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Introduction to Econometrics I Project

Using STATA, perform a regression analysis of the data provided.

The dependent variables deaths, heart, and liver, each can be regressed on alcohol as nice simple regression examples.The conventional wisdom is that wine is good for the heart but not for the liver, something that is apparent in the regressions.Because the number of observations is small, this can be a good data set to illustrate calculation of the OLS estimates and statistics.

You will be working on a project where you use multivariate regression analysis to analyze

economic data. You will be responsible for determining the research question, formulating the

regression model, finding the relevant data and papers, performing the analysis and discussing the

results. Chapter 19 in Wooldridge’s “Introductory Econometrics” has many useful examples and

suggestions for carrying out an empirical project.

Technical Details-Formats

Your final project must be submitted uploaded to a designated folder on Brightspace.

Please submit an electronic copy of your first draft for a format check by.

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 Introduction to Econometrics I Project

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).

Introduction to Econometrics I Project

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

Introduction to Econometrics I Project

).

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.

Introduction to Econometrics I Project

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.

Introduction to Econometrics I Project

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 generalto-specific approach.

3. Perform misspecification testing (RESET, Breusch-Pagan and White’s tests) in the

following order:

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.

Project Rubric

Approximate weight (%)

Technical Model description 10

Data description 15

Selection of independent variables (including F-tests) 15

Misspecification testing 10

Statistical significance (discussion) 10

Qualitative Motivation of the research question 10

Literature review 10

Economic significance of the results (discussion) 10

Layout / format 10

Introduction to Econometrics I Project

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