2. The first equation to be estimated is :

FX_i = b₀ + b₁ UR_i +u_i

Where u is a disturbance term and the i subscript represents year.

Answer these questions:

(i) In terms of economic theory what sign would you expect to find for the coefficients in the regression equation ?

(ii) Explain why we are using per capita data for food rather than the total value as the dependent variable?

(iii) Why is there a constant term in the equation with no variable attached?

(iv) Why do these types of equations have a ‘u' term ? 

3. Estimate equation (1) by OLS and present the results in a suitable table

(i) Comment on the result for the coefficient on the UR variable.

(ii) Comment on the R squared statistic.

(iii) Is the estimated value of b0 positive or negative? Does it matter for the reliability of your estimates for b1 whether b0 is positive or negative?

(iv) Examine the residuals of your estimated equation to determine whether any of your years might be considered an outlier in the regression.

(v) Calculate the elasticity of FX with respect to UR at the sample means and comment on it?

4. You are now required to estimate the following form of the model using OLS:

FX_i = b₀ + b₁ UR_i + b₂UR_i2 + u_i

where u is a classical disturbance term.

Carry out the following hypothesis tests

(i) b₀=0 against the two sided alternative at the 10% level for both equations

(ii) b₁=0 against the two sided alternative at the 5 % level for both equations

(iii) b₁ = b₂ = 0 against the one sided alternative at the 5% level for the second equation 

(iv) Establish whether your second equation has one of the following shapes:

(a) U-shaped
(b) Inverted U-shape
(c) Non-linear upward sloping
(d) Non-linear downward sloping
(e) Linear upward sloping
(f) Linear downward sloping
(g) None of the above

5. Having estimated both equations, compare their results and consider whether equation 2 is an improvement over equation 1.

6. Economists would think that the model you have estimated so far is not satisfactory in terms of the independent variables. You should now change this model by introducing up to a maximum of two additional variables. Explain why these variables have been chosen and give full sources and definitions for them. Present and interpret the regression results for this new model.