Heterogeneous Agent Model Research Articles

Computing Quantiles of Functions of the Agent Distribution Using t-Digests

We introduce t-Digests as an accurate and computationally efficient way to calculate the quantiles of functions of the agent distribution for models in which the full distribution is too large to work with directly; e.g., to calculate the Top 1% of the wealth distribution. When it is possible to fit the entire agent distribution (and a function evaluation on it) into memory, the quantiles can easily be calculated directly. Evaluating a function on the agent distribution can be done much faster using a GPU, however this frequently introduces a memory bottleneck as GPU memory is typically an order of magnitude smaller than CPU memory. For Heterogeneous Agent models the full distribution of agents may fit in CPU memory, but not in GPU memory. We partition the agent distribution into (non-overlapping) subspaces and because these subspaces are much smaller we can fit the subspaces in GPU memory one at a time. For each subspace we then evaluate the function and calculate a t-Digest. t-Digests are a form of data structure that are fast to compute, require less memory, and provide high accuracy for the quantiles of the distribution; t-Digests are a ’sketch’ of the subspace. Having computed and stored a t-Digest for each subspace we can then merge them to get a t-Digest for the full agent distribution. The resulting t-Digest is an accurate representation of the quantiles and can form the basis of Lorenz Curves as well as many other distributional and inequality statistics of interest in Economics.

Optimal policies with heterogeneous agents: Truncation and transitions

We compare two approaches in their ability to solve for optimal Ramsey policies in heterogeneous-agent models, considering the optimal provision of a public good. First, the “transition” approach makes the problem tractable by assuming a constant path for the planner's instruments. Second, the “truncation” approach uses a Lagrangian technique, solving the Ramsey problem of a finite state space model that approximates the full model. The truncation approach is shown to compute quantitatively accurate estimates of the actual values of the planner's instruments, whereas a time-inconsistency issue is found to affect the transition approach.

On the optimal reform of income support for single parents

We characterize the optimal reform of U.S. income support for low-income single parents using a life-cycle heterogeneous agent model with idiosyncratic risk and incomplete asset markets. We use the U.S. tax-transfer system as the benchmark policy and a sample of single mothers drawn from the CPS to assess reforms that maximize average expected utility among single mothers-to-be. When policy cannot be tagged by the age of the children, the optimal reform calls for an increase in out-of-work income support by about 15 percent, and a decrease in earnings subsidies to low-wage workers by roughly 50 percent. This reform delivers substantial welfare gains. Tagging policy by the age of the children makes the government’s trade-off between providing insurance to single mothers with children of pre-school age, on the one hand, and providing work incentives to those with school-age children, on the other hand, more favorable, thus increasing their scope for smoothing marginal utility throughout the life cycle. With tagging, mothers of pre-school age children get a substantial increase in out-of-work income support and no earnings subsidies. Tagging brings additional welfare gains.

A continuous heterogeneous agent model for multi-asset pricing and portfolio construction under market matching friction

We propose a novel continuous Heterogeneous Agent Model (HAM) that applies to the general n>1 risky assets. In this model, every heterogeneous investor is identified with the continuous variables reflecting their personal characteristics. The heterogeneity of the market is captured by the distribution of these variables. By introducing market friction via a matching-based pricing mechanism, we derive a pricing equation from market clearing. The equation extends the classical CAPM and specifies how the bounded rationality and heterogeneity of investors can drive the actual price of risky assets away from their CAPM price. A system of ordinary (stochastic) differential equations are derived to govern the evolution of the total wealth and market value of risky assets held by the entire market (individual investors). From the equation system, a rolling-window-based maximum likelihood algorithm is developed to calibrate the model, which turn our HAM to a forecast tool for stock returns and an adaptive adjustment strategy for portfolio construction. This bridges the theoretical study on HAMs with the empirical studies of asset pricing and portfolio theory. We apply this tool to the Chinese A-share market and make a comparative analysis on its performance. The results demonstrate that compared to the classical forecast approaches in literature, our HAM has the advantage in identifying the tail risk in real market, which results in a more profitable portfolio in a variety of different investment horizons.

Block-recursive equilibria in heterogeneous-agent models

Equilibrium models with heterogeneous agents and aggregate uncertainty are difficult to analyze since policy functions and market prices usually depend on the cross-sectional distribution over agents' state variables which is a high-dimensional object. This paper considers a general model framework in which this curse of dimensionality does not arise because equilibrium prices are determined by market entry conditions and are independent of the cross-sectional distribution (block-recursive equilibrium). The paper first establishes existence and ergodic theorems which are useful for the theoretical analysis and numerical implementation of block-recursive equilibria. Then these results are applied to models of firm dynamics with competitive or frictional input markets and to incomplete-market economies with endogenous asset market participation.

El canal de renta real y las depreciaciones contractivas en un modelo de agentes heterogéneos para América Latina

Rationale In Latin America, it is not unusual to see exchange rate depreciations in excess of 20% in a single year. Although depreciation tends to stimulate a country’s net external demand, it does not always lead to increased output. It is worth understanding which channels may explain this outcome. Takeaways •In conventional macroeconomic theory, exchange rate depreciations have expansionary effects on economic activity. However, the empirical evidence shows that, in the case of emerging market economies, devaluing the exchange rate may cause output to contract. •One channel that explains this evidence, known as the real income channel, operates through the erosion of purchasing power as a result of rising prices for imported goods, which can lead to a fall in the real consumption of households with limited access to financial markets. •This article discusses a heterogeneous agent model calibrated for the main Latin American economies that allows the importance of this channel to be measured. The results show that this channel may have a sizable macroeconomic impact, particularly on economies more open to international trade.

Coexisting Attractors in a Heterogeneous Agent Model in Discrete Time

In this paper, the discrete-time version of a continuous-time model with fundamentalists and momentum traders is presented. Our aim consists of studying the impact of cross-sectional momentum traders on the dynamics of the model. To this end, the continuous-time deterministic skeleton of the benchmark model is transformed using sophisticated discretization techniques. It is worth noting that the model does not always maintain the same characteristics after moving from continuous to discrete time. In spite of this, our discrete-time system preserves the dynamic properties of the continuous-time original model. Moreover, heterogeneity introduces an important non-linearity into the market dynamics, causing our deterministic financial model to generate erratic time series similar to the patterns observed in real markets. In particular, we show that the time series originated by the perturbed deterministic system capture some of the main stylized facts of the U.S. financial market. Converting the benchmark model from continuous time to discrete time allows the use of financial data available in discrete time.

Unemployment insurance design with repeated choices

Abstract This article characterizes the relation between the equilibrium unemployment insurance replacement rate and the frequency of its political choice. We first use a tractable analytical model to show how insurance, incentive, and redistribution effects interact at the equilibrium. We then examine a fully repeated choices equilibrium in a quantitative heterogeneous agents model and show that unemployment persistence, whether a policy is announced first or not, and the type of the political process are key determinants of the relation between the equilibrium replacement rate and the frequency of its choice. In a utilitarian welfare context, we find that the equilibrium replacement rate is higher if the policy is chosen more frequently but this relation is reversed in a median voter context.

The Matching Multiplier and the Amplification of Recessions

This paper shows that the unequal incidence of recessions in the labor market amplifies aggregate shocks. Using administrative data from the United States, I document a positive covariance between workers' marginal propensities to consume (MPCs) and their elasticities of earnings to GDP, which is a key moment for a new class of heterogeneous-agent models. I define the matching multiplier as the increase in the multiplier stemming from this matching of high MPC workers to more cyclical jobs. I show that this covariance is large enough to increase the aggregate MPC by 20 percent over an equal exposure benchmark. (JEL E21, E23, E24, E32)

The heterogeneous welfare effects of business cycles

This study investigates the welfare effects of business cycle fluctuations from a distributional perspective. To this end, we develop a quantitative heterogeneous-agent model which incorporates market incompleteness and non-convexity into the mapping from the time devoted to work to labor services. In this setup, households can insure against aggregate uncertainty using labor and savings and have substantially different labor supply elasticities. We find that the welfare effects are heterogeneous across households, with wealth-rich households benefiting most from business cycles. Wealth-rich households enjoy business cycles more than wealth-poor households, because they experience less volatile consumption and can enjoy higher average income through reallocating savings intertemporally.

Financial Frictions and the Wealth Distribution

We postulate a continuous‐time heterogeneous agent model with a financial sector and households to study the nonlinear linkages between aggregate and financial variables. In our model, the interaction between the supply of bonds by the financial sector and the precautionary demand for bonds by households produces significantendogenous aggregate risk. This risk makes the economy transition between a high‐leverage region and a low‐leverage region, which, in turn, creates state dependence in impulse responses: the same shock starting from the high‐leverage region gets propagated and amplified more than when the shock arrives when leverage is low. State dependence in impulse responses generates a time‐varying aggregate precautionary savings motive that, by moving the risk‐free rate, justifies the leverage level of the financial sector in each region. Finally, we illustrate the usefulness of neutral networks to solve for the nonlinear perceived law of motion of the model, and the importance of household heterogeneity in driving its quantitative properties.

Household Borrowing and MPCs in Heterogeneous-Agent Models

Household Borrowing and MPCs in Heterogeneous-Agent Models

Consumption Heterogeneity: Micro Drivers and Macro Implications

We document heterogeneity in the marginal propensity to consume (MPC) across household characteristics relevant to understanding heterogeneous agent models and monetary policy transmission. We find a strong negative relationship between household liquid wealth and MPC. We show that household liquid wealth predicts MPC closely for every other household characteristic we look at. We use a new empirical method that overcomes sources of bias found in the existing literature, along with administrative data from Denmark that allow us to identify heterogeneous behavior. We use our results to analyze monetary policy transmission mechanisms in both Denmark and the United States. (JEL D12, D31, E21, E43, E52, G51)

A Continuous-Time Utility Maximization Problem with Borrowing Constraints in Macroeconomic Heterogeneous Agent Models: A Case of Regular Controls under Markov Chain Uncertainty

A Continuous-Time Utility Maximization Problem with Borrowing Constraints in Macroeconomic Heterogeneous Agent Models: A Case of Regular Controls under Markov Chain Uncertainty

Full‐information estimation of heterogeneous agent models using macro and micro data

We develop a generally applicable full‐information inference method for heterogeneous agent models, combining aggregate time series data and repeated cross‐sections of micro data. To handle unobserved aggregate state variables that affect cross‐sectional distributions, we compute a numerically unbiased estimate of the model‐implied likelihood function. Employing the likelihood estimate in a Markov Chain Monte Carlo algorithm, we obtain fully efficient and valid Bayesian inference. Evaluation of the micro part of the likelihood lends itself naturally to parallel computing. Numerical illustrations in models with heterogeneous households or firms demonstrate that the proposed full‐information method substantially sharpens inference relative to using only macro data, and for some parameters micro data is essential for identification.

A Perturbational Approach for Approximating Heterogeneous Agent Models

A Perturbational Approach for Approximating Heterogeneous Agent Models

Welfare and Spending Effects of Consumption Stimulus Policies

Using a heterogeneous agent model calibrated to match measured spending dynamics over four years following an income shock (Fagereng, Holm, and Natvik (2021)), we assess the effectiveness of three fiscal stimulus policies employed during recent recessions. Unemployment insurance (UI) extensions are the clear “bang for the buck” winner, especially when effectiveness is measured in utility terms. Stimulus checks are second best and have the advantage (over UI) of being scalable to any desired size. A temporary (two-year) cut in the rate of wage taxation is considerably less effective than the other policies and has negligible effects in the version of our model without a multiplier.

Solving Heterogeneous Agent Models with the Master Equation

Solving Heterogeneous Agent Models with the Master Equation

Stuck at home: Housing demand during the COVID-19 pandemic

The COVID-19 pandemic induced an increase in both the amount of time that households spend at home and the share of expenditures allocated to at-home consumption. These changes coincided with a period of rapidly rising house prices. We interpret these facts as the result of stay-at-home shocks that increase demand for goods consumed at home as well as the homes that those goods are consumed in. We first test the hypothesis empirically using US cross-county panel data and instrumental variables regressions. We find that counties where households spent more time at home experienced faster increases in house prices. We then study various pandemic shocks using a heterogeneous agent model with general equilibrium in housing markets. Stay-at-home shocks explain around half of the increase in model house prices in 2020. Lower mortgage rates explain around one third of the price rise, while unemployment shocks and fiscal stimulus have relatively small effects on house prices. We find that young households and first-time home buyers account for much of the increase in housing demand during the pandemic, but they are largely crowded out of the housing market by the equilibrium rise in house prices.

Saving at the top and the long-run relationship between wealth and income inequality

ABSTRACT This paper analyzes the joint long-run evolution of wealth and income inequality. We find that top wealth and income shares were cointegrated over the past century in France and the US. We rationalize this finding in two macroeconomic heterogeneous agent models featuring growth and incomplete markets, respectively. In both frameworks, the co-movement of top wealth and income shares is determined by the relative saving rate at the top, i.e. the ratio of the saving rate of rich individuals to the aggregate saving rate. Our empirical results suggest that relative saving rates at the top have been fairly stable over time, thus explaining the observed tight co-movement between top wealth and income shares over the past century.