Private Debt and Idiosyncratic Volatility: A Business Cycle Analysis

I develop and estimate a heterogeneous agents business cycle model featuring aggregate and idiosyncratic shocks on the one hand, collateralized and uncollateralized debt on the other. I use the model to ask two sets of questions: (1) what has caused the large increase in private debt over GDP in the US in the last 30 years? (2) can the model account for some features of the distribution of assets and expenditure across the population? In answer to (1) , I find that most of the increase in private debt can be explained by a rise in the volatility of idiosyncratic shocks (coupled with the unit root behavior of idiosyncratic debt itself). In response to (2) , I find that the model developed can explain not only the trend but also the cyclical behavior of financial assets over time, as well as the dynamics in earnings and consumption inequality which are found in the data. (JEL E31, E32, E44, E52, R21) ∗Email: iacoviel@bc.edu. Address: Department of Economics, Boston College, Chestnut Hill, MA 02467-3806, USA. Debts of households and businesses have since the 1980s jumped out of proportion with real activity. This phenomenon has occurred alongside two separate and striking changes in economic volatility. On the one hand, aggregate volatility has fallen: in the US, the standard deviation of GDP growth has roughly halved between the period 1960-1983 and the period 1983-2002. On the other, cross-sectional risk has risen, as well as earnings inequality between and within income groups. This paper constructs a dynamic general equilibrium model to understand the interaction between the interaction between income volatility, private sector financial balances, and the distribution of consumption. In detail, I construct a three-agents general equilibrium model with idiosyncratic income shocks, aggregate income shocks and financial shocks and ask whether the model helps replicating the historical behavior of financial assets in the US in the last three decades. In particular, I address the following questions: 1. What has caused the rise in debt? Does the increase in borrowing reflect the response of agents to easing liquidity constraints, the reduction in aggregate uncertainty or the rise in individual income volatility? 2. Does the causality running from the primitive shocks to the quantity of debt feeds back into the observed macroeconomic volatility? The key model features are heterogeneity in discount rates, market incompleteness (in the form of liquidity constraints for some of the agents), idiosyncratic income shocks and financial shocks. Three agents populate the economy: they issue bonds, produce a final good using capital and labor and consume durables and non-durables. Agents 1 and 2 only differ in their idiosyncratic productivity. Idiosyncratic shocks give rise to a desire to borrow and lend. Agent 3 also differs in preferences: being more impatient, agent 3 would like to borrow at the equilibrium interest rate. This agent faces borrowing constraints tied to durable values. Changes in the tightness of borrowing constraints affect how much agent 3 borrows from 1 and 2. Using annual data on between and within-group income inequality, I estimate stochastic process for the idiosyncratic income shocks; using data on loan-to-value ratios and productivity, I estimate processes for “financial” shocks and aggregate productivity shocks. Once the shocks are estimated, I simulate the model to test whether the timing of the shocks can explain the patterns in the data, in particular the trend and the cyclical behavior of private debt, and the distribution of consumption and income across the population. The key finding of the paper lies in the ability of a heterogeneous agents model to explain at the same time two salient feature of the data: 1. On the one hand, the model can explain the timing and the magnitude of rise in private debt over GDP. Debt rises when the cross-sectional risk increases and when borrowing constraints become 2 looser. Of the total variation in debt, a large fraction is due to increased idiosyncratic uncertainty, and a smaller one to financial liberalization (time variation in the tightness of the borrowing constraints). 2. On the other, the model can reconcile the sharp increase in income inequality over the last 30 years with a modest rise in consumption inequality over the same time period.