Warrants

Endogeneity Bias

Recall that an endogenous variable is a predictor variable that is correlated with the error term in your model. There are three potential sources of this problem all of which are covered in detail in different lecture notes: Omitted variables, measurement error, and simultaneity/reverse causality. All three problems impart bias to your estimated coefficients. The purpose of this technical note is to pull together all three problems in the same place, demonstrating the interrelationships among the three.

I. Omitted Variable Bias

Suppose the true model is

(1) Y = B0 + B1X + B2Z + y

You lack data on Z so you estimate

(2) Y = B0 + B1X + (B2Z + y)

where B2Z + εy is the error in your regression. If Z is correlated with X, then you have omitted variable bias. The predictor X is clearly endogenous because it is correlated with the error.

II. Measurement Error

Measurement error occurs whenever a variable is not exactly right. We also use the term noisy variables.

Dirty data is one of the main sources of measurement error. Typos, misplaced decimal points, poor scanning equipment, and the like are common culprits. A second common source of measurement error is the use of a proxy variable in place of what your model really calls for.

Here are some examples of this type of measurement error:

• You want to measure the impact of product-level advertising on product sales. You have data on firms’ total advertising budgets. To estimate product-level budgets, you divide the total budget by the number of products. Your measure of product-level advertising is noisy.

• You are interested in the effect of your competitors’ advertising and promotion activity on your sales. However, you are using the number of radio ads they have run as a proxy for total advertising and promotion. Your measure of competitors’ advertising and promotion activity is noisy.

Note that here we are concerned with what happens when...