Time dummies and omitted variable bias

[Kaleemullah Abbasi]

Dear all,

Assume a situation in which there are only two omitted/unobservable variables. Also, assume they are time-varying and can have either a positive or a negative effect on the dependent variable.

Given the aforementioned assumptions, if time dummies are included in the regression then does this mean that there will not be any omitted variable bias because all the time-varying unobservable variables are controlled? In this case, what are the ways in which omitted variable bias, if any, could arise?

Kind regards.

[Carlo Lazzaro]

Kaleemullah:
the best way for eliciting helpfiul replies is posting what you typed and what Stata gave you back (as per FAQ). Thanks.

[Kaleemullah Abbasi]

Thanks for the reply and the guidance.

Is it possible if you can clarify this statistical issue? I will be grateful.

How can omitted variable bias arise even after including time dummies and fixed effects which capture all time-varying unobservable variables and time-invariant unobservable variables?

Kind regards.

[Clyde Schechter]

How can omitted variable bias arise even after including time dummies and fixed effects which capture all time-varying unobservable variables and time-invariant unobservable variables?

What you say here is often repeated, but it is an abbreviation, and as literally stated it is false. What is true is this:

Inclusion of panel level fixed effects automatically adjusts for any observed or unobserved effects which are constant across time within each panel. Inclusion of time indicators adjusted for any observed or unobserved effects which are constant across panels in each time panel.

But the panel and time effects do not adjust for unobserved effects which vary both over time and within panels.

[Kaleemullah Abbasi]

Thank you very much for the excellent clarification.

I will be grateful if you can answer one more query.

Literature suggests that the control variable (A), in general, has an association with the dependent variable, however, (A) does not affect any independent variables in the multiple regression, hence, there is no omitted variable bias. In this case, if there is no data available for A (due to the study being conducted in different environment/context) then which statistical techniques in Stata can be used to address any problems, if any, caused due to exclusion of (A)?

Note: (A) is time-varying and also varies within panels.

I look forward to your reply.

Kind regards.

[Clyde Schechter]

I'm not sure I fully understand your choice of words, but if A is not associated with the predictor variables in your model, then it cannot be a source of omitted variable bias, and there is no need to do anything about it on that account.

What may result from the exclusion of A, which is associated with the dependent variable, is that with A excluded the residual variance of the regression may be larger than it would be had you been able to include A. That in turn may reduce your statistical power. Without specifics and data, it is impossible to speculate whether this is an important problem or a minor one. In any case, possible approaches to dealing with this, if it is large enough to matter, is to study a larger sample, or to find a variable which might serve as a good proxy for A and for which data can be obtained.

[Kaleemullah Abbasi]

Thank you very much for the guidance. Yes, the control variable (A) does not create omitted variable bias given that it is not associated with predictor variables.

An important lesson learnt. Large samples reduce the problems arising due to exclusion of control variables that are associated with dependent variable but not with predictor variables.

Is the sample of around 1200 observations large enough to address the aforementioned issue?

I look forward to your reply.

Kind regards.

[Clyde Schechter]

Can a sample of around 1200 observations be large enough to address the aforementioned issue?

It is not possible to answer this question. There are many aspects to it that have not been specified. One is just how strongly the variable A is associated with the outcome variable. Another is how much of the variance in the outcome is accounted for by the observed predictors. Another is how the 1200 observations are divided up in terms of N (# of panels) and T (# of time periods). Another unspecified but relevant matter is how large the actual effect size(s) of your principal predictor(s) are, and with what level of precision you need to estimate those for your research goals.

[Kaleemullah Abbasi]

Thank you for the reply.

Literature suggests that the association is not well established. Although the theory suggests the variable can have an impact on dependent variable, the empirical evidence is mixed as some find significant association and some find the association to be insignificant. There are 250 firms (N) and 6 time periods. Also, 0.1 significance level is used. The adjusted r-square will vary as I am using three different ways to measure the dependent variable, however, based on literature, it will vary from 0.15 to 0.5. Sorry, I do not know about effect size given that it is not used by studies in my field to ascertain sample size.

Is the above mentioned information enough to determine whether 1200 observations are large to address the issue? Other studies in my field have used observations ranging from 700 to 1300.

I look forward to your reply.
Kind regards

[Clyde Schechter]

Well, that information doesn't really settle the question.

Let's think about it another way: suppose we had the necessary information and did the calculations and concluded that omitting A would lead to enough inflation of the standard errors of your principal predictors that it would compromise your study, what would you do? Can you get more data even if you try? Would you abandon the study? Or perhaps go for a major re-design, such as a matched-pairs analysis that might be more powerful? If you wouldn't be in a position to do any of those things, then I wouldn't worry about this issue: I'd just proceed with my analysis and hope for the best.

[Kaleemullah Abbasi]

Thanks for the reply and suggestions.

I will learn about matched pairs analysis (propensity-score matching) which is also used in my field. Also, more data can be collected.