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Working Papers

Working Papers

  • WP 19-26R | The Optimal Taxation of Business Owners

    Tom Phelan

    Original Paper: WP 19-26


    Business owners in the United States are disproportionately represented among the wealthy and are exposed to substantial idiosyncratic risk. Further, recent evidence indicates that business income primarily reflects returns to the human capital of the owner. Motivated by these facts, this paper characterizes stationary efficient allocations and optimal linear taxes on income and wealth when business income depends on innate ability, luck, and the past effort of the owner. I first show that in stationary efficient allocations, more productive entrepreneurs typically bear more risk and the distributions of consumption and firm size are approximately Pareto, with the tail of the latter typically thicker than that of the former. I then characterize optimal linear taxes when owners may save in a risk-free bond and trade shares in their businesses. The optimal utilitarian policy calls for separate taxes on firm profits, capital income, and wealth, serving distinct purposes. The tax on profits plays a redistributive role, the tax on capital income affects the incentives to retain equity and exert effort, and the tax on wealth affects the degree of consumption smoothing over time.   Read More

  • WP 21-12 | Censored Density Forecasts: Production and Evaluation

    James Mitchell Martin Weale


    This paper develops methods for the production and evaluation of censored density forecasts. Censored density forecasts quantify forecast risks in a middle region of the density covering a specified probability, and ignore the magnitude but not the frequency of outlying observations. We propose a new estimator that fits a potentially skewed and fat-tailed density to the inner observations, acknowledging that the outlying observations may be drawn from a different but unknown distribution. We also introduce a new test for calibration of censored density forecasts. An application using historical forecast errors from the Federal Reserve Board and the Monetary Policy Committee at the Bank of England illustrates the utility of censored density forecasts when quantifying forecast risks after shocks such as the global financial crisis and the COVID-19 pandemic.   Read More

  • WP 21-11 | Export-Led Decay: The Trade Channel in the Gold Standard Era

    Bernardo Candia Mathieu Pedemonte


    Flexible exchange rates can facilitate price adjustments that buffer macroeconomic shocks. We test this hypothesis using adjustments to the gold standard during the Great Depression. Using prices at the goods level, we estimate exchange rate pass-through and find gains in competitiveness after a depreciation. Using novel monthly data on city-level economic activity, combined with employment composition and sectoral export data, we show that American exporting cities were significantly affected by changes in bilateral exchange rates. They were negatively impacted when the UK abandoned the gold standard in 1931 and benefited when the US left the gold standard in April 1933. We show that the gold standard deepened the Great Depression, and abandoning it was a key driver of the economic recovery.   Read More

  • WP 21-10 | Is It Time to Reassess the Focal Role of Core PCE Inflation?

    Randal J. Verbrugge


    In this paper, I review the history of “core” PCE inflation and its rationale: remove volatile items with transitory shocks to better highlight the trend in inflation. Structural changes in the inflation process imply that, on a “reducing volatility” basis, the list of items excluded from the “core” inflation basket (aside from gasoline) is far from optimal. This is true whether one assesses volatility on the basis of a weighted component monthly, or an index monthly, or a 12-month index, or a 5-year index. In addition, I demonstrate other deficiencies of exclusion indexes. Excluded items do not just experience transitory shocks, but also have persistent trends; thus excluding them imparts a significant time-varying bias to core inflation. Meanwhile, items that are not excluded can experience volatility and moreover can cause core inflation to depart notably from trend inflation, sometimes at crucial moments. Two other prominent trend inflation measures, trimmed mean PCE inflation and median PCE inflation, gracefully address these issues, but themselves have notable time-varying bias. I discuss the source of the bias in these other measures and how to correct for bias in real time. I then summarize and extend a wide variety of evidence comparing these three trend measures. I conclude that, for a variety of considerations that are relevant for monetary policy deliberations and communication, either trimmed mean PCE inflation or median PCE inflation are superior measures.   Read More

  • WP 20-22R | Late Payment Fees and Nonpayment in Rental Markets, and Implications for Inflation Measurement: Theoretical Considerations and Evidence

    Wesley Janson Randal J. Verbrugge

    Original Paper: WP 20-22


    Statistical agencies track rental expenditures for use in the national accounts and in consumer price indexes (CPIs). As such, statistical agencies should include late payment fees and nonpayment in rent. In the US context, late payment fees are excluded from the CPI. Ostensibly, nonpayment of rent is included in the US CPI; but its treatment is deficient, and we demonstrate that small variations in nonpayment could lead to large swings in shelter inflation, and might have played a role in the 2009 measured shelter inflation collapse. They didn't: while the national nonpayment incidence is 2-3 percent, in the 1 million plus rent observations in BLS rent microdata from 2000-2016, no nonpayment is recorded. A back-of-the-envelope calculation suggests that, assuming nonpayment undermeasurement continued after 2016, CPI shelter inflation may have been overestimated by about 1 percentage point per month (annualized) in 2020. Late fees and nonpayment are difficult to measure in real time. We offer implementation suggestions that are consistent with CPI procedures.   Read More

  • WP 21-09 | Forecasting with Shadow-Rate VARs

    Andrea Carriero Todd E. Clark Massimiliano Marcellino Elmar Mertens


    Interest rate data are an important element of macroeconomic forecasting. Projections of future interest rates are not only an important product themselves, but also typically matter for forecasting other macroeconomic and financial variables. A popular class of forecasting models is linear vector autoregressions (VARs) that include shorter- and longer-term interest rates. However, in a number of economies, at least shorter-term interest rates have now been stuck for years at or near their effective lower bound (ELB), with longer-term rates drifting toward the constraint as well. In such an environment, linear forecasting models that ignore the ELB constraint on nominal interest rates appear inept. To handle the ELB on interest rates, we model observed rates as censored observations of a latent shadow-rate process in an otherwise standard VAR setup. The shadow rates are assumed to be equal to observed rates when above the ELB. Point and density forecasts for interest rates (short term and long term) constructed from a shadow-rate VAR for the US since 2009 are superior to predictions from a standard VAR that ignores the ELB. For other indicators of financial conditions and measures of economic activity and inflation, the accuracy of forecasts from our shadow-rate specification is on par with a standard VAR that ignores the ELB.   Read More

  • WP 21-07 | Municipal Markets and the Municipal Liquidity Facility

    Nicholas Fritsch John Bagley Shawn Nee


    Municipal bond markets experienced a significant amount of strain in response to the COVID-19 crisis, creating liquidity and credit concerns among market participants. During the economic shutdown resulting from the pandemic, income tax revenues were deferred and sales tax revenues decreased beginning in spring 2020, while the cost of borrowing significantly increased for municipal issuers. To aid municipal borrowing needs, the Federal Reserve implemented the Municipal Liquidity Facility (MLF) on April 9, 2020. In this analysis we describe the municipal market conditions as they evolved during 2020, we document the response by the Federal Reserve to municipal market distress with a focus on the MLF, and we conduct an event study to examine MLF-related impacts on market index yield spreads. We detail two case studies that compare yield spreads for two issuers that had sold debt to the MLF and find that yield spreads in secondary market transactions for these two issuers were notably reduced after a public announcement of intent to sell debt to the MLF. Our results present additional evidence that the MLF had a positive impact on municipal market functioning during the pandemic period.   Read More

  • WP 21-08 | Tail Forecasting with Multivariate Bayesian Additive Regression Trees

    Todd E. Clark Florian Huber Gary Koop Massimiliano Marcellino Michael Pfarrhofer


    We develop novel multivariate time series models using Bayesian additive regression trees that posit nonlinear relationships among macroeconomic variables, their lags, and possibly the lags of the errors. The variance of the errors can be stable, driven by stochastic volatility (SV), or follow a novel nonparametric specification. Estimation is carried out using scalable Markov chain Monte Carlo estimation algorithms for each specification. We evaluate the real-time density and tail forecasting performance of the various models for a set of US macroeconomic and financial indicators. Our results suggest that using nonparametric models generally leads to improved forecast accuracy. In particular, when interest centers on the tails of the posterior predictive, flexible models improve upon standard VAR models with SV. Another key finding is that if we allow for nonlinearities in the conditional mean, allowing for heteroskedasticity becomes less important. A scenario analysis reveals highly nonlinear relations between the predictive distribution and financial conditions.   Read More

  • WP 21-06 | All Forecasters Are Not the Same: Time-Varying Predictive Ability across Forecast Environments

    Robert Rich Joseph Tracy


    This paper examines data from the European Central Bank’s Survey of Professional Forecasters to investigate whether participants display equal predictive performance. We use panel data models to evaluate point- and density-based forecasts of real GDP growth, inflation, and unemployment. The results document systematic differences in participants’ forecast accuracy that are not time invariant, but instead vary with the difficulty of the forecasting environment. Specifically, we find that some participants display higher relative accuracy in tranquil environments, while others display higher relative accuracy in volatile environments. We also find that predictive performance is positively correlated across target variables and horizons, with density forecasts generating stronger correlation patterns. Taken together, the results support the development of expectations models featuring persistent heterogeneity.   Read More

  • WP 21-05 | Inflation Gap Persistence, Indeterminacy, and Monetary Policy

    Yasuo Hirose Takushi Kurozumi Willem Van Zandweghe


    Empirical studies have documented that the persistence of the gap between inflation and its trend declined after the Volcker disinflation. Previous research into the source of the decline has offered competing views while sidestepping the possibility of equilibrium indeterminacy. This paper examines the source by estimating a medium-scale DSGE model using a Bayesian method that allows for indeterminacy. The estimated model shows that the Fed's change from a passive to an active policy response to the inflation gap or a decrease in firms' probability of price change can fully account for the decline in inflation gap persistence by ruling out indeterminacy that induces persistent dynamics of the economy.   Read More