RDP 2021-07: Macroprudential Limits on Mortgage Products: The Australian Experience 4. Empirical Strategy
July 2021
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We identify policy effects with 2 types of panel data regressions. The first detects the average policy effect across all banks in the sample that is used. We supplement these estimates with falsification (i.e. placebo) tests that gauge the likelihood of falsely identifying policy effects. The second type detects policy effects that systematically differ across banks. The second type has a more robust identification strategy, so it provides a more definitive test of whether the policies caused a change in banks' behaviour. However, aggregate policy effects are less clear with this specification, hence the use of 2 separate strategies. Note that none of the specifications give more weight to banks with larger portfolios, so the outcomes should not be interpreted as aggregated effects on the banking system. (But that interpretation would be close for samples containing only the 4 large banks.) To understand aggregated effects we report aggregate time series throughout various parts of the paper.
4.1 Average effect regressions
The average effect regressions estimate the policy effects using (bank invariant) indicator variables for the 4 quarters after the policy announcement (𝕀(policy )_{t–1,…, t–4} ). Control variables remove other influences, leaving the indicator variables to capture any ‘abnormal behaviour’ in the policy period that is common across all banks in the sample. The controls include lagged dependent variables, other bank-level control variables, and system-level macroeconomic control variables.
The average effect regression equation is
In Equation (1), the lagged dependent variables are instrumented using the Arellano–Bond procedure. This involves first differencing all variables (as per Equation (1)). Bank fixed effects are therefore not included. The macro controls are GDP growth, housing price growth and the set of seasonal controls.^{[10]} The bank controls are the capital ratio and the deposit funding ratio, both lagged once to address reverse causality.
The average effect specification for mortgage interest rates is
where ${\alpha}_{b}$ is a set of bank-level fixed effects. The bank and macro controls are the same as in Equation (1), except the first 2 lags of the quarter-end change in the cash rate are added as macro controls, given that the cash rate is a very strong determinant of mortgage rates. Lagged dependent variables are included in Equation (1) but not in Equation (2), because mortgage rate changes are much less persistent than commitments growth.
The average effect regressions are repeated for mortgage types m not targeted by the policies. These non-targeted mortgages serve as a quasi control group. For example, if a decline in credit that is detected by 𝕀(policy) is instead spuriously driven by macroeconomic influences, this should be revealed by a negative policy effect in the non-targeted loan types. It is not appropriate to use non-targeted mortgages as an explicit control group in a differences-in-differences specification. This would lead to overstated policy effect estimates if banks substituted from targeted to non-targeted mortgages. However, we are still interested in the effects of the policy on non-targeted mortgages. So we examine them in separate estimations, but without including them as explicit controls in the same equation.
The main threat to identification is the possibility of system-wide influences that coincidentally affect (only) targeted mortgages when the policies are implemented, and that are not captured by the control variables. We address this in 2 ways. First, we run placebo regressions akin to the falsification tests suggested by Roberts and Whited (2013). In the placebo regressions, the 4 𝕀(policy) variables are swapped for a ‘placebo’ indicator variable that instead indicates a single non-policy quarter, to assess whether a false positive effect shows up in that quarter. This is repeated for all non-policy quarters from 2010 onward. If few of these placebo indicators are significant, the likelihood of coincidental factors causing a falsely detected policy effect is low. Due to the multiple testing problem (e.g. Bender and Lange 2001), these placebo tests warrant conservative significance thresholds, which we acknowledge informally. We also address the coincidental-influences identification threat with a qualitative analysis of economic trends that could have potentially generated false policy effects.
The average effect regressions are each run on multiple samples. One sample comprises only the 4 large banks, another sample comprises only mid-sized banks and a third sample comprises all banks.
4.2 Heterogeneous effect regressions
The heterogeneous effect regressions identify policy effects that differ across banks, in line with how close those banks are to satisfying the policy limits. Intuitively, banks above the limit should be more intensely ‘treated’ by the policy than banks below. Focusing on these differences in reactions across banks allows including fixed effects for each quarter, which in the average effect regressions would be collinear with 𝕀(policy). Quarter fixed effects remove all system-wide influences on the dependent variables, and give a stronger case for identification of the policy effects.
The heterogeneous policy effects regression equation is
Y is either CommitGrth or $\text{\Delta}$IntRate, and Treatment is a measure of how far bank b is above the limit. Treatment is lagged twice to remove reverse causality from mechanical dependence on commitments growth.^{[11]} That is, distance from the limit in a given period likely depends on commitments in that period, and therefore on commitments growth in the next period (because growth rates depend on the level in the last period). Bank and quarter fixed effects are represented by ${\alpha}_{b}$ and ${\alpha}_{t}$. The bank controls are the capital ratio and deposit funding ratio.
Footnotes
Including the cash rate as a control has little effect on the policy effect estimates. We do not include it because its true effect on commitments is likely to be slow and cumulative, and its coefficients indicate that it is picking up effects not caused by the cash rate. [10]
Treatment is chosen as a rolling measure, rather than fixed at the time of the policy announcement. This is because if a bank moves to below the benchmark soon after the policy announcement (for example), then it is unlikely to still behave as though it is above the benchmark. [11]