#### A Model Of Australia’s Household Leverage: PIMCO

**Abstract**

In a recent Viewpoint, we looked at the potential implications of rising household debt in Australia for both monetary policy and real activity. Economic theory tells us that unanticipated increases in household wealth lead to increased consumption, known as the “wealth effect”. Increases in asset prices can be caused by factors such as higher wage expectations, profits or rental yields, or alternatively, irrational exuberance. So, the key questions are: In which category do recent Australian house price increases belong? Is there a housing bubble in Australia, and how would households react to a potential decline in wealth? By many measures, like the rent-to-price ratio, Australian homes look expensive. Will Australian households deleverage as prices go down as they levered up when the going was good?

### A Model Of Australia’s Household Leverage – Introduction

While econometric models will not provide a definitive answer to these questions, the U.S. experience – both leading into the financial crisis of 2008 and the deleveraging since then – is a good laboratory. Following the global financial crisis of 2008, household deleveraging acted as a significant headwind to the U.S. economic recovery. This deleveraging happened despite zero policy rates and has compelled many researchers to focus on what drives consumer debt ratios (Eggertsson and Krugman, 2012; Guerrieri and Lorenzoni, 2011). For example, the European Central Bank (Albuquerque, Baumann and Krustev, 2014) modelled the U.S. household equilibrium debt-to-income ratio in a panel-error correction framework and identified deleveraging as a “significant headwind to consumption and activity in recent years”.

Even before the 2008 financial crisis, U.S. household leverage was of interest to policymakers and researchers. Many analysts were questioning whether higher debt levels had increased the sensitivity of consumer spending to asset price shocks. In their 2007 Federal Reserve Board discussion paper, “The Rise in U.S. Household Indebtedness: Causes and Consequences”, Karen E. Dynan and Donald L. Kohn identified rising U.S. house prices as a primary source of the continued increase in the debt-to-income ratio. They flagged the possibility of large and negative consequences for the macro economy given unexpected shocks to asset prices in a highly levered environment.

Given the impact household de-leveraging had on the U.S. economy during and after the global financial crisis, it is important to also consider what drives the Australian debt-to-income ratio. We modelled both U.S. and Australian leverage (the household debt-to-income ratio) and found that the correlations between wealth and increases in aggregate leverage in the two countries are remarkably similar. If anything, mortgage finance in Australia has even fewer frictions than in the U.S. Thus, Australian households respond faster to increases in wealth, and the sensitivity of leverage to interest rates is higher.

### Method, model and data

We fit a vector autoregressive model with exogenous variables (VARX) to understand the time series dynamics in the debt-to-income ratio. We modelled the U.S. and Australian debt-to-income ratio with:

y(t) and z(t) are zero-mean, wide-sense stationary time series of dimension n and q , respectively, where y(t) = {y1(t), y2(t),…,yn(t)}’ are nx1 observations on the endogenous variables at time t and the z(t) are q x1 observations on the exogenous variables at time t.v(t) is an nx1 stationary vector process.

We employed a model-fitting technique known as subset autoregression with exogenous variables to model the debt-to-income ratio. Full order VARX models are modified to arrive at subset VARX (SARX). A SARX is a special form of the more basic autoregression model that allows us to capture the dynamic behavior present in the data. This approach of first identifying the full model in the VARX avoids over-identifying restrictions and accidentally excluding important variables especially given the lack of strong economic theory on how restrictions should be imposed. We take a more data-driven approach given our limited a priori knowledge of what restrictions should be imposed. When using SARX models, the data drive the model while identifying both the short-run and long-run influences of variables on each other.

To account for model uncertainty, we used an informationtheoretic approach based on AIC (Akaike Information Criterion) likelihood estimates and identified the most likely models given the data set. The model likelihoods provide a measure of relative importance that allows us to rank models and variables and calculate average coefficients across models. AIC likelihoods indicate the probability that the model is the best among the whole set of candidate models. For instance, an Akaike likelihood of 0.90 for a single model tells us that it has a 90% chance of being the best one among the candidate models.

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