The Dynamic Distribution in the Fixed Cost Model: An Analytical Solution

New!! (short paper)

I derive an analytical solution to the Kolmogorov forward equation for a fixed cost model. This is a challenging PDE, because the dynamic distribution depends on the flow of resetting agents, which is endogenously determined by the distribution itself. I show there is a shortcut that allows the flow function to be derived without first finding the entire distribution of agents. This shortcut is also valuable because many aggregate variables can be written in terms of the flow function alone. As an example, I solve the canonical menu cost model. In it, the analytical solution uncovers effects that are inconsistent with existing approximation methods. Specifically, the effects of shocks are both size and history dependent. These nonlinearities are substantial; if a monetary shock is sufficiently large, it can even reverse the sign of the effect on output.

Optimal Policy Without Rational Expectations: A Sufficient Statistic Solution

New!!

How should policymakers respond to mistakes made by agents without rational expectations? I demonstrate in a general setting that the optimal policy is determined by a sufficient statistic: agents' belief distortions. This result is both simple and only semi-structural: in order to calculate policy from the belief distortion, the policymaker does not need to know the whole macroeconomic model. They only need to know how beliefs and policies distort decisions. Crucially, they do not even need to know how expectations are formed; they only need to measure them. Next, I study several examples. In a behavioral RBC model, the optimal policy is to tax capital when agents are overly optimistic about future returns. In a behavioral New Keynesian model, the optimal policy is to raise interest rates when agents misperceive the economy to be running hot.

The Rise of AI Pricing: Trends, Driving Forces, and Implications for Firm Performance

(with Min Fang, Zheng Liu, and Yajie Wang)

New!!

We document key stylized facts about the time-series trends and cross-sectional distributions of AI pricing and study its implications for firm performance, both on average and conditional on monetary policy shocks. We use the universe of online job posting data from Lightcast to measure the adoption of AI pricing. We infer that a firm is adopting AI pricing if it posts a job opening that requires AI-related skills and contains the keyword "pricing". At the aggregate level, the share of AI-pricing jobs in all pricing jobs has increased by more than tenfold since 2010. The increase in AI-pricing jobs has been broad-based, spreading to more industries than other types of AI jobs. At the firm level, larger and more productive firms are more likely to adopt AI pricing. Moreover, firms that adopted AI pricing experienced faster growth in sales, employment, assets, and markups, and their stock returns are also more sensitive to high-frequency monetary policy surprises than non-adopters. We show that these empirical observations can be rationalized by a simple model where a monopolist firm with incomplete information about the demand function invests in AI pricing to acquire information.

Incomplete Information and Investment Inaction

(with Cheng Chen, Min Fang, Takahiro Hattori, and Eugenio Rojas)

New!!

How do investment friction and information frictions interact? We study this question in a stylized continuous time model of heterogeneous firms facing incomplete information and irreversible investment. We analytically characterize how the information friction distorts firms' decision rules and stationary distribution. The two frictions interact in rich and substantial ways. At the firm level, noisier information shrinks a firm's inaction region and reduces the elasticity of investment to productivity. In the aggregate, it increases steady-state capital, increases capital misallocation, and attenuates the effect of productivity shocks on investment. Finally, we test and confirm these predictions using Japanese administrative data that match firms' forecasts to their balance sheets, incomes, and expenditures.

Macroeconomic Models with Incomplete Information and Endogenous Signals

Revise and Resubmit - Journal of Economic Theory

This paper characterizes a general class of macroeconomic models with incomplete information, which feature endogenous signal processes. These models may exhibit multiple or no equilibria, and standard algorithms can fail to converge. I introduce an Information Feedback Regularity condition to impose discipline on these models. If the condition holds, the model has desirable properties: a computable equilibrium must exist, and if stable, it is the globally unique one. I also develop an algorithm to solve the general model and provide computational resources.

Identifying News Shocks from Forecasts

(with Philip Barrett)

Submitted

We propose a method to identify the anticipated components of macroeconomic shocks in a structural VAR. We include empirical forecasts about each time series in the VAR. This introduces enough linear restrictions to identify each structural shock and to further decompose each one into "news" and "surprise" shocks. We estimate a VAR on US time series using forecast data from the SPF, CBO, Federal Reserve, and asset prices. Unanticipated fiscal stimulus and monetary policy shocks have typical effects that match existing evidence. In our news-surprise decomposition, we find that news drives around one quarter of US business cycle volatility. News explains a larger share of the variance due to fiscal shocks than for monetary policy shocks. Finally, we use the news structure of the shocks to estimate counterfactual policy rules, and compare the ability of fiscal and monetary policy to moderate output and inflation. We find that coordinated fiscal and monetary policy are substantially more effective than either tool is individually.

Equilibrium Determinacy with Behavioral Expectations

Submitted

Behavioral expectations affect determinacy in macroeconomic models. Relaxing rational expectations can make models more or less well behaved, depending on the behavioral assumptions. In some cases, multiplicity is created; in other cases, multiplicity is eliminated. Is it possible to tell exactly when there are multiple solutions? Yes: I derive a Behavioral Blanchard-Kahn sufficient condition that ensures a unique equilibrium exists. If and only if this condition or a Sunspot Admissibility condition hold, then a model's solution must be unique. These conditions depend on the spectrum of the behavioral expectation operator. I describe how to check these conditions for an arbitrary behavioral expectation, and illustrate with a large variety of popular types of expectations, heuristics, and information frictions. As an example, I demonstrate that a large class of behavioral expectations imply a unique solution to the New Keynesian model with an interest rate peg, including all strictly backwards-looking heuristics. Another class of expectations imply that asset prices exhibit non-fundamental volatility in a standard model.

Firestorm: Multiplicity in Models with Full Information

Submitted

FIRE models can feature multiple equilibria when causality is relaxed. I demonstrate how self-fulfilling equilibria arise and explore their implications in asset pricing and business cycle models, arguing that the standard FIRE framework may need to be re-evaluated.

Household Consumption and Dispersed Information

(with Eugenio Rojas)

Journal of Monetary Economics (2024)

We examine how dispersed information affects household consumption in response to aggregate income shocks in a small open economy. Our model explains two phenomena: excess volatility in consumption and low correlation between income and consumption elasticities. Using survey data, we corroborate our model’s mechanism.

Shocks to Inflation Expectations

(with Philip Barrett)

Review of Economic Dynamics (2024)

The consensus among central bankers is that higher inflation expectations can drive up actual inflation. We assess this by devising a novel method for identifying shocks to inflation expectations, estimating a semi-structural VAR where an expectation shock is identified as that which causes measured forecasts to diverge from the rational expectation. Using data for the United States, we find that a positive inflation expectation shock is contractionary and deflationary: output, inflation, and interest rates all fall. These results are inconsistent with the standard New Keynesian model, which predicts inflation and interest rate hikes. We discuss possible resolutions to this puzzle.

The Rise and Fall of Armies

Macroeconomic Dynamics (2024)

For a thousand years, income growth was associated with a rising military employment share. But this share peaked in the early 20th century, after which military employment shares fell with income growth. I argue that rising military shares were driven by structural change out of agriculture, and the recent declines are driven by substitution from soldiers towards military goods. I document evidence for this substitution effect: as countries' incomes rise, the ratio of their military expenditure share to their military employment share rises too. I introduce a game theoretic model of growth and warfare that reproduces the time series patterns of military expenditure and employment. The model also correctly predicts the cross-sectional pattern, that military employment and expenditure shares are decreasing in income during wars. Finally, I show that faster economic growth can reduce military expenditure in the long run.

Moderating Noise-Driven Macroeconomic Fluctuations Under Dispersed Information

Journal of Economic Dynamics and Control (2023)

We study the effects of aggregate income shocks in a small open economy heterogeneous agent model. By introducing a standard information friction, we are able to explain two patterns of small economies experiencing large income changes: (1) excess volatility in consumption and (2) household consumption elasticities that have low correlation with income. With a standard dispersed information structure, households cannot distinguish aggregate income shocks from idiosyncratic ones. Therefore their consumption responds excessively to aggregate income changes, which they forecast as likely to be more persistent than they would if they had full information. We demonstrate that this effect occurs at all points in the income distribution, lowering the correlation of the consumption elasticity with income. Finally, we corroborate our central mechanism using survey data on household expectations of their future income.

Urbanization, Long-Run Growth, and the Demographic Transition

Journal of Demographic Economics (2021)

Advanced economies undergo three transitions during their development: 1. They transition from a rural to an urban economy. 2. They transition from low income growth to high income growth. 3. Their demographics transition from initially high fertility and mortality rates to low modern levels. The timings of these transitions are correlated in the historical development of most advanced economies. I unify complementary theories of the transitions into a nonlinear model of endogenous long run economic and demographic change. The model reproduces the timing and magnitude of the transitions. Because the model captures the interactions between all three transitions, it is able to explain three additional empirical patterns: a declining urban-rural wage gap, a declining rural-urban family size ratio, and most surprisingly, that early urbanization slows development. This third prediction distinguishes the model from other theories of long-run growth, so I test and confirm it in cross-country data.

Behavioral Expectations Equilibrium Toolkit (BEET)

In Progress

The Behavioral Expectations Equilibrium Toolkit (BEET) is a toolkit for solving stochastic dynamic macroeconomic models with behavioral expectations in MATLAB. BEET itself is not a model-solver; for that task, it uses existing methods. Rather, BEET is a wrapper that transforms a behavioral expectations model into one that can be solved using tools designed for rational expectations.