logit model yield too high coefficient

[Marcel Issa]

I ran a logit model

 egen Banks=group(V)

[/CODE] logit Collateraldummy Age Numberofemployees Totalassets Corporationdummy Profitability Leverage Loansize Maturity GDPGrowth Duration Housebank if Loantype=="LC", vce (cluster Banks)

 
on the following data: 
input float Collateraldummy int Age byte Numberofemployees long Totalassets float Corporationdummy double(Profitability Leverage) long Loansize byte Maturity double(GDPGrowth Duration) byte Housebank str6 Loantype str14 V
1   8 28 1500 1               .0625 .95 475 10 .015                  0 0 "Credit" "Volksbank A"  
0   8 28 1500 1               .0625 .95 475 10 .015                  0 0 "Credit" "Förderbank A"
1   6 15  500 1               .0875  .5 150 10 .015               5.75 1 "Credit" "Volksbank B"  
1   6 15  500 1               .0875  .5  30  1 .015               5.75 1 "LC"     "Volksbank B"  
1   6 15  500 1               .0875  .5  20  1 .015                  6 1 "LC"     "Volksbank B"  
1  23 10  387 0   .0343558282208589 .72  80  1 .022                 10 1 "LC"     "Volksbank B"  
1  24 10  415 0  .05060240963855422 .77  80  1 .022                 11 1 "LC"     "Volksbank B"  
1  25 10  400 0  .03529411764705882  .9 120  1 .015                 12 1 "LC"     "Volksbank B"  
0  24 10  415 0  .05060240963855422 .77  60  6 .022                  1 0 "Credit" "Volksbank A"  
1  15 25  800 1  .03428571428571429  .2 100  1 .015  4.666666666666667 0 "LC"     "Private bank A"
1  15 25  800 1  .03428571428571429  .2 620 20 .015                  0 0 "Credit" "Sparkasse B"  
1  15 25  800 1  .03428571428571429  .2 230  3 .015                  5 0 "LC"     "Sparkasse A"  
0   7  8  130 0  .23333333333333334  .4  50 10 .015               4.75 1 "Credit" "Förderbank A"
0   1  3   60 0                   0   0  20 10 .005                  0 1 "Credit" "Förderbank A"
0   7  8  130 0  .23333333333333334  .4  15  3 .022                  3 0 "LC"     "Private bank A"
1  20 12  450 1              .08125 .26  50 10 .015 10.083333333333334 0 "Credit" "Volksbank B"  
1  18 12  462 1   .0819277108433735 .32 125  5 .022                  8 0 "Credit" "Volksbank B"  
1  19 12  438 1  .07549668874172186  .3 100  5 .022                  0 0 "Credit" "Private bank B"
1  20 12  450 1              .08125 .26  15  1 .015                 10 0 "LC"     "Volksbank B"  
1  19 12  438 1  .07549668874172186  .3  15  1 .022                  9 0 "LC"     "Volksbank B"  
1  18 12  462 1   .0819277108433735 .32  15  1 .022                  8 0 "LC"     "Volksbank B"  
1  19 12  438 1  .07549668874172186  .3 120  1 .022                 10 0 "LC"     "Sparkasse A"  
1  18 12  462 1   .0819277108433735 .32 120  1 .022                  9 0 "LC"     "Sparkasse A"  
0  20 12  450 1              .08125 .26  10  1 .015 10.583333333333334 0 "LC"     "Sparkasse A"  
1  15 10  320 1                 .08 .55  70  6 .015                  7 0 "Credit" "Sparkasse A"  
1  15 10  320 1                 .08 .55 100  5 .015  5.166666666666667 0 "Credit" "Private bank B"
1  10 12  277 1              .09375  .6 150  4 .015  5.083333333333333 1 "Credit" "Sparkasse A"  
1  18 25  720 1  .11388888888888889 .45 350  3 .022                 12 1 "Credit" "Sparkasse A"  
0  20 25  695 1                .105 .45 300  6 .015                 14 1 "Credit" "Sparkasse A"  
1   3  3  248 1                 .11 .44  30  4 .017                  0 0 "Credit" "Private bank A"
1   4  3  250 1  .08333333333333333  .5  50  5 .022               1.33 0 "Credit" "Private bank B"
0   3  3  248 1                 .11 .44   8  1 .017                  0 0 "LC"     "Volksbank A"  
0   4  3  250 1  .08333333333333333  .5   8  1 .022                  1 0 "LC"     "Volksbank A"  
0   4  3  250 1  .08333333333333333  .5  10  3 .022              1.083 0 "LC"     "Volksbank C"  
1   2 25  462 1 .022857142857142857 .45 100  1 .022                  0 0 "LC"     "Volksbank C"  
1   3 29  450 1 .027105263157894736  .5 200  3 .022  .5833333333333334 0 "LC"     "Volksbank C"  
1   3 29  450 1 .027105263157894736  .5 100  1 .022                  1 0 "LC"     "Volksbank C"  
1   2 25  462 1 .022857142857142857 .45 250  5 .022                  0 0 "Credit" "Private bank B"
1   4 29  440 1                .025  .5 200  5 .015 1.4166666666666667 0 "Credit" "Private bank B"
1   7  9  360 1  .18795180722891566 .25  15  1 .017                  5 1 "LC"     "Volksbank A"  
1   8  9  350 1  .18620689655172415 .25  25  1 .022                  6 1 "LC"     "Volksbank A"  
1   9  9  345 1  .18604651162790697  .3  15  1 .022                  7 1 "LC"     "Volksbank A"  
1  45 14 1000 0  .07931034482758621  .6 350  7 .005                 15 1 "Credit" "Volksbank A"  
0  50 15 1050 0  .06666666666666667  .7 300 10 .015                 20 1 "Credit" "Volksbank A"  
1  45 14 1000 0  .07931034482758621  .6 150  1 .005                 15 1 "LC"     "Volksbank A"  
1  46 15  970 0  .06785714285714285  .7 150  1 .022               16.5 1 "LC"     "Volksbank A"  
1  47 15  960 0  .06779661016949153  .7 150  1 .017              17.75 1 "LC"     "Volksbank A"  
1   7  3  350 0                .125  .5  20  1 .015                  7 1 "LC"     "Sparkasse B"  
1   7  3  350 0                .125  .5  15  5 .015                  7 1 "Credit" "Sparkasse B"  
0  25 25  500 1  .18181818181818182  .8 150 10 .015                 15 1 "Credit" "Sparkasse A"  
0  25 25  500 1  .18181818181818182  .8 400 15 .015                 15 1 "Credit" "Sparkasse A"  
0  25 25  500 1  .18181818181818182  .8  50  1 .015                 15 1 "LC"     "Sparkasse A"  
0  40 25  620 0                 .15  .2 150 10 .015                 20 1 "Credit" "Sparkasse A"  
0  40 25  620 0                 .15  .2  50  1 .015                 20 1 "LC"     "Sparkasse A"  
0  35 12  380 1  .06666666666666667  .3  25  5 .015                 15 1 "Credit" "Sparkasse A"  
1   4  7  400 0   .1368421052631579 .25 300  5 .017                  3 1 "Credit" "Volksbank A"  
0   7  9  425 0                .123  .2 250  7 .015                  6 1 "Credit" "Volksbank A"  
1   4  7  400 0   .1368421052631579 .25  50  1 .017                  3 1 "LC"     "Volksbank A"  
1   5  8  415 0  .14358974358974358  .2  80  1 .022  4.333333333333333 1 "LC"     "Volksbank A"  
1   6  9  410 0  .13368983957219252  .2  80  1 .022  5.333333333333333 1 "LC"     "Volksbank A"  
1   7  9  425 0                .123  .2  80  1 .015                  6 1 "LC"     "Volksbank A"  
1 102  6  370 0  .14285714285714285 .42  80  5 .022                 23 1 "Credit" "Sparkasse A"  
1 102  6  370 0  .14285714285714285 .42  30  1 .022                  8 0 "LC"     "Sparkasse B"  
1 103  6  375 0  .13953488372093023 .45  45  1 .022               8.75 0 "LC"     "Sparkasse B"  
0 102  6  370 0  .14285714285714285 .42  80  5 .022                  0 0 "Credit" "Förderbank B"
0  17 28 3500 1  .05495652173913043 .38 500 10 .005                 14 1 "Credit" "Sparkasse A"  
0  22 30 3625 1                 .05  .4 400  7 .022                  4 0 "Credit" "Private bank A"
1  22 30 3625 1                 .05  .4  60  2 .022                  5 0 "LC"     "Private bank B"
1  22 30 3625 1                 .05  .4  50  2 .022 .16666666666666666 0 "LC"     "Private bank B"
0  18 15 3100 1  .06538461538461539  .5 150  3 .018                  5 0 "Credit" "Private bank A"
0  18 15 3100 1  .06538461538461539  .5 130  4 .018                  4 0 "Credit" "Private bank B"
0  18 15 3100 1  .06538461538461539  .5  50  2 .018                  4 0 "LC"     "Private bank B"
1  26 35 2650 1                 .09 .21 300  5 .022                 22 1 "Credit" "Volksbank A"  
1  27 35 2710 1  .09278350515463918 .28 250  7 .017                 23 1 "Credit" "Volksbank A"  
0  29 33 2665 1               .0875 .25  50  9 .022              25.25 1 "Credit" "Volksbank A"  
0  30 33 2700 1  .08297872340425531 .25  80 10 .015 26.333333333333332 1 "Credit" "Volksbank A"  
1  27 34 2710 1  .09278350515463918 .28  80  1 .017 23.166666666666668 1 "LC"     "Volksbank A"  
1  17 26 1980 1   .0893939393939394 .26 325 10 .022                 16 1 "Credit" "Volksbank A"  
0  19 26 2050 1  .08941176470588236 .31 150  8 .022 18.333333333333332 1 "Credit" "Volksbank A"  
0  20 26 1930 1  .08857142857142856 .33 220  5 .015 19.166666666666668 1 "Credit" "Volksbank A"  
0  19 26 2050 1  .08941176470588236 .31  80  1 .022 18.166666666666668 1 "LC"     "Volksbank A"  
end

To interprete the coefficients I ran the margin command:

margins, dydx(*) atmeans

and I get for profitability and for GDPGrowth a way too high coefficient. It doesnt make any sense that a one percent increase in GDP would lead to an 161% decrease in the likelihood of collateral incidence. Does anybody have an idea of why the coefficients are so large?

[Mike Lacy]

My guess is that the problem is the interpretation of the units: GDPGrowth appears to be measured as a proportion, not a percent, since for your example data, its range is 0.005 to 0.02. A one unit change in GDPGrowth is a 100% change in one year (right?), something not plausible.

[Marcel Issa]

Hi Mike, 0.005 is devoted to a year where the economy grew by 0,5% so it is measured as percent. What do u mean by: "

A one unit change in GDPGrowth is a 100% change in one year (right?)"

[Weiwen Ng]

Hi Mike, 0.005 is devoted to a year where the economy grew by 0,5% so it is measured as percent. What do u mean by: "

A one unit change in GDPGrowth is a 100% change in one year (right?)"

I checked these data, and it ranges from 0.005 (which you said was 0.5 percentage points) to 0.022 (2.2 percentage points). So, you did input GDP growth as a fraction, not a percent. Thus, a one-unit change in GDP growth does mean a doubling of GDP. Mike was asking if this was the case. It looks like it is. The bank names look like German names, and I'm going to assume that a 100% change in GDP is not something we would expect to see in Germany (although that assumption seems like it would apply to a few other places).

You might want to do this:

gen GDPGrowth_pct = GDPGrowth * 100
 logit Collateraldummy Age Numberofemployees Totalassets Corporationdummy Profitability Leverage Loansize Maturity GDPGrowth_pct Duration Housebank if Loantype=="LC", vce (cluster Banks)
margins, dydx(GDPGrowth_pct)
Average marginal effects                        Number of obs     =         40
Model VCE    : Robust

Expression   : Pr(Collateraldummy), predict()
dy/dx w.r.t. : GDPGrowth_pct

-------------------------------------------------------------------------------
              |            Delta-method
              |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
GDPGrowth_pct |   -.037436   .1324189    -0.28   0.777    -.2969722    .2221003
-------------------------------------------------------------------------------

So, a one percentage point increase in GDP growth is associated with a 3.7 percentage point reduction in the probability of collateral incidence.

[Marcel Issa]

Many thanks for your effort. That indeed was my mistake also for profitability, leverage and even my dependent variable loanspread.