic analysis: Enormous movements in a number of series have had strong effects on parameters and forecasts constructed with standard VAR methods. We propose the use of VAR models with timevarying volatility that include a treatment of the COVID extremes as outlier observations. Typical VARs with timevarying volatility assume changes in uncertainty to be highly persistent. Instead, we adopt an outlieradjusted stochastic volatility (SV) model for VAR residuals that combines transitory and persistent changes in volatility. In addition, we consider the treatment of outliers as missing data. Evaluating forecast performance over the last few decades in quasireal time, we find that the outlieraugmented SV scheme does at least as well as a conventional SV model, while both outperform standard homoskedastic VARs. Point forecasts made in 2020 from heteroskedastic VARs are much less sensitive to outliers in the data, and the outlieradjusted SV model generates more reasonable gauges of forecast uncertainty than a standard SV model. At least preCOVID, a close alternative to the outlieradjusted model is an SV model with tdistributed shocks. Treating outliers as missing data also generates betterbehaved forecasts than the conventional SV model. However, since uncertainty about the incidence of outliers is ignored in that approach, it leads to strikingly tight predictive densities. Read More

Does the Yield Curve Predict Output?
Does the yield curve have the ability to predict output and recessions? At some times and in certain places, of course! But many details are matters of dispute: When and where does the yield curve predict successfully, which aspects of the curve matter most, and which economic forces account for the predictive ability? Over the years, an increasingly sophisticated set of tools, both statistical and theoretical, have addressed these issues. For the US, an inverted yield curve, particularly when the spread between the yield on 10year and 3month Treasuries becomes negative, has been a robust indicator of recessions in the postWorld War Two period. The spread also predicts future real GDP growth for the US, although the forecast ability varies by time period, in ways that appear to depend on monetary policy. The evidence is less clear in other countries, but the yield curve shows some predictive ability for the UK and Germany, among others. Read More

Measuring Uncertainty and Its Effects in the COVID19 Era
We measure the effects of the COVID19 outbreak on macroeconomic and financial uncertainty, and we assess the consequences of the latter for key economic variables. We use a large, heteroskedastic vector autoregression (VAR) in which the error volatilities share two common factors, interpreted as macro and financial uncertainty, in addition to idiosyncratic components. Macro and financial uncertainty are allowed to contemporaneously affect the macroeconomy and financial conditions, with changes in the common component of the volatilities providing contemporaneous identifying information on uncertainty. We also consider an extended version of the model, based on a latent state approach to accommodating outliers in volatility, to reduce the influence of extreme observations from the COVID period. The estimates we obtain yield very large increases in macroeconomic and financial uncertainty over the course of the COVID19 period. These increases have contributed to the downturn in economic and financial conditions, but with both models, the contributions of uncertainty are small compared to the overall movements in many macroeconomic and financial indicators. That implies that the downturn is driven more by other dimensions of the COVID crisis than shocks to aggregate uncertainty (as measured by our method). Read More

Nowcasting Tail Risks to Economic Activity with Many Indicators
This paper focuses on nowcasts of tail risk to GDP growth, with a potentially wide array of monthly and weekly information. We consider different models (Bayesian mixed frequency regressions with stochastic volatility, as well as classical and Bayesian quantile regressions) and also different methods for data reduction (either forecasts from models that incorporate data reduction or the combination of forecasts from smaller models). Our results show that, within some limits, more information helps the accuracy of nowcasts of tail risk to GDP growth. Accuracy typically improves as time moves forward within a quarter, making additional data available, with monthly data more important to accuracy than weekly data. Accuracy also typically improves with the use of financial indicators in addition to a base set of macroeconomic indicators. The betterperforming models or methods include the Bayesian regression model with stochastic volatility, Bayesian quantile regression, some approaches to data reduction that make use of factors, and forecast averaging. In contrast, simple quantile regression performs relatively poorly. Read More

Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions
A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and it has relied on quantile regression methods to estimate tail risks. Although much of this work discusses asymmetries in conditional predictive distributions, the analysis often focuses on evidence of downside risk varying more than upside risk. We note that this pattern in risk estimates over time could obtain with conditional distributions that are symmetric but subject to simultaneous shifts in conditional means (down) and variances (up). Building on that insight, we examine the ability of Bayesian VARs with stochastic volatility to capture tail risks in macroeconomic forecast distributions and outcomes. We consider both a conventional stochastic volatility specification and a specification with a common factor in volatility that enters the VAR’s conditional mean. Even though the onestepahead conditional predictive distributions from the conventional stochastic volatility specification are symmetric, the model estimates yield more time variation in downside risk as compared to upside risk. Results from the model that includes a volatility factor in the conditional mean and thereby allows for asymmetries in conditional distributions are very similar. Our paper also extends the recent literature by formally evaluating the accuracy of tail risk forecasts and assessing the performance of Bayesian quantile regression, as well as our Bayesian VARs, in this context. Overall, the BVAR models perform comparably to quantile regression for estimating and forecasting tail risks, complementing BVARs’ established performance for forecasting and structural analysis. Read More

NoArbitrage Priors, Drifting Volatilities, and the Term Structure of Interest Rates
We derive a Bayesian prior from a noarbitrage affine term structure model and use it to estimate the coefficients of a vector autoregression of a panel of government bond yields, specifying a common timevarying volatility for the disturbances. Results based on US data show that this method improves the precision of both point and density forecasts of the term structure of government bond yields, compared to a fully fledged term structure model with timevarying volatility and to a nochange random walk forecast. Further analysis reveals that the approach might work better than an exact term structure model because it relaxes the requirements that yields obey a strict factor structure and that the factors follow a Markov process. Instead, the crossequation noarbitrage restrictions on the factor loadings play a marginal role in producing forecasting gains. Read More

Nowcasting Tail Risks to Economic Activity with Many Indicators
This paper focuses on nowcasts of tail risk to GDP growth, with a potentially wide array of monthly and weekly information. We consider different models (Bayesian mixed frequency regressions with stochastic volatility, classical and Bayesian quantile regressions, quantile MIDAS regressions) and also different methods for data reduction (either forecasts from models that incorporate data reduction or the combination of forecasts from smaller models). Our results show that, within some limits, more information helps the accuracy of nowcasts of tail risk to GDP growth. Accuracy typically improves as time moves forward within a quarter, making additional data available, with monthly data more important to accuracy than weekly data. Accuracy also typically improves with the use of financial indicators in addition to a base set of macroeconomic indicators. The betterperforming models or methods include the Bayesian regression model with stochastic volatility, Bayesian quantile regression, some approaches to data reduction that make use of factors, and forecast averaging. In contrast, simple quantile regression and quantile MIDAS regression perform relatively poorly. Read More

Monetary Policy with Judgment
We consider two approaches to incorporate judgment into DSGE models. First, Bayesian estimation indirectly imposes judgment via priors on model parameters, which are then mapped into a judgmental interest rate decision. Standard priors are shown to be associated with highly unrealistic judgmental decisions. Second, judgmental interest rate decisions are directly provided by the decision maker and incorporated into a formal statistical decision rule using frequentist procedures. When the observed interest rates are interpreted as judgmental decisions, they are found to be consistent with DSGE models for long stretches of time, but excessively tight in the 1980s and late 1990s and excessively loose in the late 1970s and early 2000s. Read More

Nowcasting Tail Risks to Economic Activity with Many Indicators
This paper focuses on tail risk nowcasts of economic activity, measured by GDP growth, with a potentially wide array of monthly and weekly information. We consider different models (Bayesian mixed frequency regressions with stochastic volatility, classical and Bayesian quantile regressions, quantile MIDAS regressions) and also different methods for data reduction (either the combination of forecasts from smaller models or forecasts from models that incorporate data reduction). The results show that classical and MIDAS quantile regressions perform very well insample but not outofsample, where the Bayesian mixed frequency and quantile regressions are generally clearly superior. Such a ranking of methods appears to be driven by substantial variability over time in the recursively estimated parameters in classical quantile regressions, while the use of priors in the Bayesian approaches reduces sampling variability and its effects on forecast accuracy. From an economic point of view, we find that the weekly information flow is quite useful in improving tail nowcasts of economic activity, with initial claims for unemployment insurance, stock prices, a term spread, a credit spread, and the Chicago Fed’s index of financial conditions emerging as particularly relevant indicators. Additional weekly indicators of economic activity do not improve historical forecast accuracy but do not harm it much, either. Read More

A New Tool for Robust Estimation and Identification of Unusual Data Points
Most consistent estimators are what Müller (2007) terms “highly fragile”: prone to total breakdown in the presence of a handful of unusual data points. This compromises inference. Robust estimation is a (seldomused) solution, but commonly used methods have drawbacks. In this paper, building on methods that are relatively unknown in economics, we provide a new tool for robust estimates of mean and covariance, useful both for robust estimation and for detection of unusual data points. It is relatively fast and useful for large data sets. Our performance testing indicates that our baseline method performs on par with, or better than, two of the currently best available methods, and that it works well on benchmark data sets. We also demonstrate that the issues we discuss are not merely hypothetical, by reexamining a prominent economic study and demonstrating its central results are driven by a set of unusual points. Read More

Advance Layoff Notices and Labor Market Forecasting
We collect rich establishmentlevel data about advance layoff notices filed under the Worker Adjustment and Retraining Notification (WARN) Act since January 1990. We present insample evidence that the number of workers affected by WARN notices leads statelevel initial unemployment insurance claims, changes in the unemployment rate, and changes in private employment. The effects are strongest at the one and twomonth horizons. After aggregating statelevel information to a nationallevel “WARN factor” using a dynamic factor model, we find that the factor substantially improves outofsample forecasts of changes of manufacturing employment in real time. Read More

Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions
A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and has relied on quantile regression methods to estimate tail risks. In this paper we examine the ability of Bayesian VARs with stochastic volatility to capture tail risks in macroeconomic forecast distributions and outcomes. We consider both a conventional stochastic volatility specification and a specification featuring a common volatility factor that is a function of past financial conditions. Even though the conditional predictive distributions from the VAR models are symmetric, our estimated models featuring timevarying volatility yield more time variation in downside risk as compared to upside risk—a feature highlighted in other work that has advocated for quantile regression methods or focused on asymmetric conditional distributions. Overall, the BVAR models perform comparably to quantile regression for estimating tail risks, with, in addition, some gains in standard point and density forecasts. Read More

The Propagation of Monetary Policy Shocks in a Heterogeneous Production Economy
Realistic heterogeneity in price rigidity interacts with heterogeneity in sectoral size and inputoutput linkages in the transmission of monetary policy shocks. Quantitatively, heterogeneity in price stickiness is the central driver for real effects. Inputoutput linkages and consumption shares alter the identity of the most important sectors to the transmission. Reducing the number of sectors decreases monetary nonneutrality with a similar impact response of inflation. Hence, the initial response of inflation to monetary shocks is not sufficient to discriminate across models and ignoring heterogeneous consumption shares and inputoutput linkages identifies the wrong sectors from which the real effects originate. Read More

Sequential Bayesian Inference for Vector Autoregressions with Stochastic Volatility
We develop a sequential Monte Carlo (SMC) algorithm for Bayesian inference in vector autoregressions with stochastic volatility (VARSV). The algorithm builds particle approximations to the sequence of the model’s posteriors, adapting the particles from one approximation to the next as the window of available data expands. The parallelizability of the algorithm’s computations allows the adaptations to occur rapidly. Our particular algorithm exploits the ability to marginalize many parameters from the posterior analytically and embeds a known Markov chain Monte Carlo (MCMC) algorithm for the model as an effective mutation kernel for fighting particle degeneracy. We show that, relative to using MCMC alone, our algorithm increases the precision of inference while reducing computing time by an order of magnitude when estimating a mediumscale VARSV model. Read More

Has the RealTime Reliability of Monthly Indicators Changed over Time?
Economic data are routinely revised after they are initially released. I examine the extent to which the realtime reliability of six monthly macroeconomic indicators important to policymakers has remained stable over time by studying the timeseries properties of their shortterm and longterm revisions. I show that the revisions to many monthly economic indicators display systematic behaviors that policymakers could build into their realtime assessments. I also find that some indicators’ revision series have varied substantially over time, suggesting that these indicators may now be less useful in real time than they once were. Lastly, I find that substantial revisions tend to occur indefinitely after the initial data release, a result which suggests a certain degree of caution is in order when using even thricerevised monthly data in policymaking. Read More

Asymptotically Valid Bootstrap Inference for Proxy SVARs
Proxy structural vector autoregressions identify structural shocks in vector autoregressions with external variables that are correlated with the structural shocks of interest but uncorrelated with all other structural shocks. We provide asymptotic theory for this identification approach under mild αmixing conditions that cover a large class of uncorrelated, but possibly dependent innovation processes, including conditional heteroskedasticity. We prove consistency of a residualbased moving block bootstrap for inference on statistics such as impulse response functions and forecast error variance decompositions. Wild bootstraps are proven to be generally invalid for these statistics and their coverage rates can be badly and persistently missized. Read More

A Closer Look at the Behavior of Uncertainty and Disagreement: Micro Evidence from the Euro Area
This paper examines point and density forecasts of real GDP growth, inflation and unemployment from the European Central Bank’s Survey of Professional Forecasters. We present individual uncertainty measures and introduce individual point and densitybased measures of disagreement. The data indicate substantial heterogeneity and persistence in respondents’ uncertainty and disagreement, with uncertainty associated with prominent respondent effects and disagreement associated with prominent time effects. We also examine the comovement between uncertainty and disagreement and find an economically insignificant relationship that is robust to changes in the volatility of the forecasting environment. This provides further evidence that disagreement is not a reliable proxy for uncertainty. Read More

A Class of TimeVarying Parameter Structural VARs for Inference under Exact or Set Identification
This paper develops a new class of structural vector autoregressions (SVARs) with timevarying parameters, which I call a drifting SVAR (DSVAR). The DSVAR is the first structural timevarying parameter model to allow for internally consistent probabilistic inference under exact—or set—identification, nesting the widely used SVAR framework as a special case. I prove that the DSVAR implies a reducedform representation, from which structural inference can proceed similarly to the widely used twostep approach for SVARs: beginning with estimation of a reduced form and then choosing among observationally equivalent candidate structural parameters via the imposition of identifying restrictions. In a special case, the implied reduced form is a tractable known model for which I provide the first algorithm for Bayesian estimation of all free parameters. I demonstrate the framework in the context of Baumeister and Peersman’s (2013b) work on time variation in the elasticity of oil demand. Read More

Can Yield Curve Inversions Be Predicted?
An inverted Treasury yield curve—a yield curve where shortterm Treasury interest rates are higher than longterm Treasury interest rates—is a good predictor of recessions. Because of this, economists and policymakers often assess the risk of a yield curve inversion when the yield curve is flattening. I study the forecastability of yield curve inversions. Read More

Modeling TimeVarying Uncertainty of MultipleHorizon Forecast Errors
We estimate uncertainty measures for point forecasts obtained from survey data, pooling information embedded in observed forecast errors for different forecast horizons. To track timevarying uncertainty in the associated forecast errors, we derive a multiplehorizon specification of stochastic volatility. We apply our method to forecasts for various macroeconomic variables from the Survey of Professional Forecasters. Compared to constant variance approaches, our stochastic volatility model improves the accuracy of uncertainty measures for survey forecasts. Our method can also be applied to other surveys like the Blue Chip Consensus, or the Federal Open Market Committee’s Summary of Economic Projections. Read More

Endogenous Uncertainty
We show that macroeconomic uncertainty can be considered as exogenous when assessing its effects on the U.S. economy. Instead, financial uncertainty can at least in part arise as an endogenous response to some macroeconomic developments, and overlooking this channel leads to distortions in the estimated effects of financial uncertainty shocks on the economy. We obtain these empirical findings with an econometric model that simultaneously allows for contemporaneous effects of both uncertainty shocks on economic variables and of economic shocks on uncertainty. While the traditional econometric approaches do not allow us to simultaneously identify both of these transmission channels, we achieve identification by exploiting the heteroskedasticity of macroeconomic data. Methodologically, we develop a structural VAR with timevarying volatility in which one of the variables (the uncertainty measure) impacts both the mean and the variance of the other variables. We provide conditional posterior distributions for this model, which is a substantial extension of the popular leverage model of Jacquier, Polson, and Rossi (2004), and provide an MCMC algorithm for estimation. Read More

Costly Information Intermediation as a Natural Monopoly
In this paper, we show that information trade has similar characteristics to a natural monopoly, where competition may be detrimental to efficiency due either to the duplication of direct costs or the slowing down of information dissemination. We present a model and find that cooperation can be sustained through an institution that gives incentives to information exchange. Read More

Convergence of Cultural Traits with TimeVarying SelfConfidence in the Panebianco (2014) ModelA Corrigendum
We highlight that convergence in repeated averaging models commonly used to study cultural traits or opinion dynamics is not equivalent to convergence in Markov chain settings if transition matrices are timevarying. We then establish a new proof for the convergence of cultural traits in the model of Panebianco (2014) correcting the existing proof. The new proof provides novel insights on the longrun outcomes for inessential individuals. We close with a discussion of conditions for convergence in repeated averaging models with timevarying transition matrices. Read More

Testing for Differences in Path Forecast Accuracy: ForecastError Dynamics Matter
Although the trajectory and path of future outcomes plays an important role in policy decisions, analyses of forecast accuracy typically focus on individual point forecasts. However, it is important to examine the path forecasts errors since they include the forecast dynamics. We use the link between path forecast evaluation methods and the joint predictive density to propose a test for differences in system path forecast accuracy. We also demonstrate how our test relates to and extends existing joint testing approaches. Simulations highlight both the advantages and disadvantages of path forecast accuracy tests in detecting a broad range of differences in forecast errors. We compare the Federal Reserve's Greenbook point and path forecasts against four DSGE model forecasts. The results show that differences in forecasterror dynamics can play an important role in the assessment of forecast accuracy. Read More

Modeling TimeVarying Uncertainty of MultipleHorizon Forecast Errors
We develop uncertainty measures for point forecasts from surveys such as the Survey of Professional Forecasters, Blue Chip, or the Federal Open Market Committee’s Summary of Economic Projections. At a given point of time, these surveys provide forecasts for macroeconomic variables at multiple horizons. To track timevarying uncertainty in the associated forecast errors, we derive a multiplehorizon specification of stochastic volatility. Compared to constantvariance approaches, our stochasticvolatility model improves the accuracy of uncertainty measures for survey forecasts. Read More

Forecasting GDP Growth with NIPA Aggregates
This paper compiles realtime data on a variety of NIPA aggregates and uses these in simple timeseries models to construct outofsample forecasts for GDP growth. Read More

Measuring Uncertainty and Its Impact on the Economy
We propose a new model for measuring uncertainty and its effects on the economy, based on a large vector autoregression with stochastic volatility driven by common factors representing macroeconomic and financial uncertainty. Read More

Organizations, Skills, and Wage Inequality
We extend an onthejob search framework in order to allow firms to hire workers with different skills and skills to interact with firms' total factor productivity (TFP). Our model implies that more productive firms are larger, pay higher wages, and hire more workers at all skill levels and proportionately more at higher skill types, matching key stylized facts. Read More

Financial Nowcasts and Their Usefulness in Macroeconomic Forecasting
This paper considers the role of nowcasts of financial variables in making conditional forecasts of real and nominal macroeconomic variables using standard quarterly Bayesian vector autoregressions. For nowcasting the quarterly value of a variety of financial variables, we document that the average of the available daily data and a daily random walk forecast to fill in the missing days in the quarter typically outperforms other nowcasting approaches. Using realtime data and outofsample forecasting exercises, we find that the inclusion of financial variable nowcasts by themselves generally improves forecast accuracy for macroeconomic variables relative to unconditional forecasts. Read More

Partially Disaggregated Householdlevel Debt Service Ratios: Construction and Validation
We develop and estimate debt service ratio measures based on individuallevel debt payments data obtained from credit bureau data and published estimates of disposable personal income. Our results suggest that aggregate debt service ratios may have understated the payment requirements of households. Read More

Measuring Uncertainty and Its Impact on the Economy
We propose a new framework for measuring uncertainty and its effects on the economy, based on a large VAR model with errors whose stochastic volatility is driven by two common unobservable factors, representing aggregate macroeconomic and financial uncertainty. The uncertainty measures can also influence the levels of the variables so that, contrary to most existing measures, ours reflect changes in both the conditional mean and volatility of the variables, and their impact on the economy can be assessed within the same framework. Read More

Proxy SVARs: Asymptotic Theory, Bootstrap Inference, and the Effects of Income Tax Changes in the United States
We provide asymptotic theory for proxy SVARs when the VAR innovations and proxy variables are jointly αmixing. We also prove the asymptotic validity of a residualbased moving block bootstrap (MBB) for inference on statistics that depend jointly on estimators for the VAR coefficients and for covariances of the VAR innovations and proxy variables. Read More

Large Vector Autoregressions with Stochastic Volatility and Flexible Priors
In this paper we propose a new Bayesian estimation procedure for (possibly very large) VARs featuring time varying volatilities and general priors. Read More

The Natural Rate of Interest in Taylor Rules
The natural rate of interest is assumed to be constant over time in Taylor rules. Since this assumption is likely incorrect, we show how the Taylor rule can account for a variable natural rate by incorporating longterm productivity growth. Read More

Persistence Dependence in Empirical Relations: The Velocity of Money
We apply newly developed econometric tools (Ashley and Verbrugge, 2009a) for drawing inferences about persistence dependence in economic relationships to study the velocity of money. Read More

Identifying Structural VARs with a Proxy Variable and a Test for a Weak Proxy
This paper develops a simple estimator to identify structural shocks in vector autoregressions (VARs) by using a proxy variable. Read More

Do Forecasters Agree on a Taylor Rule?
We use a Taylor rule to investigate two possible reasons why forecasters’ projections for shortterm interest rates differ so much. Read More

Forecasts from Reducedform Models under the ZeroLowerBound Constraint
In this paper, I present a method for forecasting from a reducedform VAR under the zero lower bound (ZLB) for the shortterm nominal interest rate. Read More

Interest Rate Forecasts in Conventional and Unconventional Monetary Policy Periods
We analyze the accuracy of interestrate forecasts in the periods before and after the introduction of new monetary policy tools. Read More

Evaluating Conditional Forecasts from Vector Autoregressions
Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments. Read More

A Distinction between Causal Effects in Structural and Rubin Causal Models
Under different definitions, notationally similar causal effects make distinct claims about the results of interventions to the system under investigation: Read More

Majority Voting: A Quantitative Investigation
We study the tax systems that arise in a onceandforall majority voting equilibrium embedded within a macroeconomic model of inequality. Read More

Using Entropic Tilting to Combine BVAR Forecasts with External Nowcasts
This paper shows entropic tilting to be a flexible and powerful tool for combining mediumterm forecasts from BVARs with shortterm forecasts from other sources (nowcasts from either surveys or other models). Read More

Implied Taylor Rules among Forecasters
We explore whether professional forecasters appear to use a Taylor rule when they forecast the future funds rate, and if so, how similar their regression coefficients are to each other and to those in a Taylor rule that fits the historical data. Read More

Frequency Dependence in a RealTime Monetary Policy Rule
We estimate a monetary policy rule for the US allowing for possible frequency dependence (the central bank can respond differently to persistent and transitory innovations) in the unemployment and inflation rates. Read More

Estimating (MarkovSwitching) VAR Models without Gibbs Sampling: A Sequential Monte Carlo Approach
We document the effectiveness of Sequential Monte Carlo algorithms at estimating MSVAR posteriors, and we show that the use of priors with superior data fit alters inference about the presence of time variation in macroeconomic dynamics. Read More

Evaluating Conditional Forecasts from Vector Autoregressions
Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments. Read More

Have Standard VARs Remained Stable since the Crisis?
Small or mediumscale VARs are commonly used in applied macroeconomics for forecasting and evaluating the shock transmission mechanism. We conduct a similar analysis but focus on the effects of the recent crisis. Read More

Estimating Contract Indexation in a Financial Accelerator Model
This paper addresses the positive implications of indexing risky debt to observable aggregate conditions. These issues are pursued within the context of the celebrated financial accelerator model of Bernanke, Gertler and Gilchrist (1999). Read More

Privately Optimal Contracts and Suboptimal Outcomes in a Model of Agency Costs
This paper derives the privately optimal lending contract in the celebrated financial accelerator model of Bernanke, Gertler, and Gilchrist (1999). Read More

Covariates and Causal Effects: The Problem of Context
I show there is a tradeoff between identification and prediction driven by a fact I call the problem of context: Treatment always influences the outcome variable in combination with covariates. Read More

Does Nonfarm Payroll Growth Improve the Taylor Rule?
There has been a lot of interest in financial circles in finding a guidepost or rule of thumb that reflects how monetary policymakers decide how to set interest rates. Read More

Japanese Monetary Policy and the Yen
Japan’s new prime minister, Shinzo Abe, has been concerned about the yen’s appreciation and has attributed the yen’s behavior to exceptionally easy monetary policies abroad. Read More

Privately Optimal Contracts and Suboptimal Outcomes in a Model of Agency Costs
This paper derives the privately optimal lending contract in the celebrated financial accelerator model of Bernanke, Gertler, and Gilchrist (1999). Read More

RealTime Nowcasting with a Bayesian Mixed Frequency Model with Stochastic Volatility
This paper develops a method for producing currentquarter forecasts of GDP growth with a (possibly large) range of available withinthequarter monthly observations of economic indicators ... Read More

Approximating HighDimensional Dynamic Models: Sieve Value Function Iteration
We introduce a method for approximating the value function of highdimensional dynamic models based on sieves and establish results for the: consistency,rates of convergence, and bounds on the error of approximation. Read More

Gaps versus Growth Rates in the Taylor Rule
There are many possible formulations of the Taylor rule. We consider two that use different measures of economic activity to which the Fed could react.... Read More

Estimating Real GDP Growth Trends
The economy continues to expand at a slow pace. Real GDP rose at an annual rate of 1.3 percent in the second quarter of 2012, down from 2 percent in the first quarter. Read More

A Tractable Estimator for General Mixed Multinomial Logit Models
The mixed logit is a framework for incorporating unobserved heterogeneity in discrete choice models in a general way. Read More

The Macroeconomic Forecasting Performance of Autoregressive Models with Alternative Specifications of TimeVarying Volatility
This paper compares alternative models of timevarying macroeconomic volatility on the basis of the accuracy of point and density forecasts of macroeconomic variables. Read More

A Quick Look at Fed Forecasting
During the Chairman's recent press conferences, the first topic that he addressed was the Federal Open Market Committee's (FOMC) set of economic projections. Read More

Fiscal Multipliers under an Interest Rate Peg of Deterministic vs. Stochastic Duration
This paper revisits the size of the fiscal multiplier. The experiment is a fiscal expansion under the assumption of a pegged nominal rate of interest. Read More

Estimating Contract Indexation in a Financial Accelerator Model
This paper addresses the positive implications of indexing risky debt to observable aggregate conditions. These issues are pursued within the context of the celebrated financial accelerator model of Bernanke, Gertler and Gilchrist (1999). Read More

Subdued Business Lending
The financial crisis and subsequent recession caused bank profitability to decline significantly. Read More

Diagnosing Labor Market Search Models: A MultipleShock Approach
We construct a multiple shock, discrete time version of the MortensenPissarides labor market search model to investigate the basic model’s wellknown tendency to underpredict the volatility of key labor market variables. Read More

Approximating HighDimensional Dynamic Models: Sieve Value Function Iteration
We introduce a method for approximating the value function of highdimensional dynamic models based on sieves and establish results for the: consistency,rates of convergence, and bounds on the error of approximation. Read More

Common Drifting Volatility in Large Bayesian VARs
The estimation of large vector autoregressions with stochastic volatility using standard methods is computationally very demanding. Read More

Do Leading Indicators Help Predict GDP Growth Rates?
The latest GDP estimate leaves real GDP growth for 2011 far below 2010's growth rate and further emphasizes the uneven nature of the current recovery. Read More

Play by the (Taylor) Rules
The interest rate projections released after the January Federal Open Market Committee (FOMC) meeting were another step toward increased Fed transparency. Read More

Privately Optimal Contracts and Suboptimal Outcomes in a Model of Agency Costs
This paper derives the privately optimal lending contract in the celebrated financial accelerator model of Bernanke, Gertler, and Gilchrist (1999). Read More

A Medium Scale Forecasting Model for Monetary Policy
This paper presents a 16variable Bayesian VAR forecasting model of the U.S. economy for use in a monetary policy setting. Read More

Macroeconomic Models, Forecasting, and Policymaking
Models of the macroeconomy have gotten quite sophisticated, thanks to decades of development and advances in computing power. Read More

The Impact of GDP Revisions on Taylor Rule Estimations
Along with July’s advanced estimate for secondquarter GDP, the annual revisions for previous GDP estimates were released. Read More

Tests of Equal Forecast Accuracy for Overlapping Models
This paper examines the asymptotic and finitesample properties of tests of equal forecast accuracy when the models being compared are overlapping in the sense of Vuong (1989). Read More

Advances in Forecast Evaluation
This paper surveys recent developments in the evaluation of point forecasts. Read More

The Federal Reserve as an Informed ForeignExchange Trader: 19731995
We show that U.S. intervention sales and purchases of foreign exchange were incapable of forecasting dollar appreciations or depreciations. Read More

Bayesian VARs Specification Choices and Forecast Accuracy
In this paper we examine how the forecasting performance of Bayesian VARs is affected by a number of specification choices. Read More

The Demand for Income Tax Progressivity in the Growth Model
This paper examines the degree of income tax progressivity chosen through a simple majority vote in a model with savings. Read More

Purchasing Power Parity and the Dollar
In terms of purchasing power parity, the dollar seems a tad undervalued these days, but that does not mean it will soon appreciate. Exchange rates can deviate from their purchasingpowerparty levels for long periods. Read More

A Note on Sunspots with Heterogeneous Agents
This paper studies sunspot fluctuations in a model with heterogeneous households. Read More

A Conference on Liquidity in Frictional Markets
This Policy Discussion Paper summarizes the papers that were presented at the Liquidity in Frictional Markets conference in November 2008. Read More

A Monetary Approach to Asset Liquidity
This paper offers a monetary theory of asset liquidity and it explores the implications of the theory for the relationship between assets’ intrinsic characteristics and liquidity, and the effects of monetary policy on asset prices and welfare. Read More

Diagnosing Labor Market Search Models: A MultipleShock Approach
We construct a multipleshock version of the MortensenPissarides labor market search model to investigate the basic model’s wellknown tendency to underpredict the volatility of key labor market variables. Read More

Diagnosing Labor Market Search Models: A MultipleShock Approach
This paper constructs a multipleshock version of the MortensenPissarides labor market search model to investigate the basic model’s wellknown tendency to under predict the volatility of key labor market variables. Read More

The National Banking System: Empirical Observations
This paper provides a summary of the main features of U.S. financial and banking data during the period of the National Banking System (1863–1914). Read More

Technology Investment
As is well known, spending on capital equipment, particularly information technology (IT) equipment, grew rapidly in the 1990s. Read More

Inertial Taylor Rules: The Benefit of Signaling Future Policy
We trace the consequences of an energy shock on the economy under two different monetary policy rules. Read More

Japanese Monetary Policy
The Bank of Japan left its operating target, the uncollateralized overnight call rate, unchanged at 0.25 percent in January. Read More

CoMovement in Sticky Price Models with Durable Goods
Barsky, House, and Kimball (2005) demonstrate that in a standard sticky price model a monetary contraction will lead to a decline in nondurable goods production but an increase in durable goods production, so that aggregate output is little changed. Read More

The Role of Independence in the GreenLin DiamondDybvig Model
Green and Lin study a version of the DiamondDybvig model with a finite number of agents, independence (independent determination of each agent’s type), and sequential service. Read More

Forecasting with the Yield Curve: Level, Slope, and Output 18751997
Using the yield curve helps forecast real growth over the period 1875 to 1997. Using both the level and slope of the curve improves forecasts more than using either variable alone. Read More

Taylor Rules and Monetary Policy
Monetary policy is often described as a rule or strategy for changing the federal funds rate. Read More

Estimating GSP and Labor Productivity by State
In gauging the health of state economies, arguably the two most important series to track are employment and output. Read More

General Equilibrium with Nonconvexities, Sunspots, and Money
We study general equilibrium with nonconvexities. In these economies there exist sunspot equilibria without the usual assumptions needed in convex economies, and they have good welfare properties. Read More

Taylor Rules and Communication
The FOMC statement continues to assert that “monetary policy remains accommodative,” but it is difficult to judge whether or not this is the case. One approach is to calculate what the funds rate would have been in the past under similar conditions. Read More

Recovering Market Expectations of FOMC Rate Changes with Options on Federal Funds Futures
This paper demonstrates how options on federal funds futures, which began trading in March 2003, can be used to recover the implied probability density function (PDF) for future Federal Open Market Committee (FOMC) interest rate outcomes. Read More

Theory, Measurement, and Calibration of Macroeconomic Models
Calibration has become a standard tool of macroeconomics. Read More

The Forecast Ability of RiskNeutral Densities of Foreign Exchange
We estimate the process underlying the pricing of American options by using higherorder lattices combined with a multigrid method. Read More

Money in Search Equilibrium, in Competitive Equilibrium, and in Competitive Search Equilibrium
We compare three market structures for monetary economies: bargaining (search equilibrium); price taking (competitive equilibrium); and price posting (competitive search equilibrium). Read More

A Model of (the Threat of) Counterfeiting
A simple matchingmodel of money with the potential for counterfeiting is constructed. Read More

An Option for Anticipating Fed Action
Options contracts on federal funds futures, a new financial instrument introduced earlier this year, can be analyzed to gauge public expectations of future Fed actions. Read More

The Taylor Rule: A Guidepost for Monetary Policy?
Once a topic to be found only in scholarly economic journals, the Taylor rule is popping up regularly in news magazines, finance journals, and central bankers’ speeches. Does the Fed follow the rule? Should it? Read More

The Iowa Electronic Markets
In 1998, University of Iowa faculty members created their own futures markets. Read More

Another Jobless Recovery
The expansion of the 1990s began with such unexpectedly slow employment growth that commentators called it the “jobless recovery.” Read More

The Taylor Rule
Monetary policy can often be described as a rule or strategy for changing the federal funds rate in response to inflation and other indicators of real economic activity. Read More

A Simple Model of Money and Banking
The authors define money to be any object that circulates widely as a means of payment and a bank to be an agency that simultaneously issues money and monitors investments. Read More

Estimates of Scale and Cost Efficiency for Federal Reserve Currency Operations
Meeting the currency demands of depository institutions, businesses, and consumers costs the Federal Reserve more than half a billion dollars each year, yet, very little research has been devoted to understanding what factors affect such costs. Read More

Timing and Real Indeterminacy in Monetary Models
An increasingly common approach to the theoretical analysis of monetary policy is to ensure that a proposed policy does not introduce real indeterminacy and thus sunspot fluctuations into the model economy. Read More

Taylor Rules in a Model that Satisfies the Natural Rate Hypothesis
The authors analyze the restrictions necessary to ensure that the interestrate policy rule used by the central bank does not introduce real indeterminacy into the economy. Read More

Learning and the Central Bank
It is well known that sunspot equilibria may arise under an interestrate operating procedure in which the central bank varies the nominal rate with movements in future inflation (a forwardlooking Taylor rule). Read More

How Well Does the Federal Funds Futures Rate Predict the Future Federal Funds Rate?
Contrary to popular belief, federal funds futures rates do not tell us precisely where the market thinks federal funds rates will be in the future. Read More

Maximum Likelihood in the Frequency Domain: The Importance of TimetoPlan
We illustrate the use of various frequency domain tools for estimating and testing dynamic,stochastic general equilibrium models. Read More

Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy
We present a model embodying moderate amounts of nominal rigidities which accounts for the observed inertia in inflation and persistence in output. Read More

LifeCycle Income and Consumption Variability
By all accounts, economic inequality is growing — the rich are getting richer, and the poor are getting poorer. Read More

The SearchTheoretic Approach to Monetary Economics: A Primer
The authors present simple versions of models used in the searchtheoretic approach to monetary economics. They discuss results on the existence of monetary equilibria, the potential for multiple equilibria, and welfare. Read More

ForwardLooking Versus BackwardLooking Taylor Rules
This paper analyzes the restrictions necessary to ensure that the policy rule used by the central bank does not introduce real indeterminacy into the economy. Read More

Forecasts and Sunspots: Looking Back for a Better Future
Some would argue that economic forecasts are about as accurate as soothsayers and weather forecasts. Yet central banks all around the world make such forecasts and use them when conducting monetary policy. Read More

Timing and Real Indeterminacy in Monetary Models
An increasingly common approach to the theoretical analysis of monetary policy is to ensure that a proposed policy does not introduce real indeterminacy and thus sunspot fluctuations into the model economy. Read More

The Band Pass Filter
The "ideal" band pass filter can be used to isolate the component of a time series that lies within a particular band of frequencies. Read More

A Method for Taking Models to the Data
This paper develops a method for combining the power of a dynamic, stochastic, general equilibrium model with the flexibility of a vector autoregressive timeseries model to obtain a hybrid that can be taken directly to the data. Read More

Defining Capital in Growth Models
The authors analyze the measurement of the capital stock when technological advance is embodied in capital. The source of the problem is that capital is not homogeneous across vintages. Which measure of the capital stock to use? is addressed. Read More

Taylor Rules in a Limited Participation Model
We use the limited participation model of money as a laboratory for studying the operating characteristics of Taylor rules for setting the rate of interest. Rules are evaluated according to their ability to protect the economy from bad outcomes such as the burst of inflation observed in the 1970's. Based on our analysis, we argue fora rule which: (i) raises the nominal interest rate more than oneforone with a rise in inflation; and (ii) does not change the interest rate in response to a change in output relative to trend. Read More

Maximum Likelihood in the Frequency Domain: A Time to Build Example
A well known result is that the Gaussian loglikelihood can be expressed as the sum over different frequency components. Read More

Evolutionary Programming as a Solution Technique for the Bellman Equation
Evolutionary programming is a stochastic optimization procedure which has proved useful in optimizing difficult functions. Read More

Real Indeterminacy in Monetary Models with Nominal Interest Rate Distortions: The Problem with Inflation Targets
This paper demonstrates that in a standard monetary model there exists real indeterminacy whenever the nominal interest rate moves too closely with the real rate. Read More

Real Indeterminacy in Monetary Models with Nominal Interest Rate Distortions: The Problem with Inflation Targets
This paper demonstrates that in a standard monetary model there exists real indeterminacy whenever the nominal interest rate moves too closely with the real rate. Read More

Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients
This paper presents an undeterminedcoefficients method for obtaining a linear approximation to the solution of a dynamic rationalexpectations model. Read More

Appointing the Median Voter of a Policy Board
Partisan politics and elector uncertainty generate policy uncertainty and partisan business cycles. Read More

Interest Rate Option Pricing with Volatility Humps
This paper develops a simple model for pricing interest rate options. Analytical solutions are developed for European claims and extremely efficient algorithms exist for tile pricing of American options. Read More

Algorithms for Solving Dynamic Models with Occasionally Binding Constraints
We describe and compare several algorithms for approximating the solution to a model in which inequality constraints occasionally bind. Read More

A Note on Purifying Mixed Strategy Equilibria in the Search Model of Money
The simple searchtheoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y is an element of (0,1). Read More

Indeterminacy and Stabilization Policy
It has been shown that a onesector real business cycle model with sufficient increasing returns in production may possess an indeterminate steady state that can be exploited to generate business cycles. Read More

Agency Costs, Net Worth, and Business Fluctuations: A Computable General Equilibrium Analysis
An analysis of the quantitative effects of agency costs in a real business cycle model, showing that these costs can explain why output growth displays positive autocorrelation at short horizons. Read More

The Reduced Form as an Empirical Tool: A Cautionary Tale from the Financial Veil
The reducedform empirical strategy has been used for over 30 years to test the ModiglianiMiller model of corporate financial structure. Curiously, early tests almost always accepted the model, whereas subsequent tests almost always reject it. Read More

Some Monte Carlo Results on Nonparametric Changepoint Tests
For long periods since 1982, core inflation has behaved as if it were generated by a process with a fixed mean and serially independent error term. Read More

A Conference on Liquidity, Monetary Policy, and Financial Intermediation
A summary of the fifth in a series of symposiums sponsored by the Federal Reserve Bank of Cleveland. Read More

Computable GeneralEquilibrium Models and Monetary Policy Advice
This paper argues that variations of extant generalequilibrium monetary models are capable of generating realtime economic forecasts comparable in accuracy to those generated under the, standard Federal Reserve Board staff methodology. Read More

Federal Funds Futures as an Indicator of Future Monetary Policy: A Primer
Unlike most futures contracts, which are drawn on commodities or financial instruments whose price or yield is determined in competitive markets, federal funds futures rate is essentially determined by a deliberative decision of the FOMC. Read More

The Computational Experiment: an Econometric Tool
An economic experiment consists of the act of placing people in an environment desired by the experimenter, who then records the time paths of their economic behavior. Read More

Auctions with BudgetConstrained Buyers: A Nonequivalence Result
Anecdotal evidence of concern about the limited financial resources of small firms abounds in government auctions. Recent empirical work also provides evidence of the importance of capital constraints. Read More

Relative Price Movements In Dynamic General Equilibrium Models Of International Trade
We examine the behavior of international relative prices from the perspective of dynamic general equilibrium theory, with particular emphasis on the variability of the terms of trade and the relation between the terms of trade and net exports. Read More

Binomial Approximation in Financial Models: Computational Simplicity and Convergence
This paper explores the potential of transformation and other schemes in constructing a sequence of simple binomial processes that weakly converges to the desired diffusion limit. Read More

Estimating A Firm's AgeProductivity Profile Using The Present Value Of Workers' Earnings
In hiring new workers, riskneutral employers equate the present expected value of each worker's compensation to the present expected value of his/her productivity. Read More

Federal Funds Rate Volatility
The federal funds rate was unusually volatile for several months starting in late December 1990. Daytoday changes over this period were far greater than in previous years, although the difference seems to have disappeared recently (figure 1A). Read More

Forecast Accuracy and Monetary Policy
It has been suggested that the purpose of economic forecasting is to make weather forecasters look good by comparison. Read More

Cointegration and Transformed Series
A large and growing literature is concerned with the theory, estimation, and applications of cointegrating vectors and associated error correction models. Read More

Some Problems of Infinite Regress in SocialChoice Models: A Category Theory Solution
In modern Western democracies, economic and political institutions often have been criticized on moral grounds. Read More

Consumption and Fractional Differencing: Old and New Anomalies
Consumption depends on income, so testing theories of consumption involves testing theories of income. Read More

Forecasting Turning Points With Leading Indicators
The financial news media frequently point to the movement of the Composite Index of Leading Indicators (ILl) as proof of impending growth or contraction in economic activity. Read More

A TwoSector Implicit Contracting Model with Procyclical Quits and Involuntary Layoffs
An explanation of involuntary unemployment and procyclical quits based on models of implicit contracts and onthejob search. Read More

Using SMVAM as a Linear Approximation to a Nonlinear Function: A Note
A study contending that the linear statistical marketvalue accounting model (SMVAM) is a reasonable approximation of the relationship between market and book equity for firms with positive balance sheets. Read More

Learning, Rationality, the Stability of Equilibrium and Macroeconomics
The issue of how agents learn to form rational expectations has received increasing attention lately. The approach taken in many papers treats model stability as a problem in learning. Read More

Estimating Multivariate Arima Models: When is Close Not Good Enough?
The purpose of this study is to examine the forecasting abilities of the same multivariate autoregressive model estimated using two methods. The first method is the "exact method" used by the SCA System from Scientific Computing Associates. Read More

Interest Rate Rules are Infeasible and Fail to Complete Macroeconomic Models
A discussion of the circumstances under which interest rate rules are consistent with nominal determinacy in macroeconomic models. Read More

Univariate and Multivariate Arima versus Vector Autoregression Forecasting
All of these methods have been shown to provide forecasts that are more accurate than many econometric methods, which require more resources to implement. Read More

A Technique for Estimating a Cost System that Allows for Inefficiency
The presentation of a new econometric technique for estimating a system of cost and input share equations that allow for inefficiency. Read More

Monetarism and the Ml Target
The Federal Reserve has once again decreased emphasis on the Ml target as a guide for shortrun policy actions. Read More

Comparison of Univariate ARIMA, Multivariate ARIMA and Vector Autoregression Forecasting
A comparison of the forecasting abilities of univariate ARIMA, multivariate ARIMA, and VAR, and examination of whether series should be differenced before estimating models for forecasting purposes. Read More

Forecasting and Seasonal Adjustment
There have been many studies and papers written about the effects of seasonal adjustment on the relationships among variables. Read More

New Classical and New Keynesian Models of Business Cycles
A presentation of simple New Classical and New Keynesian models of economy and business cycles that illustrate central force behind fluctuations in each. Theoretical and statistical arguments for and against each model are discussed. Read More

Stochastic Interest Rates in the Aggregate Life Cycle/Permanent Income Cum Rational Expectations Model
An estimation of the life cycle/permanent income model with rational expectations that allows for uncertain future interest rates. Results provide ample evidence to reject this form of model during the postwar period. Read More

Fixprice Models for Dynamic Studies
This paper constructs fixprice (or disequilibrium) models of a simple general equilibrium macroeconomic model. Read More

Forecasting GNP Using Monthly M1
In this paper, we present an application of mu1tivariate time series forecasting in which the data consist of a mixture of quarterly and monthly series. Read More

Vector Autoregressive Forecasts of Recession and Recovery: Is Less More?
A look at the pros and cons of VAR models, and consideration of how lag lengths affect outofsample forecasts. Read More

Forecasting Using Contemporaneous Correlations
In this paper, we present a forecasting technique that uses contemporaneous correlations for forecasting in a time series model when only a subset of the variables are available for the current period. Read More

Forecasting the Money Supply in Time Series Models
In this paper, time series techniques are used to forecast quarterly money supply levels. Read More

Extension of Granger Causality in Multivariate Time Series Models
This paper proposes an extension of Granger causality when more than two variables are used in a multivariate time series model, and it is necessary to consider more than oneperiodahead forecasts. Read More