Estimating Export-productivity Cutoff Contours with Profit Data: A Novel Threshold Estimation Approach

TL;DR

This paper develops a novel method to estimate heterogeneous export-entry thresholds when fixed costs vary across firms, modeling profits as a kink in domestic sales with a threshold that depends on fixed-cost proxies through a nonparametric function $\gamma(m)$. The core contribution is a kernel-based estimation framework that extends regression-kink models from a scalar cutoff to a threshold contour, with consistency and asymptotic normality established for the second-stage coefficients. The empirical application to Chinese CASIF data shows substantial heterogeneity: higher fixed-cost proxies raise the export-threshold, and accounting for endogeneity reduces the exporter premium, altering the selection narrative relative to a homogeneous-cost benchmark. The framework is broadly applicable to discrete firm choices beyond exporting and provides a flexible tool for studying how observable firm characteristics shape heterogeneous threshold-driven decisions.

Abstract

This paper develops a novel method to estimate firm-specific market-entry thresholds in international economics, allowing fixed costs to vary across firms alongside productivity. Our framework models market entry as an interaction between productivity and observable fixed-cost measures, extending traditional single-threshold models to ones with set-valued thresholds. Applying this approach to Chinese firm data, we estimate export-market entry thresholds as functions of domestic sales and surrogate variables for fixed costs. The results reveal substantial heterogeneity and threshold contours, challenging conventional single-threshold-point assumptions. These findings offer new insights into firm behavior and provide a foundation for further theoretical and empirical advancements in trade research.

Figures (14)

• Figure 1: This figure illustrates the positive selection of firms into export market.
• Figure 2: This figure illustrates the unknown threshold contour for different functional forms of true firm-specific fixed costs, $F_{i}=F^G+1^X_{i}F^X_{i}$, as a function of an observable surrogate variable of these fixed costs, $F_i=F(m_{i})$.
• Figure 3: This figure depicts the estimated threshold $\hat{\gamma}(m)$ with $m$ referring to the $m$-th quantile of $m_i$ in the range of $m\in [0.15,0.85]$. The left panel refers to models that employ quantiles of Financial cost$_i$ and the right panel to ones that employ Fixed assets$_i$ as an observable fixed-cost metric.
• Figure 4: This figure depicts the estimated threshold $\hat{\gamma}(m)$ using Model 2, with $m$ referring to the $m$-th quantile of $m_i$ in the range of $m\in [0.15,0.85]$. The left panel refers to models that employ quantiles of Financial cost$_i$ and the right panel to ones that employ Fixed assets$_i$ as an observable fixed-cost metric.
• Figure 5: This figure depicts the estimated threshold $\hat{\gamma}(m)$ using Model 3, with $m$ referring to the $m$-th quantile of $m_i$ in the range of $m\in [0.15,0.85]$. The left panel refers to models that employ quantiles of Financial cost$_i$ and the right panel to ones that employ Fixed assets$_i$ as an observable fixed-cost metric.

Theorems & Definitions (10)

• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• proof : Proof of Theorem \ref{['thm:id']}
• proof : Proof of Theorem \ref{['thm:consistency']}
• Lemma 1
• proof : Proof of Lemma \ref{['lem:bias']}
• proof : Proof of Theorem \ref{['thm:normal']}
• proof : Proof of Theorem \ref{['thm:rootn']}