# Endogeneity justification

I'm using a fixed-effects model to analyze car prices based on product's characteristics during a five year period. Steel price is used among others explanatory variables.

How to justify possible endogeneity of steel price in the regression model?

• First and foremost,endogeneity should be supported by a strong logical argument. Why do you think steel prices are endogenous in your model? is there other research or theory available to back your claim? Once you gather this, use it to suggest good instruments. Formally you need to find a valid instrument and use a Housman-Wu test to prove that steel price is endogenous. If an instrument is not available (all to often the case) you are left with only the logic argument and must accept the possibility of endogeneity. Dec 30, 2014 at 23:01
• @Zachary Blumenfeld There is other research about price endogeneity but used in different model for different purpose. It was argued by my advisor that price of steel is endogenous and thus causing biased results. Therefore, I need to justify/rebut somehow advisor's claim. My idea was to use price of steel just as other variables that represent car's characterstics and their effect on car's overall price. Dec 30, 2014 at 23:21

A possible concern regarding endogeneity of steel prices is that car manufacturers potentially account for a large share of the overall steel demand in a given country. In that case, steel prices may not only be a determinant of car prices but car prices may as well predict steel prices. This is known as "reverse causality" (look for this term in your preferred econometrics textbook or internet search engine). Given that the relation between these two variables is varying over time the fixed effects estimator will not take care of the problem.

Using this argument you can even have an idea about the direction of the bias. If demand for cars rises (i.e. car prices rise) then the price for steel rises due to the higher demand from car manufacturers. Then the estimated coefficient of steel prices in your model will be overestimated.

edit:
Regarding your comment it seems worthwhile to discuss in general when you should expect endogeneity of a variable. The basic considerations are

• Is there a simultaneous or reverse relationship between the dependent and an explanatory variable?
• Is there an omitted variable that is both related to the dependent and one or more explanatory variables?
• Is a given explanatory variable potentially measured with error?

If you can answer any of these questions with yes on the basis of a logical argument, then you might expect endogeneity. You don't really have to justify endogeneity as Aksakal said but these are the kinds of questions that your audience (supervisor, thesis committee, etc) will be asking themselves and then they will ask you whether you have spotted those problems and if yes you you deal or intend to deal with them.

• What about telephone montly subscription and price of a call. E.g. phone plans with lower monthly fee have higher price per minute and vice versa. How to explain the claim about possible endogeneity of the price of a call in OLS regression model? Dec 30, 2014 at 23:32
• I added a more general description on how to spot potential endogeneity given your comment such that you can apply these tools to other projects beyond the car price study.
– Andy
Dec 31, 2014 at 7:24
• Thank you for your helpful responses. My thinking about "justifying" endogeneity was pretty much in the direction you have proposed. Namely, I thought to mention the potential problem of endogeneity as possible research limitation and as certainly something to deal with in future research. I hope that this will suffice. Additionally, would you argue that monthly fee and call price are inversely related? To me it seems that they are. Dec 31, 2014 at 10:43
• So you want to estimate the effect of call price per minute on monthly fees of phone plans. To be honest, I don't think this regression makes much sense because both monthly fees and minute prices are set by the network provider. It's not the case that the minute price varies in the sense of a random variable and so will not "cause" a change in the monthly price. The two just happen to be set together as a bundle. I would still argue that the two predict each other as the previous problem but this time not because of market forces but due to the design of such plans.
– Andy
Dec 31, 2014 at 11:02
• I'm using also others variables like free minutes etc. to calculate overall price and price index. The reason behind using call price is that user for a fixed montly fee is buying certain level of call price just like amount of any other features that form a bundle. I was using only features which user looks after when signing phone contract. It was argued that call price causes endogeneity. What could be a reasonable explanation? Mine is that the possible bias in the coefficients should not be exaggerated; they're are not as important as in estimating e.g. price elasticity of demand. Dec 31, 2014 at 14:35

You don't have to justify endogeneity. It is usually the other way around: you try to justify that your model does not suffer from endogeneity, because this problem is so pervasive in any economic research.

In case of steel, I'd argue that on one hand the demand for cars is inversely related to the car prices which include steel cost, on the other hand, the demand for cars creates the demand for steel increasing its price. Now, show me that it's not true, because it's the duty of the researcher to argue that this has been taken care of. However, in order to raise an issue of endogeneity I don't have to prove that it's there.