Do not calculate any descriptive statistics or estimate any model.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Part A – Cross-sectional Analysis

 

Consider the dataset PS1a-9.dta, which contains simulated data on demand for product 0. The variable q0 denotes the quantity sold of that good and p0 denotes its price. Prices of other relevant goods are denoted by p1 and p2. Other variables are denoted by x1, x2 and x3 (if they are potential explanatory variables) or z1 and z2 (if they are potential instruments for p0). Apart from product 0 (which is defined in the dataset) and income (x1), all the other variables available in the dataset are left unspecified. Assume that p0 is suspected to be endogenous and that all the other explanatory variables are exogenous.

 

1. Do not calculate any descriptive statistics or estimate any model. Thinking only in theoretical terms, and having into account the definition of product 0, provide examples of:

1.1. The goods that p1 and p2 may refer to.

1.2. The variables that x2 and x3 may represent (do not take into account their sample values, but note that

x3 is a dummy variable).

1.3. A specific factor that may be causing the possible endogeneity of p0.

1.4. The variables that z1 and z2 may represent (do not take into account their sample values).

 

2. Discuss the expected effects (positive / negative / null) that each explanatory variable defined in the dataset or in questions 1.2 and 1.3 (p0, p1, p2, x1, x2 and x3) may have on the demand for good 0.

 

3. Consider a log-linear regression model for explaining the demand for product 0. Include in the econometric model all potential explanatory variables. When necessary, use all available instruments.

3.1. Test whether p0 is indeed endogenous.

3.2. Test whether the variables zj could indeed be used as instruments for p0.

3.3. Estimate the model using the method that question 3.1. indicates as appropriate for your data (for the variance, assume homoskedasticity).

3.4. Test the individual and joint significance of all explanatory variables.

3.5. Extend the model in order to test whether the effect of the variable x2 depends on the value of x3. What can you conclude?

3.6. Assume exogeneity. Test for heteroskedasticity and for the log-linearity assumption.

Part B – Panel Data Analysis

Consider the dataset PS1b.dta, which comprises the following data for Portuguese firms:

 

• id: Firm id

• YEAR: Year

• LEV_ST: Short-term debt / (STD+LTD+Equity)

• LEV_LT Long-term debt / (STD+LTD+Equity)

• LEV: Total debt / (STD+LTD+Equity)

• COLLAT: Tangible assets / Total assets

 

• SIZE: Log(Total assets)

• PROF: EBIT / Total assets

• GROWTH: Sales growth rate

• AGE: YEAR - Foundation year

• LE: =1 if large firm

• MicE: =1 if micro firm

• SE: =1 if small firm

• MedE: =1 if medium firm

 

For your work, consider only small firms and the following variables:

• Dependent variable: LEV_ST (from now on designated by LEVERAGE)

• Base explanatory variables: COLLAT, SIZE, PROF, GROWTH and AGE

 

You may delete the other observations and variables.

 

4. Consider a panel data linear regression model for for explaining the behaviour of LEVERAGE as a function of all explanatory variables defined above. Denote the individual effects by and the idiosyncratic error

term by .

4.1. Compute the random-effects and fixed-effects estimators of this model using standard (cross-sectional) estimators for the variance.

4.2. Use a statistical test to decide between random effects and fixed effects estimators.

4.3. Re-estimate the model selected in question 4.2 using the most appropriate panel data estimator for the variance. Did the significance of the explanatory variables change?

4.4. Add as many year dummies as possible to your selected model and re-estimate it. What can you conclude?

4.5. Using the random effects estimator, test whether the effect of PROF on LEVERAGE is constant over time (assume that everything else is constant over time).

4.6. Assume that 𝐸(𝑢𝑖,𝑡+𝑗 |𝑆𝐼𝑍𝐸𝑖𝑡) = 0, |𝑗| > 2, 𝐸(𝑢𝑖,𝑡+𝑗 |𝑆𝐼𝑍𝐸𝑖𝑡) ≠ 0, |𝑗| ≤ 2 and 𝐸(𝛼𝑖 |𝑆𝐼𝑍𝐸𝑖𝑡) = 0. All other explanatory variables are strictly exogenous. Use an appropriate method to estimate the initial model under these assumptions

 

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