Difference-in-Differences With Missing Data

This brief post is a "shout out" for  Irene Botusaru (Economics, Simon Fraser University) who gave a great seminar in our department yesterday.

The paper that she presented (co-authored with Federico Guitierrez), is titled "Difference-in- Differences When the Treatment Status is Observed in Only One Period". So, the title of this post is a bit of an abbreviation of what the paper is really about.

When we conduct DID analysis, we need to be able to classify information about the behaviour/characteristics of survey respondents into a 4-way matrix. Specifically we need to be able to observe the respondents before and after a "treatment"; and in each case we need to know which respondents were treated, and which ones were not.

Usually, a true panel of data, observed at two or more time-periods, facilitates this.

However, what if we simply have repeated cross-sections of data, taken at different time-periods? In this case we aren't necessarily observing exactly the same respondents when we look at the cross-sections for two different time-periods. Typically, in the cross-section after the treatment we'll know which respondents were treated and which ones weren't. However, there will be no way of partitioning the respondents in the pre-treatment cross-section  into "subsequently treated" and "not treated" groups.

Two of the four cells in the matrix of information that we need will be missing, so conventional DID can't be performed.

This is the problem that Irene and Federico consider.

A natural response is introduce some sort of proxy variable(s) to deal with the missing data, and of course this will introduce an estimation bias, even asymptotically. This paper basically takes this approach. The result is a GMM estimation strategy, together with a test that the underlying assumptions are satisfied.

This is a really nice paper - well motivated, technically solid, and with a nice empirical example and application. I urge you to take a look at it if DID is in your econometrics tool-kit (and even if it's not!)

I'm sure that Irene and Federico would appreciate hearing about situations where you've encountered this missing data problem, and how you've responded to it.

© 2016, David E. Giles

What's in a Title?

I'm not one of those people who go in for "cute" titles for my research papers. Some people obviously do. However, they probably spend way too much of their valuable time conjuring up snappy titles in the hope that they'll come up with something that will attract people's attention.

Ultimately, it's the content of the paper that's going to matter - at least, I like to think that's true! So, most of my published papers have titles that describe what the research is about - but those titles aren't going to win any awards for creativity. I mean, really, titles such as:

A saddlepoint approximation to the distribution function of the Anderson-Darling test statistic.

Exact asymptotic goodness-of-fit testing for discrete circular data, with applications.

Bias reduction for the maximum likelihood estimator of the parameters in the half-logistic distribution.

Do you see what I mean? (Assuming you're still awake, that is.)

Daylight Saving Time - A Natural Experiment

Early this morning, most of North America "sprang forward" to embrace the coming of Spring an hour sooner than we otherwise would have done. In Canada, the province of Saskatchewan was the notable exception. Ironic really - I'd have thought that with their climate they'd be pleased to get out of winter's icy grip an hour sooner!

Several researchers have noted that the phenomenon of daylight saving time offers a rather nice "natural experiment". We didn't always abide by this custom; now we do. At least, most us do, but some of us don't. In (most of) Canada and the U.S., the duration of DST was extended a couple of years ago.

What a great opportunity to use some econometric modelling to address questions such as: "Does the use of daylight saving reduce energy usage?" After all, as I understand it, this was one of the primary motivations for the introduction of this minor time warp. This just screams out "difference-in-differences" analysis!"

Here are a few links to some studies that have addressed the above question:

• Kellogg, R. & H. Wolff, 2007. Does extending daylight saving time save energy. Evidence from an Australian experiment. IZA DP No. 2704.
• Kotchen, M. J. & L. E. Grant, 2011. Does daylight saving time save energy? Evidence from a natural experiment in Indiana. Review of Economics and Statistics, 93, 1172-1185. (2008 Working Paper here.)
• Nadarjaze, R., H. Sadeghi, & Y. Gohli, 2012. An econometric analysis of the impact of daylight saving time (DST) on electric energy consumption in Iran. Quarterly Energy Economics Review, 8, 145-160.

Are there any econometric studies that focus on the "Saskatchewan versus the rest of Canada" aspect of this? I'm not aware of any, off hand. If there are, then I'd love to hear about them.

If not, then this would make a nice student project.

© 2013, David E. Giles