Simultaneity bias in a logit model?

[Marcel Issa]

OLS yields inconsistent estimates when an explanatory variable is endogenous, because the explanatory variable is correlated with the error term. I have run a logit model of collateral regressed on loanspread. I divided my data in Lines of Crédit and other loans and yield with the inclusion of the endogenous loanspread perfect predictability in Lines of credit and highly insignificant variables but high pseudo r squared for other loans. I concluded that These results indicate biased estimates due to endogeneity, since the different results cannot be rationally explained. However, is endogeneity in fact a major problem for logit models?

* Example generated by -dataex-. To install: ssc install dataex
clear
input float Loanspread_pct byte Numberofemployees float Corporationdummy long Grossprofit float(Profitability_pct Leverage_pct) long Loansize byte Maturity float GDPGrowth_pct double Duration byte Housebank str6 Loantype float(Banks Collateraldummy)
 5.45 28 1 1600      6.25 95 475 10 1.5                  0 0 "Credit" 7 1
 1.25 28 1 1600      6.25 95 475 10 1.5                  0 0 "Credit" 1 0
 2.52 15 1  800      8.75 50 150 10 1.5               5.75 1 "Credit" 8 1
 9.14 15 1  800      8.75 50  30  1 1.5               5.75 1 "LC"     8 1
 9.07 15 1  800      8.75 50  20  1 1.5                  6 1 "LC"     8 1
 8.72 10 0  815  3.435583 72  80  1 2.2                 10 1 "LC"     8 1
 8.67 10 0  830  5.060241 77  80  1 2.2                 11 1 "LC"     8 1
 8.55 10 0  850  3.529412 90 120  1 1.5                 12 1 "LC"     8 1
 5.02 10 0  830  5.060241 77  60  6 2.2                  1 0 "Credit" 7 0
 9.42 25 1 3500 3.4285715 20 100  1 1.5  4.666666666666667 0 "LC"     3 1
 4.07 25 1 3500 3.4285715 20 620 20 1.5                  0 0 "Credit" 6 1
 9.31 25 1 3500 3.4285715 20 230  3 1.5                  5 0 "LC"     5 1
 1.76  8 0  300 23.333334 40  50 10 1.5               4.75 1 "Credit" 1 0
  .71  3 0  190         0  0  20 10  .5                  0 1 "Credit" 1 0
 9.16  8 0  300 23.333334 40  15  3 2.2                  3 0 "LC"     3 0
 3.26 12 1  800     8.125 26  50 10 1.5 10.083333333333334 0 "Credit" 8 1
 4.33 12 1  830  8.192771 32 125  5 2.2                  8 0 "Credit" 8 1
 5.17 12 1  755  7.549669 30 100  5 2.2                  0 0 "Credit" 4 1
 8.15 12 1  800     8.125 26  15  1 1.5                 10 0 "LC"     8 1
 8.26 12 1  755  7.549669 30  15  1 2.2                  9 0 "LC"     8 1
    8 12 1  830  8.192771 32  15  1 2.2                  8 0 "LC"     8 1
 8.84 12 1  755  7.549669 30 120  1 2.2                 10 0 "LC"     5 1
 8.97 12 1  830  8.192771 32 120  1 2.2                  9 0 "LC"     5 1
 8.67 12 1  800     8.125 26  10  1 1.5 10.583333333333334 0 "LC"     5 0
  3.9 10 1 1000         8 55  70  6 1.5                  7 0 "Credit" 5 1
 4.09 10 1 1000         8 55 100  5 1.5  5.166666666666667 0 "Credit" 4 1
 3.33 12 1  800     9.375 60 150  4 1.5  5.083333333333333 1 "Credit" 5 1
 2.79 25 1 1800  11.38889 45 350  3 2.2                 12 1 "Credit" 5 1
 2.45 25 1 2000      10.5 45 300  6 1.5                 14 1 "Credit" 5 0
 4.55  3 1  500        11 44  30  4 1.7                  0 0 "Credit" 3 1
 4.91  3 1  600  8.333333 50  50  5 2.2               1.33 0 "Credit" 4 1
10.05  3 1  500        11 44   8  1 1.7                  0 0 "LC"     7 0
10.02  3 1  600  8.333333 50   8  1 2.2                  1 0 "LC"     7 0
10.03  3 1  600  8.333333 50  10  3 2.2              1.083 0 "LC"     9 0
 9.84 25 1 1750 2.2857144 45 100  1 2.2                  0 0 "LC"     9 1
 9.43 29 1 1900  2.710526 50 200  3 2.2  .5833333333333334 0 "LC"     9 1
 9.62 29 1 1900  2.710526 50 100  1 2.2                  1 0 "LC"     9 1
 5.26 25 1 1750 2.2857144 45 250  5 2.2                  0 0 "Credit" 4 1
 5.12 29 1 2000       2.5 50 200  5 1.5 1.4166666666666667 0 "Credit" 4 1
 8.16  9 1  415 18.795181 25  15  1 1.7                  5 1 "LC"     7 1
 8.11  9 1  435  18.62069 25  25  1 2.2                  6 1 "LC"     7 1
 8.04  9 1  430  18.60465 30  15  1 2.2                  7 1 "LC"     7 1
 2.58 14 0 1450  7.931035 60 350  7  .5                 15 1 "Credit" 7 1
 2.27 15 0 1500  6.666667 70 300 10 1.5                 20 1 "Credit" 7 0
 8.23 14 0 1450  7.931035 60 150  1  .5                 15 1 "LC"     7 1
 8.07 15 0 1400  6.785714 70 150  1 2.2               16.5 1 "LC"     7 1
 8.05 15 0 1475  6.779661 70 150  1 1.7              17.75 1 "LC"     7 1
 8.78  3 0  400      12.5 50  20  1 1.5                  7 1 "LC"     6 1
 3.39  3 0  400      12.5 50  15  5 1.5                  7 1 "Credit" 6 1
  2.9 25 1 1100 18.181818 80 150 10 1.5                 15 1 "Credit" 5 0
  2.6 25 1 1100 18.181818 80 400 15 1.5                 15 1 "Credit" 5 0
 8.52 25 1 1100 18.181818 80  50  1 1.5                 15 1 "LC"     5 0
  2.1 25 0 2000        15 20 150 10 1.5                 20 1 "Credit" 5 0
 8.12 25 0 2000        15 20  50  1 1.5                 20 1 "LC"     5 0
 2.57 12 1 1500  6.666667 30  25  5 1.5                 15 1 "Credit" 5 0
 3.12  7 0  950  13.68421 25 300  5 1.7                  3 1 "Credit" 7 1
 2.54  9 0 1000      12.3 20 250  7 1.5                  6 1 "Credit" 7 0
 8.76  7 0  950  13.68421 25  50  1 1.7                  3 1 "LC"     7 1
 8.82  8 0  975 14.358974 20  80  1 2.2  4.333333333333333 1 "LC"     7 1
 8.87  9 0  935 13.368984 20  80  1 2.2  5.333333333333333 1 "LC"     7 1
 8.66  9 0 1000      12.3 20  80  1 1.5                  6 1 "LC"     7 1
 2.85  6 0  427 14.285714 42  80  5 2.2                 23 1 "Credit" 5 1
 9.24  6 0  427 14.285714 42  30  1 2.2                  8 0 "LC"     6 1
 9.17  6 0  430 13.953488 45  45  1 2.2               8.75 0 "LC"     6 1
  1.6  6 0  427 14.285714 42  80  5 2.2                  0 0 "Credit" 2 0
 1.91 28 1 2875  5.495652 38 500 10  .5                 14 1 "Credit" 5 0
 3.76 30 1 3000         5 40 400  7 2.2                  4 0 "Credit" 3 0
 9.36 30 1 3000         5 40  60  2 2.2                  5 0 "LC"     4 1
 9.68 30 1 3000         5 40  50  2 2.2 .16666666666666666 0 "LC"     4 1
 4.61 15 1 2600  6.538462 50 150  3 1.8                  5 0 "Credit" 3 0
 4.65 15 1 2600  6.538462 50 130  4 1.8                  4 0 "Credit" 4 0
  9.4 15 1 2600  6.538462 50  50  2 1.8                  4 0 "LC"     4 0
 2.09 35 1 2300         9 21 300  5 2.2                 22 1 "Credit" 7 1
 2.15 35 1 2425  9.278351 28 250  7 1.7                 23 1 "Credit" 7 1
 1.98 33 1 2400      8.75 25  50  9 2.2              25.25 1 "Credit" 7 0
 1.75 33 1 2350  8.297873 25  80 10 1.5 26.333333333333332 1 "Credit" 7 0
  7.8 34 1 2425  9.278351 28  80  1 1.7 23.166666666666668 1 "LC"     7 1
 2.74 26 1 1650  8.939394 26 325 10 2.2                 16 1 "Credit" 7 1
  2.7 26 1 1700  8.941176 31 150  8 2.2 18.333333333333332 1 "Credit" 7 0
 2.55 26 1 1750  8.857142 33 220  5 1.5 19.166666666666668 1 "Credit" 7 0
 8.15 26 1 1700  8.941176 31  80  1 2.2 18.166666666666668 1 "LC"     7 0
end

xtset Banks

logit Collateraldummy  Age Numberofemployees Totalassets Corporationdummy Grossprofit Profitability_pct Leverage_pct Loansize Maturity GDPGrowth_pct Duration Housebank if Loantype=="LC", vce (cluster Banks)

 xtlogit Collateraldummy  Age Numberofemployees Totalassets Corporationdummy Grossprofit Profitability_pct Leverage_pct g1 g3 Loansize Maturity GDPGrowth_pct Duration Housebank if Loantype=="Credit", re noskip vce (cluster Banks)

[Phil Bromiley]

Endogeneity is just as much a problem with logit as OLS as far as I know. Both estimators assume the x's are not correlated with the errors. If you have data from several banks, you need a panel estimator so ignore logit and focus on xtlogit etc. GSEM and (I think) User written cmp estimators will handle this properly. While the extended regression procedures will handle endogeneity, they don't handle the panel issues as far as I know.