ECONOMETRIC METHODS QUESTION 1 ALL WORKING MUST BE SHOWN IN YOU...

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ECONOMETRIC METHODS QUESTION 1 ALL WORKING MUST BE SHOWN IN YOUR ANSWER TO THIS QUESTION The following table contains data on number of bedrooms (X) and weekly rent in pounds (y) for a sample of six rental properties in Norwich. Household X y A 0 100 B 1 160 C 2 200 D 2 200 E 3 240 F 4 300 Obtain ordinary least squares estimates of 0 and 1 in the model: [10 marks] Interpret each of the two parameter estimates, and . [6 marks] Find the residuals. Which of the six properties has the highest positive residual associated with it? What conclusion can you draw about this property? [3 marks] Test the null hypothesis that the slope equals zero (1=0) against the alternative that the slope is positive (1 >0). Interpret your result. [6 marks]   QUESTION 2 For a sample of 1,700 college teachers in the USA, the following information is recorded: pay: Earnings, in thousands of dollars per year exp: Years of teaching experience male: 1 if male; 0 if female A scatter plot of pay against exp is shown below: The following regression results are obtained, with pay as the dependent variable and exp as the explanatory variable.   Interpret the estimates of the intercept and the slope in the above regression. [5 marks] The variable “male” is added to the regression, leading to the results: Interpret the coefficient of the variable “male” in the above regression. [5 marks] Conduct a t-test of the significance of the variable “male” in the above regression. Interpret the result. [5 marks] Explain why you would expect the problem of heteroskedasticity to be an issue in the above regressions. Looking at the scatter plot presented above, do you see evidence of heteroskedasticity? Explain your answer. [5 marks] The following command is used following the second regress command. The results are also shown. What do we learn from the results of this command? [5 marks] The second regression is performed again, with the robust option. The results are: Explain the purpose of the robust option, and why it is important to use it in the present situation. Which parts of the results change as a result of using robust? Does your answer to (c) change as a result of using robust? [5 marks] QUESTION 3 We have data on 52 countries in 2019. Let p_locali be the price of a Big Mac (the McDonald’s hamburger) in country i in local currency in 2019. Let ei be the exchange rate for country i against the US dollar in 2019 (that is, ei is the number of units of local currency that can be exchanged for one US dollar in 2019). Data on three of the 52 countries is shown in the following table. Country Currency p_local e Russia Rouble 130 63.84 Sweden Krone 51 9.48 Colombia Peso 11900 3227 Compute the price of a Big Mac in each of the three countries in US dollars. On this basis, which of the three currencies appears under-valued in 2019, and which appears over-valued? [7 marks]   The following regression model is estimated using data from all 52 countries in 2019 (p_usa is the price of a Big Mac in the USA in 2018): (1) Following the regression, two tests are performed. The results are as follows: Consider the two tests performed following the regression above. The first test is a test of the Law of One Price (LOP). Explain the concept of LOP. Is it rejected by the 2019 Big Mac data? Which theory is being tested by the second test? Is it rejected? [7 marks] It is claimed that LOP fails because the price is expected to be higher in countries with higher GDP. What is the name of this theory? How would you extend the model above to allow for this theory? How would you then know whether the theory is true? [6 marks] QUESTION 4 Gun ownership is currently a hotly debated topic in the USA. A survey was recently conducted on a cross-section sample of adults in the USA. The information collected was: y: 1 if individual owns a gun; = otherwise age: Age in years male: 1 if male; 0 if female income: Income in thousands of dollars per year mar: Marital status: 1 if living with parents 2 if single 3 if married 4 if separated, divorced or widowed Analysis of the data is carried out in STATA. The STATA output is shown on the next page. Consider this output, and then answer the following questions. How many individuals are in the survey, and what percentage of these individuals own a gun? [5 marks] Consider the margins command following the first logit command. Interpret the output from this command. [5 marks] Using the results from the first logit command, find the age at which the probability of gun ownership is maximised or minimised. Is it a maximum or a minimum? [5 marks] The second logit command includes a set of marital status dummies. Conduct a LR test of the importance of marital status in the gun-ownership decision. Interpret the result. [5 marks] Imagine that you are a consultant for the Coalition to Stop Gun Violence (CSGV). On the basis of the results of the second logit model, which types of individuals would you advise the CSVG to target when campaigning to bring about a reduction in gun ownership. [5 marks]   END OF PAPER Econometric Methods Formula Sheet Formula for the OLS estimators and OLS standard errors in the SLR model. Suppose we have the SLR model, y_i=β_0+β_1 X_i+u_i. The OLS estimators for β_1 and β_0 are: β ̂_1=(∑_(i=1)^n▒〖(X_i-X ̅ ) y_i 〗)/(∑_(i=1)^n▒(X_i-X ̅ )^2 ) and β ̂_0=y ̅-β ̂_1 X ̅, where y ̅ and X ̅ are the sample means of y_i and X_i respectively. Given that the OLS fitted values are, y ̂_i=β ̂_0+β ̂_1 X_i, and residuals, u ̂_i=y_i- y ̂_i, and given that MLR1-MLR5 hold, the OLS Standard Errors for β ̂_1 and β ̂_0, are se(β ̂_1 )=σ ̂√(1/(∑_(i=1)^n▒(X_i-X ̅ )^2 )) and se(β ̂_1 )=σ ̂√(1/n+X ̅^2/(∑_(i=1)^n▒(X_i-X ̅ )^2 )) with σ ̂=√((∑▒u ̂_i^2 )/(n-2)). Testing joint exclusion restrictions in the multiple regression model If q is the number of exclusion restrictions under the test and K is the number of explanatory variables in the unrestricted model (excluding the intercept), then: F-stat=((R_U^2-R_R^2)/(1-R_U^2 ))×((n-K-1)/q) has an F_(q,n-K-1) distribution under the null hypothesis that the q restrictions are true. R_U^2 and R_R^2 stand for the Unrestricted R-squared and the Restricted R-squared respectively. The logit model   Table 1: Critical values of the t-distribution SIGNIFICANCE LEVEL 1-tailed: 0.10 0.05 0.025 0.01 0.005 2-tailed: 0.20 0.10 0.05 0.02 0.01 df=n-k-1 1 3.08 6.31 12.71 31.82 63.66 2 1.89 2.92 4.30 6.97 9.93 3 1.64 2.35 3.18 4.54 5.84 4 1.53 2.13 2.78 3.75 4.60 5 1.48 2.02 2.57 3.37 4.03 6 1.44 1.94 2.45 3.14 3.71 7 1.42 1.90 2.37 3.00 3.50 8 1.40 1.86 2.31 2.90 3.36 9 1.38 1.83 2.26 2.82 3.25 10 1.37 1.81 2.23 2.76 3.17 11 1.36 1.80 2.20 2.72 3.11 12 1.36 1.78 2.18 2.68 3.06 13 1.35 1.77 2.16 2.65 3.01 14 1.35 1.76 2.15 2.62 2.98 15 1.34 1.75 2.13 2.60 2.95 16 1.34 1.75 2.12 2.58 2.92 17 1.33 1.74 2.11 2.57 2.90 18 1.33 1.73 2.10 2.55 2.88 19 1.33 1.73 2.09 2.54 2.86 20 1.33 1.73 2.09 2.53 2.85 21 1.32 1.72 2.08 2.52 2.83 22 1.32 1.72 2.07 2.51 2.82 23 1.32 1.71 2.07 2.50 2.81 24 1.32 1.71 2.06 2.49 2.80 25 1.32 1.71 2.06 2.49 2.79 26 1.32 1.70 2.06 2.48 2.78 27 1.31 1.70 2.05 2.47 2.77 28 1.31 1.70 2.05 2.47 2.76 29 1.31 1.70 2.04 2.46 2.76 30 1.31 1.70 2.04 2.46 2.75 40 1.30 1.68 2.02 2.42 2.70 50 1.30 1.68 2.01 2.40 2.68 60 1.30 1.67 2.00 2.39 2.66 70 1.29 1.67 1.99 2.38 2.65 80 1.29 1.66 1.99 2.37 2.64 90 1.29 1.66 1.99 2.37 2.63 100 1.29 1.66 1.98 2.36 2.63 125 1.29 1.66 1.98 2.36 2.62 150 1.29 1.65 1.98 2.35 2.61 200 1.29 1.65 1.97 2.35 2.60  1.28 1.64 1.96 2.33 2.58 Table 2: Critical values of the 2-distribution df  = 0.10  = 0.05  = 0.025  = 0.01  = 0.005 1 2.71 3.84 5.02 6.64 7.88 2 4.61 5.99 7.38 9.21 10.60 3 6.25 7.82 9.35 11.34 12.84 4 7.78 9.49 11.14 13.28 14.86 5 9.24 11.07 12.83 15.09 16.75 6 10.64 12.59 14.45 16.81 18.55 7 12.02 14.07 16.01 18.48 20.28 8 13.36 15.51 17.53 20.09 21.95 9 14.68 16.92 19.02 21.67 23.59 10 15.99 18.31 20.48 23.21 25.19 11 17.28 19.68 21.92 24.72 26.76 12 18.55 21.03 23.34 26.22 28.30 13 19.81 22.36 24.74 27.69 29.82 14 21.06 23.68 26.12 29.14 31.32 15 22.31 25.00 27.49 30.58 32.80 END OF MATERIALS

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