In Sports Economics, Production Functions Are Often Estimated by Relating $$Y _ { i t } = \beta _ { 0 } + \beta _ { 1 } L _ { i t } + \beta _ { 2 } M _ { i } + u _ { i t }$$

question 14

Essay

In Sports Economics, production functions are often estimated by relating the winning
percentage of teams (Y)to inputs indicating performance in certain aspects of the game.
However, this omits the quality of management.Assume that you could measure the
quality of pitching and hitting by a single index L, and that managerial ability is
represented by M, which is assumed to be constant over time.The production function
would then be specified as follows: $$Y _ { i t } = \beta _ { 0 } + \beta _ { 1 } L _ { i t } + \beta _ { 2 } M _ { i } + u _ { i t }$$ where i is an index for the baseball team, and t indexes time and all variables are in logs.
(a) Assume that managerial ability is unobservable but is positively related, in a linear way, to $L$ . Explain why the OLS estimator $\widehat { \beta } _ { 1 }$ is inconsistent in the case of a single crosssection, i.e., if you attempt to estimate the above regression for a single year. Do you expect this coefficient to over- or under-estimate $\beta _ { 1 }$ ?

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Definitions:

Geographic Area

A specific portion of the Earth’s surface characterized by distinct boundaries, which can be defined by natural or artificial features.

Bottom-Up Analysis

An approach that starts with individual elements or components to develop broader insights or aggregate outcomes, often used in financial forecasting and market analysis.

First Six Months

The initial half-year period of a specific timeframe, often used to evaluate early progress or performance.

Total Market Size

The overall demand or volume of sales potential for a particular product or service within a specified market.