The dynamic effect of trading between China and Taiwan under exchange rate fluctuations

Taiwan is an export-oriented economy whose trade performance, especially with China, is central to its growth. China has become Taiwan's largest export destination since the early 2000s. Exchange rate movements are a key linkage between domestic and international markets, affecting export prices and trade volumes. The industrial production index (IPI) serves as a coincident indicator of Taiwan's economic conditions and comoves with exports to China. The study aims to investigate whether the IPI's effect on Taiwan's export income to China depends nonlinearly on the RMB/NTD exchange rate, using monthly data from January 2001 to February 2022. Employing a Panel Smooth Transition Regression (PSTR) model with the RMB/NTD rate as the transition variable, the paper assesses threshold-dependent dynamics to inform exporters and policy makers about how exchange rate regimes modulate the IPI–exports relationship.

Prior work documents links among economic activity, exchange rates, and exports. Higher partner-country IPI correlates with greater Chinese export income (Liao and Chen, 2020). Studies across countries find various causality patterns between exports and growth (Hatemi and Irandoust, 2000; Afxentiou and Serletis, 1991). Exchange rate levels and volatility significantly influence exports, with appreciations tending to reduce export volumes and volatility dampening export demand (Ngouhouo and Makolle, 2013; Arize et al., 2000; Sharma, 2000). Regarding dynamic nonlinear modeling, TAR and STAR capture regime switching but have limitations for panel settings. PTR (Hansen, 1999) introduces threshold panels with discrete jumps, while PSTR (González et al., 2005; Fok et al., 2005) allows smooth transitions and time-varying heterogeneity in panels. Applications of PSTR show regime-dependent effects in trade and macro relationships (Heidari et al., 2014; Chiu and Sun, 2016; Béreau et al., 2012). The literature suggests a role for exchange rate regimes in conditioning export responses, motivating use of PSTR to assess how the RMB/NTD rate modulates the IPI–exports link for Taiwan–China trade.

Data: Monthly data from January 2001 to February 2022. Dependent variable ΔETM_it: rate of change of Taiwan’s export income to China by SITC category i at time t: ΔETM_it = [(ETM_it − ETM_i,t−1)/ETM_i,t−1]×100%. Independent variable ΔIPI_t: rate of change of Taiwan’s IPI: ΔIPI_t = [(IPI_t − IPI_t−1)/IPI_t−1]×100%. Transition variable EX_t: RMB to NTD exchange rate (level). Sample size reported as 4554 observations across categories and months. Modeling steps: (1) Linear panel model for benchmark: ΔETM_it = α0 + β1ΔIPI_t + ε_it. Hausman test selects fixed effects for panel specification. (2) PSTR model to capture nonlinear threshold effects with smooth transitions: ΔETM_it = α + βX_it + βX_it G(q_it; γ, c) + μ_it, where X_it = (ΔIPI_t), transition function G bounded in [0,1] is logistic: G(q_it; γ, c) = [1 + exp(−∑{j=1}^m γ_j (q_it − c_j))]^{-1}. General PSTR: ΔETM_it = α_i + ρ_i X_it + ∑{j=1}^r β_ij X_it G(q_it; γ_j, c_j) + μ_it, with r+1 regimes. The transition variable q_it is the RMB/NTD exchange rate (possibly with optimal lag chosen by AIC/BIC). Parameters estimated by nonlinear least squares after removing individual means. (3) Specification and tests: Nonlinear unit root tests with structural breaks (ADF with breaks) assess stationarity. Granger causality between ΔETM_t and ΔIPI_t. Linearity tests (Wald LM, Fisher LMF, LRT) evaluate H0: linearity vs H1: PSTR with thresholds (consider m=1,2). Test for additional thresholds proceeds until no remaining nonlinearity. Goodness-of-fit compared via R-squared, and information criteria (AIC/BIC) guide lag selection of transition variable.

• Descriptive statistics (Jan 2001–Feb 2022, N=4554): ΔETM_it shows the widest dispersion (Max 52.33, Min −1.00, SD 1.163); EX_t mean 4.463 (SD 0.330); ΔIPI_t mean 0.007 (SD 0.085).
• Hausman test favors fixed effects (Table 3), leading to fixed-effect analysis.
• Nonlinear unit root tests with structural breaks indicate stationarity for ΔETM_t, ΔIPI_t, and EX_t with significant ADF t-statistics and identified break dates (Table 4).
• Granger causality is bidirectional between ΔIPI_t and ΔETM_t (ΔIPI_t → ΔETM_t: F=15.636, p≈2e−07; ΔETM_t → ΔIPI_t: F=3.074, p=0.046) (Table 5).
• Linearity is rejected: LM/LMF/LRT reject a linear model at ≥10% for m=1 and at 5% for m=2 (Table 6). Tests for remaining nonlinearity support a single-threshold specification (no additional threshold; Table 7).
• PSTR estimates (Table 8): threshold c=4.1732 for EX_t; transition parameter γ=5.9615e+003; coefficient β on ΔIPI_t within transition term ≈0.7451 (10% significance). PSTR R-squared ≈0.2878 versus linear model R-squared ≈0.0187, indicating substantial improvement from allowing nonlinearity.
• Regime-dependent marginal effects: below the exchange-rate threshold, a one-unit increase in ΔIPI_t raises ΔETM_t by about 1.3421 units; above the threshold, by about 0.4854 units. Thus, effects are always positive but stronger when EX_t is below c (interpreted as NTD appreciation).
• Interpretation: The exchange rate condition dynamically modulates the impact of Taiwan’s IPI on export income to China; appreciation (EX below c) and expanding markets amplify the positive IPI effect, while depreciation (EX above c) weakens it. Despite fluctuations, the study indicates continued positive contributions to exports and a trade surplus.

The study directly addresses how exchange rate regimes shape the IPI–exports linkage between Taiwan and China. Evidence of nonlinearity and a single threshold in the RMB/NTD rate shows that the state of the exchange rate conditions the strength of the IPI’s effect on export income. The stronger marginal effect of ΔIPI_t on ΔETM_t when EX_t is below the threshold suggests that periods associated with NTD appreciation and expanding economic conditions enable domestic industrial momentum to translate more effectively into export gains. Conversely, when EX_t exceeds the threshold (interpreted as NTD depreciation), the positive influence of IPI persists but is materially attenuated. These findings validate the hypothesis that exchange rate fluctuations alter the transmission of domestic industrial performance to export outcomes and underscore that exchange rate policy and macro conditions jointly matter for trade performance. The improved fit of the PSTR over the linear model highlights the importance of accounting for regime-dependent dynamics. Policy implications include the role of exchange rate management as a lever that influences the marginal effect of industrial activity on exports and the advisability of avoiding real exchange rate misalignments that could dampen growth and export responsiveness.

The paper establishes a nonlinear, threshold-dependent relationship between Taiwan’s industrial production (IPI) and its export income to China, conditioned by the RMB/NTD exchange rate. Using a PSTR framework on monthly data from 2001–2022, the authors find a single exchange-rate threshold at EX=4.1732 and a large transition parameter, indicating distinct regimes. The IPI’s effect on export income is positive in both regimes but substantially stronger when the exchange rate is below the threshold (≈1.3421 per unit ΔIPI) than when above it (≈0.4854). The PSTR model markedly outperforms a linear specification in explanatory power, confirming the importance of modeling smooth transitions and heterogeneity. Economically, appreciation episodes and expanding markets magnify how domestic industrial conditions convert into export earnings, while depreciation dampens this transmission. The study highlights exchange rate policy as an important determinant of export performance and cautions against real exchange rate misalignments. The results provide actionable insights for exporters and policymakers in Taiwan’s export-led context.