[Limdep Nlogit List] Binary probit selection model with ordered probit outcome model

Sat Jan 31 21:08:05 EST 2009

Dear Limdepers,

I have been working on a research paper and I have hit a brick wall. I would very much appreciate it if you could help me find a practical solution to said problem as soon as possible, since I am running a tight deadline.

Let me explain. I am researching two things. Firstly, I am trying to determine what makes companies in the UK apply for a credit rating from agencies like S&P, Moody's, etc., in an attempt to also test for self-selection as per Moon and Stotsky (1993), Poon (2003) and Adams et al. (2003). Secondly, I am looking at the determinants of the credit ratings for rated companies (taking into account sample selection via the first step) as per too many earlier studies to list here!

Therefore, I am running two models simultaneously; one selection model (binary probit), which accounts for whether a company is rated or not and an outcome model (ordered probit), which in turn tests for the determinants of the ratings of rated companies accounting for self-selection from the selection equation (via ?, the correlation between the errors of the two models).

The problem I am facing is this: When I specify the two models and run the commands, I sometimes cannot get the outcome equation (ordered probit model) to work, due to an "Error 143: Models - Estimated variance matrix of estimates is singular". However, if I slightly change the specification of the two models (i.e. excluding certain variable combinations, due to collinearity), I can get it to work, although I do not absolutely make sense of the results. 

As you can understand, this is driving me crazy and I do not know what to do. Your help will be greatly appreciated. I attach a screenshot of a failed attempt and one of a model that did eventually give me some results. Please, let me know what you think and what I can do to rectify the problem, if anything.

--> sample;all$
--> reject;rnr=-999$
--> probit; lhs=rnr; rhs=one,intcov,roa,gear2,stdtd,quick,lnta,ncftd,earnvola...
Normal exit from iterations. Exit status=0.
+---------------------------------------------+
| Binomial Probit Model |
| Maximum Likelihood Estimates |
| Model estimated: Jan 30, 2009 at 06:30:14PM.|
| Dependent variable RNR |
| Weighting variable None |
| Number of observations 2772 |
| Iterations completed 10 |
| Log likelihood function -772.6020 |
| Restricted log likelihood -1620.323 |
| Chi squared 1695.442 |
| Degrees of freedom 8 |
| Prob[ChiSqd > value] = .0000000 |
| Results retained for SELECTION model. |
| Hosmer-Lemeshow chi-squared = 16.43816 |
| P-value= .03652 with deg.fr. = 8 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Index function for probability

Constant -19.3696715 .72790679 -26.610 .0000
INTCOV .351593D-04 .907473D-04 .387 .6984 4.23404803
ROA -.91968646 .03582285 -25.673 .0000 -1.40783056
GEAR2 -.00410652 .00157574 -2.606 .0092 .14191338
STDTD .00153961 .00088895 1.732 .0833 -41.4832213
QUICK .00092811 .00181795 .511 .6097 .22573407
LNTA .89923250 .03434504 26.182 .0000 19.3611392
NCFTD -.00051512 .00073742 -.699 .4848 -29.7768286
EARNVOLA -.149839D-06 .587505D-07 -2.550 .0108 206862.267
+-------------------------------------------+

| Partial derivatives of E[y] = F[*] with |
| respect to the vector of characteristics. |
| They are computed at the means of the Xs. |
| Observations used for means are All Obs. |
+-------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] |Elasticity|
+---------+--------------+----------------+--------+---------+----------+
Index function for probability

Constant -5.85698684 .22606789 -25.908 .0000
INTCOV .106314D-04 .274368D-04 .387 .6984 .00019718
ROA -.27809411 .01177440 -23.619 .0000 1.71497093
GEAR2 -.00124173 .00047886 -2.593 .0095 -.00077190
STDTD .00046555 .00026320 1.769 .0769 -.08459585
QUICK .00028064 .00054998 .510 .6099 .00027750
LNTA .27190925 .01094632 24.840 .0000 23.0605408
NCFTD -.00015576 .00022204 -.701 .4830 .02031686
EARNVOLA -.453083D-07 .177453D-07 -2.553 .0107 -.04105574

+----------------------------------------+

| Fit Measures for Binomial Choice Model |

| Probit model for variable RNR |
+----------------------------------------+
| Proportions P0= .728716 P1= .271284 |
| N = 2772 N0= 2020 N1= 752 |
| LogL = -772.60200 LogL0 = -1620.3228 |
| Estrella = 1-(L/L0)^(-2L0/n) = .57930 |
--> reject;cr1=-999$
--> ORDERED; Lhs=cr1; Rhs=one,lnta,intcov,ROA,gear2,quick;all;margin;Selection$
Normal exit from iterations. Exit status=0.

+---------------------------------------------+

| Ordered Probability Model |
| Maximum Likelihood Estimates |
| Model estimated: Jan 30, 2009 at 06:30:15PM.|
| Dependent variable CR1 |
| Weighting variable None |
| Number of observations 752 |
| Iterations completed 26 |
| Log likelihood function -1812.100 |
| Underlying probabilities based on Normal |
| Cell frequencies for outcomes |
| Y Count Freq Y Count Freq Y Count Freq |
| 0 114 .151 1 120 .159 2 121 .161 |
| 3 98 .130 4 106 .141 5 103 .137 |
| 6 45 .059 7 12 .017 8 31 .041 |

+---------------------------------------------+

+---------+--------------+----------------+--------+---------+----------+

|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|

+---------+--------------+----------------+--------+---------+----------+

Index function for probability

Constant -9.05734757 .67717940 -13.375 .0000
LNTA .48906715 .03163035 15.462 .0000 19.5846509
INTCOV -.00028206 .00042958 -.657 .5114 -3.71335633
ROA .00385539 .02506454 .154 .8778 -5.27641249
GEAR2 .745839D-04 .00141114 .053 .9578 -2.40968173
QUICK -.50453468 .03633599 -13.885 .0000 -1.42681132

Threshold parameters for index

Mu(1) .68355876 .04403042 15.525 .0000
Mu(2) 1.19349313 .04574868 26.088 .0000
Mu(3) 1.59145544 .04775226 33.327 .0000
Mu(4) 2.05016510 .05163259 39.707 .0000
Mu(5) 2.63003400 .06293071 41.793 .0000
Mu(6) 3.07101886 .07942038 38.668 .0000
Mu(7) 3.27670582 .09099353 36.010 .0000

Line search does not improve fn. Exit iterations. Status=3
Error 806: Line search does not improve fn. Exit iterations. Status=3
Function= .18123368199D+04, at entry, .14241092013D+04 at exit
Error 143: Models - estimated variance matrix of estimates is singular

The second, slightly better specification, when I drop the collinear variables, reads as follows:

--> sample;all$
--> reject;rnr=-999$
--> probit; lhs=rnr; rhs=one,intcov,roa,gear2,stdtd,quick,logdebt,earnvola;hold$
Normal exit from iterations. Exit status=0.
+---------------------------------------------+
| Binomial Probit Model |
| Maximum Likelihood Estimates |
| Model estimated: Jan 31, 2009 at 10:02:20AM.|
| Dependent variable RNR |
| Weighting variable None |
| Number of observations 2772 |
| Iterations completed 9 |
| Log likelihood function -838.5894 |
| Restricted log likelihood -1620.323 |
| Chi squared 1563.467 |
| Degrees of freedom 7 |
| Prob[ChiSqd > value] = .0000000 |
| Results retained for SELECTION model. |
| Hosmer-Lemeshow chi-squared = 41.06561 |
| P-value= .00000 with deg.fr. = 8 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+

Index function for probability
Constant -8.64474206 .34644257 -24.953 .0000
INTCOV .00015964 .00012392 1.288 .1977 4.23404803
ROA -.00380345 .00703352 -.541 .5887 -1.40783056
GEAR2 -.00434948 .00231111 -1.882 .0598 .14191338
STDTD -1.53962010 .06378597 -24.137 .0000 -41.4832213
QUICK .00076261 .00148270 .514 .6070 .22573407
LOGDEBT 1.53311696 .06344139 24.166 .0000 -37.0068432
EARNVOLA .110989D-06 .541204D-07 2.051 .0403 206862.267

=======================================================================
--> reject;cr1=-999$
--> ORDERED; Lhs=cr1; Rhs=one,lnsales,intcov2,ROA,gear3,acid;all;margin;Select$
Normal exit from iterations. Exit status=0.
+---------------------------------------------+
| Ordered Probability Model |
| Maximum Likelihood Estimates |
| Model estimated: Jan 31, 2009 at 10:02:21AM.|
| Dependent variable CR1 |
| Weighting variable None |
| Number of observations 752 |
| Iterations completed 27 |
| Log likelihood function -1907.432 |
| Underlying probabilities based on Normal |
| Cell frequencies for outcomes |
| Y Count Freq Y Count Freq Y Count Freq |
| 0 114 .151 1 120 .159 2 121 .161 |
| 3 98 .130 4 106 .141 5 103 .137 |
| 6 45 .059 7 12 .017 8 31 .041 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Index function for probability
Constant -3.25179462 .53814655 -6.043 .0000
LNSALES .32123631 .03454129 9.300 .0000 12.3335790
INTCOV2 -.00020248 .00042309 -.479 .6322 -.11973006
ROA .11409350 .09195667 1.241 .2147 -5.27641249
GEAR3 .00096513 .00213186 .453 .6508 -3.40442100
ACID -.44191452 .07875167 -5.611 .0000 -1.65870381

Threshold parameters for index
Mu(1) .63090498 .04153496 15.190 .0000
Mu(2) 1.09393764 .04367250 25.049 .0000
Mu(3) 1.45513864 .04592586 31.685 .0000
Mu(4) 1.88826692 .05016707 37.640 .0000
Mu(5) 2.44633015 .06141870 39.830 .0000
Mu(6) 2.87026851 .07769861 36.941 .0000
Mu(7) 3.06926831 .08911097 34.443 .0000

Line search does not improve fn. Exit iterations. Status=3
Error 806: Line search does not improve fn. Exit iterations. Status=3
Function= .19082537971D+04, at entry, .14751466855D+04 at exit
+---------------------------------------------+
| Bivar.: Ordered & Univariate Probit. |

| Maximum Likelihood Estimates |
| Model estimated: Jan 31, 2009 at 10:02:25AM.|
| Dependent variable CR1 |
| Weighting variable None |
| Number of observations 752 |
| Iterations completed 4 |
| Log likelihood function -1475.147 |
| Restricted log likelihood -1907.432 |
| Chi squared 864.5704 |
| Degrees of freedom 1 |
| Prob[ChiSqd > value] = .0000000 |
+---------------------------------------------+
+---------+--------------+----------------+--------+---------+----------+
|Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|
+---------+--------------+----------------+--------+---------+----------+
Index function for probability
Constant -3.25179462 .233494D+07 .000 1.0000
LNSALES .32123630 .03336911 9.627 .0000 12.3335790
INTCOV2 -.00020248 .00051253 -.395 .6928 -.11973006
ROA .11409350 .09276239 1.230 .2187 -5.27641249
GEAR3 .00096513 .01972754 .049 .9610 -3.40442100
ACID -.44191451 .08085354 -5.466 .0000 -1.65870381

Threshold parameters for index

Mu(1) .63090498 .05545440 11.377 .0000
Mu(2) 1.09393764 .06487182 16.863 .0000
Mu(3) 1.45513864 .07180431 20.265 .0000
Mu(4) 1.88826692 .07760632 24.331 .0000
Mu(5) 2.44633015 .08679465 28.185 .0000
Mu(6) 2.87026851 .11253792 25.505 .0000
Mu(7) 3.06926831 .11911900 25.766 .0000

Index function for probit equation
Constant -8.64474173 .400357D+14 .000 1.0000
INTCOV .00016091 .508867D+11 .000 1.0000 -3.69418028
ROA -.00380344 .635048D+11 .000 1.0000 -5.26924126
GEAR2 -.00434904 .241282D+12 .000 1.0000 -2.40547321
STDTD -1.53962352 .690621D+13 .000 1.0000 -5.06606727
QUICK .00076305 .264621D+12 .000 1.0000 -1.42343500
LOGDEBT 1.53311531 .686199D+13 .000 1.0000 .79188574
EARNVOLA .10000011 .336183D+07 .000 1.0000 539641.199
Rho(1,2) -.648819D-08 .208701D+21 .000 1.0000

Can you see anything that can be improved or anything that I am not getting???

PS: I think I have got the commands right, but please can you also check that my syntax is corect:

sample;all$
reject;rnr=-999$
probit; lhs=rnr; rhs=one,intcov,roa,gear2,stdtd,quick,lnta,ncftd,earnvola;margin;hold$
reject;cr1=-999$
ORDERED; Lhs=cr1; Rhs=one,lnta,intcov,ROA,gear2,quick;all;margin;Selection$

Your prompt response will be greatly appreciated.
Eleimon

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