ivreg

[Tobias Huber]

Do I have to use the same variables in the first stage (including one exclusion variable) as in the second stage? Becuase in my case it doesn't make sense to use all variables from the second stage in the first stage.

[Jeff Wooldridge]

If you exclude exogenous variables from the first stage then you are making explicit exclusion restrictions is what is usually a reduced form equation. In effect, you are giving that equation a more structural interpretation. You may want this, but it comes with costs. In particular, omitted relevant variables from the first stage will cause bias in the estimates.

In any case, neither -ivreg- or -ivregress 2sls- allow you to exclude variables from the first stage. That's because it assumes you are interested in the single structural equation. Asymptotically, there is no harm in including redundant variables in the first stage; it does not even affect the asymptotic variance of the 2sls estimator. That's why in almost all cases no exclusion restrictions are made in the first stage unless that equation is structural.

If you insist on making the exclusion restrictions, use -3sls- and set it up as a two-equation system. One drawback is that you might not be able to get robust standard errors, in which case you might bootstrap or use -gmm- with the optimal weighting matrix.

[Mark Schaffer]

I'm pretty sure David Roodman's cmp will let you impose these exclusion restrictions on the first stage. But like Jeff says, you really need to be sure you need to do this.

[Tobias Huber]

Thank you so much for your help!

It's just becuase I have a time invariant endogenous variable and using time dummies in the first-stage just doesn't make any sense ... so I was just wondering whether it is (economically) wrong to include the time-dummies in the first stage.

I also use a heckman-type correction for another model (where the endognous variable is a dummy variable) and with heckman it is no problem to exclude variables in the first stage, selection equation (at least that's what I learned). I again have a valid exclusion restriction variable which I include in the first but exclude in the second stage.

[Jeff Wooldridge]

If you have exogenous variables that change over time -- whether in the structural equation or the reduced form -- then you should include the time dummies in the first stage. Remember, OLS partials out the explanatory variables. So if you have

x(i) = w(i)*a + z(i,t)*b + u(i,t)

then you should include the time dummies because of the presence of z(i,t). If in a time series regression y(t) is not trending but x(t) is, you need to include a time trend to detrend x(t) -- not just to capture a trend in y(t).

Bottom line: Include the time dummies in the first stage. It makes sense unless all exogenous variables are time-constant.

[Tobias Huber]

Thank you so much!

[Carolin Schuerg]

Dear all,

may I join in with another question that (to me) seems to be related to the topic above?

I'm estimating a simultaneous equation system of the following form via 3sls (reg3 in Stata):

1. I(i,t) = CF(i,t) + Q(i,t) + S(i,t) + delta_D(i,t) + delta_CH(i,t) + lag_I(i,t) + i.firm + i.quarter + u(i,t)

2. delta_D(i,t) = CF(i,t) + Q(i,t) + S(i,t) + delta_CH(i,t) + I(i,t)+ lag_D(i,t) + i.firm + i.quarter + e(i,t)

3. delta_CH(i,t) = CF(i,t) + Q(i,t) + S(i,t) + delta_D(i,t) + I(i,t)+ lag_CH(i,t) + i.firm + i.quarter + v(i,t)

with endogenous variables being I(i,t), delta_D(i,t) and delta_CH(i,t).


The routine reg3 in stata automatically uses all exogenous variables as instruments, i.e. also the firm- and quarter-fixed effects. I am wondering whether this makes sense. When I look at the first stage results of reg3 the F-test suggests that the instruments (including fixed effects) are poor.

When I run the first stage manually excluding the fixed effects the F-test becomes much better. But I don't know how I would implement this in Stata since when I use the inst() command for defining the variables used as instruments in reg3 I get the error message "equation is not identified - does not meet order conditions". (I know that the F-test is only one indication of the instruments being adequate or poor, therefore I also use the xtivreg2 routine which shows several test statistics.)

When I use the xtivreg2 routine instead I do not get an error message using the instruments excluding the fixed effects but compared to the reg3 routine this routine does not account for the simultaneity of the three equations.

So my questions are:

1. Should I include fixed effects in the first stage using reg3?
2. If not, how can I control for the simultaneity of the three equations using a different Stata routine?

Thank you very much in advance!