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EC220: Introduction to Econometrics

Lent: Problem Set 6

计量经济学代做 Supposethat oil prices jump 25% above their previous peak value and stay at this new higher level (so that Ot = 25 and Ot＋1= Ot＋2 = .. = 0).

1.[Wooldridge, Ch 10 Problem 2] Let gGDP_tdenote the annual percentage change in gross domestic product and let snt_tdenote a short-term interest rate. Suppose that gGDP_t is related to interest rate by  计量经济学代做

gGDP_t = α_O ＋ δ_Oint_t ＋ δ1int_t—1 ＋ u_t,

where u_t is uncorrelated with snt_t, snt_t—fi, and all other past values of interest rates. Suppose that the Federal Reserve follows the policy rule:

int_t = γ_O ＋ γ₁(gGDP_t—1 — 3) ＋ v_t,

where γ₁ > 0. In behavioral terms, γ₁ > 0 means that when last year‘s GDP growth is above 3%, the Fed increases interest rates to prevent an ”overheated™ economy.

(a)If v_tis uncorrelated with all past values of snt_t  and u_t, argue  that snt_t  must  be correlated with u_t—1. (Hsnt: Lag the first equation for one time period and substitute for gGDP_t—1 in the second )    计量经济学代做

We want to show that Cov (snt_t, u_t—1) ƒ= 0.

(b)Which Gauss-Markov assumption does Covv (snt_t, u_t—1)violate?

2. Consider the stationary AR(1) model

_yt = β₁4_t—1 ＋ o_t with |β₁| < 1

where o_t is i.i.d.(0, o^X) and ε_t is independent of y_t—1, y_t—X, …

(a)Derivethe OLS estimator of β1,

(b) Is an unbiased estimator for β1? Is it BLUE? Clearly explain your answers.

(c) Is a consistent estimator for β1? Clearly explain your answer.

3.[Stockand Watson] Increases in oil prices have been blamed for several recessions in developed  Let GDP_t denote the value of quarterly gross domestic product in the US and let Y_t = 100 ln (GDP_t/GDP_t—fi) be the quarterly percentage change in GDP.  计量经济学代做

Arguably, oil prices adversely affect the economy only when they jump above their values in the recent past: Hence, let O_t equal the greater of zero or the percentage point difference between oil prices at date t and their maximum value during the past year (i.e., O_t = max(0,oil price change}).

A distributed lag regression relating Y_t and O_t, estimated over 1955 : I — X000 : IV is

(a)Supposethat oil prices jump 25% above their previous peak value and stay at this new higher level (so that O_t = 25 and O_t＋1= O_t＋2 = .. = 0). What is the predicted effect on output growth for each quarter over the next 2 years?    计量经济学代做

(b)Construct a 95% confidence interval for your answers in (a).

Whatis the predicted cumulative change in GDP growth over eight quarters?

Arobust F-statistic, used to test whether the coefficients on O_t and its lags are zero, is 49. Are the coefficients significantly different from zero? Explain your answer. Briefly indicate why a robust F-statistic was used instead of the usual F statistic.

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