3305AFE APPLIED ECONOMETRICS TIMED ASSIGNMENT 25 MARKS – APPROXIMATE LENGTH: 500-1000 WORDS DUE MAY 4th 8PM BRISBANE TIME Instructions: Answer all questions on this document under the relevant headings.Approximately half the available marks will be allocated for getting the correct numerical/mathematical answers. All other marks will relate to the exposition/interpretation of your econometric work.Upload your completed assignment to the submission portal on the Learning at Griffith website by 8pm May 4, 2021.To complete the technical questions, you may write equations by hand, or use the equation editor in MS Word. Graphically constructed answers may be drawn by hand, or produced in a software package such as MS Paint. The content covers work from the first four weeks (lectures 1-4) and the associated workshops. Question 1. [6 Marks] Regression models are a workhorse method of statistical and/or econometric analysis. These models can take the form , where is the dependent variable and the independent variable. These equations are usually fit to data using a technique known as “Ordinary Least Squares”, or OLS. Briefly explain the mechanics and intuition behind this method. Why is a model estimated using OLS considered a “line of best fit” for a given data set? Using a couple of sentences in each case, explain the meanings behind the following terms in the context of the above regression model. Regression models often employ the assumptions and . Explain the meanings of these two terms. You may like to illustrate these assumptions (or their violations) by providing graphs such as scatter plots. What implications do they have for (i) the standard errors from the model, and (ii) the Gauss-Markov Theorem? Question 2. [5 Marks] Finance professionals are often interested in minimizing risk in their portfolios by investing in assets that react differently under varying market conditions. The idea is that by buying some securities that are positively correlated with broader market movements, and some that are negatively associated with the market, the combined risk exposure will be reduced. This type of risk can be measured for a share using the market beta – a parameter from a regression model designed to measure the association between the return on the asset and the overall market performance. Market betas can be calculated using the following equation: where is the return on the asset, and is the market return. A share with a high beta will move strongly with the market, while a beta closer to zero will be less sensitive to market fluctuations. Shares with negative betas will move in the opposite direction to the broader market. Table 1 below gives an estimate for a US firm that manufactures textiles. Table 1. Asset Returns and Market Returns – Textiles Dependent Variable: ASSET RETURN Method: Least Squares Sample: 1 32 Included observations: 32 VariableCoefficientStd. Errort-StatisticProb. C0.3321080.1450822.2891110.0293MARKET RETURN0.4210840.1736152.4253870.0215 R-squared0.163938 Mean dependent var0.472250Adjusted R-squared0.136069 S.D. dependent var0.809924S.E. of regression0.752807 Akaike info criterion2.330447Sum squared resid17.00157 Schwarz criterion2.422055Log likelihood-35.28715 Hannan-Quinn criter.2.360812F-statistic5.882501 Durbin-Watson stat2.555932Prob(F-statistic)0.021521 Do your asset returns move with the market, against the market, or are uncorrelated with the market? Briefly explain. Calculate a 90% confidence interval for the market beta ( using information drawn from the output. Show all working and provide an interpretation for your result. Test the null hypothesis that there is no link between the returns on your specific asset () and the return on the market () at Give the null and alternative hypotheses, a test (t) statistic, critical value, p-value and a conclusion. Question 3. [6 Marks] A criminologist is interested in the social and economic factors that contribute to violent crime. To study this issue, she takes data on incidents of violence per 100,000 people per year, and regresses this against measures of poverty, education, income and unemployment. All variables are collected at the geographical level. The model she employs is where , , and are the poverty, education, income and unemployment variables respectively. Poverty is measured in percentage points, average education in years, income in thousands of dollars per year, and unemployment in percent. An output of her model is given below. Table 2. Economic Determinants of Violent Crime Dependent Variable: VIOLENT CRIME (Per 100,000) Method: Least Squares Sample: 1 65 Included observations: 65 VariableCoefficientStd. Errort-StatisticProb. C257.503833.126907.7732530.0000P2.6745991.0952552.4419880.0176E0.6806251.9253460.3535080.7249I-1.0151860.365762-2.7755380.0073U1.6579191.6899030.9810740.3305 R-squared0.194721 Mean dependent var247.1954Adjusted R-squared0.141035 S.D. dependent var33.41308S.E. of regression30.96736 Akaike info criterion9.777548Sum squared resid57538.64 Schwarz criterion9.944809Log likelihood-312.7703 Hannan-Quinn criter.9.843543F-statistic3.627078 Durbin-Watson stat1.992742Prob(F-statistic)0.010317 Provide an interpretation of the parameter (the coefficient on poverty). How does this interpretation differ from one obtained from a model where education, income and unemployment are excluded (i.e. the model )? Which variables appear to be the most significant determinants of violent crime? Which variable is the least significant? Provide an interpretation of this model that could be useful for a policy maker who is trying to lower violent crime in their district. What fraction of the overall variation in is explained by the covariates in the model? Make some suggestions to the criminologist as to how the model fit could be improved. Suppose a region has a poverty rate of 8%, an average educational attainment of 11.2 years, an average income of $42 (000) per year, and an unemployment rate of 7%. Provide a prediction of the rate of violent crime for this geographical area. Question 4. [8 Marks] This question uses the information from Question 3. Alongside the model estimated in Table 2, the criminologist also estimates an equation of the form and the output is given below. Table 3. Economic Determinants of Violent Crime – Null Model Dependent Variable: VIOLENT CRIME (Per 100,000) Method: Least Squares Sample: 1 65 Included observations: 65 VariableCoefficientStd. Errort-StatisticProb. C247.19544.14438359.645880.0000 R-squared0.000000 Mean dependent var247.1954Adjusted R-squared0.000000 S.D. dependent var33.41308S.E. of regression33.41308 Akaike info criterion9.871037Sum squared resid71451.79 Schwarz criterion9.904489Log likelihood-319.8087 Hannan-Quinn criter.9.884236Durbin-Watson stat2.014774 Using information drawn from Tables 2 and 3, perform an F-test for the overall significance of the model presented in Table 2. Give the unrestricted and restricted models, the null and alternative hypotheses, values for F-calc and F-crit, and a conclusion. Briefly explain the intuition behind the F-test you performed above. If and turn out to be very similar, what would this imply about the null hypothesis in an F test? The criminologist is interested in assessing the functional form of the model depicted in Table 2. She performs the RESET test and the output is provided overleaf. Using the output in Table 4, conduct the RESET test. Give the null and alternative hypotheses, the F-statistic, P-value and a conclusion. Does the model she has used have the correct functional form? Briefly give an explanation of how the RESET test works. Provide some intuition around the role of the additional non-linear terms added to the equation in assessing the specification. Table 4. RESET Test – Violent Crime Model Ramsey RESET Test Equation: UNTITLED Specification: VC C P E I U Omitted Variables: Powers of fitted values from 2 to 3 ValuedfProbability F-statistic 0.700956(2, 58) 0.5003 Likelihood ratio 1.552421 2 0.4601 F-test summary: Sum of Sq.dfMean Squares Test SSR 1357.938 2 678.9689 Restricted SSR 57538.64 60 958.9774 Unrestricted SSR 56180.71 58 968.6329 LR test summary: Value Restricted LogL-312.7703 Unrestricted LogL-311.9941 Unrestricted Test Equation: Dependent Variable: VC Method: Least Squares Sample: 1 65 Included observations: 65 VariableCoefficientStd. Errort-StatisticProb. C-24781.8821216.71-1.1680360.2476P-376.8784321.2959-1.1729940.2456E-95.6903381.59221-1.1727880.2457I143.0923121.98901.1729930.2456U-233.6525199.2176-1.1728510.2457FITTED^20.5812680.4931891.1785920.2434FITTED^3-0.0007910.000673-1.1749690.2448 R-squared0.213726 Mean dependent var247.1954Adjusted R-squared0.132387 S.D. dependent var33.41308S.E. of regression31.12287 Akaike info criterion9.815203Sum squared resid56180.71 Schwarz criterion10.04937Log likelihood-311.9941 Hannan-Quinn criter.9.907596F-statistic2.627601 Durbin-Watson stat2.023006Prob(F-statistic)0.025358
