Economics and stata

PART A: Stata Application: Reset and Chow tests (50 marks) Question 1: (40 marks) We will use the data set from Assignment 1 to perform a CHOW test to determine whether or not there was any change in the relationship between crime, the lagged clearance rate, the size of the local population and the overall unemployment rate after Mr. Rob Knecht was hired as the new Chief of Police in Edmonton. The test will be based on the following “log-log” models (NOTE: the data set includes the current value of Clearance, but the models use the lagged value of this variable). MODEL 1 ln(Crimet) = δo + δ1 ln(Clearancet-1) + δ2 ln(Popt) + δ3 ln(Unempt) + ut MODEL 2 ln(Crimet) = βo + β1 ln(Clearancet-1) + β2 ln(Popt) + β3 ln(Unempt) + β4Newchieft + β5 Newchieft * ln(Clearancet-1) + β6 Newchieft * ln(Popt) + β7 Newchieft * ln(Unempt) + νt; (a) Find out when Rob Knecht became chief of police for the City of Edmonton and create a dummy variable, Newchief, that is equal to 1 for all observations after Rob Knecht became the chief of police (i.e., do not include quarter during which he became police chief). (b) Using the same sample period as in Assignment 1 (i.e., commencing in 2009 Q2), calculate summary statistics (including correlations) for Crimet , Clearancet-1, Popt , Unempt and Newchieft for i. the full sample period; ii. the sub-sample where Newchieft=0 iii. the sub-sample where Newchieft=1. (c) Estimate the coefficients for Model 1 and Model 2. (d) Test whether or not the elasticticity of crime with respect to unemp for the period during which Chief Knecht has been in office is significantly different from zero. (e) Perform RESET tests for both models (f) Perform a CHOW test for differences across the two subsamples. Complete Part A of the Answer Worksheet and Attach your Stata log file PART B: Some Properties of Simple Regression Models with Dummy Variables (20 marks) Consider the following model, where the data are drawn from two different groups (such as two different time periods), Group A and Group B: Yt = γ0 + γ1Dt + εt i = 1, … T; where Dt = 0 for the first TA observations in the data set (Group A) 1 for the last TB (= T-TA) observations in the data set (Group B). (i) (2 marks)Find the expected value of Y for a random observation drawn from Group A (ii) (2 marks)Find the expected value of Y for a random observation drawn from Group B (iii) Use a Stata experiment where Yt = Crimet and Dt = Newchieft from Part A, to determine which of the following statements are true for this data set. For each statement clearly explain how your Stata experiment supports or refutes the statement. (a) (4 marks) ∑ [(?? − ?̅)?? ] = (????)/(?) ? ?=1 (b) (4 marks) ∑ [(?? − ?̅)?? ] = ??(?̅ ? − ?̅) ? ?=1 where ?̅ ? is the average value of Y for the subset of observations belonging to group B (c) (2 marks) If we use OLS to estimate the model, the estimate of γ0 will be ?̅ ? (d) (2 marks) If we use OLS to estimate the model, the estimate of γ1 will be ?̅ ? -?̅ ? (e) (4 marks) A “Chow” test, which in this case is simply the F-test for overall significance, indicates that there are significant differences in the average value of Y across the two time periods. Attach your Stata log file to your answers to Part B. PART C: Preliminary Data and Literature Review Work on Research Report (30 marks) (1) Collect the data that you will need to estimate your model. The sample size should be at least 30 observations. Report the exact sources (4 marks) of your data (including web site addresses and series numbers if applicable). (2) (4 marks) Calculate the minimum, maximum, and average values for all of your variables and the correlations of each of your explanatory variables with your dependent variable. Present these values in a table using the general format from Assignment 1. Submit the corresponding Stata logs for these calculations. (3) (2 marks) Create a Stata plot with your dependent variable on the vertical axis and the main explanatory variable corresponding to your main research question on the horizontal axis. (4) (10 marks) Write a paragraph (at least 1/3 of a page single spaced or at least 2/3 of a page double-spaced) describing the highlights of your results from (2) and (3) (5) (10 marks) Write a paragraph (at least 1/3 of a page single spaced or at least 2/3 of a page double-spaced) describing one or more major results or ideas from one of the articles that you will be using for your literature review. Provide a complete reference for the article (See, for example, the references on the class website.) Note: Wikipedia and other similar websites such as Investopedia are not appropriate sources for your literature review. NOTE: If you have changed topics, PART C for Assignment #2 will only be marked if you also hand in a revised version of PART C from Assignment # 1. Assignment #2 Answer Worksheet Due Date: March 23, 2017 (in class) Name: __________________ Student ID ______________ (A1) (2 marks) Rob Knecht became the Chief of Police for the City of Edmonton on ________________. Enter dates as Month/Day/Year (for example November 30,1999). (A2) (8 marks) Summary Statistics 1. Full Sample: 2009 Q2 through 2016 Q3 crime lagged clearance pop unemp Newchief Sample Average Minimum Maximum Standard Deviation Correlation with crime Sub-Sample 1: Observations from 2009 Q2 through 2016 Q3 where Newchief=0 crime lagged clearance pop unemp Newchief Sample Average Minimum Maximum Standard Deviation Correlation with crime Sub-Sample 2: Observations from 2009 Q2 through 2016 Q3 where Newchief=1 crime lagged clearance pop unemp Newchief Sample Average Minimum Maximum Standard Deviation Correlation with crime (A4) Complete the following tables (12 marks =6 marks per Model) Model 2 Results ?̂0 [se(?̂0 )] ?̂1 [se(?̂1 )] ?̂2 [se(?̂2 )] ?̂3 [se(?̂3 )] ?̂4 [se(?̂4 )] ?̂5 [se(?̂5 )] ?̂6 [se(?̂6 )] ?̂7 [se(?̂7 )] # of observations R 2 F test of overall significance (p-value) RESET (p-value) Model 1 Results ?̂0 [se(?̂0 )] ?1 ̂ [se(?1 ̂ )] ?̂2 [se(?2 ̂ )] ?̂3 [se(?3 ̂ )] # of observations R 2 F test of overall significance (p-value) RESET (p-value) (A5) (6 marks) According to the RESET test results, the functional form for: Model 1 appears to be adequate: _YES / NO___(circle one) Model 2 appears to be adequate: _YES / NO___(circle one) (A6) (10 marks) Construct a 95% Confidence interval for the elasticity of crime with respect to the unemployment rate for the period after Chief Knecht took office. Interpret this interval from the perspective of an economist (i.e., What do we learn about the elasticity from this C.I.?): ANSWER: (A7) (12 marks) Perform a CHOW test for whether or not the relationship is the same in both subsamples. Include all of the following steps:  Indicate the null and alternative hypotheses: H0 and Ha ;  provide the appropriate critical value from your statistical tables;  provide the value of the test statistic from your Stata output;  indicate whether you have decided to reject or not reject your null hypothesis;  interpret your decision in the context of the model. ANSWER: