xtthreshold – Threshold estimation for interactive fixed effects models.

xtthreshold depvar indepvars1 | [indepvars2] [if] [in], threshold(thresvar) [csa(varlist1) grid(integer)]

• Data must be tsset or xtset before using xtthreshold.
• Variables may include time-series operators (see tsvarlist help).
• Requires the moremata package.

Variable Notes:

• thresvar: thresholding variable.
• indepvars1: variables affected by the threshold.
• indepvars2: variables not affected by the threshold.
• varlist1: variables added as cross-section averages.

• Description
• Options
• Postestimation
• Examples
• References
• About, Authors and Version History

We consider a panel dataset over cross-sectional units i and time t, with three sets of independent variables:

• x(i,t): unaffected by the threshold
• w(i,t): effects depend on whether z(i,t) is above or below threshold v
• z(i,t): the thresholding variable

The model is defined as:

The error term has an interactive fixed effect structure:

Where:

• g(i): factor loading
• f(t): common factor
• ε(i,t): iid noise

The estimator uses cross-sectional averages to span the factor space (see Ditzen & Karavias, 2025).

xtthreshold follows Ditzen et al. (2025) to:

1. Estimate the threshold v using a grid over z(i,t)
2. Estimate coefficients b₁, g₁, and g₂
3. Choose v minimizing the sum of squared residuals (SSR)

• threshold(thresvar): defines the thresholding variable Z
• csa(varlist1): adds variables as cross-section averages
• grid(integer): length of the threshold grid (default: 100)

You can use estat to explore and visualize results:

estat split         // Splits variables in indepvars1 at threshold
estat graph lr      // Graphs LR test across thresholds

Download data from the GitHub repository.

xtthreshold gdppcgr govspend khanvar | open popgr grosscap, threshold(khanvar) grid(400) csa(govspend khanvar open popgr grosscap)

estat split

xtdcce2 gdppcgr govspend_0 khanvar_0 govspend_1 khanvar_1 open popgr grosscap, cr(govspend khanvar open popgr grosscap)

estat graph lr

• Ditzen, J. & Karavias, Y. (2025)
  Interactive, Grouped and Non-separable Fixed Effects: A Practitioner’s Guide to the New Panel Data Econometrics
  Link

• Ditzen, J., Karavias, Y. & Westerlund, J. (2025)
  Threshold Regression in Interactive Fixed Effects Panel Data and the Impact of Inflation on Economic Growth
  Link

Jan Ditzen
Free University of Bozen-Bolzano
📧 jan.ditzen@unibz.it
🌐 Webpage

Yiannis Karavias
Brunel University
📧 yiannis.karavias@brunel.ac.uk
🌐 Webpage

Joakim Westerlund
Lund University
📧 joakim.westerlund@nek.lu.se
🌐 Webpage

Run the following command in Stata to install:

net from https://janditzen.github.io/xtthreshold/

• Requires Stata version 16 or higher.

Version 0.1 – 24.07.2025