IV-PROBIT with binary endogenous variable and binary instrument

[Cansu Oymak]

Hello There,

I am exploring the causal effect of maternal education on child health. My dependent variable is binary. It indicates whether children under 6 months of age are exclusively breastfef (1=exclusiveky breastfed; 0=otherwise).
To account for the endoeneity of maternal education, I utilize a compulsory education law. My IV is also a binary variable. It is reform exposure and it indicates whether the mothers were exposed the law. My education variable is also dummy and it shows whether the mothers received 8 years of education or not (1=8 yearsor more; 0= less than 8 years). I am using 2 rounds of Turkish DHS. I pooled them. I am using STATA 14.

My code is as follows:

ivprobit exclusive_BF (completionof8years=reformexpsosure) X1 X2 X3 ... where X1 X2 and X3 are my explanatory variables.

However, stata says that ivprobit assumes that the endogenous covariates are continuous and so are not appropriate for use with discrete endogenous covariates.

As a result, my code becomes useless (I guess?).

Can anybody please help me? How can I run ivprobit model and interpret the results?

Thank you so much

[Joro Kolev]

Stata tells you correctly that -ivprobit- (which is not an IV estimator at all, it is a control function or maximum likelihood estimator) is not appropriate for your situation. -ivprobit- is appropriate for continuous endogenous regressor.

Use either -biprobit-, or linear regression -ivregress-.

[Cansu Oymak]

Stata tells you correctly that -ivprobit- (which is not an IV estimator at all, it is a control function or maximum likelihood estimator) is not appropriate for your situation. -ivprobit- is appropriate for continuous endogenous regressor.

Use either -biprobit-, or linear regression -ivregress-.

Dear Joro Kolev, thank you so much for your reply. However, I am a bit confused about the biprobit. How can I implement my insturment using biprobit?

[Joro Kolev]

Like this. I load data and I create dummies for both the dependent variable and the endogenous regressor:

.  webuse hsng2, clear
(1980 Census housing data)

. summ hsngval

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
     hsngval |         50       48484    15770.24      31100     119400

. gen hsngvaldummy = hsngval>r(mean)

. summ rent

    Variable |        Obs        Mean    Std. Dev.       Min        Max
-------------+---------------------------------------------------------
        rent |         50      234.76    35.35335        180        368

. gen rentdummy = rent>r(mean)

Then linear regression:

. ivregress 2sls rentdummy pcturban (hsngvaldummy = faminc i.region)

Instrumental variables (2SLS) regression          Number of obs   =         50
                                                  Wald chi2(2)    =      62.78
                                                  Prob > chi2     =     0.0000
                                                  R-squared       =     0.5450
                                                  Root MSE        =     .33619

------------------------------------------------------------------------------
   rentdummy |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
hsngvaldummy |   .7432537   .1833852     4.05   0.000     .3838253    1.102682
    pcturban |   .0089092   .0047618     1.87   0.061    -.0004239    .0182422
       _cons |  -.3891662   .2817598    -1.38   0.167    -.9414053    .1630729
------------------------------------------------------------------------------
Instrumented:  hsngvaldummy
Instruments:   pcturban faminc 2.region 3.region 4.region

And then biprobit:

. biprobit (rentdummy hsngvaldummy pcturban) (hsngvaldummy pcturban faminc i.region), nolog

Seemingly unrelated bivariate probit            Number of obs     =         50
                                                Wald chi2(7)      =      28.46
Log likelihood = -19.478371                     Prob > chi2       =     0.0002

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
rentdummy    |
hsngvaldummy |   2.269605   .5418049     4.19   0.000     1.207687    3.331523
    pcturban |   .0600618   .0238045     2.52   0.012     .0134058    .1067178
       _cons |  -4.825022   1.634003    -2.95   0.003    -8.027609   -1.622435
-------------+----------------------------------------------------------------
hsngvaldummy |
    pcturban |   .0475946    .059457     0.80   0.423    -.0689391    .1641283
      faminc |   .0014891   .0006342     2.35   0.019     .0002461    .0027321
             |
      region |
    N Cntrl  |  -.6791572    1.58226    -0.43   0.668     -3.78033    2.422015
      South  |    .561397   29.04296     0.02   0.985    -56.36176    57.48455
       West  |   3.720021    1.70954     2.18   0.030     .3693845    7.070657
             |
       _cons |   -34.8199    12.0947    -2.88   0.004    -58.52507   -11.11473
-------------+----------------------------------------------------------------
     /athrho |  -14.15105    2426.15    -0.01   0.995    -4769.318    4741.016
-------------+----------------------------------------------------------------
         rho |         -1   4.96e-09                            -1           1
------------------------------------------------------------------------------
Wald test of rho=0: chi2(1) = .000034                     Prob > chi2 = 0.9953

.

Dear Joro Kolev, thank you so much for your reply. However, I am a bit confused about the biprobit. How can I implement my insturment using biprobit?

[Cansu Oymak]

Like this. I load data and I create dummies for both the dependent variable and the endogenous regressor:

. webuse hsng2, clear
(1980 Census housing data)

. summ hsngval

Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
hsngval | 50 48484 15770.24 31100 119400

. gen hsngvaldummy = hsngval>r(mean)

. summ rent

Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
rent | 50 234.76 35.35335 180 368

. gen rentdummy = rent>r(mean)

Then linear regression:

. ivregress 2sls rentdummy pcturban (hsngvaldummy = faminc i.region)

Instrumental variables (2SLS) regression Number of obs = 50
Wald chi2(2) = 62.78
Prob > chi2 = 0.0000
R-squared = 0.5450
Root MSE = .33619

------------------------------------------------------------------------------
rentdummy | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
hsngvaldummy | .7432537 .1833852 4.05 0.000 .3838253 1.102682
pcturban | .0089092 .0047618 1.87 0.061 -.0004239 .0182422
_cons | -.3891662 .2817598 -1.38 0.167 -.9414053 .1630729
------------------------------------------------------------------------------
Instrumented: hsngvaldummy
Instruments: pcturban faminc 2.region 3.region 4.region

And then biprobit:

. biprobit (rentdummy hsngvaldummy pcturban) (hsngvaldummy pcturban faminc i.region), nolog

Seemingly unrelated bivariate probit Number of obs = 50
Wald chi2(7) = 28.46
Log likelihood = -19.478371 Prob > chi2 = 0.0002

------------------------------------------------------------------------------
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
rentdummy |
hsngvaldummy | 2.269605 .5418049 4.19 0.000 1.207687 3.331523
pcturban | .0600618 .0238045 2.52 0.012 .0134058 .1067178
_cons | -4.825022 1.634003 -2.95 0.003 -8.027609 -1.622435
-------------+----------------------------------------------------------------
hsngvaldummy |
pcturban | .0475946 .059457 0.80 0.423 -.0689391 .1641283
faminc | .0014891 .0006342 2.35 0.019 .0002461 .0027321
|
region |
N Cntrl | -.6791572 1.58226 -0.43 0.668 -3.78033 2.422015
South | .561397 29.04296 0.02 0.985 -56.36176 57.48455
West | 3.720021 1.70954 2.18 0.030 .3693845 7.070657
|
_cons | -34.8199 12.0947 -2.88 0.004 -58.52507 -11.11473
-------------+----------------------------------------------------------------
/athrho | -14.15105 2426.15 -0.01 0.995 -4769.318 4741.016
-------------+----------------------------------------------------------------
rho | -1 4.96e-09 -1 1
------------------------------------------------------------------------------
Wald test of rho=0: chi2(1) = .000034 Prob > chi2 = 0.9953

.

I really appreciate for the syntax and the logical explanation. However, should I need to interpret marginal effects to talk about "odds ratio"? or can I simply interpret the causal effect just using biprobit? Thank yuo so much.

[Joro Kolev]

You might want to check out -margins- for marginal effects and interpretations. Odds ratios are only for logistic regression.

If I had to evaluate the endogenous dummy manually, and my estimated structural equation is F(a*dummy + b'x), where F() is the normal CDF, I would set the control variables x at some values, say their means, lets call the vector of x predictors set at their means x*, and I would evaluate

F(a + b'x*) - F(b'x*).

I really appreciate for the syntax and the logical explanation. However, should I need to interpret marginal effects to talk about "odds ratio"? or can I simply interpret the causal effect just using biprobit? Thank yuo so much.

[Cansu Oymak]

You might want to check out -margins- for marginal effects and interpretations. Odds ratios are only for logistic regression.

If I had to evaluate the endogenous dummy manually, and my estimated structural equation is F(a*dummy + b'x), where F() is the normal CDF, I would set the control variables x at some values, say their means, lets call the vector of x predictors set at their means x*, and I would evaluate

F(a + b'x*) - F(b'x*).

I am very thankful for your prompt and explanatory replies ! I guess I got it !

[Diti Roy]

Hello,

I tried running biprobit model with a binary independent and dependent variable and also my IV is a binary variable and I am running the regression with the 'if' command. However, after the nth iteration, STATA is showing me this output "Hessian is not negative semidefinite". Can anybody help, please?

With Ivregress 2SLS, the model is working but to interpret the estimates I need to look at margins. right? My coefficient from Iv regress 2SLS output and margins are coming as 31.92 and I don't know how to interpret this. Any input is highly appreciated

[Mustafa Coban]

Hi,

there is a new package rbiprobit that handles recursive bivariate probit models

ssc install rbiprobit

So, if your outcome variable is binary and your endogenous treatment variable is also binary, you can use rbiprobit to get coefficient estimates, to compute marginal effects and to compute treatment effects.

Here, a short example for computation of the average treatment effect and the marginal effects of x2 on the joint probability p11

rbiprobit (y1 = x1 x2), endog(y2 = x2 x3)
rbiprobit tmeffects, tmeff(ate)
rbiprobit margdec, dydx(x2) predict(p11) effect(total)

While biprobit will give you the correct coefficient estimates if you fit a recursive model, it won't give you the correct predictions, treatment effects and marginal effects.

[Trang Thu Vu]

Hi Mustafa,

Thanks much for sharing the new package rbiprobit. I can apply it for my IV regression with binary outcome and endogenous variables.

Would you recommend any command to test for the weakness of the IV following the rbiprobit?

Best,
Trang

[Mustafa Coban]

Hi Trang Thu Vu,

to the best of my knowledge, there is currently no way of testing weakness of IVs in nonlinear settings like rbiprobit. This might due to the fact that such models are even identified if there is no IV at all. In that case, identification is based solely on the distributional assumption of the model. I'm currently working on version 1.2 of the package that will allow users to test the normality assumption of the model.

[Joro Kolev]

It is acceptable to test/examine the weakness of the instruments in the linear setting, even though you might end up using these instruments in a nonlinear model.

Mustafa is right that this is not exactly correct because the nonlinear model might be ideantified even without any instruments, but this is known as identification through functional form, and is frowned upon. Therefore one can still examine the weakness of the instruments in the linear first stage with available methods for linear models -- although not exactly correct, this is informative.

[Mustafa Coban]

I agree with Joro. It is better to have any test statistic, even if it is based on linear models, than to have no test statistic. It's true that identification through functional form is not the best way to get published but once you have an approriate IV rbiprobit may have better performance than e.g. ivprobit

[Chanda Moon]

Thank you everyone for the nice guidence.
I have similar confusion and need help.

I am exploring causal effect of household water quality and child health indicators (ARI, diarrhea, malnutrition- where diarrhea and Infant mortality are binary and malnutrition is continuous outcomes). Water quality is main regression and categorical variable based on bacterial contamination (low, medium, and high risk). 2 Instruments, one is continuous at district level elevation & 2nd is (interaction) max average temperature X interview month.

My code is as follows:

ivreg2 diarrhea (WQ= mean_elevation c.max_tem#i.Interview_month) X2 X3 dist_sanitation_coverage i.province i.year, cluster (village)

similar code for other outcomes. Does this model is correct using 2SLS model

[Joro Kolev]

I think this is wrong. If I understand what you are saying WQ is a categorical variable bacterial contamination (low, medium, and high risk). You cannot put categorical variables in the regression like this, you need to expand them into dummy variables.

So your command should be something like

ivreg2 diarrhea (i.WQ= mean_elevation c.max_tem#i.Interview_month) X2 X3 dist_sanitation_coverage i.province i.year, cluster (village)

or if Stata does not accept this syntax, first generate the dummies manually, and then include them. E.g.,

gen WQhigh = WQ=="high"
gen WQmedium = WQ=="medium"

ivreg2 diarrhea (WQhigh WQmedium= mean_elevation c.max_tem#i.Interview_month) X2 X3 dist_sanitation_coverage i.province i.year, cluster (village)

What I have written above is pseudo code because you do not say or show how WQ is encoded. I assumed that it is a string variable with the level names as strings.