Question

In a demand function estimation of a good X, a researcher collected data on various households’ consumption of good X (\( Q_x \)) for various price levels. The researcher also collected data on household income (\( M \)) and household size (\( S \)). The estimated regression result is \[ \log Q_x = -0.345(0.111) - 1.543(2.345) \log P_x + 1.123(0.012) \log M + 0.234(0.123) \log S, \] where \( P_x \) is price per unit of X. The values in the parentheses are the standard errors of the estimated coefficients. From the estimation, one can conclude that

• A. the demand for good X is highly elastic
• B. X is an inferior good
• C. the estimated price elasticity of demand is not statistically significant
• D. the estimated price elasticity of good X is 2.345

Hint:

In regression analysis, the significance of a coefficient is determined by comparing the coefficient to its standard error. If the coefficient is less than twice the standard error, it is statistically insignificant.

Answer 1

The Correct Option is C

Step 1: Interpret the Regression Coefficients.
The coefficient of \( \log P_x \) is \( -1.543 \), which indicates the price elasticity of demand for good X. Since the standard error for this coefficient is 2.345, it suggests that the price elasticity estimate is statistically insignificant because the coefficient is not significantly different from zero. Step 2: Analyze the Inferiority of Good X.
The coefficient for \( \log P_x \) is negative, indicating that as the price of good X increases, the quantity demanded decreases, which is typical of most goods. Since the coefficient is negative and not significantly statistically significant, we cannot conclude that the good is highly elastic or has a positive price elasticity. Step 3: Conclusion.
- (B) X is an inferior good: This could be inferred from the negative coefficient of \( \log M \), which suggests that demand for X decreases as income rises, a typical characteristic of inferior goods.
- (C) The estimated price elasticity of demand is not statistically significant: The standard error for \( \log P_x \) is large relative to the coefficient, indicating statistical insignificance.