Event studies are widespread in economics and finance to determine the effect of an event on a stock price, but they are almost always based on frequentist reasoning. An OLS regression -- over a reference period which is distinct from the event window -- is usually used to determine the parameters required to model the normal return for an asset. One then determines the statistical significance of cumulative abnormal returns ($\text{CAR}$) on asset $i$ following an event during a specified event window from $T_1$ to $T_2$. A hypothesis test is used to determine whether these returns are significant and thus indeed abnormal or not. Thus:

$H_0 : \text{CAR}_i = 0$, where

$\text{CAR}_i = \sum_{t=T_1}^{T_2} \text{AR}_{i,t} = \sum_{t=T_1}^{T_2} \left( r_{i,t} -\mathbb{E}[r_{i,t}] \right)$, and

$\mathbb{E}[r_{i,t}]$ is the return on the asset predicted by the model.

If our number of observations is large enough, we can assume asymptotic normality of the distribution of asset returns, but this may not be verified for a smaller sample size.

It can be argued that because of this, single-firm, single-event studies (as required for example in litigation) should follow a Bayesian approach, because the assumption of infinitely many repetitions is much "further from being verified" than in the case of multiple firms. Yet, the frequentist approach remains common practice.

Given the scarce literature on this subject, my question is how to best approach an event study -- analogous to the methodology outlined above and summarised in MacKinlay, 1997 -- using a Bayesian approach.

Although this question arises within the context of empirical corporate finance, it is really about the econometrics of Bayesian regression and inference, and the differences in reasoning behind frequentist and Bayesian approaches. Specifically:

1. How should I best approach the estimation of the model parameters using a Bayesian approach (assuming a theoretical understanding of Bayesian statistics, but little to no experience in using it for empirical research).

2. How do I test for statistical significance, once cumulative abnormal returns have been computed (using the normal returns from the model)?.

Event studies are widespread in economics and finance to determine the effect of an event on a stock price, but they are almost always based on frequentist reasoning. An OLS regression -- over a reference period which is distinct from the event window -- is usually used to determine the parameters required to model the normal return for an asset. One then determines the statistical significance of cumulative abnormal returns ($\text{CAR}$) on asset $i$ following an event during a specified event window from $T_1$ to $T_2$. A hypothesis test is used to determine whether these returns are significant and thus indeed abnormal or not. Thus:

$H_0 : \text{CAR}_i = 0$, where

$\text{CAR}_i = \sum_{t=T_1}^{T_2} \text{AR}_{i,t} = \sum_{t=T_1}^{T_2} \left( r_{i,t} -\mathbb{E}[r_{i,t}] \right)$, and

$\mathbb{E}[r_{i,t}]$ is the return on the asset predicted by the model.

If our number of observations is large enough, we can assume asymptotic normality of the distribution of asset returns, but this may not be verified for a smaller sample size.

It can be argued that because of this, single-firm, single-event studies (as required for example in litigation) should follow a Bayesian approach, because the assumption of infinitely many repetitions is much "further from being verified" than in the case of multiple firms. Yet, the frequentist approach remains common practice.

Given the scarce literature on this subject, my question is how to best approach an event study -- analogous to the methodology outlined above and summarised in MacKinlay, 1997 -- using a Bayesian approach.

Although this question arises within the context of empirical corporate finance, it is really about the econometrics of Bayesian regression and inference, and the differences in reasoning behind frequentist and Bayesian approaches. Specifically:

1. How should I best approach the estimation of the model parameters using a Bayesian approach (assuming a theoretical understanding of Bayesian statistics, but little to no experience in using it for empirical research).

2. How do I test for statistical significance, once cumulative abnormal returns have been computed (using the normal returns from the model)?

3. How can this be implemented in Matlab?

Event studies are widespread in economics and finance to determine the effect of an event on a stock price, but they are almost always based on frequentist reasoning. An OLS regression -- over a reference period which is distinct from the event window -- is usually used to determine the parameters required to model the normal return for an asset. One then determines the statistical significance of cumulative abnormal returns ($CAR$) on asset $i$ following an event during a specified event window from $T_1$ to $T_2$. A hypothesis test is used to determine whether these returns are significant and thus indeed abnormal or not. Thus:

$H_0 : CAR_i = 0$, where

$CAR_i = \sum_{t=T_1}^{T_2} AR_{i,t} = \sum_{t=T_1}^{T_2} \left( r_{i,t} -\mathbb{E}[r_{i,t}] \right)$, and

$\mathbb{E}[r_{i,t}]$ is the return on the asset predicted by the model.

If our number of observations is large enough, we can assume asymptotic normality of the distribution of asset returns, but this may not be verified for a smaller sample size.

It can be argued that because of this, single-firm, single-event studies (as required for example in litigation) should follow a Bayesian approach, because the assumption of infinitely many repetitions is much "further from being verified" than in the case of multiple firms. Yet, the frequentist approach remains common practice.

Given the scarce literature on this subject, my question is how to best approach an event study -- analogous to the methodology outlined above and summarised in MacKinlay, 1997 -- using a Bayesian approach.

Although this question arises within the context of empirical corporate finance, it is really about the econometrics of Bayesian regression and inference, and the differences in reasoning behind frequentist and Bayesian approaches. Specifically:

1. How should I best approach the estimation of the model parameters using a Bayesian approach (assuming a theoretical understanding of Bayesian statistics, but little to no experience in using it for empirical research).

2. How do I test for statistical significance, once cumulative abnormal returns have been computed (using the normal returns from the model)?.

Event studies are widespread in economics and finance to determine the effect of an event on a stock price, but they are almost always based on frequentist reasoning. An OLS regression -- over a reference period which is distinct from the event window -- is usually used to determine the parameters required to model the normal return for an asset. One then determines the statistical significance of cumulative abnormal returns ($\text{CAR}$) on asset $i$ following an event during a specified event window from $T_1$ to $T_2$. A hypothesis test is used to determine whether these returns are significant and thus indeed abnormal or not. Thus:

$H_0 : \text{CAR}_i = 0$, where

$\text{CAR}_i = \sum_{t=T_1}^{T_2} \text{AR}_{i,t} = \sum_{t=T_1}^{T_2} \left( r_{i,t} -\mathbb{E}[r_{i,t}] \right)$, and

$\mathbb{E}[r_{i,t}]$ is the return on the asset predicted by the model.

If our number of observations is large enough, we can assume asymptotic normality of the distribution of asset returns, but this may not be verified for a smaller sample size.

It can be argued that because of this, single-firm, single-event studies (as required for example in litigation) should follow a Bayesian approach, because the assumption of infinitely many repetitions is much "further from being verified" than in the case of multiple firms. Yet, the frequentist approach remains common practice.

Given the scarce literature on this subject, my question is how to best approach an event study -- analogous to the methodology outlined above and summarised in MacKinlay, 1997 -- using a Bayesian approach.

Although this question arises within the context of empirical corporate finance, it is really about the econometrics of Bayesian regression and inference, and the differences in reasoning behind frequentist and Bayesian approaches. Specifically:

1. How should I best approach the estimation of the model parameters using a Bayesian approach (assuming a theoretical understanding of Bayesian statistics, but little to no experience in using it for empirical research).

2. How do I test for statistical significance, once cumulative abnormal returns have been computed (using the normal returns from the model)?.