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st: Test for significance of total effects in a system of simultaneous equations


From   Johannes Muck <Johannes.Muck@dice.uni-duesseldorf.de>
To   statalist@hsphsun2.harvard.edu
Subject   st: Test for significance of total effects in a system of simultaneous equations
Date   Wed, 12 Jun 2013 18:14:18 +0200

Dear Statalisters,

I am estimating a system of  two equations with ivreg2:

(1) y = a_1*z + a_2*x1 + a_3*x2 + a_4*i1

(2) z = b_1*y + b_2*x1 + b_3*x2 + b_4*i2

Where y and z influence each other, x1 and x2 are exogenous variables
influencing both dependent variables, and i1 and i2 serve as instruments for
y and z, respectively.

To quantify the effects of x1 and x2 on y and z, I calculated the total
effects, i.e. for x1 on y this is:

total_x1 = (a_2 + a_1*b_2)/ (1-a_1*b_1)

Now my question is: How can I test, whether total_x1 is significantly
different from zero?

Or, in other words, is it somehow possible to store the results from
estimating (1) and (2), say as est1 and est2, and then type something like:


lincom ([est1]a_2+[est1]a_1*[est2]b_2)/(1-[est1]a_1*[est2]b_1)


[Background information : y and z are fractional variables, i.e. bound to
[0,1]. As this implies heteroskedasticy (see Papke and Wooldridge, 1996, p.
621), I don?t use reg3 (reason given here:
http://statalist.1588530.n2.nabble.com/reg3-option-robust-td5647547.html),
but rather additionally estimate a fractional probit model using the ?frm-
command.]

Thank you very much for your help!

Best,

Johannes Muck
Doctoral Researcher
Düsseldorf Institute for Competition Economics


References: 
Papke, L. W., and Wooldridge, J. M. (1996), ?Econometric Methods for
Fractional Response Variables With an Application to 401 (K) Plan
Participation Rates?, Journal of Applied Econometrics 11 (6), 619-632.



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