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A Unified Framework of Business Cycles and Household Portfolios: Income Risks, Asset Liquidity, and Inequality

Periodic Reporting for period 3 - LiquidHouseCycle (A Unified Framework of Business Cycles and Household Portfolios: Income Risks, Asset Liquidity, and Inequality)

Reporting period: 2020-06-01 to 2021-11-30

Households face large idiosyncratic income risks and use their wealth to self insure. In doing so, they make portfolio choices we can summarize grosso modo as choices between liquid (safe and nominal) and illiquid (risky and real) assets. These choices have the potential to create strong aggregate repercussions as investments in real assets create an immediate demand for goods, while liquid nominal savings only when someone else uses the funds to invest or consume. As a result, portfolio choices are key for economic dynamics and important for the propagation of monetary and fiscal policy. Moreover, household portfolio positions and the liquidity of assets itself become an important determinant of aggregate savings and investment. Yet, they are widely disregarded in standard business cycle models today.

The proposed research, therefore, develops a novel framework that allows us to understand this nexus - a framework that studies business cycles, household portfolios, income risks, and asset liquidity in unison. This novel framework allows us to address a wide array of important macroeconomic questions of our time: how wealth inequality and stabilization policies interact, how monetary policy redistributes, how a housing freeze can create a recession as big as the last one, and finally, why crises are particularly severe in times of high household debt.

To develop this framework, empirical and theoretical work has to go hand in hand: First, I document the historical movements in the distribution of household (and firm) portfolios to understand how and whose portfolio positions change over the cycle and in response to shocks. Second, I document the cyclical movements in asset liquidity. Third, I develop a theoretical framework that allows us to understand the implications of changes in asset liquidity in a setup with incomplete markets and nominal rigidities.
So far, work has concentrated on the methodological underpinnings of the project. The first difficulty in the project is that it involves business cycle models with heterogeneous households that differ along many dimensions. To tackle this issue, I have developed a solution method (together with Ralph Luetticke) [1] which allows us to solve this class of models relatively quickly and represent them by a linear state-space model. The corresponding paper has been resubmitted to a leading field journal after revision.
The advances we made in terms of methodology then allowed to estimate the model with standard Kalman filter techniques using Bayesian maximum likelihood inference. In two papers [2,3], Ralph Luetticke, Benjamin Born, and I then use this technique to estimate a business cycle model with assets of different liquidity and household heterogeneity in wealth and income.

First [2], we ask how business cycle shocks shape income and wealth inequality once we allow for these two central features of the aggregate economy and in how far the modeled feedback from business cycles and inequality change our inference about the driving forces behind the cycle. We find that business cycle shocks explain a large part of the rising wealth inequality – a slowly moving and accumulative variable. This paper is now available as a CEPR discussion paper.

In the second piece of work [3], we focus in more detail on the question of fluctuations in liquidity being drivers of the business cycle. We find they are to some extent and in particular, the long slump and low interest rates after the great recession are driven by an increase in liquidity demand because of high income risks and low liquidity of illiquid assets and by the inability of the financial sector to produce sufficiently liquid assets out of leveraging illiquid ones. We are in the process of preparing a CEPR discussion paper which summarizes our findings.

Still, along the lines of the fifth objective, Lisa Dähne and Lucas ter Steege have analyzed how uncertainty fluctuations and policy shocks affect consumer credit and through this channel the aggregate economy. Results have been summarized in [4].

In addition, I started to work with Pablo Guerron, Jens Herold, Ralph Luetticke, Keith Kuester on the extension of the model economy to cover an overlapping generation structure, in line with the planned work under objective 6.

With regard to the part of the project that documents the business cycle frequency fluctuations in household portfolio compositions, Lisa Daehne and I first concentrated on the development of the methodology for dealing with the higher dimensional filtering problem. The basic approach that we chose is a Kalman filtering one. Analogously to what we have developed in [1] the most promising approach in simulation study is to apply a discrete cosine transform (DCT) to the percentiles of the marginal wealth distribution and their copula to reduce the number of latent state variables that enter the filter. We pre-process the data applying the DCTs and retain that wave-length where the variance of the coefficients is highest.

Just as households, also firms face a portfolio choice problem. One important dimension of this choice lies on the liability side of firms' balance sheets: the portfolio choice between different financing sources. Project [5] studies this problem and its interaction with aggregate fluctuations. The main theoretical innovation of this project is to develop a dynamic model of production, financing, and costly default, in which firms are allowed to choose between the debt of different maturities. By allowing firms to choose between short-term and long-term liabilities, the model is able to match the empirical maturity structure of firm debt. The model is also successful in replicating the sluggish adjustment of firm debt over the business cycle. Joachim Jungherr and Immo Schott have completed a working paper version of this project. A leading field journal has asked the authors to submit a revised version.

[1] Bayer, Christian and Ralph Luetticke (2020): “Solving heterogeneous agent models in discrete time with many idiosyncratic states by perturbation methods”, CEPR Discussion Paper No. 13071-2.
[2] Bayer, Christian, Benjamin Born, and Ralph Luetticke (2020) “Shocks, Frictions, and Inequality in US Business Cycles”, CEPR Discussion Paper No. 14364.
[3] Bayer, Christian, Benjamin Born, and Ralph Luetticke (2020) “Household Portfolio Liquidity and the Business Cycle”, mimeo
[4] Dähne, Lisa and Lucas terSteege (2020): "Income risk and consumer bankruptcy over the business cycle”, mimeo.
[5] Jungherr, Joachim and Immo Schott (2020): „Slow Debt, Deep Recessions“, mimeo
The methodology piece [1] and the two estimation papers [2,3] go substantially beyond what is state of the art. Until the end of the project, I am aiming to extend this work and respond to feedback from presentations and journal submission.

With respect to the overlapping generations extension of our baseline model, the focus lies in understanding the challenges for monetary policy that come with an aging population. A population that lives longer needs to carry more savings for old age and thus the income effects of monetary policy become more important, potentially dampening its capacity for effective monetary policy. In particular, we expect from what we have as preliminary results that aging limits substantially the effectiveness of unconventional monetary policy that works through a commitment to lower rates in the future.

With respect to the project group’s work on firm-level debt portfolios, the main theoretical innovation of [4] is to develop a dynamic model of production, financing, and costly default, in which firms are allowed to choose between the debt of different maturities. As explained above, this slow adjustment of firm debt amplifies and prolongs aggregate fluctuations. This opens up room for welfare-improving stabilization policies. Currently, ongoing work includes studying the role of firm heterogeneity for the mechanisms outlined above.

Finally, the part of the project, where we develop tools to study portfolio distributions of households and firms at business cycle frequency from mixed frequency data can be expected to enhance our understanding of the empirical distribution of household savings rates and firm investment sensitivities based on their portfolio of assets and liabilities. So far, however, we have only developed a prototype for the estimator, which we have tested on simulated data