I'd like to estimate the effect of fuel price (which I assume is exogenous)
on distance driven. As a control, I would like to include the fuel
efficiency of the driver's car. Although efficiency is likely to be
endogenous, leaving it out of the specification runs the risk of
imparting omitted bias on my fuel price estimate. But since it is
*just* a control, I'm inclined to leave efficiency as is in the model
and not worry about whether it is endogenous. Wise move?
Any insights would be appreciated!

Before tackling the metrics, think about a likely motivation for the research question.  Suppose the government is considering a rise in the gas tax.  Policy-makers would like to know how this will affect driving habits and fuel consumption.  The government is unlikely to forbid people from buying a new more fuel efficient car in response to the tax, in fact they probably would like to encourage that.  So who needs to know what the causal effect of a price rise is conditional on being locked in to my current vehicle?  I think this observation neatly answers Colin’s  question.  Prices will go up, driving behavior will change for a number of reasons.  There is no scenario where only one response is all that’s allowed (driving in the same car). Then there is the econometric problem that conditioning on fuel efficiency will not actually answer the question of how driving behavior changes for those who don’t buy a more fuel efficient car.  That’s the bad control problem described in MHE – but that’s just metrics.

JA

New versions of and extensions to the Baum-Schaffer-Stillman packages
ivreg2, xtivreg2, ranktest and xtoverid, and a new program, ivreg29, are
now available from ssc.

The main extensions and upgrades are:

1.  2-way clustering.

2-way clustering, introduced by Cameron, Gelbach and Miller (2006) and
Thompson (2009), is now supported.  2-way clustering, e.g.,

	ivreg2 y x1 x2, cluster(id year)

or
	ivreg2 y (x = z1 z2), gmm2s (cluster id year)

allows for arbitrary within-cluster correlation in two cluster
dimensions.  In the examples above, standard errors and statistics are
robust to disturbances that are autocorrelated (correlated within
panels, clustering on id) and common (correlated across panels,
clustering on year).  In the second example, estimates also are
efficient in the presence of arbitrary within-panel and within-year
clustering.  As with 1-way clustering, the numbers of clusters in both
dimensions should be large.

2.  Angrist-Pischke first-stage F statistics

ivreg2 and xtivreg2 now provide Angrist-Pischke first-stage F
statistics.  Angrist and Pischke (2009, pp. 217-18) introduced
first-stage F statistics for tests of under- and weak identification
when there is more than one endogenous regressor.  In contrast to the
Cragg-Donald and Kleibergen-Paap statistics, which test the
identification of the equation as a whole, the AP first-stage F
statistics are tests of whether one of the endogenous regressors is
under- or weakly identified.

3.  SEs that are robust to autocorrelated across-panel disturbances

Following Thompson (2009), cluster-robust and kernel-robust SEs can be
combined and applied to panel data to produce SEs that are robust to
arbitary common autocorrelated disturbances.  This can also be combined
with 2-way clustering to provide SEs and statistics that are robust to
autocorrelated within-panel disturbances (clustering on panel id) and to
autocorrelated across-panel disturbances (clustering on time combined
with kernel-based HAC).

4.  ivreg2 has been Mata-ized

... and is noticably faster, in particular with time series and the CUE
(continuously-updated) GMM estimator.

5.  ivreg29 for users who don't yet have Stata 10 or 11

ivreg2 requires Stata 10 or later.  For those who have only Stata 9, we
have provided a new program, ivreg29.  ivreg29 is basically the previous
version of ivreg2 plus support for AP F-statistics and some minor bug
fixes.  ivreg29 does not support the other features described above.

For full details and examples, see the new help files accompanying the
programs.

I am estimating Y = b0+ b1*X1 +b2* X2 + b3*X1*X2 + X3

Many thanks in advance for your response and best regards,

thanks for your question Daniela.  Models with multiple endogenous variables are indeed hard to identify and the results can be hard to interpret.

So we don’t usually like to see them – for one thing it’s not clear why you’re tackling two causal questions at the same time; one is hard enough.
You may have noticed that the only model with more than one endogenous regressor in MHE is the peer effects regression (equation 4.6.6, based on Acemoglu and Angrist, 2000).  Here we have both individual and state-level schooling endogenous in a wage equation.

But we are really only interested in the peer effect in this case – the effect of state average schooling. Individual schooling is there because we realize that any instrument for average schooling must also be correlated with individual schooling.  We therefore try to fix this violation of the exclusion restriction by treating individual schooling as endogenous as well. This is the best reason for having a second endog variable that I can think of.  And the model may work – in the case of schooling we have enough instruments.  But not very often, I would think.

More generally, it doesn’t make sense to think of one endogenous variable as a “control” when looking at the effects of another, at least not a good one (in the sense in which we use the terms good and bad control in chapter 3).  So any time someone shows me a problem with more than one endogenous variable, my first question is always: why?

How should you construct a first stage F stat to measure instrument strength when you have more than one endogenous variable?  Not by following the instructions we gave at the bottom of page 218.  Althought the theoretical expressions that motivate the p. 218 procedure are right, the computational algorithm we gave is not.

Specifically, where it says:

“regress the first-stage fitted values (for x_2) on the other first-stage fitted values and any exogenous covs . . .”

it should read:

“regress x_2 on the other first stage fitted values and any exogenous covs . . .”

If you do what we originally wrote, you’ll get an R2 of one, always a cause for concern.

Thanks guys for cleaning this up!

In sections 5.3-5.4, there is a great discussion of using
fixed effects vs. a lagged dependent variable with panel data. I am
having trouble reconciling some of this discussion with a section in a
recent paper by Imbens and Wooldridge (2008) titled “Recent
Developments in the Econometrics of Program Evaluation.” On page 68 of
their paper (as published by IZA in 2008) they suggest that it might
be better in some circumstances with two periods of data to use first
differencing and a lag of the dependent variable (assuming
unconfoundedness given lagged outcomes). I understand your discussion
of instrumenting for lagged variables if you have more than two
periods, but with two periods, how do you react to adding a lag (the
baseline value of the dependent variable) after first differencing
with only two periods of data? I have had difficulty finding support
for this approach elsewhere and given that you have given much thought
to this issue, I was wondering what your opinion might be.

The way I see it, once you add a lagged dependent variable to a differenced model, you are really doing lagged-dep-var control and not fixed effects.  Steve may disagree (he’s generally less dogmatic than me).  This is not always exactly true but it is a theorem for the simple example we use to contrast f.e. and lagged-dep-var control in Section 5.4

Here’s that again:

two periods
no covariates
the treatment, D_it, is zero for everybody in period 1 and switched on for some in period 2 (think of a training program that some people participate in between periods; period 1 is before, period 2 is after (similar to Ashenfelter and Card, 1985)

ignoring constants,  fixed effects estimation fits

(1) Y_it – Y_it-1 = aD_it + error

lagged dependent variable estimation fits

(2) Y_it = gY_it-1 + bD_it + error

As I understand it, the Imbens-Wooldridge proposal is to throw Y_it-1 into equation (1):

(3) Y_it – Y_it-1 = dY_it-1 + cD_it + error

But in this case, c is (algebraically) the same as b.  Why ? The coefficient c is

c= COV(Y_it – Y_it-1, D_it*)/V(D_it*)

where D_it* is the residual from a regression of D_it on Y_it-1.  But this residual is orthogonal to Y_it-1, hence

c= COV(Y_it – Y_it-1, D_it*)/V(D_it*) = COV(Y_it, D_it*)/V(D_it*) = b in equation (2)

So I say: “You wanna do fixed effects?  no lagged dependent variable, please (or at least be prepared to instrument it if you include one).  You wanna control for  lagged dependent variables?  Then, just do it!

– JDA

Macartan Humphreys of Columbia University has shown why regression estimates of treatment effects can often be expected to fall between the average effect on the treated and the average effect on controls.   His theorem goes like this:  Let D denote treatment, let p(X) denote the propensity score E[D|X], and let M(X) denote the covariate-specific treatment effects, E[Y1-Y0|X].   Suppose that M(X) varies in a monotone way with p(X) (either weakly increasing or weakly decreasing). Then OLS estimates of the treatment effect in model using saturated control for covariates (i.e., the sort of regression discussed in Section 3.3.1 of MHE) will lie between E[Y1 - Y0| D=1] and E[Y1-Y0| D=0].  Read all about it in his working paper.

Why is a treatment effect likely to be monotone in the propensity score?  This happens in the Angrist (1998) study of the effects of military service because those who benefit the most from military service are least likely to be qualified and therefore least likely to be treated.  In other cases, where self-selection is more important than qualifications (as in the Roy [1951] model), those most likely to benefit from treatment may be the most likely to get treated.  Either case is fine as long as it’s one or the other.

Why is this useful?  It’s one more reason why OLS is a good summary statistic for program impact.  Check out this figure from Macartan’s paper, which illustrates the OLS-is-in-between property using the Angrist (1998) data:

Figure 3 from Humphreys (2009)

The figure shows how OLS estimates of the effects of voluntary military service are almost always between matching estimates of effects on veterans and matching estimates of effects on non-veterans.  This happens because covariate-specific estimates of veteran effects are either unrelated to the propensity score or they are a weakly decreasing function of the propensity score.

Hi Guys:

I agree that the issue I am raising is conceptually different, but as a practical matter, the “bad control” issues and “baby with the bathwater problem” both fall under a larger heading of “can more controls ever make things worse.” Your discussion of bad control may lead some students to believe that the answer is “only if the extra controls are endogenous.”

If you ever have a second edition, I think there is an argument for dealing with all aspects of the “can more controls ever make things worse” question all in one place.

Point taken! We hope to fix this in the next edition . . .