st: interpretation reciprocal causation ivprobit cdsimeq

[<Marianne.LEFEBVRE@ec.europa.eu>]

Dear Stata list

As I am new here, I would like to understand how to improve my question sent ten days ago in order to get your feedback. It is about the interpretation of the results of two estimations procedures ivprobit. Do not hesitate to let me know if this is not the good place to ask such questions or good question format.
Thanks a lot
Best,
Marianne Lefebvre

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Marianne.LEFEBVRE@ec.europa.eu
Sent: Friday, October 19, 2012 2:30 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: interpretation reciprocal causation ivprobit cdsimeq

Dear Stata listers
 
I have run the following regressions using ivprobit and cdsimeq and I am not too sure about the interpretation. please see my question in capital letters below. Thanks a lot for your help.


 In order to account for the potential endogeneity between insurance decision (binary variable) and economic performance (continuous), we adopt a 2SLS estimation technique where total gross margin is instrumented. We use Newey's (1987) minimum-chi-squared estimator (ivprobit twostep option). We find that economic performance, as defined by the total gross margin, significantly explains insurance adoption (table 1).  Post-estimation tests: We ran the joint significance test of the instruments in the first stage regression (F-statistic>10). The Amemiya-Lee-Newey test of overidentifying restrictions is not significant (chi2=2.025, p-value= 0.1547). The Wald test of exogeneity for IVprobit estimations allows to reject the null hypothesis of exogeneity of the instruments (chi2=7.45, p-value= 0.0064). 

Then, we verify whether there is reciprocal causation between insurance use and economic performance (total gross margin). To obtain this result, we rely on the two-stage probit least squares estimation method described in (Maddala 1983) for simultaneous equations models in which one of the endogenous variables is continuous (total gross margin) and the other endogenous variable is dichotomous (insurance use) (cdsimeq command in Stata http://www.stata-journal.com/article.html?article=st0038). We find that economic performance (total gross margin) significantly explains insurance adoption but the reverse effect is not significant (table 2). 

IS IT CORRECT TO CONCLUDE AS FOLLOWS?
The result suggests that the endogeneity bias between insurance decision and economic performance is due to omitted variables, and not reciprocal causation. It therefore justifies the use of the ivprobit model where economic performance is instrumented to explain insurance decision, rather than the (Maddala 1983)  estimation procedure (cdsimeq).

Table 1: 2SLS Probability to adopt insurance, with instrumentation of gross margin

First step
Number of obs =     144
R-squared     =  0.2453
Adj R-squared =  0.1946

grossmargin                             Coef.   Std. Err.      t    P>t     [95% Conf. Interval]

q3_individual farms             -228188.2***   112400.5    -2.03   0.044    -450496.7   -5879.677
q4_totaluaa_sq                      .1313854 ***  .0329142     3.99   0.000     .0662869    .1964839
nuts2_32                                51374.23   95259.15     0.54   0.591    -137031.8    239780.2
nuts2_33                                16731.56   100579.9     0.17   0.868      -182198    215661.2
nuts2_34                                10620.46   100359.5     0.11   0.916    -187873.1      209114
nuts2_41                                 7942.025   127155.7     0.06   0.950    -243549.8    259433.8
nuts2_42                                  93651.27    99561.3     0.94   0.349    -103263.6    290566.2
q4_ratiorent                           -33656.87   82139.63    -0.41   0.683    -196114.8      128801
q21_noninsuranmeasures       -56509.8   68454.26    -0.83   0.411    -191900.4     78880.8
_cons                                       292010.1   154708.1     1.89   0.061    -13975.68    597995.8

Second step
Number of obs   =       144
Wald chi2(8)    =     29.93
Prob > chi2     =    0.0002

insurance2011                                             Coef.   Std. Err.      z    P>z     [95% Conf. Interval]

I_grossmargin                       3.88e-06***   1.43e-06     2.72   0.006     1.09e-06    6.68e-06
nuts2_32                                -1.805997   .5538496    -3.26   0.001    -2.891522   -.7204715
nuts2_33                                   -1.224679   .5420211    -2.26   0.024    -2.287021   -.1623367
nuts2_34                                   -.9044687   .5287984    -1.71   0.087    -1.940894     .131957
nuts2_41                                  -2.162879   .7412688    -2.92   0.004    -3.615739   -.7100187
nuts2_42                                   -3.11869   .7796749    -4.00   0.000    -4.646824   -1.590555
q4_ratiorent                               1.127435   .4558475     2.47   0.013     .2339906     2.02088
q21_noninsuranmeasures          -.7945278   .3990442    -1.99   0.046     -1.57664   -.0124156
_cons                                          .4889867   .4838786     1.01   0.312     -.459398    1.437371

Wald test of exogeneity:     chi2(1) =     7.45           Prob > chi2 = 0.0064
Test of overidentifying restrictions: Amemiya-Lee-Newey minimum chi-sq statistic     Chi-sq(1)= 2.025     P-value = 0.1547



Table 2: two-stage probit least squares estimation (cdsimeq) – 
SECOND STAGE REGRESSIONS WITH CORRECTED STANDARD ERRORS


------------------------------------------------------------------------------
 grossmargin |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
I_insur~2011 |  -15809.74   28736.81    -0.55   0.583    -72623.96    41004.48
q3_individ~s |  -239284.4   113697.5    -2.10   0.037    -464070.5   -14498.42
q4_totalua~q |   .1351443   .0322533     4.19   0.000     .0713778    .1989108
       _cons |   264916.4   104230.9     2.54   0.012     58846.34    470986.5
------------------------------------------------------------------------------
------------------------------------------------------------------------------
insuran~2011 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
I_grossmar~n |   2.67e-06***   1.07e-06     2.50   0.012     5.77e-07    4.77e-06
    nuts2_32 |  -1.634341   .5218917    -3.13   0.002     -2.65723   -.6114523
    nuts2_33 |  -1.201044   .5233067    -2.30   0.022    -2.226706   -.1753817
    nuts2_34 |  -.8801489   .5140605    -1.71   0.087    -1.887689    .1273911
    nuts2_41 |  -2.143736   .7280761    -2.94   0.003    -3.570739   -.7167331
    nuts2_42 |  -2.832533   .6944463    -4.08   0.000    -4.193622   -1.471443
q4_ratiorent |    1.11448    .445112     2.50   0.012     .2420765    1.986884
q21_nonins~s |   -.755226    .381161    -1.98   0.048    -1.502288   -.0081642
       _cons |    .483358   .4681395     1.03   0.302    -.4341785    1.400894
------------------------------------------------------------------------------



Marianne Lefebvre

Joint Research Centre: The European Commission's in-house science service 
Institute for Prospective Technological Studies
Agriculture and Life Science in the Economy
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