Econ3338.01: Introduction to Econometrics I Project InstructionsTechnical Details – Formats Your final project must be submitted uploaded to a designated folder on Brightspace by December 15 2020. Please submit an electronic copy of your first draft for a format check by December 6 2020. If any important part of the paper is missing or is not properly presented you will receive an email within 3 – 4 days. 1. Cover page. The cover page should be structured as follows: Name B00# Date Project Title Prepared for ECON 3338.01: Introduction to Econometrics 2. Length. The maximum length including figures tables and references should not exceed 12 pages. 3. Font size and space. The text should be double – spaced with size 12 font. 4. Equations. Use an equation editor (built – in in MS Word) to specify your model(s) and number all equations in your text sequentially (1 2 etc) . Proposed Outline 1. Introduction In this section describe the research question and explain why it is important. Focus on the dependent variable. Provide a brief description of what you will do in your project (in each section) without getting into detail.2. Literature review Provide a short review of journal articles and/or books that are closely related to your project. Include the complete reference for each reviewed study in the reference section. 3. Methodology This section must discuss in detail what you will do in this project. You should mention the questions that you will answer and how you plan to do so. For example you write that you will investigate the effect of education and experience on wages. This will be done by considering a multivariate linear model to be estimated by OLS. If there is a similar paper in the literature you must explain the difference between your work and the cited paper. Is it in the methodology? Do you include more independent variables in your analysis? Do you use a different estimation technique? Do you have a different data set? Remember to write the regression that you plan to run using the following format: 𝑤𝑎𝑔𝑒𝑖 = 𝛼 + 𝛽𝑒𝑑𝑢𝑖 + 𝑢𝑖 Focus on the independent variables. For each independent variable explain why you have included it in the model and whether you expect it to have a positive or negative impact on the dependent variable. 4. Description of the data In this section you describe your data set in detail: the variables their nature (continuous categorical or binary 0/1) time period that they span the number of observations and the source of the data. Summary statistics should be provided either in tables or figures depending on the type of data. The full range of summary statistics (mean/variance/min/max/skewness/kurtosis) can be provided for continuous variables. Binary or categorical variables can be reported using frequency tables or pie charts. Provide some discussion of the descriptive statistics of the dependent and independent variables. If you notice some patterns in your data interesting or strange mention them here. You can also include some preliminary analysis about the relationship between variables of interest using scatterplots between pairs of variables. 5. Results In section 3 you have explained your methodology . In this section you should estimate the models based on your data and report the results. The regression outputs and specification tests must be provided and discussed. In the class you will learn how to estimate the models and how to do inference for the models (i.e. testing hypotheses about the values of the parameters of your model based on OLS estimates) . You are asked to use what you have learned to estimate your models and make inference. In this section you will also discuss the model specification and potential biases. You may consider additional independent variables that matter for explaining the dependent variable or use different nonlinear transformations of existing variables. If you have regressed the same variable of interest on different independent variables you should discuss which resulting model is better in terms of the goodness of fit (𝑅 2 and 𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅 2 ) . You need to be aware that your results would be reliable if OLS assumptions are satisfied. After running the regressions you should test for functional misspecification and heteroskedasticity . Note: Detailed instructions for this section as well as relevant STATA commands will be posted later on Brightspace 6. Conclusion This is the final section of your project. You should provide a summary of what you have done. In one or at most two paragraphs state the questions that you wished to answer and your main findings (independent variables that have some effects on the dependent variables and magnitude of each effect) . How can you use these results for policy making (practical purposes)? You may also provide suggestions for further research (i.e. including other variables considering different functional forms using different estimators etc. ) . 7. References You should list all cited studies that are related to your research questions following the Chicago Manual of Style as follows: Andrews D. and E. Zivot (1992) Further Evidence on the Great Crash the Oil – Price and the Unit – Root Hypothesis Journal of Business & Economic Statistics 10 251 – 270. Appendix Including tables and figures in the main text may lead to some difficulties regarding the layout of your work. Instead you may place all your tables and figures at the end of the file. All tables and figures should be labeled (e. g . Table 1 Figure 5 etc. ) and must have a title. When you discuss the results in the text use table and figure numbers to refer to them. In Section 5 refer to relevant tables and figures when discussing the results as follows: “ The results of running the regression. ……. can be found in Table 2. The parameter estimate for education is statistically insignificant…. ” If you move all tables and figures to the Appendix the Appendix should have two separate sections: one for tables and one for figures. Tables and figures should not be copy – pasted from the software output. You should create your own tables and graphs. Instructions for Section 5 “ Results ” What independent variables should you include in your models? Sometimes you have a theory that determines which independent variables you should include in your model (for example you may try to quantify the parameters in a Cobb – Douglas production function: the independent variables are labor and physical capital) . In other cases you do not have such a theory but you have a large set of independent variables that you believe can be used to explain your dependent variable. In such a case you are not sure which variables you should include and which not. You can proceed in the following way:  Begin with all independent variables that you think are relevant and that do not have near multicollinearity issues. If applicable you may consider cross products of these variables (you need to justify why you did so) .  Estimate your model with all of them.  Check the output. Some of the parameter estimates may be statistically insignificant. Consider the hypothesis that they are jointly insignificant (F – test) . If so remove the independent variables associated with these parameters. Otherwise consider all the hypotheses that are related to subgroups of these coefficients.  Estimate your model again and repeat the hypothesis testing . The coefficient estimates should not be considerably different (especially their sign) compared to the previous models or else you may have an omitted variables bias. Examine again if the OLS assumptions are satisfied. This procedure is called general – to – specific approach. In Section 5: 1. Estimate your regression model as discussed above. 2. What is the adjusted R – squared? Do you deem it to be large enough? Could you add more independent variables? Note that if you decide to explore the case of using more independent variables by including them in the “ updated ” model please use the general  to – specific approach. 3. Perform misspecification testing (RESET Breusch – Pagan and White ’ s tests) in the following :  If functional form is found to be a problem when using RESET change the specification by applying logarithms to suitable variables or by adding squared terms of some of the independent variables.  Estimate the “ updated ” model and check again for functional form using RESET. Select the model that looks less misspecified.  Check the “ updated ” model for heteroskedasticity (B – P and White ’ s tests) .  If heteroskedasticity is not an issue then you are ready to discuss your regression output results.  If heteroskedasticity is found then re – estimate your “ updated ” model using robust standard errors. Note: In misspecification tests the null hypothesis is that there is no problem with the specification. 4. Discuss the regression output.  Report the result of the goodness – of – fit test and the adjusted R – squared from the STATA regression output.  Individual parameter estimates: statistical interpretation o If you found a variable to be significant report it and mention the significance level. In the regression output the null is that the individual parameter is equal to zero (statistically insignificant) . o If a variable of interest is insignificant report it as well (do not delete it from the model) . It means that based on the data set you have found no statistical evidence of an effect of this independent variable on the dependent variable. o Reminder: if you have two or more independent variables that are individually insignificant and you consider removing them from the specification check whether they are jointly insignificant. If the F – test of this restriction does not reject the null you can remove them from the model.  Individual parameter estimates: economic interpretation o You can now interpret the parameter estimates in economic terms i.e. what effects the independent variables have on the dependent variable. Do you think that the effects are large? o Provide economic interpretation for both statistically significant and insignificant parameter estimates. Interpret them accordingly . Important: whenever you perform hypothesis testing the p – value is relevant to the null hypothesis. a. p – value<1%: reject the null hypothesis at the 1% significance level b. 1%< p - value<5%: reject the null hypothesis at the 5% significance level c. 5%< p - value<10%: reject the null hypothesis at the 10% significance level d. P - value>10%: do not reject the null hypothesis.