Nonlinear regression

[Fredrick Pavlecki]

Hello guys,

I was recently trying to replicate an approach from Barber, Brad M. and Huang, Xing and Odean, Terrance, Which Factors Matter to Investors? Evidence from Mutual Fund Flows (May 18, 2016).

In that paper the author first run the following regression:

where F are flows for fund p in month t and MAR p,t−s represents the lagged market-adjusted return for the fund at lag s, where s = 1 to 18 months. X is a matrix of control variables and µt are time-fixed effects.

The authors see that there is a decay in coefficients the more back in time they go. To capture this decay they say that they model "the flow-return relation using an exponential decay model, with decay rate λ":

"The key parameters of interest in this model are b, which measures the relation between a weighted sum of the previous eighteen monthly market-adjusted returns, and λ, which measures the decay in the return-flow relation over time."

I was a bit unsure how do you estimate λ coefficient as I feel a bit lost at the moment? I believe that they use nl to run a restricted model, but I am not sure.

Would really appreciate any help.

[FernandoRios]

This is an example for a simplified version:

nl (F={a}+{b}*l.mar+{b}*exp(-{lm})*l2.mar+{b}*exp(-2*{lm})*l3.mar)

This may help

[Fredrick Pavlecki]

This is an example for a simplified version:

nl (F={a}+{b}*l.mar+{b}*exp(-{lm})*l2.mar+{b}*exp(-2*{lm})*l3.mar)

This may help

Thank you Fernando. I was wondering if there is a way to include time-fixed effects? As far as I understand nl doesn't support them

[Fredrick Pavlecki]

I am curious if anyone had experience of estimating a similar non-linear regression with fixed effects using the gmm operator?

[FernandoRios]

There were a few posts about gmm with fixed effects in the past, and the answer is that it isn't feasible.
You can always add fixed effects as dummies, for as you may know, there is a limitation into how many dummy variables you can add to a model.
For the nl. You can add time fxed effects just by adding something like : {tfe:i.year}
HTH

[Fredrick Pavlecki]

There were a few posts about gmm with fixed effects in the past, and the answer is that it isn't feasible.
You can always add fixed effects as dummies, for as you may know, there is a limitation into how many dummy variables you can add to a model.
For the nl. You can add time fxed effects just by adding something like : {tfe:i.year}
HTH

Thank you Fernando. I tried running:

 
 nl (F={a}+{b}*l.mar+{b}*exp(-{lm})*l2.mar+{b}*exp(-2*{lm})*l3.mar+{tfe:i.year})

but it returns me that factor-variable operators not allowed.

Do you know what can be the issue here?

[George Ford]

This is old, but here the solution for future reference:

{tfe: y2020 y2021 y2022}

you have to list out the dummy for each fixed effect.