Question

A researcher is interested in estimating the supply function of an online car rental service provider as a function of its average price (Price, measured by the average per kilometre price charged for the month of October, 2017). He has data on the price charged and the number of cars available on the road for rent, (Car), for the 200 cities in the U.S. in which the provider operates. However, given that there is simultaneous causality between Price and Car due to the interactions between demand and supply, the supply function cannot be estimated consistently by an OLS regression of Car on Price. He, therefore, uses Income (measured by the per capita GDP of a given city in the U.S. for 2017) as an instrument which satisfies the two conditions of instrument validity. He uses the two stage least squares (TSLS) estimator of the coefficient on Price which enables him to estimate the supply function. Suppose, the sample covariance between Car and Income, Scar, Income is 1.45, and the sample covariance between Price and Income, Sincome, Price is 2.45. Let β₁ᵀˢᴸˢ be the population slope coefficient on price and B₁ be the two stage least squares (TSLS) estimator of β₁.

Answer 1

The researcher uses the two-stage least squares (TSLS) estimator to estimate the supply function of an online car rental service provider. Per capita GDP is used as an instrument to address the simultaneous causality between price and the number of cars available for rent. The researcher estimates the population slope coefficient using the TSLS estimator.

Step-by-step explanation:

In economics, the concept of supply refers to the relationship between the price of a product and the quantity of that product that producers are willing and able to supply to the market. The supply function represents this relationship, and it is typically estimated using regression analysis. However, in cases where there is simultaneous causality between price and quantity, instrumental variable techniques like two-stage least squares (TSLS) are used to obtain consistent estimates.

In this case, the researcher uses per capita GDP as an instrument for the average price of car rentals, which satisfies the two conditions of instrument validity. The TSLS estimator, denoted as B₁, allows the researcher to estimate the population slope coefficient, β₁ᵀˢᴸˢ, which represents the relationship between price and the supply of cars in the online car rental service market.

The sample covariance between the number of cars available on the road and income is denoted as Scar,Income and is equal to 1.45, while the sample covariance between price and income, Sincome,Price, is equal to 2.45.