Do I have to bootstrap the dummy variables used for event dates in an event study?

Question

I am doing a project where i am trying to estimate the effect of the inclusion of a stock in an ETF on its returns, meaning that i am trying to see how the inclusion of a stock in a given ETF affects that stocks returns, I have collected return data on more than 150 equities, their event dates (when they were included in the ETF and so on).

my design is this, i have divided the sample into the estimation periot starting 130 days before the inclusion and the forecast window which inclused 10 days.

I am using the Multivariable Regression Model (MVRM) technique and the market model with dummy variables, the market model's dependant variable is the firms returns on the left hand side of the equation and on the right hand side of the equation qe have the market returns represented by the returns of the S&P500 index and 10 dummy variables where every dummy takes the value of 1 for the observations within the forecast interval.

More can be read on the model in Karafiath 1988.

I want to do determine the distribution of the sum of the dummy estimators which pretty much represents the cummulative abnormal returns in this case by bootstrapping.

Now my question is this:

Do i have to use a bootstrap method by simply resampling with replacement from the Dependant Variable (firm i's returns) and the market returns (S&P500's returns) and once i have drawn a sample I run a regression with the resampled values of those two and estimate the the coefficients of the dummies and save them, then draw another sample from the DepVar and IndVar and again run a regression and estimate the coefficients of the dummy variables and save them and repeat this process 10 000 times and then construct the empirical distribution of the dummy variables?

OR

Should i draw 10 000 samples and run the regression for all the variables in the regression including the dummies?

will this second case imply that when resampling from the dummy variable which is basically a bunch of zeros with only one 1 at the position of the date in the forecast interval, would this mean it will randomly assign the number 1 to some other non forecast interval because that would not make sense.

Thanks in Advance.

Answer 1

One way is to rely on a simple block bootstrap procedure. That is, you can draw $n$ contiguous blocks of length $t^{bs}$ (both LHS and RHS variables) which result in an overall bootstrapped sample of length $T$, which should be identical to the length of your original sample.

Then repeat your estimation for each bootstrap sample and save your results, e.g. 10000 times. Thus, inference is based on the distribution of your coefficients.

From my personal experience, dummy variables often result in singular (or nearly singular) matrices within your estimation procedure. However, you can either manually add these observations to your bootstrap sample or alternatively discard all samples resulting in numerical errors.