Errata Dynamic General Equilibrium Modelling, Springer: Berlin August 2015

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1 Errata Dynamic General Equilibrium Modelling, Springer: Berlin August 2015 Chapter 1.1 p. 9/10: Figure 1.1 was computed for the parameter values T = 59, α = 0.50, and ρ = 0.35 and not as stated on p.9 for α = 0.35 and ρ = 0.5. Chapter 1.2 p. 15: equation (1.13 should be v(k = max 0 K f(k u(f(k K +βv(k. p. 30: the Lagrangian should be L = β [u(c t t +λ t (f(k t C t K t+1 t=0 +µ t C t +ω t+1 K t+1 ]. Chapter 1.3 p. 36: The derivative of L with respect to K 1 should be: Chapter 1.4 L K 1 = E 0 { λ 0 +ω 1 +βλ 1 (1 δ +Z 1 f (K 1 } = 0, p. 59: in equation (1.43 the index of r is missing. Thus, this equation should read: K t+1 K t w t N t +(r t δk t C t. p. 63:] the exponent in the second equation from the top of the page is not η but +η. Thus, the equation should be 0 = (Z s+1 t N 1 α Z s t N 1 α ( 1 Nt+s 1 N t+s+1 t+s+1k α t+s+1 +(1 δk t+s+1 ak t+s+2 t+s kt+s α +(1 δk t+s ak t+s+1 θ(1 η ( βa η η 1 δ +αz s+1 t Nt+s+1k 1 α t+s+1 α 1. 1

2 Appendix 2 p. 76: The growth factor of F(X t,1, g F must be smaller not greater than on. Thus: g F := F(X t+1,1 F(X t,1 = constant < 1 p. 78: equation (A.2.3, the first line on the rhs of this equation should be C 1 η v 1 (1 N 1 η +v 2 (1 N if η 1. The brace below the term u 11 ( /u 1 ( C should not span the term dc/c, thus: u 21 ( u 2 ( C dc }{{} ξ Problem 1.2 C = u 11( u 1 ( C }{{} η dc C + da A p. 81: in the mylist of the planers problem, line 12 from the top, this equation should be A t = A t 1 e µ+ǫt. Problem 1.3 p.82: in the statement of the planer s problem, 1 N 0 (not 1 N 0, in the second line below the statement of the planer s problem σ ξ = 0.01 (and not σ γ, in line c: σ ξ (and not σ x i. Chapter 2.3 p. 111: the matrix in the second line of equation (2.51 should be W xλ (and not W xx. Chapter 2.4 p. 134: In Table 2.3, α = 0.27 (and not α = Appendix 4 p. 144: equation (A.4.8 should be y t := Y [ t = Z t Nt 1 α k α P At t n t +(1 n t π ] [ j t F (1 ϕ P At +ϕ π ]. A t P t π t P t π t 2

3 p. 146: equation (A.4.10d should be α ˆN t +ŵ t = αˆk t +ĝ t +Ẑt. equation (A.4.10e should be (α 1 ˆN t + ˆr t = (α 1ˆk t +ĝ t +Ẑt. equation (A.4.10f should be ŷ t ϑ(1 α ˆN t = ϑαˆk t +ϑẑt +(1 ϑĵ t. the next to last line should be: from equation (A.4.8. The six equations (A.4.10a through (A.4.10f... Chapter 4.3 p. 212: the equation step 4 should be R(γ,K 0 := β [Ĉ1 Ĉ 0 ] η(1 δ +αk α p. 217: the last equation should be φ(z,k := β z z g(e z+ǫ,z,k(2πσ 2 1/2 e (1/2σ2 ǫ 2 dǫ. p. 214: there are some missing rows in Table 4.1. The table should appear as follows: Chapter 5.1 p. 243: the expression for the Lagrangian should be { L = E 0 β t [u(c t +λ t (1 ǫt=ub t +(1 τr t a t t=0 +1 ǫt=e(1 τw t +a t a t+1 c t ]} p. 243: equation (5.5 should be u (c t β = E t [u (c t+1 (1+(1 τr t+1 ]. 3

4 Table 4.1 Coefficient Least Squares Galerkin Collocation α = 0.28, β = 0.994, δ = 1, η = 1 γ γ γ γ γ Distance a α = 0.28, β = 0.994, δ = 0.011, η = 2 γ γ γ γ γ Distance b a to analytic solution; b to solution from value function iteration. Chapter 5.3 p. 284: equation (5.38 should be γ 0 (1 n t γ 1 c η t = 1 τ y 1+τ c w t e. In the paragraph below this equation, in the second line instead of σ = 1 it should be η = 1. Chapter 6.3 p. 320: the condition with respect to the stationary interest rate r should be ( 1 α N r = αz K p. 325: the transition probability matrices are: ( Γ(ǫ Z = Z g,z = Z g,ǫ = ( Γ(ǫ Z = Z b,z = Z b,ǫ = ,. 4

5 Chapter 7.2 p. 405: The lower left panel of Figure 7.11 does not show the impulse response of the aggregate capital stock (it is aggregate consumption. Here is the correct Figure: Figure 7.11: Impulse responses in the OLG model Chapter 8.2 p. 431: In the definition of orthogonal polynomials, equation (8.30, the statement if and only if refers to the case i j only, i.e., there is no special requirement for the case i = j (except in the definition of orthonormal polynomials. In equation (8.33, the second line on the right of the brace should read: π if i = j 0. 2 p. 435: equation (8.44, the upper summation index must be m instead of n and i,j < m Chapter 8.3 p. 445: the first equation on this page should be f( x+h f( x h = 2f (1 ( xh+ ( f (3 (ξ 1 +f (3 (ξ 2 h 3 6. p. 450: the next to last equation should be E(f(z := (2πσ 2 1/2 f(ze [ (z µ2 /2σ 2] dz. 5

6 p.451: equation (8.65 should be E(f(z π 1/2 n i=1 The next line should be: ( ω i f 2σxi +µ. For i = 2,...,5 the integration nodes x i and weights ω i are given in Table 8.2. The Table on this page should be Table 8.2 n x i ω i Source: Judd (1998, Table 7.4 Chapter 8.5 p. 458: Equation (8.76 should be x s+2 = x s+1 x s+1 x s f(x s+1 f(x s f(x s p. 461: second paragraph, FixvMN2 should be FixvMN. The source code of this program is in the file Toolbox.src. The source code of the program FixvMN1 is in the file Ch8_Toolbox.src. p. 459: Next to last line: In the definition of the Lipschitz property, the statement should be: for all x 1,x 2 N(x s. 6

7 Chapter 9.2 p. 495: the first element in the second row of the matrix P 2 should be 0.09 instead of Chapter 9.4 p. 504: equation (9.19: min (g t T t=1 T T 1 (y t g t 2 +λ [(g t+1 g t (g t g t 1 ] 2. t=1 t=2 p. 505: the entry in the second row and fourth column of the matrix K should be 1 and not zero. 7