LAB-2.Econ 301Bilkent University

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Çankaya University - Balgat Campus *

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301

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Economics

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Nov 24, 2024

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pdf

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Econ 301 Bilkent University Fall 2023 Econometrics Department of Economics Lab Exercise 2 The relationship between average hourly earnings (ahe) and consumer prices (cpi) is modelled as follows: log( 𝑐𝑝𝑖) 𝑖 = 𝛽 0 + 𝛽 1 log (𝑎ℎ𝑒) 𝑖 + 𝑢 𝑖 and the data is presented in file lab02.xls. a) Find the range of values and compute the mean and variance of the variables in the model. b) Graph the above line graph of average hourly earnings and consumer prices. Visually do you expect to see a positive or negative relationship between average hourly earnings and consumer prices in the USA? c) Estimate the above model. What are the interpretations of 𝛽 ̂ 0 and 𝛽 ̂ 1 . d) Write out the fitted (estimated) relationship. Compute the fitted value of cpi for October 2023. e) Plot (graph) the actual, fitted values of cpi and the residual values for that model. f) Rename the residual of the estimation conducted, ie Genr resid2=resid . g) Prove numerically that 𝑐𝑝𝑖 𝑡 = 𝑐𝑝𝑖 𝑡 ̂ + 𝑢 𝑡 ̂
h) Compute the sum of squared residuals, and R 2 of the regression. Interpret the coefficient of determination. i) Compute the estimated unbiased variance of the error term, ie. 2 ˆ .What is the formula? j) Test the significance of the average hourly earnings variable. 𝐻 𝑜 : 𝛽 1 = 0 𝐻 1 : 𝛽 1 ≠ 0 What is your conclusion? k) Test the following hypothesis: 𝐻 𝑜 : 𝛽 1 = 1 𝐻 1 : 𝛽 1 ≠ 1 at the 5% significance level. l) Test the following hypothesis: 𝐻 𝑜 : 𝛽 1 ≤ 1 𝐻 1 : 𝛽 1 > 1 at the 5% significance level. m) Construct a 95% confidence interval for 𝛽 1 . n) What do you think about the unbiasedness property? Does the OLS estimator provide an unbiased estimator of the effect of the average hourly earnings?
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