Difference-in-Difference

[Jo Smith]

Hi - I'm examinig the relationship between external auditor tenure and audit quality over ten years ending 2018. I've done 2SLS as an Endogeneity test, but I'm asked to do Diff-in-Diff test as well. I read about this test and find that it is used to recover the treatment effects stemming from sharp changes in the economic environment, or government policy, e..g. a change in regulation during the study period. This is not the case in my study.
Any ideas whether this test can be done without existence of such exogenous shock,, or any ideas on alternative test to be considered.
Thanks you

[Rhys Williams]

In the standard diff-in-diff one compares two groups, treatment and control, across 2 time periods. The treatment group has had some policy applied and you want to see how the policy affects the treatment relative to the control. It's not enough to simply compare treatment and control in the second period, you need to compare with the difference of the first period also (hence the name). To use such a methodology you need to ensure the parallel trends assumption holds.

This set-up can be extended, or generalised, to more than two units and over more time periods (staggered implementation is also possible but a bit messy).

What exactly is it you are trying to investigate? Also, diff-in-diff is not a test, it is an econometric methodology used to evaluate the impact of a policy. If you don't have an exogenous shock then it isn't certain that you are finding a causal effect, although in principle no policy is truly exogenous.

Best,
Rhys

[Jo Smith]

Thank you Rhys for your reply,
I'm trying to test whether the length of auditor tenure affects audit quality. So, I would like to use Diff-in-DIff as an Endogeneity test (to control for causality in particular). Throughout my reading about this method, I find it only work if there is an external shock. However, I find studies use it without existence of exogenous shock and also they compare their two splitted samples for the same period of time.
Do you think that I can use it, even without the existence of an exogenous shock? what if the finding from this method does not support my main results? can I scrap it then (and justify) or keep it?
You said it is a method not a test: do this mean that we have to split the sample into two groups (treatment and control) and then run the typical OLS test for each group?
Regards,
Jo

[Rhys Williams]

Hi Jo,

I am not aware of the literature which uses D-in-D to test endogeneity. My use of D-in-D comes from comparing the outcomes of a treatment group with a control group where such groups are either individuals who have received different treatment (e.g. particular medicine) or countries which have different laws (for example). To a large extent the treatment in this case would be considered exogenous, although in reality it probably isn't: laws don't come from thin air, they are voted on by politicians responding to certain events/feelings and so the enactment of a law may not be exogenous but nonetheless you want to test the impact of the law by comparing with a similar country.

You're trying to test how the length of auditor tenure impacts audit quality - what is your dataset, is it individual auditors or countries/regions with different audit rules?

Best,
Rhys

[Jo Smith]

Thank you Rhys,
My data set includes individual auditors from one country(the UK). Individual auditors' tenure is the independent variable while fees paid to auditors (audit fees) are the dependent variable. i.e does tenure affect fees? the problem is that there is no any exogenous shock relevant to the setting of the study during the study period.
Regards,
Jo

[Rhys Williams]

And do you have panel data (i.e. same individual auditors for each year)? It might be that you want to use something like fixed effects rather than a difference-in-difference approach?

Best,
Rhys

[Jo Smith]

yes. it is panel data includes UK listed companies (sample of 200 company) over 10 years. individual auditors (who audit these firms) are not same over all years, they keep changing, on average, every three years.

[Rhys Williams]

Well if you have panel data then I would suggest using fixed effects. That is running a regression of form:

Y = a + bX + cIndividuals + dYear + error

That is, you regress your dependent variable (tenure) on independent variable (fees) but control for the individual audit firm and time (normally you control for time but this will probably be perfectly correlated with tenure so maybe don't do this). You can do this in stata using:

xtset individuals time
xtreg Y X i.year, fe cluster(individuals)

As I mention, you might not include "i.year" (if it is perfectly correlated with tenure). You can include any control vars you like. You also should investigate whether you need to cluster over individual auditors/firms, I would imagine you do.

Hope this is helpful.

Best
Rhys

[Jo Smith]

Thank you Rhys for such clarification.