# 经济代写|产业经济学代写Industrial Economics代考|ECON3400

## 经济代写|产业经济学代写Industrial Economics代考|The choice of appropriate instrumental variables

I assume that the vectors of physical characteristics $w_{j m}$ and $x_{j m}$ are exogenous and consequently orthogonal to the error-terms $w_{j m}$ and $\xi_{j m}$. This exogeneity assumption is the main identification assumption for estimation of the pricing and the demand equations. The assumption seems reasonable in the short run, because firms cannot quickly adjust the characteristics of their cars marketed. In the long run, when firms can choose the characteristics of their cars, this assumption may be more problematic.
Prices and market shares are endogenous and correlated with the error terms $\omega_{j m}$ and $\xi_{j m}$ even in the short run. This is because they are simultaneously determined in the Bertrand-Nash equilibrium. In homogeneous-goods models of supply and demand, instruments are readily available: there are generally enough exogenous variables that affect marginal cost and not demand, and exogenous variables that affect demand but not marginal cost. In the present model with product differentiation, most exogenous variables, the observed physical characteristics, affect both marginal cost and demand. Indeed, it is even possible that $w_{j m}=x_{j m}$, in which case no traditional instruments can be used. Fortunately, there are other instruments available. Because the pricing equation holds for all cars simultaneously, constituting a Nash equilibrium, the physical characteristics of each car’s competitors are correlated with its own price and demand. Consequently (functions of) these variables may be used as instruments. Pakes (forthcoming) and Berry, Levinsohn, and Pakes (1995) discuss the general question of how to obtain efficient instruments when any functions of the competitors’ characteristics are potential candidates. I use their results to include the following instruments: the elements of the vectors of exogenous variables $x_{j m}$ and $w_{j m}$, the average of the elements of $x_{j m}$ and $w_{j m}$ across other cars owned by the same firm, and the average of the elements of $x_{j m}$ and $w_{j m}$ across other cars not owned by the same firm. The precise elements of the vectors $x_{j m}$ and $w_{j m}$ are discussed in detail in the data discussion below. I added the following instrument to the list just mentioned: the number of dealers per firm in each country. This variable may be viewed as exogenous at the pricing stage, and at the same time highly correlated with prices and sales.

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

Groups are defined according to their class (with one of the groups being the outside good), and subgroups according to their country of origin, foreign or domestic. I used the quasi-likelihood ratio test of Gallant and Jorgenson (1979) to test for several alternative specifications of the nested logit model, all of which were rejected at traditional 5 per cent significance levels, as discussed in detail in Verboven (1994). First, the data rejected the special cases of both the competitive, hedonic pricing model with zero markups, and the simple logit model with non-localized competition $\left(\sigma_1=\sigma_2=0\right)$. Second, the data rejected a more sophisticated version of the nested logit model, with an extra nest indicating whether to buy a car from a ‘high’ category (collecting the three highest classes) or a ‘low’ category (collecting the three lowest classes). Third, the data rejected a version of the nested logit model with an extra nest (at the top of the tree) indicating whether to buy the outside good or a car from one of the other classes. ${ }^{26}$ Fourth, the data rejected an alternative ordering of the nesting structure, in which groups are defined according to country of origin and subgroups according to class. This specification led to an estimate of $\sigma_1$ significantly below $\sigma_2$, an undesirable result in terms of McFadden’s random utility maximization. These various rejections are roughly consistent with Goldberg (1995), who uses micro-level data on the US car market. I also estimated a specification in which cars belonging to the same subgroup behave as a collusive coalition. This specification was rejected by the data at a 10 per cent significance level.

## 经济代写|产业经济学代写工业经济学代考|实证结果

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