14.5 Panel

Declare panel data

You must xtset your data before you can use other xt commands.

xtset panelvar timevar [, tsoptions] declares the data to be a panel in which the order of observations is relevant. When you specify timevar, you can then use time series operators (e.g., L, D).

tsoptions can be specified using

  • unit of timevar, e.g., yearly, quarterly.
  • delta(#) specifies the time increment between observations in timevar units.

Example

To set a panel dataset:

// string variables not allowed in varlist; need to convert them to numeric
. egen float country_id = group(iso)
. egen float year_id = group(year)

. xtset country_id year_id, yearly

Panel variable: country_id (strongly balanced)
 Time variable: year_id, 1 to 59
         Delta: 1 year

Menu

Statistics > Longitudinal/panel data > Setup and utilities > Declare dataset to be panel data

  • panelvar panel variable that identifies the unit
  • timevar optional time variable that identifies the time within panels

Use describe to show an overview of data structure.

Sometimes numbers will get recorded as string variables, making it impossible to do almost any command.

destring [varlist], {gen(newvarlist) | replace} [options]
  • gen(newvarlist) generate new variables for each variable in varlist.
  • replace replace string variables with numeric variables
  • ignore("chars") specifies nonnumeric characters be removed.
// from logd_gdp to rad, convert to numeric, replace "NA" with missing
destring logd_gdp-rad, replace ignore(`"NA"')

14.5.1 xtreg

xtreg is Stata’s feature for fitting linear models for panel data.

xtreg is only used for one-way cluster SE estimation, such as individual, firm, or country fixed effects. For two-way cluster SE estimation, use the reghdfe command

xtreg, fe estimates the parameters of fixed-effects models:

xtreg depvar [indepvars] [if] [in] [weight] , fe [FE_options]

Menu: Statistics > Longitudinal/panel data > Linear models > Linear regression (FE, RE, PA, BE, CRE)

Options:

  • vce(robust) use clustered variance that allows for intragroup correlation within groups.

    vce stands for variance-covariance estimation.

    By default, SE uses OLS estimates, which is invalid in presence of heteroskedasticity or serial correlation. Use vce(robust) to get robust SE.

    Other vce types include vce(bootstrap) and vce(jackknife).

  • vce(cluster clustvar) use cluster-robust variance that allows for intragroup correlation within groups.

    The clustvar variable must be a variable that identifies the clusters.

What xtreg, fe does is known as the within estimator to the following model:

\[ y_{it} = \alpha + \bx_{it}\bbeta' + \nu_i + \varepsilon_{it} \]

where \(\nu_i\) is the unobserved individual effect; \(\varepsilon_{it}\) is the error term with the usual assumptions (mean 0, uncorrelated with itself, uncorrelated with \(\bx\), uncorrelated with \(\nu\), and homoskedastic).

14.5.1.1 Goodness-of-fit

Three versions of R-squared are reported in the output of xtreg, fe:

R-squared Description
Regular \(R^2 = \frac{\var(\hat{y}_{it})}{\var(y)_{it}}\) \(\hat{y}_{it} = \hat{\alpha} + \hat{\bx}_{it}\hat{\bbeta}'\)
Between \(R^2 = \frac{\var(\hat{\bar{y}}_i)}{\var(\bar{y}_t)}\) \(\hat{\bar{y}}_i = \hat{\alpha} + \bar{\bx}_{it}\hat{\bbeta}'\)
Within \(R^2 = \frac{\var(\hat{\tilde{y}}_{it})}{\var(\tilde{y}_{it})}\) \(\hat{\tilde{y}}_{it} = \hat{y}_{it} - \hat{\bar{y}}_i = (\bx_{it} - \bar{\bx}_i)\hat{\bbeta}'\)

where

\[ \bar{y}_i = \frac{1}{T_i}\sum_{t=1}^{T_i} y_{it}, \]

and

\[ \bar{\bx}_i = \frac{1}{T_i}\sum_{t=1}^{T_i} \bx_{it}. \]

estat mundlak performs a Mundlak specification test to help decide whether to use a fixed-effects or random-effects model. The null hypothesis is that the random-effects model is appropriate.

14.5.2 High-dimensional fixed effects

For instance, we may want to study the effect of import tariffs (imports) on yearly trade volume (trade) and include year, country, and industry as controls.

This can be achieved using xtreg, fe absorb(year country industry), but it is slower than areg or reghdfe.

14.5.3 Test for serial correlation

However, Wooldridge (2002, 319–320) derives a simple test for autocorrelation in panel-data models. Drukker (2003) provides simulation results showing that the test has good size and power properties in reasonably sized samples.

There is a community-contributed program, called xtserial, written by David Drukker to perform this test in Stata. To install this community-contributed program, type

. search xtserial
. net sj 3-2 st0039         (or click on st0039)
. net install st0039        (or click on click here to install)

To use xtserial, you simply specify the dependent and independent variables:

. xtserial depvar indepvars

A significant test statistic indicates the presence of serial correlation.