The Matching Function and Nonlinear Business Cycles

Joint with Joshua Bernstein and Nathaniel Throckmorton

[Online Appendix, Working Paper, Slides]

Journal of Money, Credit and Banking, forthcoming

Abstract: This paper seeks to understand the general equilibrium effects of time-varying geopolitical risk in oil markets. Answering this question requires simultaneously modeling several features including macroeconomic disasters and geopolitically driven oil production disasters, oil storage and precautionary savings, and the endogenous determination of uncertainty about output and the price of oil. We find that oil price uncertainty tends to be driven by macroeconomic uncertainty. Shifts in the probability of a geopolitically driven major oil supply disruption have meaningful effects on the price of oil and the macro economy, but the resulting oil price uncertainty is not a major driver of fluctuations in macroeconomic aggregates.

A Simple Explanation of Countercyclical Uncertainty

Joint with Joshua Bernstein, Michael Plante, and Nathaniel Throckmorton

[Online Appendix, Working Paper, Slides]

AEJ: Macroeconomics, October 2024, Volume 16, Issue 4, Pages 143-171

Abstract: This paper documents that labor search and matching frictions generate countercyclical uncertainty because the inherent nonlinearity in the flow of new matches makes employment uncertainty increasing in the number of people searching for work. Quantitatively, this mechanism is strong enough to explain uncertainty and real activity dynamics, including their correlation. Through this lens, uncertainty fluctuations are endogenous responses to changes in real activity that neither affect the severity of business cycles nor warrant policy intervention, in contrast with leading theories of the interaction between uncertainty and real activity dynamics. 

Valuation Risk Revalued

Joint with Oliver de Groot and Nathaniel Throckmorton

[Online Appendix, Working Paper]

Quantitative Economics, May 2022, Volume 13, Issue 2, Pages 723-759

Abstract: This paper shows the success of valuation risk—time-preference shocks in Epstein-Zin utility—in resolving asset pricing puzzles rests sensitively on the way it is introduced. The specification used in the literature is at odds with several desirable properties of recursive preferences because the weights in the time-aggregator do not sum to one. When we revise the specification in a simple asset pricing model the puzzles resurface. However, when estimating a sequence of increasingly rich models, we find valuation risk under the revised specification consistently improves the ability of the models to match asset price and cash-flow dynamics. 

Cyclical Net Entry and Exit

Joint with Joshua Bernstein and Nathaniel Throckmorton

[Working Paper, Slides, Dallas Fed Economics Blog]

European Economic Review, July 2021, Volume 136, Article 103752

Abstract: This paper examines how the interplay between cyclical net entry and exit of firms and search and matching frictions affect business cycle dynamics. We show cyclical net entry and exit reallocates inputs across firms and destroys jobs in recessions, which amplifies and skews business cycle dynamics. The model matches the volatility and skewness of real activity, the fast rise and slow decline in unemployment that occurs in recessions, and the counter-cyclical variation in macroeconomic uncertainty. Cyclical net entry and exit generates a 20% increase in volatility, 40% increase in skewness, and 55% increase in the welfare cost of business cycles.

Complementarity and Macroeconomic Uncertainty

Joint with Tyler Atkinson, Michael Plante, and Nathaniel Throckmorton

[Working Paper, Dallas Fed Economics Blog]

Review of Economic Dynamics, April 2022, Volume 44, Pages 225-243

Abstract: Macroeconomic uncertainty regularly fluctuates in the data. Theory suggests complementarity between capital and labor inputs in production can generate time-varying endogenous uncertainty because the concavity in the production function influences how output responds to productivity shocks in different states of the economy. This paper examines whether complementarity is a quantitatively significant source of time-varying endogenous uncertainty by estimating a nonlinear real business cycle model with a constant elasticity of substitution production function and exogenous volatility shocks. When matching labor share and uncertainty moments, we find at most 16% of the volatility of uncertainty is endogenous. An estimated model without exogenous volatility shocks can endogenously generate all of the empirical variation in uncertainty, but only at the expense of significantly overstating the volatility of the labor share. 

The Zero Lower Bound and Estimation Accuracy

Joint with Tyler Atkinson and Nathaniel Throckmorton

[Online Appendix, Working Paper, Code, Slides]

Journal of Monetary Economics, November 2020, Volume 115, Pages 249-264

Abstract: During the Great Recession, central banks lowered their policy rate to the zero lower bound (ZLB), calling into question linear estimation methods. There are two alternatives: estimate a nonlinear model that accounts for precautionary savings effects of the ZLB or a piecewise linear model that is faster but ignores the precautionary savings effects. This paper compares their accuracy using artificial datasets. The predictions of the nonlinear model are typically more accurate than the piecewise linear model, but the differences are usually small. There are far larger gains in accuracy from estimating a richer, less misspecified piecewise linear model.

Uncertainty Shocks in a Model of Effective Demand: Comment

Joint with Oliver de Groot and Nathaniel Throckmorton

[Online Appendix, Working Paper, Code, Slides]

Econometrica, July 2018, Volume 86, Issue 4, Pages 1513-1526

Abstract: Basu and Bundick (2017) show an intertemporal preference volatility shock has meaningful effects on real activity in a New Keynesian model with Epstein and Zin (1991) preferences. We show when the distributional weights on current and future utility in the Epstein-Zin time-aggregator do not sum to 1, there is an asymptote in the responses to such a shock with unit intertemporal elasticity of substitution. In the Basu-Bundick model, the intertemporal elasticity of substitution is set near unity and the preference shock only hits current utility, so the sum of the weights differs from 1. We show when we restrict the weights to sum to 1, the asymptote disappears and preference volatility shocks no longer have large effects. We examine several different calibrations and preferences as potential resolutions with varying degrees of success.

The Zero Lower Bound and Endogenous Uncertainty

Joint with Michael Plante and Nathaniel Throckmorton

[Online Appendix, Working Paper, Slides, Economic Letter, WSJ, LSE]

Economic Journal, June 2018, Volume 128, Issue 611, Pages 1730-1757

Abstract: This paper examines the correlation between uncertainty and real GDP growth. We use the volatility of real GDP growth from a VAR, stock market volatility, survey-based forecast dispersion, and the index from Jurado et al. (2015) as proxies for uncertainty. In each case, a stronger negative correlation emerged in 2008. We contend the zero lower bound (ZLB) on the federal funds rate contributed to our finding. To test our theory, we estimate a New Keynesian model with a ZLB constraint to generate a data-driven, forward-looking uncertainty measure. The correlations between that measure and real GDP growth are close to the values in the data.

Forward Guidance and the State of the Economy

Joint with Benjamin Keen and Nathaniel Throckmorton

[Working Paper, Slides, Chicago Booth Review]

Economic Inquiry, October 2017, Volume 55, Issue 4, Pages 1593-1624

Abstract: This paper analyzes forward guidance in a nonlinear model with a zero lower bound (ZLB) on the nominal interest rate. Forward guidance is modeled with news shocks to the monetary policy rule, which capture innovations in expectations from central bank communication about future policy rates. Whereas most studies use quasi-linear models that disregard the expectational effects of hitting the ZLB, we show how the effectiveness of forward guidance nonlinearly depends on the state of the economy, the speed of the recovery, the degree of uncertainty, the policy shock size, and the forward guidance horizon when households account for the ZLB.

Is Rotemberg Pricing Justified by Macro Data?

Joint with Nathaniel Throckmorton

Economic Letters, December 2016, Volume 149, Pages 44-48

Abstract: Structural models used to study monetary policy often include sticky prices. Calvo pricing is more common but Rotemberg pricing has become popular due to its computational advantage. To determine whether the data supports that change, we estimate a nonlinear New Keynesian model with a zero lower bound (ZLB) constraint and each type of sticky prices. The models produce similar parameter estimates and the filtered shocks are nearly identical when the Fed was not constrained, but the Rotemberg model has a higher marginal data density and it endogenously generates more volatility at the ZLB, which helps explain data from 2008-2011.

The Consequences of an Unknown Debt Target

Joint with Nathaniel Throckmorton

[Working Paper, Slides]

European Economic Review, August 2015, Volume 78, Pages 76-96

Abstract: Several proposals to reduce U.S. debt reveal large differences in their targets. We examine how an unknown debt target affects economic activity using a real business cycle model in which Bayesian households learn about a state-dependent debt target in an endogenous tax rule. Recent papers use stochastic volatility shocks to study fiscal uncertainty. In our setup, the fiscal rule is time-varying due to unknown changes in the debt target. Households infer the current debt target from a noisy tax rule and jointly estimate the transition probabilities. Three key findings emerge from our analysis: (1) Limited information about the debt target amplifies the effect of tax shocks through changes in expected tax rates; (2) The welfare losses are an order of magnitude larger when both the debt target state and transition matrix are unknown than when only the debt target state is unknown to households; (3) An unknown debt target likely reduced the stimulative effect of the ARRA and uncertainty about the sunset provision in the Bush tax cuts may have slowed the recovery and led to welfare losses.

The Zero Lower Bound, the Dual Mandate, and Unconventional Dynamics

Joint with William Gavin, Benjamin Keen and Nathaniel Throckmorton

[Working Paper, Slides]

Journal of Economic Dynamics and Control, June 2015, Volume 55, Pages 14-38

Abstract: This article examines monetary policy when it is constrained by the zero lower bound (ZLB) on the nominal interest rate. Our analysis uses a nonlinear New Keynesian model with technology and discount factor shocks. Specifically, we investigate why technology shocks may have unconventional effects at the ZLB, what factors affect the likelihood of hitting the ZLB, and the implications of alternative monetary policy rules. We initially focus on a New Keynesian model without capital (Model 1) and then study that model with capital (Model 2). The advantage of including capital is that it introduces another mechanism for intertemporal substitution that strengthens the expectational effects of the ZLB. Four main findings emerge: (1) In Model 1, the choice of output target in the Taylor rule may reverse the effects of technology shocks when the ZLB binds; (2) When the central bank targets steady-state output in Model 2, a positive technology shock at the ZLB leads to more pronounced unconventional dynamics than in Model 1; (3) The presence of capital changes the qualitative effects of demand shocks and alters the impact of a monetary policy rule that emphasizes output stability; and (4) In Model 1, the constrained linear solution is a decent approximation of the nonlinear solution, but meaningful differences exist between the solutions in Model 2.

Finite Lifetimes, Long-term Debt and the Fiscal Limit

[Working Paper, Slides]

Journal of Economic Dynamics and Control, February 2015, Volume 51, Pages 180-203

Abstract: The U.S. faces exponentially rising entitlement obligations. I introduce a fiscal limit—a point where higher taxes are no longer a feasible financing mechanism—into a Perpetual Youth model to examine how intergenerational redistributions of wealth, the average duration of government debt, and entitlement reform impact the consequences of explosive government transfers. Three key findings emerge: (1) Growing government transfers cause more severe and more persistent stagflation than in representative agent models that do not capture intergenerational transfers of wealth; (2) A longer average duration of government debt pushes the financing of government liabilities into the future and reduces the short-run impacts of explosive transfers; (3) The time it takes the economy to rebound from a period of growing transfers increases exponentially with the number of years it takes to pass entitlement reform.

The Zero Lower Bound: Frequency, Duration, and Numerical Convergence

Joint with Nathaniel Throckmorton

[Working Paper, Slides]

The B.E. Journal of Macroeconomics, January 2015, Volume 15, Issue 1, Pages 157-182

Abstract: When monetary policy faces a zero lower bound (ZLB) constraint on the nominal interest rate, a minimum state variable (MSV) solution may not exist even if the Taylor principle holds when the ZLB does not bind. This paper shows there is a clear tradeoff between the expected frequency and average duration of ZLB events along the boundary of the convergence region—the region of the parameter space where our policy function iteration algorithm converges to an MSV solution. We show this tradeoff with two alternative stochastic processes: one where monetary policy follows a 2-state Markov chain, which exogenously governs whether the ZLB binds, and the other where ZLB events are endogenous due to discount factor or technology shocks. We also show that small changes in the parameters of the stochastic processes cause meaningful differences in the decision rules and where the ZLB binds in the state space.

Accuracy, Speed and Robustness of Policy Function Iteration

Joint with Nathaniel Throckmorton and Todd Walker

[Working Paper, Code, Toolbox, Mini-Course Slides]

Computational Economics, December 2014, Volume 44, Issue 4, Pages 445-476

Abstract: Policy function iteration methods for solving and analyzing dynamic, stochastic general equilibrium models are powerful from both a theoretical and computational perspective. Despite obvious theoretical appeal, significant startup costs and a reliance on a grid-based method have limited the use of policy function iteration as a solution algorithm. We reduce these costs by providing a user-friendly suite of MATLAB functions that introduce multi-core processing and Fortran via MATLAB's executable function. We demonstrate why policy function iteration is particularly useful in solving models with regime-dependent parameters, recursive preferences, and binding constraints. We examine a canonical real business cycle model and a new Keynesian model that features regime switching in policy parameters, Epstein-Zin preferences, and monetary policy that occasionally hits the zero-lower bound to highlight the attractiveness of our methodology. We compare our advocated approach to other familiar computational methods, highlighting the tradeoffs between accuracy and speed.

Quantitative Effects of Fiscal Foresight

Joint with Eric Leeper and Todd Walker

AEJ: Economic Policy, May 2012, Volume 4, Issue 2, Pages 115-144

Abstract: Changes in fiscal policy typically entail two kinds of lags: the legislative lag—between when legislation is proposed and when it is signed into law—and the implementation lag—from when a new fiscal law is enacted and when it takes effect. These lags imply that substantial time evolves between when news arrives about fiscal changes and when the changes actually take place—time when households and firms can adjust their behavior. We identify two types of fiscal news—government spending and changes in tax policy. We identify news concerning taxes through the municipal bond market, and news concerning government spending through the Survey of Professional Forecasters. The main contribution of the paper is a mapping from reduced-form estimates of news into a DSGE framework. We argue that news about fiscal policy is a time-varying process. We demonstrate that ignoring the time variation can have important consequences in a conventional macroeconomic model.