Alternative Matching Method

A growing literature expresses concern regarding the use of propensity score matching (PSM). King & Nielsen (2016) assess the ability of PSM to reduce bias relative other matching methods. They find that PSM may not reduce bias sufficiently, and that in some cases it can increase bias. The poor performance of PSM can arise from the fact that a match on the propensity score does not translate into a match on all covariates. Pruning observation based on propensity score differences thus can exacerbate bias, by increasing imbalance on important covariates. I follow best practices in selecting covariates with a theoretical foundation, using a wider caliper (10%) to minimize the effect of data pruning, and confirming bias reduction by comparing the covariates before and after matching. Nevertheless, it may still be the case that PSM results in poor matching that affects my results. To address this concern, this section tests the hypotheses using a form of coarsened exact matching (CEM).

For each pronouncement, I select the three most important covariates in the propensity score model by comparing their t-stats and partial R2_{s, and partition the sample in to}

quintiles based on each of the selected covariates. I then match each securitizing BHC with a non-securitizing BHC in the same quintile, for each of the three covariates. I perform this matching sequentially based on the importance of the covariates. Similar to the PSM, I perform this matching separately for each pronouncement during the year the pronouncement is issued, and separately for public and private BHCs.

For example, for FAS 125 and public BHCs, I first match each securitizing BHC to a pool of non-securitizing BHCs that are in the same size (i.e., LOGASSET S) quintile.

Table 5.9: Alternative Definition of Composite Mortgage Risk Score

FAS 125 FAS 140 FIN 46(R) FAS 166

I. : DiD for H1 Expected Sign + - - - AV GM RSCORE −0.093 0.156∗ −0.109 0.20∗∗ SAV GM RSCORE −0.007 0.009∗∗ −0.004 0.008∗∗ N HIGHRISK 0.004 0.022 −0.017 0.031∗∗ $HIGHRISK 0.002 0.007 −0.019 0.017 II. QDiD for H2

Expected Sign - + + +

AV GM RSCORE 0.048 −0.233 −0.055 0.090 SAV GM RSCORE 0.009 −0.007 0.015 0.001 N HIGHRISK 0.046 −0.009 −0.060† 0.006 $HIGHRISK 0.037 0.007 −0.046 −0.015 III. QDiD for H3

Expected Sign + - - -

AV GM RSCORE −0.224 0.049 0.022 0.153 SAV GM RSCORE −0.013 0.001 0.001 0.007∗∗ N HIGHRISK −0.010 0.003 0.007 0.037∗ $HIGHRISK −0.007 −0.012 0.019 0.044∗ IV. QDiD for H4

Expected Sign + - - -

AV GM RSCORE −0.185 −0.096 0.022 0.096 SAV GM RSCORE −0.011 0.001 −0.002 0.002 N HIGHRISK −0.032 −0.012 −0.017 0.027† $HIGHRISK −0.031 −0.016 0.013 0.040∗ This table presents the results of the sensitivity analyses when using an alternative defi- nition of composite mortgage risk score (M RSCORE), which relies only on components that consistently pass all validation tests in chapter 4. Similar to the other sensitivity tests, I present only the DiDs for H1 and the QDiDs for H2, H3, and H4. Refer to ta- bles5.2and 5.4for descriptions of DiD and QDiD, respectively. ∗∗∗_, ∗∗_,∗_, † _represent p-values below 1%, 5%, 10%, and 20%, respectively, from the mean tests comparing the corresponding values to zero. All variables are as defined in appendixA.1.

I then restrict the pool to all non-securitizing BHCs that are in the same ROA quintile, and finally to those in the same LEV ERAGE quintile. If multiple matches remain after the three rounds of quintile matches, I choose the non-securitizing BHC in the pool with the smallest difference in the third matching covariate (LEV RAGEin the above example) with the treatment BHC. In all the cases, I find at least one matching non-securitizing BHC after the first and second round of quintile matching. However, in some cases, I find no matches after the third-level quintile matching. In this case, I select the matching BHCs from the pool in the previous step by comparing actual values of the covariate for the third step and choosing the non-securitizing BHC in the second pool with the smallest difference in the third covariate. In the above example, if there are no matches on LEV ERAGE

quintiles, I select a control BHC in the pool of matching non-securitizing BHCs based on the first two quintile (LOGASSET S and ROA) that has the closest LEV ERAGE value to the treatment BHC.

Table5.10presents the results using the alternative matching strategy and the primary two-year test window in panel A, and the alternative matching strategy and the four-year test window in panel B. When using the two-year window, I find little evidence supporting my hypotheses. As in the previous cases in tables 5.2 to 5.6, most of the DiDs or QDiDs are not statistically significant or go in the opposite direction to my prediction. The only exceptions are the positive DiD inN HIGHRISK around FAS 125, the positive QDiD in

AV GM RSCOREaround FAS 166 & 167, and the negativeQDiDinSAV GM RSCORE, all which are significant at 10% (one-tailed). I find mixed evidence when using the four- year test window. Consistent with H1, I find significantly positive DIDs around FAS 125 and significantly negative DIDs around FIN 46 for all risk measures. Contrary to H1, I find positive DiDs around FAS 140 and FAS 166 & 167. The result for H2 are either insignificant or contrary to the prediction. I find evidence supporting H3 around FAS 125 and FAS 140 but not around FIN 46 and FAS 166 & 167. The results for H4 are almost always insignificant or contrary to my prediction. In general, similar to the other sensitivity tests, changing the matching strategy does not seem to significantly change my conclusions.

Table 5.10: Alternative Matching Strategy

Panel A: Two-year Window Panel B: Four-year Window

FAS 125 FAS 140 FIN 46 FAS 166 FAS 125 FAS 140 FIN 46 FAS 166 I. : DiD for H1 Expected Sign + - - - + - - - AV GM RSCORE 0.005 0.011 −0.097 −0.032 0.064∗∗∗ 0.161∗∗∗ −0.029∗∗∗ 0.038∗∗∗ SAV GM RSCORE 0.001 −0.003 0.000 0.000 0.001∗∗∗ 0.0002∗∗∗ −0.002∗∗∗ −0.001∗∗∗ N HIGHRISK 0.021† 0.015 0.000 −0.009 0.014∗∗∗ 0.030∗∗∗ −0.001∗∗∗ 0.015∗∗∗ $HIGHRISK 0.011 0.002 −0.005 0.001 0.007∗∗∗ 0.010∗∗∗ −0.002∗∗∗ 0.017∗∗∗ II. : Q-DiD for H2

Expected Sign - + + + - + + +

AV GM RSCORE 0.303 −0.199 −0.072 0.224† 0.216 −0.045 −0.175 0.203 SAV GM RSCORE 0.014 −0.007† −0.003 0.001 0.015 −0.007 0.000 0.008 N HIGHRISK 0.055 −0.038 −0.058∗ 0.002 0.044∗∗ −0.041∗∗∗ −0.054 0.023 $HIGHRISK 0.107 −0.030 −0.082∗∗ −0.014 0.088 −0.028∗∗ −0.074† 0.007 III. : Q-DiD for H3

Expected Sign + - - - + - - -

AV GM RSCORE 0.077 −0.128 0.129 0.115 0.135† −0.109∗∗ 0.048∗∗ −0.081 SAV GM RSCORE 0.004† 0.000 0.001 0.000 0.002 0.001∗∗∗ −0.002∗∗ 0.004 N HIGHRISK −0.009 0.004 0.051∗∗ 0.024 0.003† −0.014∗ 0.019∗∗∗ 0.026 $HIGHRISK −0.013 0.010 0.034 0.032† 0.002† −0.008∗∗ 0.018∗∗∗ 0.030 IV. : Q-DiD for H4

Expected Sign + - - - + - - -

AV GM RSCORE −0.049 −0.252 −0.050 −0.027 −0.113 −0.100∗ 0.093 −0.075 SAV GM RSCORE 0.000 0.000 −0.002 −0.003† −0.002† −0.003 −0.001 −0.003 N HIGHRISK −0.012 0.002 0.034† 0.020 −0.044 0.022 0.043∗∗ 0.013 $HIGHRISK −0.004 −0.026 0.039† 0.018 −0.038 0.012 0.055∗∗∗ 0.010 This table presents the results obtained when using the alternative matching technique in section5.5.4. Panel A contains the results when the alternative matching method is used with the primary two-year test window, and panel B presents the results when the alternative matching method is used with the alternative four-year test window. I present only the DiDs for H1 and the QDiDs for H2, H3, and H4. Refer to tables5.2and5.4for descriptions of DiD and QDiD, respec-

∗∗∗ ∗∗ ∗ †