a)
Economic interpretation for the equation.
a)
Explanation of Solution
If the output elasticity with respect to idea is ½, it implies that the percentage point increase of idea will lead to a 0.5 percentage increase in the output level. Also, the discovery of new ideas will lead to a growth rate in idea to diminish. It can be derived as follows:
b)
Growth rate of knowledge in the economy.
b)
Explanation of Solution
The growth rate of knowledge implies the growth rate of idea in the economy. Then, derive the growth rate of idea as follows:
c)
Growth rate of output per person in the economy.
c)
Explanation of Solution
Derive the growth rate of output per person in the economy as follows:
Where,
Take logs and rewrite the equation as follows:
Suppose
Therefore, the growth rate of output per person is calculated as follows:
d)
Output per person at each point in time.
d)
Explanation of Solution
Suppose,
The stock of knowledge can be equated as follows:
The production function per worker can be derived as follows:
Want to see more full solutions like this?
Chapter 6 Solutions
Macroeconomics (Fourth Edition)
- Consider the regression model Yi = β0 + β1Xi + ui.a. Suppose you know that β0 = 0. Derive a formula for the least squaresestimator of β1.b. Suppose you know that β0 = 4. Derive a formula for the least squaresestimator of β1?arrow_forward(Econmetrics) Q.1 How can you test for general misspecification of model if it would have only (any of) two independent variables?arrow_forwardTrue or False? WLS is preferred to OLS when an important variable has been omitted from the model.arrow_forward
- A. B. Consider data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The following simple regression was estimated using data on n = 1,388 births: bwght = 119.772 (0.572) n = 1,388, 0.514 cigs (0.091) R² = 0.0227, where standard errors are shown in parenthesis. What percent of the variation in birth weight is explained by cigs? What is the predicted birth weight when cigs = 0? What about when cigs = 20 (one pack per day)? Comment on the difference.arrow_forwardEconometrics Thomas Eisensee and David Stromberg wanted to measure how much news coverage of a foreign disaster impacted the amount of disaster relief provided by the U.S. government. They argue that the simple relationship would be biased. Let X = Minutes of News Coverage and Y= Disaster Aid. Choose a variable X2 that could bias the simple relationship. This variable should impact the amount of coverage and impact the amount of aid for reasons other than purely news coverage. Eisensee and Stromberg introduce an instrument Z = During the Olympics. Explain how Z could satisfy the relevant and exogenous criteria. Explain how you could use Z to estimate the impact of X on Y free from X2 bias. Hint: you should mention two stages.arrow_forwardSuppose the Sherwin-Williams Company has developed the following multiple regression model, with paint sales Y (x 1,000 gallons) as the dependent variable and promotional expenditures A (x $1,000) and selling price P (dollars per gallon) as the independent variables. Y=α+βaA+βpP+εY=α+βaA+βpP+ε Now suppose that the estimate of the model produces following results: α=344.585α=344.585, ba=0.102ba=0.102, bp=−11.192bp=−11.192, sba=0.173sba=0.173, sbp=4.487sbp=4.487, R2=0.813R2=0.813, and F-statistic=11.361F-statistic=11.361. Note that the sample consists of 10 observations. 1.) According to the estimated model, holding all else constant, a $1,000 increase in promotional expenditures decrease or increase sales by approximately 102,813 or 11,192 gallons. Similarly, a $1 increase in the selling price decrease or increase sales by approximately 813,11,192 or 102 gallons. 2.)Which of the independent variables (if any) appears to be statistically significant (at the 0.05…arrow_forward
- Consider the following regression model and corresponding output for a dataset with n = 104 observations: y=ß₁+ß2x2+ß³¸*¸+4 3 4x4+u Variable β Std. Error t P>|t| X2 -0.012 0.006 -2.289 0.022 X3 0.596 0.014 41.139 0.000 X4 0.52 1.06 Constant 8.860 1.766 5.017 0.000 What is the marginal effect of x4 on y? (approximate at least to 3 decimal places)arrow_forwardConsider the following model: yhat = 2.6+-0.9x² The prediction of y is yhat. What is the estimated marginal effect of x on y when x=2.7? PLZ MAKE SURE THIS IS RIGHT!!!arrow_forwardConsider the regression model Yi = β0 + β1X1i + β2X2i + β3(X1i * X2i) +ui. a. ΔY>/ΔX1 = β1 + β3X2 (effect of change in X1, holding X2 constant).b. ΔY/ΔX2 = β2 + β3X1 (effect of change in X2, holding X1 constant).c. If X1 changes by ΔX1 and X2 changes by ΔX2, then ΔY =(β1+β3X2)ΔX1 + (β2 + β3X1)ΔX2 + β3ΔX1ΔX2.arrow_forward
- We have a pooled cross section of data with data from 2009 and 1999 on women’s wages and their years of education. We consider the model: wage = β0 + β1Year2009 + β2educ + β3Year2009 × educ + u where wage is the hourly wage and educ is the years of education. Year2009 is a dummy variable equal to 1 in the year 2009 and 0 otherwise. Which of the following measures the change in the effect of education on the wage between 1999 and 2009? a) β0 b) β1 + β2 + β3 c) none of these answers d) β1 + β3 e) β3arrow_forwardConsider the model: yt = α0 + b0st + b1st-1 + b2st-2 + b3st-3 + ut. What is the effect of a permanent change in s on y?arrow_forwardWhat is the model constant when the dummy variable equals 1 in the following equations, where x1 is a continuous variable and x2 is a dummy variable with a value of 0 or 1? a. Ŷ = 4 + 8x1 + 3x2 b. Ŷ = 7 + 6x1 + 5x2 c. Ŷ = 4 + 8x1 + 3x2 + 4x1x2arrow_forward
- Managerial Economics: Applications, Strategies an...EconomicsISBN:9781305506381Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. HarrisPublisher:Cengage Learning