Panel Data Coarsened Exact Matching

CEM matches units by requiring them to fall in the same coarsened covariate bins, guaranteeing balance by construction without estimating a propensity model. Propensity score matching collapses all covariates into a single scalar and then matches on that score, which can mask residual imbalance on individual covariates. In panel settings, CEM can incorporate pre-treatment time series directly into the strata definition, whereas propensity matching typically requires the researcher to summarise the history into summary statistics.

Pruning improves internal validity by ensuring treated and control units are genuinely comparable, but it reduces the number of units in the analysis. The ATT estimate then applies only to the matched subpopulation — not all treated units. Researchers should report the fraction of treated units retained and assess whether the matched sample is representative of the broader population they care about.

Matching on pre-treatment covariates reduces observable imbalance, but time-invariant unobserved heterogeneity may still differ across units. Adding unit fixed effects in the outcome model after matching provides an additional layer of control, so the combination is generally recommended for panel data. The two approaches target different sources of confounding.

Including more pre-treatment periods improves the quality of matching on trends but increases the dimensionality of the strata, which accelerates pruning. A practical balance is to include enough periods to capture the pre-treatment trajectory — often two to four lagged outcome values — and to rely on within-unit differencing for residual trend adjustment.

There is no universal rule. Common approaches use quantile-based bins (quartiles or deciles), substantively meaningful cutpoints, or automated selection based on data density. Researchers should report sensitivity of results to alternative binning choices as part of the robustness analysis.