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I need to complete an assignment for Industrial Organization course where one of the tasks is to estimate a discrete choice demand model. This means I basically need to estimate a linear model:

$log(s_j) - log(s_0) = X_j \beta - \alpha p_j + \xi_j$

where $s_j$ is the market share for product $j$, $s_0$ - market share for outside option, $X_j$ contains observed characteristics for product $j$, $p_j$ is the price and $\xi_j$ are the unobserved product characteristics.

We have a panel dataset on European car market (few markets spanning few decades with few hundred products) which could be obtained from here. I exploit the panel nature of the data and construct instruments for price by averaging price of product $j$ in other markets, similarly as in the famous paper by Hausman (1994).

The problem and the main question is that after using IV instead of simple OLS I get significant but positive price coefficient, which is hardly to be expected. Does this tell me that the instruments are not appropriate for this case?

Note: the market size is assumed to be population/4 (set by the assigment), in the product characteristics I include horsepower (hp), length (le), width (wi), height (he) and variable of fuel efficiency (li); the price variable used is princ which is price relative to per capita income; I also use dummy variables for market and year (so that trend is controlled for each market basically).

Here is the snippet of the code (maybe i'm doing something wrong while calculating?):

##load libraries
library(foreign)
library(data.table)
library(AER)

##load data
data <- data.table(read.dta("https://feb.kuleuven.be/public/ndbad83/frank/cars/cars.dta",
                            convert.date = FALSE, convert.factors = FALSE))

##potential market size in each market and each year is pop/4
##estimate shares and dependent variable that will be used for regression
data[, share := qu / (pop / 4), by = c("ye", "ma")]
data[, share0 := 1 - sum(share), by = c("ye", "ma")]
data[, yy := log(share) - log(share0), by = c("ye", "ma")]

##keep data for regression
data.regression <- data[, list(ye, ma, yy, co, hp, le, wi, he, li, princ)]

##instrument the price
data.regression <- data.regression[, {

  ##copy the data for processing
  dat <- copy(.SD)

  ##loop over markets
  for(market in unique(dat$ma)){

    ##instruments - mean price of same product in other markets
    ins <- dat[ma != market, mean(princ)]
    dat[ma == market, p.ins := ins]
  }

  ##return
  dat

}, by = c("ye", "co")]


##lm model
summary(lm(yy ~ princ + hp + le + wi + he + li + factor(ma):factor(ye) - 1, data.regression))

##iv model
fit <- ivreg(yy ~ princ + hp + le + wi + he + li + factor(ma):factor(ye) - 1 | 
               p.ins + hp + le + wi + he + li + factor(ma):factor(ye) - 1, 
             data = data.regression)
summary(fit)
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    $\begingroup$ If I remember correctly, the identifying assumption of the Hausman instrument is that demand for a given car in country A is independent from demand for the same car in country B. With the European car market being very integrated this is unlikely to hold because if you have a shock that affects all markets (e.g. a currency shock - particularly relevant for the Euro zone) this breaks the identification strategy. $\endgroup$ – Andy Apr 25 '15 at 11:09
  • $\begingroup$ yes, you are right, but since the data spans 1970-1999 its hard to believe (for me) that integration was so strong at that time. how could differently I instrument the prices if this is the case? $\endgroup$ – Sarunas Apr 25 '15 at 11:20
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    $\begingroup$ In 1992 they implemented the single market program, so it might be a concern. There are other potential instruments, see for instance this answer (at the bottom): stats.stackexchange.com/questions/86715/berry-inversion/… $\endgroup$ – Andy Apr 25 '15 at 11:58
  • $\begingroup$ hey @andy, if you would elaborate a bit on how I could use other products' characteristics as instruments for price I would accept it as an answer: for example, say I use 5 characteristics for regression - should I take means, sums of rival products characteristics or some different function? does this mean I would end up with 5 instruments for the price variable? I understand the concepts but not the details and would be grateful for example/clarification $\endgroup$ – Sarunas Apr 25 '15 at 15:46
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Hausman type instruments
(I quickly recap what was said in the comments to have a complete answer.)
The Hausman type instruments require that demand for a given car in country A is independent from demand for the same car in country B. With the European car market being very integrated this is unlikely to hold because if you have a shock that affects all markets (e.g. a currency shock - particularly relevant for the Euro zone) this breaks the identification strategy.

Cost shifters
Different countries in Europe have different levels of unionization, so the wage setting process differs between them. One potential instrument are workers' wages in the car industry. Changes to the wages of these workers certainly affects the price for the given brand but not the demand for that car (unless the own workers of the given brand make up a sizable fraction of the buyers which is unlikely). Since you have panel data this is potentially a good instrument because you can exploit the time and spatial variation in those wages. The assumption required here is that the European labor market is not too tightly integrated such that a wage change in France would affect wages in Spain (not a too heroic assumption, especially for your time period).

Other products' characteristics
Have a look at

  • Berry, Levinson and Pakes (1995), "Automobile prices in market equilibrium", Econmetrica, 63, 4, 841-90.

which is the paper where they introduced the random coefficients logit model (as an extension to the Berry logit that you are estimating), and their application is the estimation of demand for Humvees. They instrument the price of car $j$ with the product characteristics of the $k$ rival cars (so they have a vector of $X_k$ different instruments [usually more than one], depending on which characteristics you pick).

What assumptions do you need to make for this? What is needed is an assumption of oligopolistic competition (not unrealistic for the car market - few producers but many buyers). This assumption allows you to make the case for a mean-independence assumption between $X$ and $\xi$, i.e. product characteristics are independent of the error. For firm $j$ this is not necessarily true because their cars' characteristics certainly depend on the error, for instance because of unobserved quality. However, under oligopolistic competition firm $j$'s price $p_j$ is a function of other firms' product characteristics which in turn are uncorrelated with firm $j$'s quality.

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