Fixed Effects

[John Cavin]

Dear Statalists,

How can I decide, which of following fixed effects make more sense, when I would like to find out, whether men or women are better (better means a higher return) as investors in funds?

1. Time fixed effect
2. Style fixed effect (Style means e.g. small caps, large caps etc.)
3. Investor fixed effect
4. Funds fixed effect

Some Information about my file:

I have panel data with round about 500 investor_ids for a time period of ten years. Some investors have more than one funds per year.
Some funds are managed by different investors in different years, but only by one investor each time when they are managed.

My regression looks like following:

reg return man (dummy 1 if man) controllvar1 controllvar2 ... i.year i.style i.investor i.funds, robust

How can I decide which effects to combine/use? I hope it is understandable.

Thanks a lot!

[Phil Bromiley]

This depends on what you want to control for. The fixed effects picks up anything that is constant within the domain that the effect is based on. So, an investor fixed effect will control for (hold constant) stable investor differences and only use within-investor variation to estimate the equation.

So, you cannot have an investor fixed effect since sex is constant within investors. You can have any of the three others depending on what you think is most important and what you want to hold constant.

Note that with fund effects, you'll be throwing out the information for investors who stay with a fund and only that fund for the entire observation period - for such investors the dummy will pick up both stable fund and stable investor characteristics.

Often, you are well advised to look for normal practice in your field.

[Clyde Schechter]

Let me be provocative and suggest the opposite of what Phil Bromiley suggests: go radically in the opposite direction of normal practice in your field!

That is, from watching Statalist, I have the impression that longitudinal data are nearly always treated with fixed effects estimation in the fields of finance, and usually also in economics.* And there are some good reasons for doing that, particularly if you strongly prefer unbiasedness over efficiency and focus your skepticism about modeling assumptions on certain technical aspects of structure. But the fixed effects estimators have some important limitations, and the project you are describing seems to go beyond the capabilities of a fixed effects regression.

As best I can understand it (I know next to nothing about finance), your time effects are nested inside investor and fund effects. The latter two do not appear to have a nesting relationship, nor are they crossed: they appear to be a multiple membership model. But regardless, they are clearly an additional hierarchical level. Since the fixed-effects estimators can only accommodate two levels, no matter how you "slice" it you are building a model by putting your data into a Procrustean bed. (I've said nothing about style effect, but it looks to me like it's just a dichotomous or polytomous attribute of the fund, and doesn't contribute a separate level.)

I think if you want to do this "right," you need to go to the mixed-effects models in Stata. The multiple-membership aspect of the investor and fund effects are not ideally suited to these commands, which work best with pure nesting and almost as well with crossed effects. Multiple-membership can be modeled by coding as if the effects were crossed, but the estimation may be very slow and inefficient (in terms of computing time, not in terms of estimate variance). If you have access to HLM7 software and know how to use it, I have heard that it handles multiple-membership models better than Stata's commands--but I have never used it myself and don't know how to.

Now, there are downsides to this approach. First, these models are not widely used in finance and may not be well understood by a finance audience. Second, I'm guessing that you yourself don't know much about them and would face a steep learning curve here. Third, there are assumptions in these models that may not be met by your data (which, I think, is why these models have not gained much popularity in finance and economics). Fourth, if your data contains large numbers of funds and investors, the estimation could be very slow, or maybe even exceed Stata's limits. Despite all of these, it might be worth looking into. You might want to ask some colleagues in your discipline whether this would fly or not in your environment.

*An alternative explanation for my observations would be that the people in those disciplines who use the mixed-effects models freely are numerous but do not post on this Forum. But that strikes me as less plausible.

[Katherine Adams]

Hello,

I have a question related to the topic of this thread (https://www.statalist.org/forums/for...s-model/page4; #53).

I will appreciate any help!

[Carlo Lazzaro]

Katherine:
the link you provided seems to be broken.

[Katherine Adams]

Oh, I am sorry.

https://www.statalist.org/forums/for...es-model/page4

[David Benson]

Hi Katherine,

As Phil and Clyde both indicated, fixed-effects (at least for the men vs the women) won't work because sex is constant within investors. Also, if a man and a woman invest in the same mutual fund over the same time period, both will earn equal returns. Thus, I would look for ways that the men and women might invest differently (for example, men tend to be more overconfident about their ability to pick stocks / mutual funds so they may trade more often, or are less willing to cut their losses -- both leading to lower returns for men ).

Thus, I can imagine with your data you could look for several differences between the way men and women invest:

1. Men choose riskier mutual funds than women on average (i.e. more likely to invest in a gold fund or emerging markets fund)
2. The man's overall mutual fund portfolio is riskier than the woman's
3. Men trade more than women
4. Men hold on to a mutual fund for less time (related to #3)
5. For a given style fund (i.e. large-cap stocks) men are more likely to choose one with higher expense ratio, or more likely to choose an actively-managed fund over an index fund.

I don't know if this would help, but you'll want to look at Barber & Odean (2001) (you probably already have) and see how they set up their model.
The Quarterly Journal of Economics, Volume 116, Issue 1, 1 February 2001, Pages 261–292, https://doi.org/10.1162/003355301556400
https://www.jstor.org/stable/2696449

Theoretical models predict that overconfident investors trade excessively. We test this prediction by partitioning investors on gender. Psychological research demonstrates that, in areas such as finance, men are more overconfident than women. Thus, theory predicts that men will trade more excessively than women. Using account data for over 35,000 households from a large discount brokerage, we analyze the common stock investments of men and women from February 1991 through January 1997. We document that men trade 45 percent more than women. Trading reduces men's net returns by 2.65 percentage points a year as opposed to 1.72 percentage points for women.

You might also take a look at:
Are men better investors than women? Gender differences in mutual fund and pension investments (2008). Journal of Financial Services Marketing LINK
It has a nice review of the literature.

This paper reviews prior studies on gender differences for financial consumers. Results are inconclusive and more research is needed to clarify when and why there are gender differences. This paper also analyses how the Swedish population has allocated their pension investments within the state pension system as well as the results from a nationally representative sample of consumers. There are less significant differences between expert men and women. Most differences are between novice men and women. Men are both more profit-oriented and more motivated to make financial investments than women are.

[Katherine Adams]

Hello David,

I am afraid that your answer does not refer to my question...

Mine is as follows:
https://www.statalist.org/forums/for...es-model/page4

(posts ## 51, 55, 57)

[David Benson]

Sorry - I was responding to John Cavin's (which was from Mar 2016 -- yikes!). Sorry!