Is this right? Regression analysis using LSDV and dif-in-dif

[Tobias Christiansen]

Hello,

I'm currently trying to investigate the effect of aging on economic output and what the role of the low interest rates experienced over the past decade are. I use panel data for 169 countries from 1990-2014. I'm currently regressing the following;

y_i,t = gdp per capita
A_i = A dummy which equals 1 if the ratio of old (age 65+) to young (age 20-64) has gone up over the period 1990-2014 in a specific country
L_i = A dummy which equals 1 if the country has experienced low interest rates over the period
X_i,t = Additional controls
First sum is a set of country dummies.
Second sum is a set of year dummies
u_i,t is an error term

i) I've included year dummies to account for secular changes that are not being modeled (these are as i understand aggregate/global changes and not country specific).
ii) I've included country dummies to allow for each and every country to differ. This resembles the Least Sqaure Dummy Variable regression, which is another way of doing a fixed effect estimation. In other words this should remove any country specific fixed (time invariant) effects.
iii) The frist part of the regression (β₁ ... β₄) is thought to be a dif-in-dif approach.
iiii) X_i,t are control variables for things that are thought to change over time on country level

I have a three questions:
1) Is it okay to combine an dif-in-dif approach with a LSDV regression?
2) The first part of the regression resembles a dif-in-din estimator, however, as countries do not hit the lower zero bound for the nominal interest at the same time I do not have a specific period in which countries go from 'normal' interest rates to low (dif-in-dif usually investigate the effect of a treatment that occurs at a specific time). Most countries did indeed experience low interest rates after the financial crisis of 2008. Should i use this year as a dividing point, or is this not necessary?
3) Some of the underlying independent variables may be endogenous. That is, the aging variable I use to define my dummy may be endogenous as gdp growth may lead to a larger share of old people as it could increase life expectancy, or it could increase the inflow of immigrants seeking job etc. Is it possible to use instrumental variables in this setting. An instrument for the aging variable would be birthrates from fx 1960-1980. This would purge the variable from the before mentioned endogeneity, but I'm not sure how to incorporate this when I'm actually regressing dummy variables.

I hope you can help

/Tobias

[David Benson]

Hi Tobias,

Welcome to Statalist! Note that I don’t do macroeconomics, so this might be worth what you paid for it. :-) Others may chime in and disagree.

Regarding your first two questions:

1) Is it okay to combine an dif-in-dif approach with a LSDV regression?

2) The first part of the regression resembles a dif-in-din estimator, however, as countries do not hit the lower zero bound for the nominal interest at the same time I do not have a specific period in which countries go from 'normal' interest rates to low (dif-in-dif usually investigate the effect of a treatment that occurs at a specific time). Most countries did indeed experience low interest rates after the financial crisis of 2008. Should i use this year as a dividing point, or is this not necessary?

In my mind, since low interest rate treatment is what you care about (and it happens at different times), why not just do the fixed variable approach and not call it “diff-in-diff?”

Also, I would include the variable as the actual interest rate rather than a “A dummy which equals 1 if the country has experienced low interest rates over the period.” Ditto for the ratio of old (age 65+) to young (age 20-64). (Including them as a dummy variable is the classic way to include a treatment effect in diff-in-diff, but (a) you don’t have a traditional diff-in-diff because treatment occurs at different times and (b) from a policy point of view you care about an estimate of “for each percentage point increase in interest rates, GDP decreases by X% (or whatever)…”

Plus, collapsing a continuous variable down to 0/1 throws away information.

Regarding your third question:

3) Some of the underlying independent variables may be endogenous. That is, the aging variable I use to define my dummy may be endogenous as GDP growth may lead to a larger share of old people as it could increase life expectancy, or it could increase the inflow of immigrants seeking job etc. Is it possible to use instrumental variables in this setting. An instrument for the aging variable would be birthrates from fx 1960-1980. This would purge the variable from the before mentioned endogeneity, but I'm not sure how to incorporate this when I'm actually regressing dummy variables.

I suspect the change in life span is not enough to “move the needle” in most cases (at least in most developed countries). For example, the life expectancy of a man in the US in 1990 was 73, in 2000 was 75, and in 2015 was 76.3 years. See here and here. I suspect for developing nations controlling for change in life span would become more important.

You could also test to see whether low interest rates had the same effect countries with declining life expectancies (like Russia).

I also don’t know how much immigration changed the ratio of old to young in a country, but surely you could get that info online somewhere to see whether it was large enough to matter (and if so, to control for it).

• More than GDP growth you might look at things like whenever the EU adopted the “Free movement of persons” (1992?). Apparently the idea of the “Polish plumber” became a big deal in UK & France (and elsewhere I’m sure) once that went into effect. Just for fun, I looked up “Polish Plumber” on Wikipedia, and it noted that “Statistics for 2003–2007 estimated that two million East and Central European immigrants arrived in the UK and that half of them were Polish.” (https://en.wikipedia.org/wiki/Polish_Plumber ) (UK total pop at the time was ~60 million. Going from 60 million to 62 million would be a 3.3% increase in population).

Hope that helps!

[David Benson]

Tobias, I'm posting this separately because my last post was already getting to be too long. You might find the following entries to be helpful:

See these Statalist entries:

• Diff-n-Diff (DD) Panel data with many time periods Link
• Difference in Difference model with multiple treatment periods Link
• How to use difference in difference with many yearly observations and dummy-variables? Link

Other Readings:

• Imbens/Wooldridge page 8, Lecture Notes 10, Summer ’07 (available at: http://www.nber.org/WNE/lect_10_diffindiffs.pdf )

• Bertrand, Duflo, & Mullainathan (2004). “How Much Should We Trust Differences-In-Differences Estimates?” The Quarterly Journal of Economics, Volume 119, Issue 1, 1 February 2004, Pages 249–275, https://doi.org/10.1162/003355304772839588

• Autor “Outsourcing at Will: The Contribution of Unjust Dismissal Doctrine to the Growth of Employment Outsourcing.” Journal of Labor Economics , Vol. 21, No. 1 (January 2003), pp. 1-42 https://www.jstor.org/stable/pdf/10.1086/344122.pdf using when states adopted “unjust dismissal” doctrines (which occurred at different times).