The OLS Slope Estimator Is Not Defined If There Is

question 52

Essay

The OLS slope estimator is not defined if there is no variation in the data for the explanatory variable. You are interested in estimating a regression relating earnings to years of schooling. Imagine that you had collected data on earnings for different individuals, but that all these individuals had completed a college education (16 years of education). Sketch what the data would look like and explain intuitively why the OLS coefficient does not exist in this situation.

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Definitions:

Variable Ratio

A reinforcement schedule in which a response is rewarded after a random number of responses, leading to a high resistance to extinction.

Fixed Interval

A schedule of reinforcement where the first response is rewarded only after a specified amount of time has elapsed, leading to a pattern of responses.

Variable Interval

Variable interval refers to a type of reinforcement schedule in operant conditioning where a response is rewarded after an unpredictable amount of time has passed, leading to a steady and resistant response rate.

Variable Ratio

A schedule of reinforcement where a response is reinforced after an unpredictable number of responses, making it highly resistant to extinction.