Instructions:
·Answer all questionson this documentunder 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.
3305AFE APPLIED ECONOMETRICS TIMED ASSIGNMENT 25 MARKS – APPROXIMATE LENGTH: 500-1000 WORDS DUE MAY 4th 8PM BRISBANE TIME Lochlan Charlton S5092763 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 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 Variable Coefficient Std. Error t-Statistic Prob. C 0.332108 0.145082 2.289111 0.0293 MARKET RETURN 0.421084 0.173615 2.425387 0.0215 R-squared 0.163938 Mean dependent var 0.472250 Adjusted R-squared 0.136069 S.D. dependent var 0.809924 S.E. of regression 0.752807 Akaike info criterion 2.330447 Sum squared resid 17.00157 Schwarz criterion 2.422055 Log likelihood -35.28715 Hannan-Quinn criter. 2.360812 F-statistic 5.882501 Durbin-Watson stat 2.555932 Prob(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 Variable Coefficient Std. Error t-Statistic Prob. C 257.5038 33.12690 7.773253 0.0000 P 2.674599 1.095255 2.441988 0.0176 E 0.680625 1.925346 0.353508 0.7249 I -1.015186 0.365762 -2.775538 0.0073 U 1.657919 1.689903 0.981074 0.3305 R-squared 0.194721 Mean dependent var 247.1954 Adjusted R-squared 0.141035 S.D. dependent var 33.41308 S.E. of regression 30.96736 Akaike info criterion 9.777548 Sum squared resid 57538.64 Schwarz criterion 9.944809 Log likelihood -312.7703 Hannan-Quinn criter. 9.843543 F-statistic 3.627078 Durbin-Watson stat 1.992742 Prob(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 Variable Coefficient Std. Error t-Statistic Prob. C 247.1954 4.144383 59.64588 0.0000 R-squared 0.000000 Mean dependent var 247.1954 Adjusted R-squared 0.000000 S.D. dependent var 33.41308 S.E. of regression 33.41308 Akaike info criterion 9.871037 Sum squared resid 71451.79 Schwarz criterion 9.904489 Log likelihood -319.8087 Hannan-Quinn criter. 9.884236 Durbin-Watson stat 2.014774 · 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 Value df Probability F-statistic 0.700956 (2, 58) 0.5003 Likelihood ratio 1.552421 2 0.4601 F-test summary: Sum of Sq. df Mean 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 Variable Coefficient Std. Error t-Statistic Prob. C -24781.88 21216.71 -1.168036 0.2476 P -376.8784 321.2959 -1.172994 0.2456 E -95.69033 81.59221 -1.172788 0.2457 I 143.0923 121.9890 1.172993 0.2456 U -233.6525 199.2176 -1.172851 0.2457 FITTED^2 0.581268 0.493189 1.178592 0.2434 FITTED^3 -0.000791 0.000673 -1.174969 0.2448 R-squared 0.213726 Mean dependent var 247.1954 Adjusted R-squared 0.132387 S.D. dependent var 33.41308 S.E. of regression 31.12287 Akaike info criterion 9.815203 Sum squared resid 56180.71 Schwarz criterion 10.04937 Log likelihood -311.9941 Hannan-Quinn criter. 9.907596 F-statistic 2.627601 Durbin-Watson stat 2.023006 Prob(F-statistic) 0.025358