Tables 9 and 10 provide estimations of the HMR model based on the two-stage approach suggested by WTO (2012). For each model specification, we run a Probit (trade propensity) model with the random effect to estimate the probability of the exporting behavior and calculate the inverse Mill’s ratio (imr),7 which is later added into a nonlinear least square (NLS) regression for the second-stage outcome estima-tion. Following Helpman et al. (2008), Briggs (2013) and Lee and Park (2016), we consider the degree of communality of religion (REL) as exclusion restrictions (i.e., cost variable that enters into the first stage, but not in the second-stage regression) to help identification, because regressors are allowed to have different effects on
7 WTO (2012) points out that the use of the Probit model with the fixed effect in the first stage esti-mation may induce “incidental parameters problem,” which leads to inconsistent estiesti-mation of all parameters of the model. One possible solution is to use the random effect (see Cameron and Trivedi, 2005).
Table 8: Robustness Check for Traditional Estimation Model specificationOLSRandom EffectFixed Effect (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12) Dependent variablelnYln(Y+1)lnYln(Y+1)lnYln(Y+1)lnYln(Y+1)lnYln(Y+1)lnYln(Y+1) PR0.98*** (0.10)0.81*** (0.14)0.52*** (0.10)0.17 (0.15)0.93*** (0.21)0.33 (0.23)0.79*** (0.21)0.40* (0.24)1.03*** (0.23)0.26 (0.29)0.97*** (0.24)0.51 (0.33) lnGDP1.42*** (0.07)2.59*** (0.09)1.41*** (0.06)2.64*** (0.09)1.46*** (0.15)2.87*** (0.20)1.44*** (0.13)2.73*** (0.19)2.17*** (0.61)3.66*** (1.12)2.28*** (0.73)3.81*** (1.39) lnPOP−0.52*** (0.06)−1.15*** (0.09)−0.35*** (0.06)−1.04*** (0.09)−0.65*** (0.15)−1.39*** (0.22)−0.48*** (0.13)−1.21*** (0.22)−6.65*** (1.54)−3.69* (2.20)−5.86*** (1.55)−4.19 (2.85) lnDIST−2.76*** (0.08)−3.27*** (0.12)−2.18*** (0.09)−2.74*** (0.12)−2.78*** (0.28)−3.23*** (0.37)−2.40*** (0.29)−3.13*** (0.37) FTA−1.25*** (0.35)0.52 (0.39)−1.09*** (0.43)0.37 (0.40)−0.72 (0.52)−0.13 (0.26)−0.70 (0.50)−0.23 (0.28)−0.52 (0.55)−0.13 (0.26)−0.54 (0.54)−0.27 (0.31) HX6.32*** (0.43)4.84*** (0.69)3.71*** (1.11)0.93 (1.66)2.17 (1.34)−0.49 (1.90) Time FEYesYesYesYesYesYesYesYesYesYesYesYes Importer FENoNoNoNoNoNoNoNoYesYesYesYes Observations147219021353163414721902135316341472190213531634 R2 0.7640.7350.8120.7570.7620.7330.8040.7520.2790.1360.3080.151 Notes: Robust standard errors are reported in parentheses. *** Significant at 1 percent level. ** Significant at 5 percent level. * Significant at 10 percent level.
the extensive and intensive margins of trade.
Columns (1) to (4) of Table 9 show four different model specifications in which results of each stage, as Probit and NLS, of the HMR model are reported for the impact of PRs differences (PRD). The estimates in Columns (1) and (3) show that export elasticity is around −0.88 to −0.96, i.e., a 10% reduction in PRs differences between Taiwan and a destination country with lower PRs protection level (PRDP) results in a range of 8.8% to 9.6% increase in Taiwan’s semiconductor exports. On the other hand, the impact of patent rights difference between Taiwan and a destina-tion country with higher PRs protecdestina-tion level (PRDN) on Taiwan’s semiconductor exports is negative but insignificant, as shown in Columns (1) and (3). Generally, differences in PRs between Taiwan and the trading countries with lower PRs level (PRDP) do not have a significant effect on Taiwan’s semiconductor exporting firms’
binary decision to export semiconductor goods in the first stage. However, in stage two, firms already engaging in semiconductor trade will increase the volume of semiconductor exports as the patent regime in the trade partner countries becomes stronger or more similar to Taiwan’s. An increase in the volume of trade could correspond to an introduction of new high-tech varieties or an increase in the volume of existing varieties. When adding HX in Columns (2) and (4), the impact of PRDN becomes significant and the magnitude of PRDP coefficients change substantially, increasing from −0.88 in Column (3) to −1.82 in Column (4). This finding implies the estimates of PRDP and PRDN are quite sensitive to the inclusion of the new variable when the importer fixed-effect is not controlled.8 On the other hand, the results in all specifications of Table 10 support a positive and significant impact of PRs protection level of the destination country (PR) on Taiwan’s semiconductor exports, no matter whether HX is included or the time fixed-effect is controlled.
These findings further confirm the positive impact of PR and a negative impact of PRDP on the semiconductor exports, as illustrated in results from PPML and OLS, although the magnitude of the impact changes.
Country size has a positive influence on exports, while distance has a negative sign. The impacts of FTA are negative and significant in all model specifications of Tables 9 and 10. In Columns (1) and (3) of both tables, the significant coefficient of the inverse Mill’s ratio (imr) confirms that correcting for sample selection bias is justified. The estimated results show that the significant coefficient of (P+imr),
8 Unlike in the PPML and fixed effect models, we are unable to control for the importer fixed-effect in the HMR model. STATA program stops when it excludes some importer fixed-effect for particular countries in the first-stage estimation and results in some missing observations, which consequently renders the second-stage estimation.
δ, is positive, which indicates that heterogeneity matters and that higher trade vol-umes are driven by a greater proportion of exporters to a particular destination.
These results from subsections 5.2 to 5.4 also provide two interesting empiri-cal insights. First, in the traditional gravity model, the results with lnY and ln(Y+1) Table 9: HMR Estimation of the Impact of the Differences in PRs Protection
Model specification
(1) (2) (3) (4)
Probit NLS Probit NLS Probit NLS Probit NLS
Dependent
variable EX lnY EX lnY EX lnY EX lnY
PRDP −0.11
Observations 1902 1472 1634 1353 1902 1472 1634 1353
R2 0.444 0.761 0.481 0.801 0.463 0.765 0.504 0.813
Notes: Robust standard errors are reported in parentheses.
*** Significant at 1 percent level. ** Significant at 5 percent level. * Significant at 10 percent level.
Table 10: Robustness Check for HMR Estimation
Model specification
(1) (2) (3) (4)
Probit NLS Probit NLS Probit NLS Probit NLS
Dependent
variable EX lnY EX lnY EX lnY EX lnY
PR 0.21***
Observations 1902 1472 1634 1353 1902 1472 1634 1353
R2 0.443 0.767 0.476 0.806 0.459 0.766 0.498 0.810
Notes: Robust standard errors are reported in parentheses.
*** Significant at 1 percent level. ** Significant at 5 percent level. * Significant at 10 percent level.
are very different, and this occurs because the traditional gravity model does not handle zeros well, simply assuming ln(Y+1) and ignoring the nonlinearity associ-ated with Y=0. Second, the HMR specification might have trouble dealing with incorporating the importer fixed-effect, but the fixed-effect is more easily included in a PPML framework.