Principal Component Analysis

In the main section, I used the standardized value of the capital stringency index as the depen- dent variable. Therefore, I implicitly assumed that all questions that enter into the calculation of the index have equal waits in determining the stringency of bank capital regulation. How- ever, some of the regulation dimensions measured by the index can more easily be adopted by regulators and vary less across countries, whereas implementation of some other components could be more challenging for regulators, and hence vary to a larger extent across countries. For example, on average 99% of countries answered Question 3.1.1 (“Is the minimum capital ratio risk weighted in line with the Basle guidelines?”) in Table 2.1 as “Yes”, whereas only 46% of them did so for Question 3.3 (“Does the minimum ratio vary as a function of market risk?”).

In that regard, one may prefer an index that attaches greater weights to components of regulation that vary more across countries, and smaller weights to components vary less across countries. Principal Component Analysis (PCA) exactly does that. Principal component analysis is an orthogonal transformation of (possibly) correlated variables, the index compo- nents here, into a number of linearly uncorrelated variables, calledprincipal components. This transformation is defined in such a way that the first principal component is the “most infor- mative”, which means, it accounts for as much of the variability in the data as possible. The first principal component in this case explains about 42% of the variation in the index data. I estimate both the static and dynamic models using the first principal component of the capital stringency index as the dependent variable. The results of the static model is presented in Table 2.5. Again, my focus in on the fixed effects regression, but the pooled OLS estimation results are presented for comparison. The results do not change qualitatively compared to the results in Table 2.3 where the standardized value of the index is used. The fixed effects model

Table 2.5: Results for the Statics Model with Principal Component Analysis

(1) (2) (3)

VARIABLES Pooled OLS Pooled OLS Fixed Effects

GDP growth -0.072* -0.076** -0.091** (0.058) (0.048) (0.012) Government-owned banks -0.006 -0.005 -0.029*** (0.413) (0.463) (0.008) Concentration ratio -0.003 -0.004 -0.031*** (0.545) (0.452) (0.009) Legal origin UK -0.149 (0.830) Legal origin FR -0.377 (0.565) Legal origin GE -0.231 (0.727) Constant 0.643 0.972 2.719*** (0.107) (0.257) (0.000) Observations 245 244 245 R-squared 0.030 0.038 0.130 Number of code 81

1 _{The dependent variable is the first principal component of the capital stringency}

index. The range of the principal component is [−2.52,1.78]. For the pooled OLS regressions, standard errors are clustered at the country level to take into account the highly likely within country correlation in error terms.

2 _{GDP growth, government-owned banks and concentration ratio are expressed in}

percentages.

3 _{GDP growth is 3 year average growth rate for yearst, t−1 andt−2 whereas the}

capital stringency index represents the state of the capital regulation the end of yeart.

4 _{Legal origin variables are dummies that do not change over time, and hence they}

are dropped in the fixed effect regressions as a result of the within transformation.

5 _{Robust p values in parentheses. *** p<0.01, ** p<0.05, * p<0.1}

estimates negative and significant effect of all three variables on the stringency of capital reg- ulations. Given that the range of the principal component is [−2.52,1.78] with mean 0.16 and standard deviation 1.57, the economic magnitude of the coefficients are similar to the those obtained in Table 2.3.

Table 2.6 presents the results of dynamic panel data models using Principal Component Analysis. Similar to Table 2.4, the first and third columns are estimated under the assumption that all three regressors are strictly exogenous with respect to the time varying heterogeneity (it), and the second and fourth columns are estimated under the assumption that GDP growth and concentration ratio are predetermined variables, i.e that the error term is uncorrelated

Table 2.6: Results for the Dynamic Model with Principal Component Analysis Difference GMM System GMM (1) (2) (3) (4) L.capital stringency pc 0.122 0.140 0.021 0.109 (0.705) (0.512) (0.925) (0.503) GDP growth -0.221*** -0.268*** -0.209*** -0.260*** (0.000) (0.000) (0.000) (0.000) Government-owned banks -0.018 -0.027 -0.022 -0.023 (0.498) (0.293) (0.461) (0.393) Concentration ratio -0.015 0.014 -0.016 -0.014 (0.452) (0.675) (0.424) (0.567) Constant 2.254 0.833 2.341 2.389 (0.121) (0.674) (0.117) (0.136) Observations 86 86 161 161 Number of code 52 52 72 72 1

The dependent variable is the principal component of the capital stringency index. The range of the principal component is [−2.52,1.78] with mean 0.16 and standard deviation 1.57.

2 _{Column (1): Two-step GMM estimation where all three right-hand side variables are}

treated as strictly exogenous with respect to time-varying heterogeneityit. Column (2):

Two-step GMM estimation where GDP growth and concentration ratio are treated as predetermined variables with respect to time-varying heterogeneityit. Columns (3) and

(4) repeat the estimations in Column (1) and (2) with Two-Step System GMM where levels Equation (2.2) is estimated along side with the first difference model given by Equation (2.3).

3 _{GDP growth, government-owned banks and concentration ratio are expressed in percent-}

ages.

4 _{GDP growth is 3 year average growth rate for yearst, t−1 andt−2 whereas the capital}

stringency index represents the state of the capital regulation the end of yeart.

5

Standard errors are Windmeijer corrected robust. Robust p values in parentheses. *** p<0.01, ** p<0.05, * p<0.1

with the current and lagged values of these regressors, but it can be correlated with future values of these regressors.

The coefficient of GDP Growth is highly significant across all specifications, and it is at least twice as large as the coefficients estimated by static models. Coefficients of the two other explanatory variables (government-owned banks and concentration ratio) and the lagged de- pendent variable are not significantly different from zero. Those results are qualitatively the same as the results obtained with the standardized value of the index in Table 2.4. Further- more, the quantitative effects of the coefficients also do not change significantly when the first principal component of the index is used.

meaningful and statistically highly significant negative effect of GDP growth rate on the strin- gency of bank capital regulations. Government-owned banks has a significant negative effect in static fixed effects models, but under more reasonable dynamic models, it is significant only if the levels of the stringency index is used as the dependent variable. Statistical significance of this coefficient is not robust to using the standardized value or the first principal component of the capital stringency index. Lastly, concentration ratio has a significant negative effect on the stringency of capital regulations in static models, but never has a significant effect in dynamic models.