Explain and comment the results reported in the Table. In particular, discuss the economic interpretation of the estimated coefficients

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

In the Gretl output above you can find the estimation output of the regression of the percentage growth rate (year-on-year) of the EURO AREA unit labor cost, pc_ULC, on the period 1971:Q1- 2017:Q4 (quarterly observations) on the following variables:

URX = the Euro Area unemployment rate (tot # of unemployment/tot labor force);

pc_HICP = year-on-year percentage growth rate of the index of consumer prices, i.e. the inflation rate.

a) Explain and comment the results reported in the Table. In particular, discuss the economic interpretation of the estimated coefficients.

b) Are the standard errors valid? Why?

c) What is the F(2,185) reported in the Table? Explain which is the underlying theory.

d) Is this estimated model correctly specified? Motivate your answer

e) Suppose that we are interested in testing the null hypothesis:

H0: 𝛽𝑈𝑅𝑋 = −50, 𝛽𝑝𝑐𝐻𝐼𝐶𝑃 = 1 Write this null hypothesis in the form 𝑅𝛽 = 𝑟

f) The test in e) has produced the following output:

Restriction set 1: b[URX] = -50

2: b[pc_HICP] = 1

Test statistic: Robust F(2, 185) = 8.04736, with p-value = 0.000445474

Explain the results and the underlying theory.

g) The Q-stat test for the autocorrelation of the residuals associated with the estimated model produces the following output

Explain and interpret the results.

h) In light of your comment in (g), is it necessary to amend the specification of the model and if the answer is yes how would you amend it?

i) Discuss whether URX and pc_HICP are possibly endogenous regressors and in case they can be how would you address the estimation of this model?

j) Consider the Gretl ouput of model 2 in the Table below. pc_COMM denotes the year-on- year percentage change in the prices of commodities, including OIL. (pc_COMM_1 and pc_COMM_2 denote the first and second lag of the variable). This variable, with first and second lag, is used as an instrument for pc_HICP. Comment on the results reported in the Table. In particular, according to the results of the three tests below, what can we conclude about the Instrumental Variable strategy employed, the validity of the instruments and the endogeneity of pc_HICP? 

Problem 2

Discuss the problem of testing linear hypotheses in a regression model in small samples. Discuss a practical (concrete) example.

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