# 经济代写|产业经济学代写Industrial Economics代考|ECON3516

## 经济代写|产业经济学代写Industrial Economics代考|Econometric considerations and data

The model to be estimated consists of pricing equation (4) and demand equation (7), with the appropriate substitutions using $(5),(6),(8)$, and (9). I estimated the model using the non-linear three-stage least-squares estimator (NL3SLS) of Gallant and Jorgenson (1979). This is an estimator for a system of simultaneous, non-linear, implicit equations. In particular, the NL3SLS estimator allows the error terms, $\omega_{j m}$ and $\xi_{j m}$ to be correlated. Such a correlation may be expected given that unobserved physical characteristics may influence both marginal cost and demand. Furthermore, the NL3SLS estimator takes into account the possible endogeneity of variables such as sales and prices, $q_{j m}$ and $p_{j m}$, through appropriately chosen instrumental variables.

Details of the NL3SLS estimator, and of the quasi-likelihood ratio test used for hypothesis testing, are found in Gallant and Jorgenson (1979).

Before the NL3SLS estimator can be used, a computational problem must be resolved. The error terms, $\omega_{j m}$ and $\xi_{j m}$ enter non-linearly in the pricing equation (4) and the demand equation (7). To avoid the need for computationally burdensome simulation methods, the demand and pricing equations are therefore first transformed in such a way that the error terms enter linearly. This idea was proposed by Berry (1994), in a more simple version of the nested logit model and with single-product firms. The transformations are given in the appendix. For simplicity, it is assumed that the multi-product firms only take into account the cross-demand derivatives of the cars they own in the same subgroup. ${ }^{19}$ This yields the following model, first for demand, then for pricing, that is taken to the data
\begin{aligned} \ln \left(q_j / L_m\right)=& \ln \left[1=Q_m / L_m\right]+\sigma_1 \ln \left(q_j / Q_{h g m}\right)+\sigma_2 \ln \left(Q_{h g m} / Q_{g m}\right) \ &+x_{j m} \beta-\alpha \frac{\left(p_{j m}\right)^\mu-1}{\mu}+\xi_m+\xi_{j m} \end{aligned}
and
$$\ln p_{j m}+\ln \left(1-m_{j m}\right)=w_{j m} \gamma+\gamma_q Q_j+\ln \left(1+t_m\right)+\tau_m+\omega_m+\omega_{j m}$$

## 经济代写|产业经济学代写Industrial Economics代考|Identification problems

The pricing equations (11)-(13) reveal some identification problems. It is not possible to separately identify the market-specific fixed effects $\omega_m$ or the multipliers $\lambda_{f m}^a$ or $\lambda_{f m}^r$ from $\tau_m$. The market-specific fixed effects, which are estimated using market-specific dummy variables, should therefore be interpreted with care. They reflect both crosscountry differences in the marginal cost of operating in the various countries $\left(\omega_m\right)$ and cross-country differences in percentage deviations of the wholesale price from the consumer price $\tau_m$. Similarly, the Lagrange multipliers should be interpreted with care. They are identified only up to a factor $\left(1+\tau_m\right)$. A high estimate of the multipliers may therefore partly reflect a high $\tau_m$. The inability to obtain a separate identification for $\tau_m$ makes it impossible to accurately compute the absolute wholesale markups received by the firms, i.e., $p_{j m}^w-\partial C_j / \partial q_{j m}$. Fortunately the relative wholesale markups can easily be computed from the estimates, despite the identification problems. Indeed, it may be verified that the relative markup for a car $j$ in market $m$ equals
$$\frac{p_{j m}^w-\partial C_j / \partial q_{j m}}{p_{j m}^w}=m_{j m}$$
where $m_{j m}$ is defined by (12) and can easily be computed from the estimates. The estimates of the relative wholesale markups can then be used to quantify the presence of international price discrimination.

To estimate the Lagrange multipliers (multiplied by $\left(1+\tau_m\right)$ ), I assume that $\lambda_{f m}^a=\lambda_m^a$ and $\lambda_{f m}^r=\lambda_m^r$ for all Japanese firms subject to the import quota in market $m^{20}$ The Lagrange multipliers are then estimated using dummy variables identifying the Japanese cars operating in market $m$. There is a potential identification problem because these dummy variables may also capture some unobserved marginal costs that are specific to firms of Japanese origin. ${ }^{21}$ To have an idea of the importance of this identification problem, I also estimated a Lagrange multiplier for Japanese firms selling in Belgium, even though there is no import quota against Japanese cars in that country. I will interpret an insignificant estimate of the Lagrange multiplier for Belgium as evidence that the estimated Lagrange multipliers for the other countries capture the effect of the quota constraint rather well.

## 经济代写|产业经济学代写工业经济学代考|计量经济的考虑和数据

\begin{aligned} \ln \left(q_j / L_m\right)=& \ln \left[1=Q_m / L_m\right]+\sigma_1 \ln \left(q_j / Q_{h g m}\right)+\sigma_2 \ln \left(Q_{h g m} / Q_{g m}\right) \ &+x_{j m} \beta-\alpha \frac{\left(p_{j m}\right)^\mu-1}{\mu}+\xi_m+\xi_{j m} \end{aligned}

$$\ln p_{j m}+\ln \left(1-m_{j m}\right)=w_{j m} \gamma+\gamma_q Q_j+\ln \left(1+t_m\right)+\tau_m+\omega_m+\omega_{j m}$$

## 经济代写|产业经济学代写工业经济学代考|识别问题

$$\frac{p_{j m}^w-\partial C_j / \partial q_{j m}}{p_{j m}^w}=m_{j m}$$
，其中$m_{j m}$由(12)定义，可以很容易地从估计中计算出来。然后，对相对批发加价的估计可以用来量化国际价格歧视的存在

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