Panel Data Guide

Panel Data Analysis Guide

Estimate and interpret fixed effects, random effects, and dynamic panel models using Stata, R, and Python for longitudinal/panel datasets.

What Is Panel Data?

Panel data (also called longitudinal or cross-sectional time-series data) tracks the same units (individuals, firms, countries) across multiple time periods. This structure enables:

• Controlling for unobserved heterogeneity (time-invariant omitted variables)
• Studying dynamic relationships (how X at time t affects Y at time t+1)
• Increased statistical power through more observations

Data Structure

| unit_id | year | gdp_growth | investment | trade_openness |
|---------|------|-----------|------------|----------------|
| USA     | 2015 | 2.9       | 20.5       | 28.3           |
| USA     | 2016 | 1.7       | 20.1       | 27.1           |
| USA     | 2017 | 2.3       | 20.8       | 27.5           |
| CHN     | 2015 | 6.9       | 43.3       | 39.9           |
| CHN     | 2016 | 6.7       | 42.7       | 37.2           |
| CHN     | 2017 | 6.9       | 43.1       | 38.1           |

Key notation:

• i = unit (cross-sectional dimension): i = 1, ..., N
• t = time period: t = 1, ..., T
• Y_it = dependent variable for unit i at time t

Model Specification

Pooled OLS

Y_it = alpha + beta * X_it + epsilon_it

Ignores panel structure; assumes no unit-specific effects. Rarely appropriate.

Fixed Effects (FE) Model

Y_it = alpha_i + beta * X_it + epsilon_it

Each unit has its own intercept (alphai) that captures all time-invariant unobserved heterogeneity. The "within" estimator removes alphai by demeaning.

Random Effects (RE) Model

Y_it = alpha + beta * X_it + u_i + epsilon_it

The unit-specific effect ui is treated as random and uncorrelated with Xit.

Estimation in Stata

Setting Up Panel Data

* Declare panel structure
xtset country_id year

* Summarize within and between variation
xtsum gdp_growth investment trade_openness

Panel Diagnostics (Stata)

* Check for gaps in panel
gen gap = year - l.year if l.year != .
tab gap  // Should be all 1's for balanced annual panels

* Create balanced subsample
by country_id: gen T_i = _N
keep if T_i == max_T  // Keep only units observed in all periods

* Attrition analysis
gen in_panel = 1
tsfill, full
replace in_panel = 0 if missing(in_panel)

Fixed Effects

* Fixed effects regression
xtreg gdp_growth investment trade_openness, fe

* Store results for Hausman test
estimates store FE

* Fixed effects with robust standard errors (clustered by unit)
xtreg gdp_growth investment trade_openness, fe vce(cluster country_id)

* Test joint significance of fixed effects
testparm i.country_id

Two-Way Fixed Effects with reghdfe

* Entity and time fixed effects (fast, memory-efficient)
reghdfe gdp_growth investment trade_openness, ///
    absorb(country_id year) cluster(country_id)

* Two-way clustering (entity and year)
reghdfe gdp_growth investment trade_openness, ///
    absorb(country_id year) cluster(country_id year)

Random Effects

* Random effects regression
xtreg gdp_growth investment trade_openness, re

* Store results for Hausman test
estimates store RE

Hausman Test (FE vs. RE)

* Hausman specification test
hausman FE RE

* If p  0.05: RE is consistent and efficient, prefer RE

Robust Hausman Test (Mundlak Approach)

* Mundlak (1978): add group means to RE model (robust to heteroskedasticity)
foreach var of varlist investment trade_openness {
    bysort country_id: egen m_`var' = mean(`var')
}
xtreg gdp_growth investment trade_openness ///
    m_investment m_trade_openness, re cluster(country_id)
test m_investment m_trade_openness
* Rejection => FE preferred; failure to reject => RE acceptable

First Differences

* First-differenced regression (alternative to FE)
reg D.gdp_growth D.investment D.trade_openness, vce(cluster country_id)

Estimation in R (plm Package)

library(plm)

# Convert to panel data frame
pdata  0.10) | Reported automatically |
| Hansen J | Instruments are valid | Fail to reject (p > 0.10) | Reported automatically |
| Diff-in-Hansen | Level instruments valid | Fail to reject (p > 0.10) | Reported automatically |
| Instrument count | -- | N_instruments < N_groups | Check output |

### Difference-in-Differences (DID)

```stata
* Basic DID with two-way fixed effects
xtreg outcome treated##post, fe vce(cluster unit_id)

* Event study specification
xtreg outcome i.relative_time##treated, fe vce(cluster unit_id)

Standard Error Options

* Entity-clustered (default choice for firm/country panels)
xtreg gdp_growth investment trade_openness, fe cluster(country_id)

* Driscoll-Kraay standard errors (cross-sectional dependence)
xtscc gdp_growth investment trade_openness i.year, fe lag(3)

* Diagnostic tests for SE selection
xtreg gdp_growth investment trade_openness, fe
xttest3           // Modified Wald test for heteroskedasticity
xtserial gdp_growth investment trade_openness  // Wooldridge test for serial correlation
xtcsd, pesaran abs  // Pesaran CD test for cross-sectional dependence

Instrumental Variables in Panel Data

* IV with fixed effects (xtivreg)
xtivreg gdp_growth (investment = tax_incentive foreign_aid) ///
    trade_openness i.year, fe first

* Report Kleibergen-Paap rk Wald F for weak instruments

Reporting Results

Table X: Panel Regression Results (Fixed Effects)
Dependent Variable: GDP Growth (%)

                      (1)         (2)         (3)
                      FE          RE          Two-way FE
Investment           0.125***    0.118***    0.131***
                    (0.032)     (0.029)     (0.035)
Trade Openness       0.045**     0.051**     0.038*
                    (0.018)     (0.017)     (0.020)

Entity FE             Yes         No         Yes
Time FE               No          No         Yes
Observations          850         850        850
R-squared (within)   0.234       0.228      0.267
Hausman test (p)       --        0.003        --

Notes: Robust standard errors clustered at the country level in
parentheses. * p<0.10, ** p<0.05, *** p<0.01.

References

• Wooldridge, J.M. (2010), Econometric Analysis of Cross Section and Panel Data, 2nd ed., MIT Press
• Arellano & Bond (1991), "Some Tests of Specification for Panel Data," RES 58(2)
• Blundell & Bond (1998), "Initial Conditions and Moment Restrictions in Dynamic Panel Data Models," JoE 87(1)
• Roodman (2009), "How to Do xtabond2: An Introduction to Difference and System GMM in Stata," SJ 9(1)
• Cameron & Trivedi (2005), Microeconometrics: Methods and Applications, Cambridge University Press

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: wentorai
• Source: wentorai/research-plugins
• License: MIT

Install and usage instructions live in the source repository linked above.