Professor Ryus Econometrics On Omitted Variable Bias Endogeneity

Professor Ryu’s Econometrics On Omitted Variable Bias, Endogeneity : Farmer’s Example in Leamer (AER, 1983) I. The farmer wants to know the relationship between fertilizer level and the resulting yield. 1

Professor Ryu’s Econometrics II. But, the farmer only has data on (y, F). He does not have data on L. He runs a simple OLS. 2

Professor Ryu’s Econometrics III. Mc. Donalds ads: “What you want is what you get. ” How about the farmer? Does he get what he wants? 3

Professor Ryu’s Econometrics But, REALITY BITES! As the farmer does not have data on L, he is tempted to run the following simple (short) regression To understand what the farmer is doing, let us compute 4

Professor Ryu’s Econometrics 5

Professor Ryu’s Econometrics In general, what the farmer gets is not what he wants. (The farmer is now farming, not ordering a Big Mac) 6

Professor Ryu’s Econometrics Ø To sum up, the farmer wanted to estimate (for the purpose of determining the optimal fertilizer level to maximize profit) Ø But, he ended up estimating * which is in general different from 7

Professor Ryu’s Econometrics Special Cases : (1) If the farmer applied “randomization, ” 1=0 and thus he gets * = (no bias). (2) If “Lighting” was “irrelevant” in the sense that =0, again the farmer gets what he wants * = (no bias). (3) Otherwise, *. 8

Professor Ryu’s Econometrics Consider a general case that (a) “Lighting” is “relevant” for determining yield in the sense that > 0, and (b) The farmer applies a bigger amount of fertilizers under shades than under the sun in the sense that δ 1 < 0 c. f. E(Li | Fi ) = δ 0 + δ 1 Fi Then, we have * < (under-estimation bias) 9

Professor Ryu’s Econometrics Alternative Interpretation: “F (fertilizer level)” is an endogenous variable which is simultaneously determined with the yield due to the common influence of the “L (lighting)”. Endogeneity Bias arises. Mathematically , where Thus, OLS estimates will be biased! Endogeneity Bias! 10

Professor Ryu’s Econometrics Messages of the Farmer’s Example: (1) Control for Relevant Variables (“L”) (2) If you do not have data on the relevant variables, try randomization with respect to the variable at hand “F” (randomized controlled). (3) If neither data on the relevant variables and nor randomized controlled (“F” and “L” are correlated), the short regression will give you biased estimates. 11