Panel Regression: Cross-Sectional Dependence and Clustering
Summary
The document discusses a fixed-effects panel regression relating mutual fund characteristics to monthly fund alpha. Its central statistical concern is that monthly returns may be correlated across funds in the same period. If standard errors treat those observations as independent, the effective amount of information can be overstated and uncertainty understated. The response recommends clustering by date or using another method that accommodates cross-sectional correlation; it also points to portfolio time series and Fama–MacBeth estimation as related ways to use time variation.
The exchange also cautions that fixed effects control unobserved heterogeneity only when it is constant over time, an assumption that may not fit changing fund characteristics. The discussion offers general guidance rather than a full model specification. In particular, it does not establish that a particular clustering choice is sufficient for every error structure, and the panel's time and cross-sectional dimensions should inform inference.
Key ideas
- Fund returns observed in the same month can share shocks, creating cross-sectional error dependence.
- Ignoring correlated errors can make standard errors too small even when the dataset has many rows.
- Date clustering is suggested to account for common monthly dependence across funds.
- Fixed effects address unobserved heterogeneity only when that heterogeneity is stable over time.
- Portfolio time-series analysis and Fama–MacBeth estimation are mentioned as alternative approaches to inference.
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# Disadvantages of large panel
# Disadvantages of large panel
I am currently researching if some fund characteristics such as (fund size, fund family size, capital flows, and fund age) explains fund performance measured (monthly alpha).
Therefore, I am using a fixed effect panel regression where the dependant variable is monthly fund performance; the independent variables are lagged monthly fund characteristic. I perform a fixed effect regression and cluster by (ID) to adjust standard errors for cross-sectional dependence and heteroscedastic residuals.
My sample size is 350 funds with 120 observation for each fund (10 years). In total, I have around 42,000 observations.
Are there any disadvantages and/or benefits for using a large panel dataset?
You're help is appreciated.
## Answer by Matthew Gunn (score 4, accepted)
https://quant.stackexchange.com/a/35464
In general, more data is better than less data.
On the topic of your specific scenario, you want to cluster by date or use some other procedure to produce consistent standard errors in the presence of cross-sectional correlation.
Monthly returns are basically uncorrelated over time but exhibit significant cross-sectional correlation.
## With large quantities of data, treating correlated error terms as uncorrelated can massively understate standard errors!
#### Example:
Let's say I have $i=1,\ldots,50$ people recording the results of me flipping a coin 20 times ($t=1,\ldots,20$). Let $y_{it}$ be person $i$'s recorded result of flip $t$. I have $20 \cdot 50 = 1000$ observations.
My model is: $$ y_{it} = \mu + \epsilon_{it}$$
If I treat each $\epsilon_{it}$ as uncorrelated, I'm going to massively understate my standard errors. In reality, I have basically 20 independent observations, not 1,000. For each time $t$, the $\epsilon_{it}$ will be significantly correlated.
#### Basically the same thing happens with returns
For any time period $t$, returns ${R}_{it}$ are correlated. There's huge cross-sectional correlation.
Hence, you'd want to cluster by date. There are other methods of course to deal with cross-sectional correlation.
The same logic is behind: - forming portfolios and using time-series variation in portfolio returns - the Fama-Macbeth procedure of running $T$ cross-sectional correlations and taking the time-series average and standard deviation to compute estimates and standard errors.
## Answer by jd8 (score 1)
https://quant.stackexchange.com/a/35466
See this comment from the wiki page on fixed effects models:
> In statistics, a fixed effects model is a statistical model in which the model parameters are fixed ... Such models assist in controlling for unobserved heterogeneity when this heterogeneity is constant over time.
Emphasis on the time constancy of unobserved heterogeneity is my own. Do you believe that the unobserved heterogeneity in mutual fund characteristics is constant over time? This could be a reasonable dimension on which less is more.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.