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Gerald O’Neal’
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9 ( U t = jt c ln c t + j t ln h t ϕ ) 1 + η (n t + s t ) 1+η c t h t j c t j t n t s t c t c h t c f t c t = [ ( ) v 1 θ 1 ( θ c h θ t + (1 v) 1 θ c f t ) θ 1 ] θ θ 1 θ. θ v P t p h t P t h P t c t + p f t b t + q H t h t + p l tl t =(1 + r t 1 )p f t N t 1 N t b t 1 + qt H (1 δ h ) N t 1 h t 1 N t N t 1 + w t n t d t 1 + (p l t + R N t) l N t 1 l t 1 + π t t N t t N t N t 1 N t c t b t h t qt H l t p l t w t n t d t n t d t (1 + r t 1 )b t 1 Rtl l t 1

10 (1 δ h )h t 1 π t d t d t = ( N t 1 d t 1 s t ) ϕs N 2ϕs 1 t + (1 δ d ) N t 1 d t 1 N t N t (d t 1 s t ) ϕs δ d ϕ s < 1 ϕ s = 1/2 t µ t λ t λ t + µ t w t n t + βe t λ t+1 [ j c t /c t µ t = ϕ (n t + s t ) η N t 1 + µ t w t d t 1 N t = ( N t 1 ϕ (n t + s t ) η N + λ t ϕ t d t 1 s t ) ϕs s s t ] = ϕ s (s t+1 N t N t+1 d t ) ϕ s d t + (1 δ d ) N t N t+1 = p f t+1 N t µ t + βe t µ t+1 (1 + r p f t ) = N t t+1 qt H 1 + j t (h t µ t ) + βe N t µ t+1 ( ) t (1 δh )qt+1 H = N t+1 µ t p l N t µ t+1 ( ) t + βe t p l N t+1 µ t+1 + Rt+1 l = t N n t d t 1 t 1 N t = en t w t

11 en t en y t en H t en t = en y t + en H t y t p h t x t π y t = p h t y t w t en y t x t y t = a t (u t N t 1 N t k t 1 ) α (en y t ) 1 α. k t = (1 δ(u t ))k t 1 N t 1 N t + a i tι(x t /x t 1 ). δ() u t ι(x t /x t 1 ) a i q t = E t β N t N t+1 µ t+1 µ t 1/a i t = q t ι(x t, x t 1 ) x t αp h t ( p h y t+1 t+1 + βe t ) + q t+1 (1 δ(u t+1 )) k t ( ) µt+1 ι(x t+1, x t ) q t+1 µ t x t y t u t = q t δ (u t )k t m t t π H t π H t = q H t H t w t en H t R l tl t 1 p h t m t

12 qt H w t Rt l H t = a H t ( Nt 1 l t 1 N t ) ξl en H t 1 ξ l ξ mm ξ m t a H t (1 ξ ξ m )q H t H t en H t = w t ξ l q H t H t l t 1 = R l t ξ m q H t H t m t = p h t H t = h t (1 δ h ) N t 1 N t h t 1 l t = 1.

13 y t m t = v ( p h t ) θ (ct + x t ) + ex h t. ( ) θ ex h t = v rert y p h t t yt y t = c t + x t + m t + p f t b t p f t (1 + r t 1 ) N t 1 N t b t r t = (1 + r t )e ϕ b(b t b) a t = ρ a a t 1 + ϵ at a H t = ρ h a H t 1 + ϵ ht j t = ρ j j t 1 + ϵ jt j c t = ρ jc j c t 1 + ϵ jct a i t = ρ i a i t 1 + ϵ it y f t = ρ y y f t 1 + ϵ yf t v t = ρ v v t 1 + ϵ vt

14 v t ln (N t /N t 1 ) d t [ ] [ ] ˆd t = ϕ s δ d ˆdt 1 v t + ŝ t + (1 δ d ) ˆdt 1 v t [ ] [ ] ˆd t = ϕ s δ d ˆdt 1 (1 χ)v t + ŝ t + (1 δ d ) ˆdt 1 (1 χ)v t χ

16 x t+h x t x t 1 x t 2 x t 3 h = ,

17 .125 1/ , i α ρ yf ρ v ϵ yf ϵ v

18 χ χ η γ acu ac ϕ b

19 GDP I res X C pop wa M q h CP I GDP γ

20 y = HAM(log(GDP/pop W A )) H = HAM(log(I res /pop W A )) x = HAM(log(X/pop W A )) c = HAM(log(C/pop W A )) q h = HAM(log(P h /CP I)) v = HAM(M/pop W A ) y = HAM(log(GDP )) HAM() log() σ σ i /σ y Y t, Y t 1

21 α N α h N δ N η Γ θ N γ β acu β ac N ϕ b Γ 1 ρ a β ρ ah β ρ y β ρ j β ρ jc β ρ i β ρ v β ϵ a Γ 1 ϵ h Γ 1 ϵ yf Γ 1 ϵ j Γ 1 ϵ i Γ 1 ϵ jc Γ 1 ϵ v Γ 1 χ δ h β δ d ϕ s j n + s ξ m H/c

22 ϵ a ϵ h ϵ yf ϵ j ϵ i ϵ jc ϵ v χ = 1.85

25 χ χ

26 χ χ (.5, 1) A y t = A(L)y t 1 + u t. A k + 1 k + 1 y t k A(L) A 1 L+A 2 L A p L p L Ly t = y t 1 u t Σ u A 1 Σ u (A 1 )

27 α N α h N δ N η Γ θ N γ β acu β ac N ϕ b Γ 1 ρ a β ρ ah β ρ y β ρ j β ρ jc β ρ i β ρ v β ϵ a Γ 1 ϵ h Γ 1 ϵ yf Γ 1 ϵ j Γ 1 ϵ i Γ 1 ϵ jc Γ 1 ϵ v Γ 1 χ δ h β δ d ϕ s j n + s ξ m H/c

28 ϵ a ϵ h ϵ yf ϵ j ϵ i ϵ jc ϵ v χ = 1

30 Net migrants/quarter, 15,, Non-Australia Australia Total Net migrants/quarter, 15,, 5, 5, -5, -5, -, -, -15, ,

31 Percent Net working age migration (SA) / working age population (SA) Hamilton-filtered net working age migration (SA) / working age population (SA) Hamilton-filtered net working age migration (NSA) / working age population (NSA)

32 Deviation from steady state Deviation from steady state Deviation from steady state Deviation from steady state Deviation from steady state Deviation from steady state Total output Consumption Goods production GDP Quarters Quarters.15 Investment 7-3 Total effective hours Total Goods Construction Quarters Quarters Bonds Terms of trade Quarters Quarters

33 Deviation from steady state Deviation from steady state Deviation from steady state Deviation from steady state Deviation from steady state Deviation from steady state Deviation from steady state Deviation from steady state -3 Wage 6-4 Migration Quarters Quarters 6-3 Marginal product of capital -3 Housing per capita Quarters Quarters 3-3 Price of housing Construction Quarters Quarters -3 Skill acquisition Human capital Quarters Quarters

34 Contribution of v to variance Contribution of v to variance Contribution of v to variance Contribution of v to variance Contribution of v to variance Contribution of v to variance χ 6 GDP Consumption Investment Residential Investment Real House Prices Wages χ

35 .4 Consumption GDP Real House Prices Investment Migration Real Exchange Rate Residential Investment.2 Real Wages step 68% CI IRF

40 q H h c µ = 1/c = ϕ (n + s) η + (1/c)wd = ϕ (n + s) η (ds) ϕs + λϕ s [ s ] (sd) ϕ s λ = (1/c)wn + βλ ϕ s + (1 δ d ) d 1 = (ds)ϕs + (1 δ d ) d 1 = β(1 + r) = j (1 β(1 δ h )) p l = β ( p l + R l) n = (1 β(δ d(ϕ s 1) + 1) s ϕ s δ d n + s = 1/3 n = (n + s) n s n + 1 s s = (n + s) s y 1/β (1 δ) = k α c k = y k δ k n = (y k )1/(α 1) n y k c c 1 h δ h q H = y n h k n = 1 + ny n h n h

42 Deciles of ey_f

44 Deciles of alpha_h

Asset Pricing. Chapter IX. The Consumption Capital Asset Pricing Model. June 20, 2006

Asset Pricing. Chapter IX. The Consumption Capital Asset Pricing Model. June 20, 2006 Chapter IX. The Consumption Capital Model June 20, 2006 The Representative Agent Hypothesis and its Notion of Equilibrium 9.2.1 An infinitely lived Representative Agent Avoid terminal period problem Equivalence