Tang Associate Professor
Economics Department
William & Mary

Nathaniel A. Throckmorton
Recent Working Papers

A Simple Explanation of Countercyclical Uncertainty
with Joshua Bernstein, Mike Plante, and Alex Richter
[Revised: October 2022][FRB Dallas Working Paper 2109]

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.

The Matching Function and Nonlinear Business Cycles
with Joshua Bernstein and Alex Richter
[Revised: July 2022][FRB Dallas Working Paper 2201]

The Cobb-Douglas matching function is ubiquitous in labor search and matching models, even though it imposes a constant matching elasticity that is inconsistent with recent empirical evidence. To examine the implications of this discrepancy, this paper first uses a general constant returns to scale matching function to derive conditions that determine how the cyclicality of the matching elasticity amplifies or dampens nonlinear labor market dynamics. It then shows that modest cyclical variation in the matching elasticity, in line with the recent estimates, generates large differences in higher-order moments and has significant effects on optimal policy.

Published Papers

Valuation Risk Revalued
with Oliver de Groot and Alex Richter
Quantitative Economics, May 2022, Volume 13, Pages 723-759
[FRB Dallas Working Paper 1808]

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 violates several desirable properties of recursive preferences because the weights in the Epstein-Zin 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.

Complementarity and Macroeconomic Uncertainty
with Tyler Atkinson, Mike Plante, and Alex Richter
Review of Economic Dynamics, April 2022, Volume 44, Pages 225-243
[FRB Dallas Working Paper 2009, Dallas Fed Economics]

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.

Cyclical Net Entry and Exit
with Joshua Bernstein and Alex Richter
European Economic Review, July 2021, Volume 136
[FRB Dallas Working Paper 2018, Dallas Fed Economics]

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.

The Zero Lower Bound and Estimation Accuracy” [Slides]
with Tyler Atkinson and Alex Richter
Journal of Monetary Economics, November 2020, Volume 115, Pages 249-264
[Online Appendix, FRB Dallas Working Paper 1804, W&M News, UT TACC News]

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” [Slides]
with Oliver de Groot and Alex Richter
Econometrica, July 2018, Volume 86, Pages 1513-1526
[Online Appendix, Code, FRB Dallas Working Paper 1706]

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” [Slides]
with Mike Plante and Alex Richter
Economic Journal, June 2018, Volume 128, Pages 1730-1757
[Online Appendix, FRB Dallas Working Paper 1405, WSJ: Real Time Economics, Economic Letter, LSE Business Review]

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” [Slides]
with Benjamin Keen and Alex Richter
Economic Inquiry, October 2017, Volume 55, Pages 1593-1624
[FRB Dallas Working Paper 1612, WSJ: Real Time Economics, Chicago Booth Review]

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?
with Alex Richter
Economics Letters, December 2016, Volume 149, Pages 44-48

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” [Slides]
with Alex Richter
European Economic Review, August 2015, Volume 78, Pages 76-96

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” [Slides]
with William Gavin, Benjamin Keen, and Alex Richter
Journal of Economic Dynamics and Control, June 2015, Volume 55, Pages 14-38

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.

The Zero Lower Bound: Frequency, Duration, and Numerical Convergence” [Slides]
with Alex Richter
The B.E. Journal of Macroeconomics, January 2015, Volume 15, Pages 157-182

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” [Slides]
with Alex Richter and Todd Walker (Supported by NSF Grant SES 096221)
Computational Economics, December 2014, Volume 44, Pages 445-476
[Code, Toolbox]

Policy function iteration methods for solving and analyzing dynamic stochastic general equilibrium models are powerful from a theoretical and computational perspective. Despite obvious theoretical appeal, significant startup costs and a reliance on grid-based methods 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. Within the class of policy function iteration methods, we advocate using time iteration with linear interpolation. 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 on the nominal interest rate to highlight the attractiveness of our methodology. We compare our advocated approach to other familiar iteration and approximation methods, highlighting the tradeoffs between accuracy, speed and robustness.

Other Working Papers

The Business Cycle Mechanics of Search and Matching Models
with Joshua Bernstein and Alex Richter
[August 2020][FRB Dallas Working Paper 2026]

This paper provides new insights into the business cycle mechanics of search and matching models. We develop a novel identification scheme based on the matching elasticity that allows these models to perfectly match a range of labor market moments. Our estimated linear model also matches several non-targeted moments including the Beveridge curve and the decomposition of inflows and outflows of unemployment. A structural decomposition reveals job separation rate shocks explain 40% of unemployment volatility. The nonlinear version of our model generates state-dependent dynamics that produce empirically consistent fluctuations in output growth uncertainty, 37% of which stem from separation rate shocks.

COVID-19: A View from the Labor Market
with Joshua Bernstein and Alex Richter
[April 2020][FRB Dallas Working Paper 2010, Dallas Fed Economics, W&M News]

This paper examines the response of the U.S. labor market to a large and persistent job separation rate shock, motivated by the ongoing economic effects of the COVID-19 pandemic. We use nonlinear methods to analytically and numerically characterize the responses of vacancy creation and unemployment. Vacancies decline in response to the shock when firms expect persistent job destruction and the number of unemployed searching for work is low. Quantitatively, under our baseline forecast the unemployment rate peaks at 19.7%, 2 months after the shock, and takes 1 year to return to 5%. Relative to a scenario without the shock, unemployment uncertainty rises by a factor of 11. Nonlinear methods are crucial. In the linear economy, the unemployment rate "only" rises to 9.2%, vacancies increase, and uncertainty is unaffected. In both cases, the severity of the COVID-19 shock depends on the separation rate persistence.

A New Way to Quantify the Effect of Uncertainty
with Alex Richter
[May 2018][FRB Dallas Working Paper 1705]

This paper develops a new way to quantify the effects of aggregate uncertainty that accounts for exogenous and endogenous sources. First, we use Bayesian methods to estimate a nonlinear New Keynesian model with stochastic volatility and a zero lower bound constraint on the nominal interest rate. We discipline the model by matching data on uncertainty, in addition to common macro time series. Second, we use the Euler equation to decompose output into expected output and the expected variance and skewness of output. We then filter a time series for each term. Our method captures the effects of higher-order moments over horizons beyond 1 quarter by recursively decomposing expected output. Over a 1-quarter horizon, output uncertainty reduced output less than 0.01% every quarter, similar to volatility shocks in our model. Over horizons that remove the influence of expected output, output uncertainty on average reduced output 0.06% and the peak effect was 0.15% during the Great Recession, similar to structural VAR estimates. Other higher-order moments had much smaller effects on output.

Are Nonlinear Methods Necessary at the Zero Lower Bound?
with Alex Richter
[February 2017][FRB Dallas Working Paper 1606]

This paper examines the importance of using nonlinear methods to capture the zero lower bound (ZLB) on the Fed's policy rate. While it may seem obvious to impose the ZLB, ex-ante it is unclear how large of an effect the ZLB has on parameter estimates, since it was only hit once in recent history. The parameters and marginal likelihoods from a linear and nonlinear model are similar, but the linear model does not fit the data as well and predicts counterfactually large policy shocks when the Fed is constrained. A quasi-linear model performs better than a linear model but it still generates less volatility at the ZLB and is not as conducive to estimation. When we add a banking sector to create an interest rate spread, the ZLB is even more important.

Income Inequality and Current Account Imbalances
with Mike Kumhof, Claire Lebarz, Romain Ranciere, and Alex Richter
[December 2012][IMF F&D Article, IMF Working Paper No. 12/8]

Econometric evidence shows that when higher income inequality and financial liberalization are added to a set of conventional explanatory variables, they predict significantly larger current account deficits in a cross-section of advanced economies. To study this mechanism, we develop a DSGE model where investors' income share increases at the expense of workers, and where workers respond by obtaining loans from domestic and foreign investors. This supports aggregate demand but generates current account deficits, especially if domestic financial markets are simultaneously liberalized. In emerging markets, because domestic workers cannot borrow, investors deploy their surplus funds abroad, leading to current account surpluses.