On high-quality development and two-tier stochastic frontier analysis

This paper replicates, reevaluates, and extends the two-tier stochastic frontier analysis (2TSF) of the High-Quality Development (HQD) indicator in China proposed by Lei et al. (2024). We first conduct a successful replication of the study’s main estimation results. We then investigate methodological issues involving the construction of the HQD variable, inconsistencies in the data, and the application of the two-tier stochastic frontier framework. Specifically, 2330 missing observations for HQD were set equal to the value 1, far larger than the recorded values of the other observations. This resulted in creating an artificial upper bound and in inflating the sample from 13,533 to 15,863 observations. Methodologically, the specification exhibits an internal inconsistency by assigning regulatory effects to both observed regressors and unobserved components, undermining the interpretability of the latent variables. These concerns speak to broader questions in the emerging HQD literature regarding the interpretation, scaling, and empirical treatment of the indicator. Guided by this critical assessment, we exclude the imputed observations in the original sample and implement a correlated random effects (CRE) 2TSF panel data model that explicitly accounts for correlation between firm-level heterogeneity and observed regressors. Under this corrected specification, key regulatory variables reverse sign relative to the original estimates, altering the study’s substantive conclusions. Our results emphasize the importance of carefully specifying and constructing the HQD indicator and explicitly motivating the use of a two-tier stochastic frontier framework. Moreover, when correlation between regressors and unobserved components is unavoidable, a CRE formulation as proposed here is more appropriate.