Estimate Coefficient and Discount Factor on a Cumulative Discounted Sum

[Andres Deloera]

Hi! I would like to estimate a regression where one of the regressors of interest is the discounted cumulative sum of a variable over the last several periods, but where the regression simultaneously estimates the discount factor for that sum and the coefficient on the variable. In practice I would like to do this twice, once including an interaction of the entry within the sum with an indicator for if the entry occurred after treatment. I would also like to include fixed effects based on entity and time characteristics. I've included a simplified example of the type of regression I'd like to run in an ideal world, but can't figure out how to implement in Stata. In the example, the goal would be to estimate the Betas, Delta and Gamma, and the FEs simultaneously. I hoped the ARDL package might help here, but would appreciate any advice to get that or some other method to work. Thanks!!