gmmexamples - Example: stylized consumption function...

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Example: stylized consumption function (Campbell and Mankiw (1990) c t = δ 0 + δ 1 y t + δ 2 r t + ε t ,t =1 ,...,T = δ 0 z t + ε t L =3 where c t = the log of real per capita consumption (excluding durables), y t = the log of real disposable income, and r t = the ex post real interest rate (T-bill rate - in f ation rate). Note: See Zivot and Wang (2005), Chapter 21 for S-PLUS code to replicate this example.
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Assumptions { c t , y t ,r t } are stationary and ergodic { ε t ,I t } is a stationary and ergodic martingale di f erence sequence (MDS) where I t = { c s , y s ,r s } t s =1 denotes the observed information set at time t. Endogeneity and Instruments The variables y t and r t are likely to be contemporaneously correlated with ε t Because { ε t ,I t } is a stationary and ergodic MDS, E [ ε t | I t 1 ]=0 which implies that any variable in I t 1 is a potential instrument. For any variable x t 1 I t 1 , { x t 1 ε t } is an uncorrelated sequence. Data: Annual data over the period 1960 to 1995 taken from Wooldridge (2002)
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: Testing the Permanent Income Hypothesis The pure permanent income hypothesis (PIH) due to Hall (1978) states that c t is a martingale so that c t = ε t is a MDS. Hence, the PIH implies the linear restrictions H 0 : δ 1 = δ 2 =0 which are of the form R δ = r with R = Ã 010 001 ! , r = Ã 0 0 ! rank(
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This note was uploaded on 08/23/2010 for the course ECON 583 taught by Professor Zivot during the Fall '09 term at University of West Alabama-Livingston.

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gmmexamples - Example: stylized consumption function...

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