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Dealing with endogenous independent variables (Car Industry Project)? Watch

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    I am running a regression on vehicle demand (vehicle registrations in 2011) with the following independent variables:
    Assembly location
    Price
    Alloy wheels*
    Transmission*
    Number of seats
    Number of doors
    Driven wheels (front, rear or 4x4)
    Maximum speed
    0-62mph
    Fuel type*
    Fuel capacity
    CO2 emissions
    Vehicle tax
    Insurance group
    Customer ratings
    Air conditioning*
    Adult safety
    Child safety
    Cruise control*
    Alarm*
    Climate control*
    Rear parking sensor*
    Central locking*
    Leather interior*
    BHP

    *= Dummy variables

    The paper is looking at consumer preferences, in particular how they consider the origin of the vehicles they're looking to buy. Do consumers want a domestically produced car or do they not care?

    I have a few queries and guidance with any of them would be more than appreciated as I am really struggling- despite hours of research. (I have taken only one econometrics course whilst at University and so, have very little knowledge on such matters)

    1. As price is endogenous, how do I control for this? I was given a little pointer and told to run a separate regression with the remaining independent variables and price as the dependent variable but I wasn't sure how this would help? I know that given there is more than one endogenous variable, it is often preferred to tackle the causal questions separately. Have also looked into running a two-stage least-squares regression whereby lagged price is used to calculate a proxy for price that is uncorrelated with the measurement errors of demand (registrations). This proxy could then be substituted for the original price variable and estimated again?

    2. Customer review scores are also endogenous so I'm not sure how to control for this? Again, received a little pointer from a friend who mentioned something about reduced form regressions to run a review score model but I'm not sure what I'd do next?

    Once again, ANY help on this would really be appreciated.
    (I've read so many papers but given my lack of knowledge on the subject, I'm finding it quite difficult to work my way round what they're saying so figured this could help!)


    On a lighter note- was thinking of titling the paper something along the lines of:
    Consumer Perceptions: Does the provenance of vehicles affect an individual's purchasing journey.Again, clutching at straws here and it probably isn't funny in the slightest (I doubt the pun is even noticeable). Should I steer clear of such titles? (Haha, another pun!!)
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    demand is a function of price but price is also a function of demand. So you get simultaneous equation bias.

    if you run a regression of price on variables that determine price (and hence are correlated with price) but also aren't determinants of demand (uncorrelated with demand) then you can use these relevant and exogenous variables as instruments. this will isolate the part of price that isn't correlated with demand which you can use in your second stage least squares.

    im not great at thinking of instruments but as you said previous prices are unlikely to be a determinant of future demand and obviously are correlated with current prices. note that you can run regressions to find out if the instruments are relevant i.e F statistic in the first stage, if its greater than 10 its a good sign and you can also run a J test (residuals as a function of the instruments) to make sure they aren't correlated with demand.

    this is why i believe you were told to 'run a separate regression with the remaining independent variables and price as the dependent variable' as to find the relevant instruments (regressors that are significant). but only run a regression on the independent variables which are insignificant in determining demand (and hence exogenous).

    maybe something like the wage rate in the car production sector could be used as an instrument, arguably a determinant of the price of the car and exogenous to demand. as i said its hard to think of instruments.

    hope i haven't said anything you don't already know. as i said i think the hardest part is just thinking of instruments. possibly googling 'supply and demand instruments for price' or something might give you some insight.
 
 
 
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