SECTION I  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 estim.

1. SECTION I
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

2. 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

3. 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)

4. 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.