The file **(DATA FOR SECTION 1)** provided to you for this section contains a sample data set on two quarterly time series, namely, and . Using Gretl econometric software, you will have to find an equation describing the underlying relationship between these variables. To do that, proceed as follows:

- Obtain OLS estimates for the regression model . Then, explain why this model violates OLS assumptions and the consequences of these violations. Carefully explain your evidence.
- Propose an appropriate model for describing the between and (always assuming that depends on ) that will be consistent with OLS assumptions.
- Compute the elasticity coefficient for how reacts to based on the model you propose (using the sample mean of ).

Notes:

- In parts (a) and (b), you are expected to perform: (1) Graphical and formal testing of normality of residuals; (2) Graphical and formal testing of heteroscedasticity; (3) Analysis of serial autocorrelation through autocorrelograms and formal testing; (4) Analysis of coefficient
*t*-statistics in both models; (5) statistical analysis of linearity of regression coefficients; and (6) If necessary, make a brief comparison between competing models. - For part (b), your modelling options are:
- Different non-linear functional forms, such as: the log-log, log-level or level log models, the reciprocal functional form, the quadratic functional form and the cubic functional form.
- Use of dummy variables, including: an outlier intervention dummy (no more than one), intercept-coefficient dummies, slope-coefficient dummies, and seasonal dummies.

- Report your workings using Gretl’s command log.

**Question III. (Research question on cost functions) **

Microeconomic theory states that the cost of production should be a function of input factors, i.e. . Sometimes, firms find it difficult to identify all relevant input factors and their cost, and such task is even more difficult for researchers that can only access a subset of the information that the firm has. In these cases, a common empirical approach that bypasses this issue is the estimation of cost functions that depend upon the firm’s output level rather than input factors. The latter is justified in microeconomic theory as input factors and output and linked through a production function. In this question, you will have to conduct an investigation on literature using this approach following these steps:

- Based on microeconomic theory and using graphs and equations, explain the expected shapes of the of short-run curves for total cost function , the average cost function and the marginal cost function when plotted against output ().
- Based on the functional forms for OLS regression discussed in class, suggest regression models for estimating each of the three functions in (a). Explain carefully the expected signs of each coefficient estimate.
- Provide a summary of empirical research based on the methodology discussed in (b). Explain how the regression estimations were used for practical analysis in the cases you have reviewed. Then, provide your own conclusions on the potential usefulness of cost curves for economic analysis.

**SECTION IV**

**Question IV.A.** Graddy (2006) uses a 2-stage-least-squares (2SLS) instrumental-variable (IV) procedure to estimate the demand for fish in the Fulton market, based on the following simultaneous-equation specification:

Demand: ,

Supply:

The notation is described in the data set file provided to you and also in Graddy (2006). Considering this information:

- Use summary statistics and graphs to provide a preliminary analysis of the data used in Graddy (2006). (3 Marks)
- Replicate the results in columns (2) and (4) of Table 2 in Graddy (2006). Provide a Gretl Command Log Report and Gretl output for your estimations. (4 Marks)
*Notes: Although the intercept coefficient estimator is not reported in Table 2 of Graddy (2006), it has been used to produce these results. You should be able to obtain the exact same coefficient estimators on Gretl. However, the coefficients’ standard errors will be slightly different, due to the use of a specific method for estimating robust s.e. in the paper.* - Discuss the strategy and steps for estimating the above model with a 2SLS approach. In your discussion, estimate and explain the
*reduced form*model associated with the above system of equations and explain the role of the variable in the estimation procedure. (4 Marks) - Compare the OLS and IV demand estimates. Which one is the most reliable and why? (3 Marks)
- Explain how Graddy (2006) uses these results in Table 2 her analysis. (3 Marks)
- According to the IV demand equation, what would be the demand for fish on a Monday when all explanatory variables are equal to their sample means? How would your estimate change if the day under consideration was Tuesday? (3 Marks)

Reference: Graddy, K. (2006), “The Fulton Fish Market,” *Journal of Economic Perspectives* 20(2): 207-220.