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Re: st: Coefficient Constraints as Counterfactuals

From   Nick Cox <>
Subject   Re: st: Coefficient Constraints as Counterfactuals
Date   Fri, 11 Jan 2013 00:05:56 +0000

Suppose your model is

y = b_0 + b_1 x_1 + b_2 x_2

but for some reason you consider b_2 known (say 42). Then

y = b_0 + b_1 x_1 + 42 x_2

Then it is also true that

y - 42 x_2 = b_0 + b_1 x_1

and we form

y - 42 x_2 = y* (say)

and regress y* on x_1 to get estimates of b_0 and b_1. Clearly there
is an assumption in there about zero average errors.

y - 42 would make no sense if only on dimensional grounds. (It seems
common that people in many fields of statistical science don't use
dimensional thinking: see for a
recommendation of a paper by David Finney (1917-  ).)


On Thu, Jan 10, 2013 at 10:06 PM, Matthew C Mahutga
<> wrote:
> Thanks William and Nick.
> -linest- doesn't work for xtpcse, but I'm not sure why. It yields predicted values way beyond the observed bounds of the response.
> It works great for regress and xtreg (at least in my application) and is very intuitive to use. This does seem to be a nice approach insofar as it accommodates the covariance between parameters. But in my case, I'm engaging in pure unadulterated hypotheticals, and would actually prefer to keep the observed parameters fixed ;o).
> I attempted -estadd- or -eret2- to try to impose constraints post-facto, but had to admit they are beyond me.
> The procedure outlined by Nick gives intuitive results (at least for my purposes), but I'm still not exactly clear if I'm supposed to subtract from y (response, outcome, dependent) the constrained coefficient, or rather the product of the constrained coefficient and its covariate. My reading of his initial email leads me to believe it's the latter.
> Thanks for your help!
> Matthew
> -----Original Message-----
> From: [] On Behalf Of Richard Williams
> Sent: Thursday, January 10, 2013 12:23 PM
> To:;
> Subject: RE: st: Coefficient Constraints as Counterfactuals
> Here is an example using -linest- (which, of course, requires that you install -linest-. It is from the STB and can be found with -findit-)
> use "";, clear logit warmlt3 yr89 male white age ed test yr89 = -.5, coef constraint 1 yr89 = -.5 linest, c(1) modify logit warmlt3 yr89 male white age ed, constraint(1)
> Note that the test command and linest produce the same coefficients.
> Further imposing constraints after estimation gives different results than imposing constraints before estimation -- but they are supposed to be asympotically equivalent (like the difference between a LR chi square and a Wald chi-square).
> I don't know if it works with xtpcse, but you can try it.
> At 02:18 PM 1/10/2013, Matthew C Mahutga wrote:
>>Hi Nick.
>>Thanks for this and for asking me to clarify.
>>I'm using xtpcse with a first order autocorrelation correction.
>>Do I understand you correctly that if my original model (with other
>>covariates omitted) is
>>Y = b0 + b1x1+b2x2+b3x1*x2
>>And I want to estimate the predicted values of a model in which b1 =
>>b1+b3, then I would regress Y^(=y-b1+b3x1) on x2 and the rest of the
>>covariates and then estimated the prediction?
>>Thanks again,
>>-----Original Message-----
>>[] On Behalf Of Nick Cox
>>Sent: Thursday, January 10, 2013 10:41 AM
>>Subject: Re: st: Coefficient Constraints as Counterfactuals
>>If you want say to -regress- such that
>>y = b_0 + b_1 x_1 + 42 x_2
>>then calculate
>>y - 42 x_2
>>and -regress- on x_1. Naturally, this isn't universal, but what could
>>be universal across all possible estimation commands? Moral:
>>You should tell us more about the command you are using.
>>On Thu, Jan 10, 2013 at 6:25 PM, Matthew C Mahutga
>><> wrote:
>> > I have a question that I hope has an easy answer that escapes me.
>> >
>> > I am using  estimation command that does not support the
>> constraints option, but I would like to constrain a select group of
>> coefficients. For example, one model includes an interaction term
>> between a given socioeconomic process and a dummy variable for
>> institutional regime. I would like to ask questions like "what would
>> the trend in my outcome look like if the socioeconomic process had the
>> larger of the two conditional (i.e. by regime type) effects".
>> >
>> > Is there a universal means by which to set a given coefficient to
>> a fixed value prior to model estimation. Or, can I estimate predicted
>> values using stored results but change the coefficient on one
>> covariate beforehand?

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