Question 1

Can we estimate the following equation using standard linear regression techniques: Y_i = β₀ + β₁X_i + β₂X_i² + U_i?

Accepted Answer

The equation is linear in parameters β₀, β₁, and β₂, which allows for estimation using standard linear regression techniques.

Question 2

Suppose you've run a regression relating log(Output) to log(Worker Hours) in Excel. You are willing to make the necessary assumptions to deduce causality and run hypothesis tests. Your results are as follows: $$\begin{array} { l c c c c } 
& \text { Coefficients } & \text { Standard Error } & t \text { Stat } & P \text {-value } \
\hline \text { Irtercept } & 17.4583044 & 28.47075584 & 0.613201297 & 0.541240031 \
\text { Log(Worker Hours) } & 2.699483287 & 0.711729096 & 3.792852225 & 0.000264681
\end{array}$$ How should you interpret the coefficient on Log(Worker Hours) of 2.69?

Accepted Answer

Given the regression is in log-log form, a 1% increase in Worker Hours leads to a 2.69% increase in Output, which is the correct interpretation of the coefficient on Log(Worker Hours).

Question 3

Suppose you've regressed profits on price, assuming a quadratic functional form. Your regression equation is: Profits_i = β₀ + β₁Price_i + β₂Price_i² + U_i. What is the marginal effect of price in this equation?

Accepted Answer

The marginal effect of price in a quadratic regression equation is found by taking the derivative of the equation with respect to price. This results in β₁ + 2β₂ * Price, matching choice D.

Question 4

Suppose the fitted (assumed causal) regression line for your data is as follows: Log(Output) = 6.2 + 0.4 × Log(Labor) + 0.5 × Log(Capital)
Interpret the coefficient on Log(Labor).

Accepted Answer

The coefficient on Log(Labor) in a log-log regression model represents the elasticity of the dependent variable with respect to the independent variable. Therefore, a 1% increase in labor, holding capital constant, leads to a 0.4% increase in output.

Question 5

Which of the following regressions would yield a coefficient estimate that would be directly interpreted as the price elasticity of demand?

Accepted Answer

The coefficient estimate in option B is directly related to the logarithm of price, which is consistent with the formula for price elasticity of demand. Specifically, the coefficient estimate on the logarithm of price in option B would be equal to the absolute value of the price elasticity of demand.

Question 6

The percentage change in one variable with a percentage change in another is known as a(n):

Accepted Answer

The percentage change in one variable with a percentage change in another is known as elasticity.

Question 7

Suppose the relationship between temperature and demand for electricity is non-linear, due to the high demand for electricity when it is both very cold and very hot outside. What is the risk of estimating the effect of price on demand for electricity by the regression equation: Electricity Consumption_t = α₀ + α₁Price_t + α₂Temperature_t + U_t?

Accepted Answer

The non-linear relationship between temperature and demand for electricity will cause the estimate of the effect of price on demand (represented by α₁) to be biased. This is because the effect of temperature on demand is also included in the regression equation and may be correlated with the effect of price.

Question 8

Which of the following cannot be estimated using traditional linear regression techniques?

Accepted Answer

Traditional linear regression techniques can estimate all the given models because they all can be linearized. Models A and B involve the logarithm of Y, which is a common transformation in linear regression to stabilize variance and model multiplicative relationships. Model C involves a logarithmic transformation of X, which is also a standard approach to handle non-linear relationships between X and Y in a linear regression framework.

Question 9

Why is the use of polynomial functional forms typical in trying to estimate non-linear functional forms?

Accepted Answer

Polynomial functional forms offer a high degree of flexibility when estimating non-linear functional forms. They can capture a wide range of shapes and have multiple coefficients that can be adjusted to fit different data patterns.

Quiz 7: Basic Methods for Establishing Causal Inference

Can we estimate the following equation using standard linear regression techniques: Y_i = β₀ + β₁X_i + β₂X_i² + U_i?

Suppose you've regressed profits on price, assuming a quadratic functional form. Your regression equation is: Profits_i = β₀ + β₁Price_i + β₂Price_i² + U_i. What is the marginal effect of price in this equation?

Suppose the fitted (assumed causal) regression line for your data is as follows: Log(Output) = 6.2 + 0.4 × Log(Labor) + 0.5 × Log(Capital) Interpret the coefficient on Log(Labor) .

Which of the following regressions would yield a coefficient estimate that would be directly interpreted as the price elasticity of demand?

The percentage change in one variable with a percentage change in another is known as a(n) :

Which of the following cannot be estimated using traditional linear regression techniques?

Why is the use of polynomial functional forms typical in trying to estimate non-linear functional forms?

Quiz 7: Basic Methods for Establishing Causal Inference

Can we estimate the following equation using standard linear regression techniques: Yi = β0 + β1Xi + β2Xi2 + Ui?

Suppose you've regressed profits on price, assuming a quadratic functional form. Your regression equation is: Profitsi = β0 + β1Pricei + β2Pricei2 + Ui. What is the marginal effect of price in this equation?

Suppose the fitted (assumed causal) regression line for your data is as follows: Log(Output) = 6.2 + 0.4 × Log(Labor) + 0.5 × Log(Capital) Interpret the coefficient on Log(Labor) .

Which of the following regressions would yield a coefficient estimate that would be directly interpreted as the price elasticity of demand?

The percentage change in one variable with a percentage change in another is known as a(n) :

Which of the following cannot be estimated using traditional linear regression techniques?

Why is the use of polynomial functional forms typical in trying to estimate non-linear functional forms?

Can we estimate the following equation using standard linear regression techniques: Y_i = β₀ + β₁X_i + β₂X_i² + U_i?

Suppose you've regressed profits on price, assuming a quadratic functional form. Your regression equation is: Profits_i = β₀ + β₁Price_i + β₂Price_i² + U_i. What is the marginal effect of price in this equation?