ECON2005 Applied Econometrics Assignment - University of Nottingham, UK

The assignment - Your objective is to find an answer to the question: Do female directors improve the financial performance of companies?

The data

The dataset you have been given is called GenderDirectorsData.dta. In the dataset, each observation is a company in a year. All of the companies are UK registered. Approximately 1/5th of the observations are for companies in 2008. Approximately 1/5th of the observations are for companies in 2010. Approximately 1/5th of the observations are for companies in 2012. Approximately 1/5th of the observations are for companies in 2014. Approximately 1/5th of the observations are for companies in 2016. Included in the data that you have for each company-year observation are: two measures of the profitability of the company; a measure of the company's size; the number of company directors; and the number of female company directors.

The two profitability measures are Return on Assets (roa) and the Tobin's Q ratio (tobinsq). Return on Assets is an indicator of how efficient a company's management is at using its assets to generate earnings. It is measured in percentage points. The Tobin's Q ratio equals the market value of a company divided by the replacement cost of its assets.

Significance level -

Work with significance level α = 0.05. However, keep an eye on p-values and comment where appropriate.

1. Setting up

Download the GenderDirectorsData.dta from Moodle.

Open STATA, open a doedit window and start a new dofile with a clear command, a capture log close command, a cd command, a log command, and then a use command that will open GenderDirectorsData.dta. (Remember to save your dofile.)

2. The data

Use desc, sum and graph commands to get to know the dataset and the variables it contains.

3. Regression analysis of the relationship between profitability and the female share in a directorate

You are going to start your regression analysis by estimating the three models.

However, before you estimate these models:

3.1 Write out the two-sided and one-sided hypotheses that you will want to test after estimating each model.

3.2 Explain why it is useful to include y10_i, y12_i, y14_i and y16_i in each of the models.

3.3 Explain why there is not a fourth model that takes ln(roa)_i as its dependent variable.

3.4 Now, estimate Model 1_ROA, Model 1_TQ, and Model 1_LTQ and, after each estimation, conduct a White's test of the null hypothesis that the errors are homoscedastic. Write up the test results. (Hint: Before the estimations, you need to generate three new variables.)

3.5 Depending on your test results for 3.4, either tabulate your first set of estimations or re-estimate the three models, this time, asking STATA to provide heteroscedasticity-robust standard errors and tabulate these new estimations. Call the table "Table 1: Regression analysis of the relationship between profitability and female share in a directorate". The table must include coefficient estimates, standard errors and indicators of significance and, for eachmodel, the coefficient of determination (R²) and the number of observations. Make sure your reader knows whether the standard errors in the table have been adjusted to account for heteroscedasticity or not.

3.6 Now, write up the tests of the hypotheses that you set out in 3.1 and the interpretation of any of the significant coefficients among α₁, β₁, γ₁. (Hint: The interpretations need to be both correct and useful.)

4. Regression analysis of the relationship between profitability and female presence in a directorate

4.1 Some have argued that just one female is required on a directorate in order for any resulting positive effects to be observed. Investigate this by replacing the variable pfdir_i with the variable fdpres_i in each of the models and estimating again. After each estimation, conduct a White's test of the null hypothesis that the errors are homoscedastic and look at the results.

4.2 Depending on your test results for 4.1, either tabulate your first set of estimations that include fdpres_i or re-estimate the three models, this time, asking STATA to provide heteroscedasticity-robust standard errors and tabulate these new estimations. Call the table "Table 2: Regression analysis of the relationship between profitability and female presence in a directorate". See 3.5 for a list of what the table must include. Make sure your reader knows whether the standard errors in the table have been adjusted to account for heteroscedasticity or not.

4.3 Now, write up the results presented in Table 2. Your write-up should include relevant hypothesis tests and interpretations for any significant coefficients on fdpres_i.

4.4 What do you conclude from a comparison of your Tables 1 and 2? Decide which out of the six model specifications you have estimated so far is your preferred model specification. State and explain your decision.

5. Has the effect of female directors on financial performance changed over time?

Some have argued that the effect of female directors on company profitability varies depending on the state of the economy as a whole. At the start of the time-period covered by your dataset, the UK economy was entering a deep recession. GDP growth became positive again in 2010 and, with the exception of a couple of quarters in 2012, remained positive until the end of the time-period. So you can investigate whether the effect of female directors on company profitability varies depending on the state of the economy as a whole by looking at whether the effect of female directors on profitability varies across the years in your preferred model.

To do this you need to add four interaction terms to your preferred model specification. Each interaction term will involve either pfdir_i or fdpres_i (which depends on what your preferred model specification is) and one of the year dummy variables. There will be one interaction term involving each of the year dummy variables.

5.1 Write out the augmented version of your preferred model, i.e., your preferred model specification but with the four new interactions included.

5.2 Add four gen commands to your dofile to generate the four interaction terms.

5.3 Estimate the augmented version of your preferred model. Adjust the standard errors to account for heteroscedasticity if required. Produce another table of regression results, this time including your preferred model in one column and the augmented version of your preferred model in a second column. Call the table "Table 3: Has the effect of female directors on financial performance changed over time?" See 3.5 for a list of what the table must include. Make sure your reader knows whether the standard errors in the table have been adjusted to account for heteroscedasticity or not.

5.4 Conduct an F-test of the null hypothesis that the coefficient on each and every one of the four interaction terms is equal to zero.

5.5 Write up the results presented in Table 3, focusing primarily on the F-test that you conducted in 5.4 and the conclusion you draw from the test result.

6. Omitted variables

6.1 Finally, give some thought to potentially important determinants of profitability that have been omitted from the models that you have estimated. Might any of them be leading to omitted variable bias in the coefficients that relate to your research question? Can you comment on the possible direction of the bias?

Attachment:- Applied Econometrics Assignment Files.rar