Crowdsourcing Method for Linguistic Experiments
4.2 Semantic Similarity Rating Data Example
Structural gravity models are the workhorse of empirical trade literature. They have strong theoretical foundations, a remarkable fit with the data, and they have been widely used by the applied literature to explain bilateral trade flows (Heid, Larch, and Yotov2020; Carrère, Mrázová, and Neary 2020; Arkolakis, Costinot, and Rodríguez-Clare 2012). They were initially developed as an intuitive way to understand trade flows (Tinbergen1962; Shepherd2016). The basic idea is that trade between country i and j directly depend on the size of their economies and inversely dependent on their distance - i.e. the costs of trading.
4.4. MODEL SPECIFICATION CHAPTER 4
In recent years, scholars have developed a wide range of econometric practices allowing to con-sistently identifying the determinants of international trade in the framework of theory consistent structural gravity equation (cfr. Larch et al. 2019; Anderson and Van Wincoop 2003). We adopt most of these techniques, including a Pseudo Poisson Maximum Likelihood estimation to address issues of heteroscedasticity and zeros in trade data (cfr. Santos Silva and Tenreyro 2006, 2011;
Head and Mayer2014); three-way fixed effects to control for changes in the multilateral resistance’
term and to address endogeneity concerns regarding the variables of interest (Anderson and Van Wincoop 2003; Feenstra 2004; Baier and Bergstrand 2007) and interacting bilateral fixed effects with a trend term to account for bilateral unobserved time-varying heterogeneity (Larch et al. 2019;
Bergstrand, Larch, and Yotov2015). Moreover, we employ a wide range of robustness checks, in-cluding phase-ins of agreements, reverse causality, and country-selection biases. Finally, we base our inferences on standard errors that are clustered by all the dimension of the panel: exporter, importer, and time (multi-way clustering). Indeed, while the standard approach has been to cluster errors at the country pair level, Egger and Nigai (2015) and Larch et al. (2019) have demonstrated that in panel settings, not accounting for the possible auto-correlation of the errors across time within countries can lead to false inferences. The baseline specification we adopt to estimate the effects of child labour on exports towards China is the following:
Tij,t= exp
Where Tij,t are nominal exports flows, between a state i and a country j in a given year t. αi,t, αj,t are exporter-year importer-year fixed effects. They control for all the time-varying characteristics of the importer and the exporter, such as GDP or exchange rates, and for the multilateral resistance terms described by Anderson and Van Wincoop (2003; Feenstra 2004;
Carrère, Olarreaga, and Raess 2017). αij are state-county pair fixed effects that account for all the time-invariant bilateral characteristics that may affect export patters, such as geographical distance, or common colonial ties. Three-way fixed is the standard approach used in the literature to identify the causal impact of policy variables on bilateral trade flows (cfr. Yotov et al. 2016;
Anderson, Larch, and Yotov 2019). Indeed, Baier and Bergstrand (2007) demonstrated that bilateral fixed effect could address most of the endogeneity concerns.
Using three-way fixed effects is considered a theory-consistent and endogeneity-robust approach to gravity estimation. The issue, however, is that these fixed effects do not allow to estimate
the effects of any country/state level variables - such as child labour - on bilateral exports.
Indeed, state-level variables are perfectly collinear with the exporter-year importer-year fixed effects. To overcome this issue and examine the effects of child labour on exports, we build on two recent papers. Beverelli et al. (2018) and Heid, Larch, and Yotov (2020) demonstrated that it is possible to identify the effects of country-level variables in the context of a structural gravity model with three-way fixed effects interacting the state-level variable of interest with a dummy identifying the importer.31 Equation 4.5 follows the same logic interacting the share of children working in the state (CLi,t) with a dummy identifying if the importer is China (CHNj).32 This interaction varies on the i, j and t dimension and it is hence identified in the presence of three-way fixed effects. β1 will capture the differential impact that child labour has on exports towards China relative to the rest of the world. We expect this coefficient to be positive, indicating that having more children working favours exports towards China (Hypothesis 3 ). The idea is that on average in Chinese companies may reward states with lower production costs, even if this comes at the price of having more children involved in the production.
To examine the spatial effects of child labour, we adopt a similar strategy. β2 estimates the effects of increasing child labour in competitors states. It is the result of the interaction between the Chinese dummy CHNj and Pz6=iW CLi,t. More precisely, this variable captures the spatially weighted sum of competitors states (z) engagement in child labour. More analytically this is thus defined: Pz6=iW CLi,t = Pz6=iWiz,t × CLz,t, where the share of children working in the competitor CLz,t is weighted by the level of competition between i and z (Wiz,t). If Hypothesis 4 is correct β2 should be negative, indicating that, all else equal, the more a state has close competitors engaging with child labour the less the state will target the Chinese market.33
A potential concern with Equation4.5is that there might be bilateral time-varying unobserved heterogeneity affecting our estimates. The inclusion of bilateral fixed effects (αij) only captures bilateral time-invariant heterogeneity, but it is unable to control for state-country pair character-istics changing over time. For instance, qualitative evidence suggests that bilateral transportation costs changed over-time. According to a recent study by United Nations Conference on Trade and
31Their focus is to understand the effects of institutional quality and non-discriminatory trade policies on international trade; hence they interact the exporter-level variables with a dummy identifying intra-national trade.
32The dummy takes the value of 1 if the importer is China and 0 otherwise.
33To note that to ease the interpretation in the context of a PPML, we take the natural logarithm of this variable to use it in the model (cfr. Santos Silva and Tenreyro2006).
4.4. MODEL SPECIFICATION CHAPTER 4
Development (UNCTAD) (2019), between 2010 and 2015 freight rates of shipping cargo between Santos (Sao Paulo) and Shanghai declined by over 79%. This decline positively impacts trade from all over Brazil; however, it favours particularly exports from states where large international ports are based. International shipping expenses account for almost the entirety of the transportation expenses for these states, but for cerrado regions domestic carrying costs remain extremely high.
For instance, the domestic transportation costs of soybeans harvested in Mato Grosso is estimated to be 25–30% of the soybeans’ total cost at the port (United States International Trade Commission (USITC) 2012 at p. XXIV). Since there have been limited improvements in the Brazilian trans-port infrastructure, bilateral transtrans-portation costs have changed at different rates for coastal states compared to more remote regions of Brazil (Confederação Nacional do Transporte - CNT2015).34 Given that bilateral transportation costs changed over time, not accounting for them creates an omitted variable bias, that is likely to downward bias our estimates (Wooldridge 2010). Indeed, (larger) declines in transportation costs are likely to be associated with an increase in exports to-wards China and negatively associated with child labour. States facing a loss in competitiveness due to a slower decline in transportation costs (remote regions), may look for alternative ways to remain competitive resisting the reduction of children working. Aiming to capture bilateral unob-servable more flexibly, we follow Bergstrand, Larch, and Yotov (2015) and Larch et al. (2019) in interacting the pair fixed effects (αij) with a time trend (T rend). This approach allows accounting for all the pair specific heterogeneity that trends over time, including time-varying transportation costs. Hence, the alternative model specification we use is:
Tij,t= exp
34Indeed, improvements in the transport infrastructure of the country are not comparable to improvements in international shipping. According to United States International Trade Commission (USITC) (2012), the lack of these infrastructures is one of the main causes negatively affecting the competitiveness of Brazil in international exports.
For instance, the paved highways in Brazil are only 15% of the network, and according to some review, over 69% of these paved roads had problems (Araújo, Campos, and Bandeira2013). Moreover, also the waterway and the railway network are scarcely developed and mostly concentrated in the southern regions of the country (cfr. United States International Trade Commission (USITC)2012).