We created the following variables:
\(\text{discontinue}_{ikt}\) equals one when the relationship between firm \(i\) and bank \(k\) is active in quarter \(t\) but inactive exactly 4 quarters after.
\(\text{discontinue2}_{ikt}\) equals one when the relationship between firm \(i\) and bank \(k\) is active in quarter \(t\) but inactive in any quarter of the following year.
\(\text{acq}_{ikt}\) equals 1 if firm \(i\) has an exclusive relationship with an acquirer bank \(k\) that merged some time the following year.
\(\text{targ}_{ikt}\) equals 1 if firm \(i\) has an exclusive relationship with a target bank \(k\) that merged some time the following year.
\(\text{roam}_{it}\) ratio of assets to amount
\(\text{ropp}_{it}\) ratio of PP&E to amount
\(\text{multiple}_{it}\) identifies firms in multiple relationships
\(\text{merger}_{ikt}\) if bank \(k\) is one of the merged banks
Are relationships withe merging banks terminated at a higher rate than with other banks?
##
## ===========================================================================================
## Dependent variable:
## -------------------------------------------------------------------------
## discontinue discontinue2 discontinue
## (1) (2) (3) (4) (5) (6)
## -------------------------------------------------------------------------------------------
## merger -0.141*** -0.291*** -0.294*** -0.370*** -0.314*** -0.294***
## (0.007) (0.018) (0.018) (0.007) (0.016) (0.018)
##
## ingresos_24d 0.001*** 0.001***
## (0.0001) (0.0001)
##
## total_wf_2d 0.0001** 0.0001**
## (0.00002) (0.00002)
##
## Constant -0.891*** -1.109*** -1.078*** -0.011** -0.299*** -1.078***
## (0.005) (0.014) (0.013) (0.005) (0.012) (0.013)
##
## -------------------------------------------------------------------------------------------
## Observations 369,623 66,927 66,906 369,623 66,927 66,906
## Log Likelihood -217,419.900 -35,762.310 -35,792.310 -252,579.300 -44,656.480 -35,792.310
## Akaike Inf. Crit. 434,843.700 71,530.620 71,590.620 505,162.600 89,318.950 71,590.620
## ===========================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Are firms in business with several banks less likely to have relationships discontinued?
##
## ==============================================================================
## Dependent variable:
## ------------------------------------------------------------
## discontinue
## (1) (2) (3) (4) (5)
## ------------------------------------------------------------------------------
## merger -0.147*** -0.293*** -0.292*** -0.324*** -0.297***
## (0.007) (0.019) (0.019) (0.020) (0.018)
##
## multiple -0.428*** -0.412*** -0.380*** -0.381*** -0.388***
## (0.007) (0.029) (0.029) (0.031) (0.029)
##
## ingresos_24d 0.001***
## (0.0001)
##
## mp_10d 0.002***
## (0.0003)
##
## activo_totald 0.001***
## (0.0001)
##
## total_wf_2d 0.0001***
## (0.00002)
##
## Constant -0.656*** -0.746*** -0.752*** -0.737*** -0.734***
## (0.007) (0.029) (0.029) (0.030) (0.029)
##
## ------------------------------------------------------------------------------
## Observations 369,623 66,927 66,236 59,379 66,906
## Log Likelihood -215,750.200 -35,664.710 -35,241.000 -31,693.840 -35,705.210
## Akaike Inf. Crit. 431,506.300 71,337.410 70,489.990 63,395.680 71,418.410
## ==============================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Are firms in business with several banks less likely to have relationships discontinued?
##
## =============================================================================
## Dependent variable:
## -----------------------------------------------------------
## discontinue2
## (1) (2) (3) (4) (5)
## -----------------------------------------------------------------------------
## merger -0.113*** -0.377*** -0.371*** -0.426*** -0.370***
## (0.021) (0.035) (0.035) (0.037) (0.035)
##
## multiple -0.510*** -0.315*** -0.361*** -0.339*** -0.360***
## (0.021) (0.036) (0.036) (0.038) (0.036)
##
## ingresos_24d -0.002***
## (0.0002)
##
## mp_10d -0.002***
## (0.0004)
##
## activo_totald -0.001***
## (0.0002)
##
## total_wf_2d -0.0002***
## (0.00003)
##
## Constant 2.716*** 2.632*** 2.600*** 2.640*** 2.607***
## (0.018) (0.036) (0.036) (0.038) (0.036)
##
## -----------------------------------------------------------------------------
## Observations 129,235 37,901 37,463 33,795 37,889
## Log Likelihood -35,689.160 -12,547.090 -12,462.420 -11,232.250 -12,590.240
## Akaike Inf. Crit. 71,384.320 25,102.180 24,932.850 22,472.510 25,188.480
## =============================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Are firms in business with several banks less likely to have relationships discontinued?
##
## =============================================================================
## Dependent variable:
## -----------------------------------------------------------
## discontinue
## (1) (2) (3) (4) (5)
## -----------------------------------------------------------------------------
## merger 0.136*** -0.048** -0.052** -0.029 -0.047**
## (0.012) (0.021) (0.022) (0.023) (0.021)
##
## nrel -0.190*** -0.107*** -0.113*** -0.110*** -0.112***
## (0.006) (0.009) (0.008) (0.009) (0.008)
##
## ingresos_24d -0.0005***
## (0.0002)
##
## mp_10d -0.0001
## (0.0003)
##
## activo_totald 0.0001
## (0.0002)
##
## total_wf_2d -0.0001**
## (0.00003)
##
## Constant 1.052*** 0.801*** 0.799*** 0.788*** 0.806***
## (0.013) (0.024) (0.024) (0.025) (0.024)
##
## -----------------------------------------------------------------------------
## Observations 129,235 37,901 37,463 33,795 37,889
## Log Likelihood -79,018.150 -24,863.140 -24,604.460 -22,162.650 -24,857.470
## Akaike Inf. Crit. 158,042.300 49,734.290 49,216.920 44,333.300 49,722.940
## =============================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Are firms in business with several banks less likely to have relationships discontinued?
##
## =============================================================================
## Dependent variable:
## -----------------------------------------------------------
## discontinue2
## (1) (2) (3) (4) (5)
## -----------------------------------------------------------------------------
## merger -0.122*** -0.386*** -0.382*** -0.438*** -0.381***
## (0.021) (0.035) (0.035) (0.037) (0.035)
##
## nrel -0.234*** -0.122*** -0.149*** -0.143*** -0.150***
## (0.008) (0.013) (0.012) (0.013) (0.012)
##
## ingresos_24d -0.002***
## (0.0002)
##
## mp_10d -0.001***
## (0.0004)
##
## activo_totald -0.001***
## (0.0002)
##
## total_wf_2d -0.0001***
## (0.00003)
##
## Constant 2.909*** 2.701*** 2.706*** 2.746*** 2.720***
## (0.022) (0.039) (0.039) (0.042) (0.039)
##
## -----------------------------------------------------------------------------
## Observations 129,235 37,901 37,463 33,795 37,889
## Log Likelihood -35,645.470 -12,540.520 -12,443.560 -11,213.230 -12,568.390
## Akaike Inf. Crit. 71,296.940 25,089.040 24,895.120 22,434.450 25,144.780
## =============================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Are relationships with acquirer banks more likely to survive?
##
## =====================================================
## Dependent variable:
## -----------------------------------
## discontinue
## (1) (2) (3)
## -----------------------------------------------------
## acq -0.197*** -0.402*** -0.400***
## (0.023) (0.050) (0.050)
##
## multiple -0.378*** -0.254*** -0.267***
## (0.013) (0.024) (0.023)
##
## ingresos_24d -0.001***
## (0.0002)
##
## total_wf_2d -0.0001**
## (0.00003)
##
## acq:multiple -0.255*** -0.209*** -0.208***
## (0.040) (0.069) (0.069)
##
## Constant 0.992*** 0.762*** 0.756***
## (0.008) (0.018) (0.018)
##
## -----------------------------------------------------
## Observations 129,235 37,901 37,889
## Log Likelihood -78,973.330 -24,757.330 -24,759.060
## Akaike Inf. Crit. 157,954.700 49,524.660 49,528.120
## =====================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Are relationships with acquirer banks more likely to survive?
##
## =====================================================
## Dependent variable:
## -----------------------------------
## discontinue2
## (1) (2) (3)
## -----------------------------------------------------
## acq -0.286*** -0.604*** -0.595***
## (0.040) (0.075) (0.075)
##
## multiple -0.460*** -0.287*** -0.334***
## (0.022) (0.040) (0.039)
##
## ingresos_24d -0.002***
## (0.0002)
##
## total_wf_2d -0.0002***
## (0.00003)
##
## acq:multiple -0.448*** -0.364*** -0.357***
## (0.058) (0.095) (0.095)
##
## Constant 2.690*** 2.505*** 2.482***
## (0.015) (0.032) (0.032)
##
## -----------------------------------------------------
## Observations 129,235 37,901 37,889
## Log Likelihood -35,547.500 -12,453.260 -12,498.750
## Akaike Inf. Crit. 71,103.010 24,916.530 25,007.500
## =====================================================
## Note: *p<0.1; **p<0.05; ***p<0.01##
## =================================================================
## Dependent variable:
## -----------------------------------------------
## discontinue
## (1) (2) (3) (4)
## -----------------------------------------------------------------
## targ 0.568*** 0.905*** 0.910*** 1.024***
## (0.042) (0.075) (0.075) (0.149)
##
## multiple -0.384*** -0.265*** -0.279*** -0.276***
## (0.013) (0.024) (0.023) (0.024)
##
## acq -0.183*** -0.382*** -0.380*** -0.378***
## (0.023) (0.051) (0.051) (0.051)
##
## ingresos_24d -0.001***
## (0.0002)
##
## total_wf_2d -0.0001** -0.0001**
## (0.00003) (0.00003)
##
## multiple:acq -0.249*** -0.197*** -0.196*** -0.199***
## (0.040) (0.069) (0.069) (0.069)
##
## targ:multiple -0.156
## (0.172)
##
## Constant 0.978*** 0.743*** 0.736*** 0.734***
## (0.008) (0.018) (0.018) (0.019)
##
## -----------------------------------------------------------------
## Observations 129,235 37,901 37,889 37,889
## Log Likelihood -78,873.640 -24,672.540 -24,673.450 -24,673.040
## Akaike Inf. Crit. 157,757.300 49,357.080 49,358.910 49,360.080
## =================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01##
## =================================================================
## Dependent variable:
## -----------------------------------------------
## discontinue2
## (1) (2) (3) (4)
## -----------------------------------------------------------------
## targ 15.131 15.380 15.383 15.125
## (65.948) (114.977) (115.329) (206.740)
##
## multiple -0.472*** -0.304*** -0.351*** -0.351***
## (0.022) (0.040) (0.039) (0.039)
##
## acq -0.256*** -0.575*** -0.566*** -0.566***
## (0.040) (0.075) (0.075) (0.075)
##
## ingresos_24d -0.002***
## (0.0002)
##
## total_wf_2d -0.0002*** -0.0002***
## (0.00003) (0.00003)
##
## multiple:acq -0.436*** -0.347*** -0.340*** -0.340***
## (0.058) (0.095) (0.095) (0.095)
##
## targ:multiple 0.362
## (249.352)
##
## Constant 2.661*** 2.476*** 2.452*** 2.452***
## (0.015) (0.032) (0.032) (0.032)
##
## -----------------------------------------------------------------
## Observations 129,235 37,901 37,889 37,889
## Log Likelihood -35,251.310 -12,330.260 -12,375.770 -12,375.770
## Akaike Inf. Crit. 70,512.610 24,672.530 24,763.540 24,765.540
## =================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01The following table shows the results of estimating 3 multinomial logits (so each pair of columns is a single result with “Stayed” as the base case) with different controls
## # weights: 15 (8 variable)
## initial value 406072.369974
## iter 10 value 296089.391828
## iter 20 value 259488.149492
## iter 30 value 256429.344568
## final value 256406.538055
## converged## # weights: 18 (10 variable)
## initial value 406072.369974
## iter 10 value 265836.168757
## iter 20 value 250924.520107
## iter 20 value 250924.519832
## iter 20 value 250924.519825
## final value 250924.519825
## converged## # weights: 18 (10 variable)
## initial value 406072.369974
## iter 10 value 267518.040417
## iter 20 value 252988.532974
## iter 20 value 252988.532058
## iter 20 value 252988.531965
## final value 252988.531965
## converged## # weights: 21 (12 variable)
## initial value 73526.824644
## iter 10 value 45935.765537
## iter 20 value 44294.700090
## iter 20 value 44294.699875
## iter 20 value 44294.699853
## final value 44294.699853
## converged##
## ===============================================================================================================
## Dependent variable:
## ---------------------------------------------------------------------------------------------
## Switched Dropped Switched Dropped Switched Dropped Switched Dropped
## (1) (2) (3) (4) (5) (6) (7) (8)
## ---------------------------------------------------------------------------------------------------------------
## targ 0.538*** 0.175*** 0.500*** 0.206*** 0.520*** 0.203*** 0.295*** 0.218***
## (0.051) (0.027) (0.051) (0.027) (0.051) (0.027) (0.095) (0.064)
##
## acq -0.167*** -0.141*** -0.060* -0.205*** -0.100*** -0.198*** -0.258*** -0.318***
## (0.033) (0.014) (0.033) (0.014) (0.033) (0.014) (0.067) (0.041)
##
## acqtarg -1.042*** -1.431*** -1.364*** -1.130*** -1.443*** -1.017*** -3.039*** -1.068***
## (0.161) (0.077) (0.160) (0.077) (0.161) (0.078) (0.500) (0.124)
##
## multiple 1.234*** -0.630*** 0.609*** -0.689***
## (0.024) (0.008) (0.076) (0.031)
##
## nrel 0.154*** -0.191***
## (0.004) (0.003)
##
## log(ingresos_24d) 0.070*** 0.052***
## (0.011) (0.007)
##
## Constant -3.006*** -1.090*** -3.906*** -0.762*** -3.413*** -0.680*** -3.245*** -1.005***
## (0.009) (0.004) (0.022) (0.006) (0.016) (0.007) (0.075) (0.029)
##
## ---------------------------------------------------------------------------------------------------------------
## Akaike Inf. Crit. 512,829.100 512,829.100 501,869.000 501,869.000 505,997.100 505,997.100 88,613.400 88,613.400
## ===============================================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01## # weights: 27 (16 variable)
## initial value 73526.824644
## iter 10 value 47143.378889
## iter 20 value 44583.297597
## iter 30 value 44564.418933
## final value 44564.414713
## converged## # weights: 30 (18 variable)
## initial value 73526.824644
## iter 10 value 46579.826434
## iter 20 value 44481.724427
## iter 30 value 44280.753276
## final value 44280.697807
## converged## # weights: 30 (18 variable)
## initial value 73526.824644
## iter 10 value 55834.275035
## iter 20 value 45936.763003
## iter 30 value 44725.166952
## iter 40 value 44510.623911
## iter 50 value 44506.967720
## iter 60 value 44403.719538
## final value 44401.454275
## converged##
## ===========================================================================================
## Dependent variable:
## -----------------------------------------------------------------
## Switched Dropped Switched Dropped Switched Dropped
## (1) (2) (3) (4) (5) (6)
## -------------------------------------------------------------------------------------------
## acq -0.300** -0.054 -0.237** -0.161** -0.342*** -0.097
## (0.117) (0.065) (0.118) (0.065) (0.117) (0.065)
##
## targ 0.725*** 0.426*** 0.738*** 0.422*** 0.724*** 0.426***
## (0.155) (0.107) (0.157) (0.106) (0.155) (0.106)
##
## acqtarg -2.243** -0.722*** -2.318** -0.569** -2.144** -0.618**
## (0.988) (0.258) (0.988) (0.258) (0.987) (0.258)
##
## multiple 0.610*** -0.687***
## (0.076) (0.031)
##
## nrel -0.088*** -0.092***
## (0.009) (0.006)
##
## log(ingresos_24d) 0.093*** 0.027*** 0.077*** 0.061*** 0.140*** 0.077***
## (0.011) (0.007) (0.011) (0.007) (0.012) (0.008)
##
## acq:log(ingresos_24d) 0.002 -0.098*** -0.010 -0.079*** -0.002 -0.103***
## (0.042) (0.026) (0.043) (0.026) (0.042) (0.026)
##
## targ:log(ingresos_24d) -0.205*** -0.102** -0.212*** -0.098** -0.205*** -0.102**
## (0.063) (0.042) (0.065) (0.042) (0.063) (0.042)
##
## acqtarg:log(ingresos_24d) -0.283 -0.148* -0.267 -0.182** -0.267 -0.131
## (0.346) (0.086) (0.346) (0.086) (0.345) (0.086)
##
## Constant -2.727*** -1.561*** -3.262*** -1.026*** -2.494*** -1.317***
## (0.031) (0.019) (0.076) (0.030) (0.038) (0.024)
##
## -------------------------------------------------------------------------------------------
## Akaike Inf. Crit. 89,160.830 89,160.830 88,597.400 88,597.400 88,838.910 88,838.910
## ===========================================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Degryse et al. are concerned that being a firm with multiple relationships is endogenous to the decision of discontinuing. So, following Rivers and Vuong via Wooldridge, estimate a LPM on a first step with multiple as covariate and some exclusions restrictions. The residuals of the firs step are then included as explanatory variable on a probit for discontinue. The hope is that they turn out to be not statistically significant because then endogeneity is not really a problem.
Sadly for us it is (so far).
The fist two columns show the results of the two-step procedure and the third column is there for reference because the estimate on multiple there is what we suspect to be endogenous.
So our story seems to be along the lines of:
Suppose the number of relationships increases the chances of discontinuing (a firm with more alternative banks more readily leaves the bank that merged when something changed- it might even be that the website is not what they were used to). So the real effect of a dummy identifying firms with multiple relationships on the probability of discontinuing is positive.
Now suppose firm’s manager ability translates into more relationships and more continuation (she quickly embraces the new website).
Since we do not observe manager ability and it correlates with multiple, using multiple as covariate will capture the manager’s ability (which reduces likelihood of discontinuing) and hence we get a negative sign despite multiple having a positive real effect on the probability of discontinuing.
##
## ========================================================================
## Dependent variable:
## ----------------------------------------------------
## multiple discontinue
## OLS probit logistic
## (1) (2) (3)
## ------------------------------------------------------------------------
## merger -0.0001 -0.184*** -0.321***
## (0.002) (0.012) (0.020)
##
## multiple 0.520*** -0.377***
## (0.030) (0.031)
##
## ingresos_24d 0.00003 0.002*** 0.003***
## (0.0001) (0.0005) (0.001)
##
## ppye_28d 0.00001 0.0004 0.001
## (0.00005) (0.0003) (0.0004)
##
## total_wf_2d 0.00000* -0.00003* -0.00001
## (0.00000) (0.00001) (0.00002)
##
## inventarios_puc14d -0.0001 -0.003*** -0.004***
## (0.0001) (0.001) (0.001)
##
## activo_totald -0.00001 -0.0001 -0.0002
## (0.00003) (0.0002) (0.0003)
##
## costoventas_puc61d 0.00003 -0.001** -0.002**
## (0.0001) (0.001) (0.001)
##
## propbankdebt -0.616***
## (0.003)
##
## total_debt -0.0003***
## (0.0001)
##
## resid -1.332***
## (0.043)
##
## Constant 1.124*** -1.152*** -0.765***
## (0.002) (0.029) (0.031)
##
## ------------------------------------------------------------------------
## Observations 58,757 58,757 58,757
## R2 0.435
## Adjusted R2 0.435
## Log Likelihood -30,712.490 -31,243.350
## Akaike Inf. Crit. 61,444.970 62,504.690
## Residual Std. Error 0.225 (df = 58747)
## F Statistic 5,026.537*** (df = 9; 58747)
## ========================================================================
## Note: *p<0.1; **p<0.05; ***p<0.01