Time-varying beta

[Sander Hakvoort]

Dear all,

I am currently studying mutual equity fund returns in regard to the four-factor model of Carhart (1997). I have monthly fund and market returns from January-2000 up until now. The basic function is this: Rit-Rft=α+β0i(X1t)+β1i(X2t)+β2i(X3t)+β3i(X4t)+ ϵit.

I would now like to create time-varying betas, meaning the individual betas are a linear regression and dependent on a set (four) of lagged predetermined variables (Zt-1).

This would transform each beta into: βit=β0i + [β1Z(t-1,1) + β2Z(t-1,2) + β3Z(t-1,3) + β4Z(t-1,4)]

This is in line with the research by Otten & Bams (2004), resulting in time-variant betas and increasing the explanatory power of the model.

My Question: I can not find a a command to perform such a regression in Stata. Does anyone have experience with this, or know the answer?

Thanks in advance for all the help, and if you have any further questions then please feel free to ask them.

Sander H.

Otten, R., & Bams, D. (2004). How to measure mutual fund performance: economic versus statistical relevance. Accounting & finance, 44(2), 203-222.

[Phil Bromiley]

Welcome to Statalist. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

I suspect you can do this with ml or nl by writing an evaluator program. However, if all you want is to let the b's vary by year c.z##i.year would do that for you. Alternatively, you might be able to do this by substituting the beta equation into the return equation.