Panel data: xtset, xtreg, fixed and random effects — Stata Module 9

Panel data — repeated observations on the same units (firms, countries, individuals) over time — is where Stata is at its best. xtset declares the panel structure; xtreg fits panel models; the within-transformation that powers fixed effects is one command and one option.

xtset — declare the panel

stata

xtset bank_id year                  // panel ID + time variable
xtdescribe                          // panel structure: balanced or not
xtsum lending_rate                   // within / between / overall variance

xtreg with fixed effects

stata

xtreg lending_rate deposit_rate, fe                       // bank fixed effects
xtreg lending_rate deposit_rate i.year, fe                // bank FE + year FE
xtreg lending_rate deposit_rate, fe vce(cluster bank_id)  // clustered SEs

What the within transformation actually does

Fixed effects are equivalent to subtracting the bank-specific mean from each variable, then running OLS on the de-meaned data. This 'within' estimator removes any time-invariant bank characteristics — they get differenced out. The cost: any time-invariant predictor is unidentified (you can't include 'bank size at IPO' as a regressor when it never varies within bank).

Random effects

stata

xtreg lending_rate deposit_rate, re      // random effects
hausman fe re                            // Hausman test: FE vs RE

Random effects assumes the bank effect is uncorrelated with the regressors. The Hausman test compares FE and RE estimates. If they differ significantly, the random-effects assumption is rejected — use FE.

reghdfe — high-dimensional fixed effects

stata

* User-written, fast, recommended for multi-way FE
ssc install reghdfe
reghdfe lending_rate deposit_rate, absorb(bank_id year) cluster(bank_id)

Time-series operators

stata

xtset bank_id year
generate lag_rate = L.lending_rate         // L. lag
generate lead_rate = F.lending_rate        // F. lead
generate diff_rate = D.lending_rate        // D. first difference

Two-way clustering needs a special command

xtreg only does one-way clustering. For two-way (e.g., cluster by both bank and year), use reghdfe or ivreg2 with cluster(bank year). The choice can change the SEs by 30-50%.

Exercise

Declare a panel with bank_id and year, then fit a fixed-effects model of lending_rate on deposit_rate.