Do cultural differences affect the trade of cultural goods? A study in trade of music

Abstract

This study investigates the impact of cultural differences on trade decision and trade volume of cultural goods, using the data of traded music compact discs (CDs). According to ethnomusicological and civilization classifications, we classify countries into several groups and make novel variables that properly represent the cultural differences. We use the gravity model of trade proposed in Helpman et al. (The Quarterly Journal of Economics 123(2):441–487, 2008), which is utilized to avoid selection and endogeneity biases of estimation. In addition, we exploit an identifying assumption on the types of consumers, so that one of the cultural variables can satisfy the exclusion restriction in our two-stage estimation procedure. Our empirical hypothesis is that the trade volume of music is larger between two countries with greater cultural familiarity. The empirical results show that cultural differences have significant influences on the trading decision and volume of music traded in addition to the traditional determinants of trade. This finding supports our hypothesis that cultural familiarity promotes the cultural goods trade.

Appendix A

In this section, we will explain how to treat the incidental parameter problem of our two-stage estimation procedure. Our estimation procedure contains two equations.

First, we estimate the trade decision equation. The problem is occurred because our model has fixed effects of importer and exporter. This is the typical case of incidental parameter problem. Fernández-Val and Weidner (2016) propose the bias correction way for nonlinear models that contain two-way fixed effects, and we follow their way to correct the bias. The criterion function of the first-stage equation is

$$\begin{aligned} Q_1=\sum _{i=1}^I \sum _{j=1}^Jf_{1,ij}(\theta _1, \alpha _{1,i}, \gamma _{1,j} ; X_{1,ij}), \end{aligned}$$

(8)

where $\theta _1$ is a $K\times 1$ parameter and $\alpha _{i,i}, \gamma _{1,j}$ are fixed effects country i and j, respectively.

Fernández-Val and Weidner (2016) show that for the bias corrected estimator

$$\begin{aligned} {\tilde{\theta }}_1={\hat{\theta }}_1-W_1^{-1}(B_{1,i}+B_{1,j}), \end{aligned}$$

(9)

it is guaranteed that

$$\begin{aligned} \sqrt{IJ}({\tilde{\theta }}_1-\theta _{1,0})\xrightarrow {d}N(0, \Sigma _1). \end{aligned}$$

(10)

This is the strictly exogenous components of $X_{1,ij}$ case. For the detail of correction terms $W_1, B_{1,i}$, and $B_{1,j}$, see Fernández-Val and Weidner (2016).

Then, we estimate the outcome equation. The two-stage estimation bias correction way with one-way fixed effect is proposed in Fernández-Val and Vella (2011). We expand their way to our two-stage estimation with two-way fixed effects model. The criterion function of second-stage equation is

$$\begin{aligned} Q_2=\sum _{i=1}^I \sum _{j=1}^Jf_{2,ij}(\theta _2, \zeta , \alpha _{2,i}, \gamma _{2,j}; X_{2,ij}, \lambda _{ij}) \end{aligned}$$

(11)

where $\theta _2$ is a $M\times 1$ parameter vector, $\lambda _{ij}$ is a $L\times 1$ control variables vector, and $\zeta$ is a $L\times 1$ coefficient vector. In our case, $\lambda _{ij}$ can be written as $\lambda _{ij} = (z_{ij}, z_{ij}^2, z_{ij}^3, z_{ij}\eta _{ij}, z_{ij}^2\eta _{ij}, z_{ij}^3\eta _{ij}, \eta _{ij})$. We can show that for the bias corrected estimator

$$\begin{aligned} {\tilde{\theta }}_2={\hat{\theta }}_2-W_2^{-1}(B_{2,i}+B_{2,j}), \end{aligned}$$

(12)

it is guaranteed that

$$\begin{aligned} \sqrt{IJ}({\tilde{\theta }}_2-\theta _{2,0})\xrightarrow {d}N(0, \Sigma _2), \end{aligned}$$

(13)

where

$$\begin{aligned} W_2= & {} \sum _{i=1}^{I}\sum _{j=1}^{J}d_{ij} \cdot \begin{pmatrix} {\tilde{X}}_{2,ij}\\ {\tilde{\lambda }}_{ij} \end{pmatrix} \cdot \begin{pmatrix} {\tilde{X}}_{2,ij}\\ {\tilde{\lambda }}_{ij} \end{pmatrix}' \end{aligned}$$

(14)

$$\begin{aligned} B_{2,i}= & {} -{\mathbb {E}}_{J}\left[ d_{it}\cdot \begin{pmatrix} {\tilde{X}}_{2,ij} \\ \tilde{\lambda _{ij}} \end{pmatrix} \cdot \frac{v_{2,ij}}{{\mathbb {E}}_{I}[d_{ij}]}\right] -{\mathbb {E}}_{J}\left[ d_{it}\cdot \begin{pmatrix} {\tilde{X}}_{2,ij} \\ \tilde{\lambda _{ij}} \end{pmatrix} \cdot \frac{v_{2,ij}}{{\mathbb {E}}_{I}[d_{ij}]} \cdot \zeta ' \cdot \lambda _{ij,\pi }\cdot \psi _{1,i}^{(J)}\right] \nonumber \\&-{\mathbb {E}}_{J}\left[ d_{it}\cdot \begin{pmatrix} {\tilde{X}}_{2,ij} \\ \tilde{\lambda _{ij}} \end{pmatrix} \cdot \left( \zeta ' \cdot {\tilde{\lambda }}_{ij,\pi } \cdot \beta _{1,i}+ \zeta ' \cdot {\tilde{\lambda }}{ij,\pi \pi } \cdot \frac{\sigma _{11,i}}{2} \right) \right] - \begin{pmatrix} 0\\ {\mathbb {E}}_{J}[d_{ij} \cdot {\tilde{\lambda }}_{ij,\pi } \cdot \zeta ' \cdot {\tilde{\lambda }}_{ij,\pi }] \end{pmatrix} \cdot \sigma _{11,i} \nonumber \\&+ \begin{pmatrix} 0\\ {\mathbb {E}}_{J} \left[ d_{ij} \cdot v_{2,it} \cdot \left( {\tilde{\lambda }}_{ij,\pi } \cdot \left( \psi _{1,ij}^{(J)} + \beta _{1,i} \right) +{\tilde{\lambda }}_{ij,\pi \pi } \cdot \frac{\sigma _{11,i}}{2} \right) \right] \end{pmatrix}, \end{aligned}$$

(15)

$$\begin{aligned} B_{2,j}= & {} -{\mathbb {E}}_{I}\left[ d_{it}\cdot \begin{pmatrix} {\tilde{X}}_{2,ij} \\ \tilde{\lambda _{ij}} \end{pmatrix} \cdot \frac{v_{2,ij}}{{\mathbb {E}}_{I}[d_{ij}]}\right] -{\mathbb {E}}_{I}\left[ d_{it}\cdot \begin{pmatrix} {\tilde{X}}_{2,ij} \\ \tilde{\lambda _{ij}} \end{pmatrix} \cdot \frac{v_{2,ij}}{{\mathbb {E}}_{I}[d_{ij}]} \cdot \zeta ' \cdot \lambda _{ij,\pi }\cdot \psi _{1,i}^{(I)}\right] \nonumber \\&-{\mathbb {E}}_{I}\left[ d_{it}\cdot \begin{pmatrix} {\tilde{X}}_{2,ij} \\ \tilde{\lambda _{ij}} \end{pmatrix} \cdot \left( \zeta ' \cdot {\tilde{\lambda }}_{ij,\pi } \cdot \beta _{1,j}+ \zeta ' \cdot {\tilde{\lambda }}{ij,\pi \pi } \cdot \frac{\sigma _{11,j}}{2} \right) \right] - \begin{pmatrix} 0\\ {\mathbb {E}}_{I}[d_{ij} \cdot {\tilde{\lambda }}_{ij,\pi } \cdot \zeta ' \cdot {\tilde{\lambda }}_{ij,\pi }] \end{pmatrix} \cdot \sigma _{11,j} \nonumber \\&+ \begin{pmatrix} 0\\ {\mathbb {E}}_{I} \left[ d_{ij} \cdot v_{2,it} \cdot \left( {\tilde{\lambda }}_{ij,\pi } \cdot \left( \psi _{1,ij}^{(I)} + \beta _{1,j} \right) +{\tilde{\lambda }}_{ij,\pi \pi } \cdot \frac{\sigma _{11,j}}{2} \right) \right] \end{pmatrix} . \end{aligned}$$

(16)

The “tilde” marks represent the regression residuals of the variables on the two-way fixed effects, $d_{ij}$ is the indicator in the selection equation, and

$$\begin{aligned} \lambda _{ij,\pi }&=(1, 2z_{ij}, 3z_{ij}^2, \eta _{ij}+z_{ij}\eta _{ij,\pi }, 2z_{ij}\eta _{ij}+z_{ij}^2\eta _{ij,\pi }, 3z_{ij}^2\eta _{ij}+z_{ij}^3\eta _{ij,\pi }, \eta _{ij,\pi }), \\ \lambda _{ij,\pi \pi }&=(0, 2, 6z_{ij}, 2\eta _{ij, \pi }+z_{ij}\eta _{ij, \pi \pi }, 2\eta _{ij}+4z_{ij}\eta _{ij, \pi }+z_{ij}^2\eta _{ij, \pi \pi }, 6z_{ij}\eta _{ij}+6z_{ij}^2\eta _{ij, \pi }+z_{ij}^3\eta _{ij, \pi \pi }, \eta _{ij, \pi \pi }). \end{aligned}$$

$\eta _{ij, \pi }$ and $\eta _{ij, \pi \pi }$ are values of $\eta _{ij}$ differentiated by fixed effects once and twice, respectively. $\psi _{ij}^{(I)}, \psi _{ij}^{(J)}, \beta _{1,i}, \beta _{1,j}, \sigma _{11,i}$, and $\sigma _{11,j}$ are defined in a way similar to Fernández-Val and Vella (2011).