This study equips the following three types of model specifications for examining the vertical trade in the manufacturing and machinery industries: (1) the traditional gravity setting (Eq. 1), (2) the structural gravity setting using the directional time-varying fixed effects (Eq. 2), and (3) the structural gravity setting using the logistics performance of host countries instead of the host country’s time-varying fixed effects. The models for the estimations are specified as follows:
$$\ln {\text{FVA}}_{ij,t} = \alpha_{0} + \, \alpha_{1} \ln {\text{DIS}}_{ij} + \alpha_{2} \ln {\text{GDP}}_{i,t} + \alpha_{3} \ln {\text{GDP}}_{j,t} + \alpha_{4} \ln {\text{GAP}}_{ij,t} + \varepsilon_{ij,t}$$
(1)
$${\text{FVA}}_{ij,t} = \, \exp \left[ { \, \beta_{0} + \, \mu_{ij} + \, \pi_{i,t} + \, \chi_{j,t} + \, \beta_{1} \ln {\text{GAP}}_{ij,t} } \right] + \varepsilon_{ij,t}$$
(2)
$${\text{FVA}}_{ij,t} = \exp \left[ { \, \gamma_{0} + \, \mu_{ij} + \gamma_{1} \ln \, LPI_{i,t} + \, \chi_{j,t} + \, \gamma_{2} \ln {\text{GAP}}_{ij,t} } \right] + \varepsilon_{ij,t}$$
(3)
where the subscripts i, j, and t denote host countries (receiving foreign value added in exports), origin countries (offering foreign value added in exports), and trading years, respectively; FVA is the vertical trade measured by foreign value added in exports; DIS is the geographical distance between host countries and origin countries; GDP is gross domestic product; GAP is the gap in per capita GDP between host countries i and origin countries j; μij is the pair fixed effects between countries i and j; πi,t and χj,t are the time-varying fixed effects of countries i and j, respectively; LPI is the logistics performance index; ε is an error term; αi (i = 0,1, …, 4), βi (i = 0,1), and γi (i = 0,1,2) are estimated coefficients of Eqs. (1), (2) and (3), respectively; and ln shows a logarithm form.
Equation (1), the traditional gravity setting, is based on Kimura et al. (2007). Kimura et al. (2007) modified the standard gravity equation to account for the elements that affect cross-border fragmentation, by incorporating location advantages and service-link costs in the equation, both factors that Jones and Kierzkowski (1990, 2005) identified as the determinants of fragmentation in their theory. The location advantages are reflected in the variable GAP as a proxy for the differential in the total level of factor prices in an economy, and the service-link costs are represented by the geographical distance between exporters and importers, DIS, due to the scarcity of their statistical information.Footnote 8 For the estimation methodology, ordinary least squares (OLS) estimators are applied in this study, as in Kimura et al. (2007).
Equation (2), the structural gravity setting, conforms to the following recommendations of Piermartini and Yotov (2016), except for the existence of GAP representing location advantages. First, the time-varying fixed effects of countries i and j, πi,t and χj,t are incorporated in the equation to control for the unobservable multilateral resistances initially addressed by Anderson and van Wincoop (2003). The time-varying fixed effects absorb both countries’ GDPs as well as all other observable and unobservable country-specific characteristics that influence bilateral trade (this study treats Indonesia as a benchmark country). Second, the pair fixed effects between countries i and j, μij, are introduced to the equation to account for the effects of all time-invariant bilateral trade costs, as Agnosteva et al. (2014) demonstrated. The pair fixed effects absorb the geographical distance, DIS, as well as any other time-invariant bilateral elements such as the presences of contiguous borders, a common official language, and colonial ties. Third, the PPML is applied to the estimation to manage the possibility of zero trade flows and heteroscedasticity of trade data, as Santos Silva and Tenreyro (2006) suggested.Footnote 9 Equation (2) also applies the OLS estimator as a robustness check for the PPML estimator, as Head and Mayer (2014) recommended.
The question is where the service-link costs are positioned in this equation. As mentioned in the introduction, the service-link costs contain not only bilateral trade costs such as transportation costs but also country-specific costs such as the costs for operating in a given country. Thus, the service-link costs occupy some portions of the time-varying fixed effects of host and origin countries (πi,t, χj,t) and the pair fixed effects (μij).Footnote 10 This study focuses on the time-varying logistics performance of the host country side as one part of the service-links costs. Thus the major concern in Eq. (2) in this study is the volume of the time-varying fixed effects of host countries (πi,t), and together with the estimation results of Eq. (3), this study demonstrates the contribution of the host country’s logistics performance to the country-specific fixed effects (Fig. 3).
Equation (3), in this context, replaces the time-varying fixed effects (πi,t) with the logistics performance (LPI i,t) of the host countries. The coefficient γ1 is used to compute the contribution of the host country’s LPI i,t to πi,t. The PPML is applied to the estimation with Eq. (3).