For this question you will be using the data “Spain Phillips,” i.e. data for the inflation and unemployment rate in Spain

(i) Use the Spain data to estimate the model in equation [11.19] contained in Example 11.5 dealing with the Phillips curve. [“Expectations Augmented Phillips Curve”]. Create any necessary variables.

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Report your estimated equation (including R^{2}). Briefly define the “natural rate of unemployment” [using cited outside resources if necessary] and explain how your textbook author uses this estimated model to get an estimate of the natural rate of unemployment from this model. What is the estimated “natural rate of unemployment” based on your model?

(ii) Conduct a four-step Durbin-Watson test for serial correlation for this model. Based on this result, is it reasonable to, as the textbook suggests, estimate this model assuming “TS.1’ through TS.5’ hold”?

(iii) In Chapter 15: C7 the authors suggest an IV estimation for this model. Why might IV estimation be necessary? Test the “appropriateness” of the instrument the question suggests, show/explain. Estimate the model using the IV estimation outlined in this question. Report your estimated model and compare it with the OLS results you obtained in (i). Does the (point) estimate of the “natural rate of unemployment” change with this estimation? Show/ Explain.

FOR THIS QUESTION: you DO NOT have to answer the questions in the textbook for Chapter 15: C7 specifically, just use the question to inform your own work. Please use STATA to estimate the IV regression.

(iv) Do you suspect that either the inflation rate or the unemployment rate has a unit root? Defend your viewpoint with specific evidence using the **two** methods from our homework assignment. Formally four-step hypothesis test where appropriate.

(v) Some economists complain that unit root tests have low power. Explain **specifically** what that means in terms of unit root hypothesis testing and why that is not a good characteristic of a hypothesis test.

#2. For this question you will be using the data set “fertilfinal.” Note that this dataset [FERTIL1.RAW] is discussed in your textbook in Example 13.1.

(i) Using the base model presented in the regression output in Table 31.1 (excluding the six time dummies) run the regression model for *kids* first using the data for 1974 and then for the data using 1984 (i.e. two different cross-section regressions). Report these estimated models and highlight three key differences between these two regressions. Can you directly compare the R^{2} values for these three models? Explain why or why not.

(ii) For this part of the question you will ONLY use the data for the years 1982 and 1984. Conduct a four-step hypothesis test for a “Chow Test of Structural Change” using these two years. Again, use the “base model” set of X-regressors, the same set you used in (i). Set α = 0.05. IMPORTANT: Please use the format of the test that is consistent with Chow test you used before in this class, do not use the “interactions” approach. Note that both are discussed in Example 13.2.

(iii) As discussed in 13: C1 (iii), conduct a four-step hypothesis for heteroskedasticity in the base model (as given in Table 13.1), note that this test is based on whether the variance of u “changes over time” but not with the other variables. *[Hint: Conduct a Breusch-Pagan F-test in STATA.] *Set α = 0.05.

#3. For this question you will be using the data set “jtrain.”

(i) Using this data, estimate the model as given in Chapter 14: C3 first with then without fixed effects. Fill in this table using the output for the two estimated models and briefly compare the results. Add an explanation, where possible, for why FE might have caused the change(s) you observe.

Independent Variables | Pooled OLS | Fixed Effects |

grant |
( ) |
( ) |

grant |
( ) |
( ) |

ln(employ) |
( ) |
( ) |

d88 |
( ) |
( ) |

d89 |
( ) |
( ) |

(ii) Using the STATA output for fixed effects estimation, conduct a four-step hypothesis test for the joint significance on the fixed effects.

Appendix (software output):

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