University of Groningen. Life cycle behavior under uncertainty van Ooijen, Raun

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1 University of Groningen Life cycle behavior under uncertainty van Ooijen, Raun IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2016 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): van Ooijen, R. (2016). Life cycle behavior under uncertainty: Essays on savings, mortgages and health [Groningen]: University of Groningen, SOM research school Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

4 Life cycle behavior under uncertainty Essays on savings, mortgages and health PhD thesis to obtain the degree of PhD at the University of Groningen on the authority of the Rector Magnificus Prof. E. Sterken and in accordance with the decision by the College of Deans. This thesis will be defended in public on Thursday 21 January 2016 at 12:45 hours by Raun van Ooijen born on 7 November 1983 in Oss

5 Supervisor Prof. R.J.M. Alessie Co-supervisor Dr. A.S. Kalwij Assessment Committee Prof. M. De Nardi Prof. R.H. Koning Prof. A.H.O. van Soest

36 y k y k+1 [y k, y k+1 ] : k = 1,..., 5 (, 15], ( 15, 5], ( 5, 5], (5, 15], [15, ) p p(1 p)

37 y k y k+1

38 Y Y R R = 0 R = 1 (R = 1) (R = 1) (R = 1 X) = Φ(X β), R X Φ P r(r = 1) R

39 Fi r(y) = P i(y y R = r) p r ik, k = 1,, 5 pr ik = p(y k Y i y k+1 R = r) r = {0, 1} p r ik F r ik(y k ) = P r i (Y y k R = r) k l=1 p r il. i µ r i σr i µ r i, σ r i 6 k=1 [ ( Fik(y r ln(yik ) µ r )] 2 i k ) Φ σi r, µ r i = E[ln(Y i ) R = r] σi r2 = [ln(y i ) R = r] E[Y i R] = exp(µ r i σr i 2 ) [Y i R] = exp(2µ r i + 2σr i 2 ) exp(2µ r i + σr i 2 ) Y Y X = x [Y X = x] = E[Y 2 X = x] (E[Y X = x]) 2 E(Y 2 X = x) = E[E(Y 2 R, X = x)] = E(Y 2 R = 0, X = x)p r(r = 0 X = x) + E(Y 2 R = 1, X = x)p r(r = 1 X = x) E(Y 2 R = r, X = x) = [Y R = r, X = x] + (E[Y R = r, X = x]) 2 Y E(Y X = x) =

40 E[E(Y R, X = x)] = P r(r = 0 X = x)e(y X = x, R = 0) + P r(r = 1 X = x)e(y X = x, R = 1)

41 s 5 s i = β 0 + δ a ai + β 1 i + β 2 µ i + x iθ + ϵ i, a=2 a µ i x i

42 s i = β δ a ai + β 1 i + β 2 µ i + β 3 0 i + β 4 µ 0 i + x iθ + ϵ i, a=2 i 1 i 0 i 0 i

43 ˆβ1 / s = /.121 =.0158

46 Expects a reform (fraction) Uncertain about a refrom (fraction) Election Election Follow up survey Spring Agreement Questionnaire Election Election 2003w1 2005w1 2007w1 2009w1 2011w1 2013w1 2015w1 < < < < < <

47 P r(r = 1) Density Pr(reform) < < < < < >

48 H 0 : µ 1 = µ 2 = µ 3 H 0 : µ = µ H 0 : 1 = 2 = 3 H 0 : =

49 a b SD( t t 1 ) t 2012Q1 2008Q1

50 µ µ 0 µ 0 < < < < < R 2

51 %

60 < >

61 < >

80 Density Linear prediction (mortgage risk)

81 > 100%

84 χ 2 p p p χ 2 p p p χ 2 p p p

85 χ 2 p p p χ 2 p p p χ 2 p p p

86 χ 2 F p

87 χ 2 F p χ 2 F p χ 2 F p χ 2 F p

88 χ 2 F p χ 2 F p χ 2 F p χ 2 F p

89 p p χ 2 p

92 µ 1 µ 2

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133 300 (a) Married 300 (b) Widowed euro euro Age Age 300 Married 300 Widowed euro euro Age Age 300 Married 300 Widowed euro euro Age Age

134 200 Married 200 Widowed euro euro Age Age 200 Married 200 Widowed euro euro Age Age 70 Married 70 Widowed Ownership rate % Ownership rate % Age Age

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139 70 Married 70 Widowed Ownership rate % Ownership rate % Age Age 70 Married 70 Widowed Ownership rate % Ownership rate % Age Age 70 Married 70 Widowed Ownership rate % Ownership rate % Age Age

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141 Widowed Upper income tertile Middle income tertile Bottom income tertile 1000 euro Age Homeowner Renter Widowed euro Age

142 t t + 2 % t t + 2 % t t + 2 t t + 2

143 t t + 2 % t t + 2 % t t + 2 t t + 2

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145 1000 euro Net Worth (mean) 1000 euro Net Worth (median) No No No No Minor Minor No Minor Severe No Minor/Severe Dead No Severe Severe Net Financial Wealth (mean) 120 Net Financial Wealth (median) euro euro Ownership % Fraction of total assets %

146 e e < < < >

147

148 SRH SRH SRH SRH SRH

149 SRH SRH SRH SRH SRH SRH

150 SRH SRH SRH SRH x SRH SRH SRH

151 SRH SRH SRH SRH SRH SRH SRH SRH x

152 SRH x y x β ŷ = x ˆβ SRH β β SRH ˆβ

153 i t x it yit x it y it = x itβ + ε it, t = 1,..., T, ε it SRH x it ε it x it N(0, 1) β ε it ε it c i u it ε it = c i + u it c i NID(0, σc 2 ) u it N(0, σu) 2 cov(c i, u it ) = 0, t = 1,..., T. σ 2 u = 1 σ 2 c var(ε it ) = 1 u it u it u it = γu it 1 + ζ it ζ it NID(0, σ 2 ζ). var(ε it ) = 1 σ 2 ζ = σ2 u (1 γ 2 ) = (1 σ 2 c ) (1 γ 2 )

154 SRH SRH it y it SRH it = L λ g L 1 < y it λ g L, L = 1,, 5; g = 1,..., G, λ g = (λ g 1, λg 2, λg 3, λg 4 ) g λ g 0 = λg 5 = g β β SRH θ = (β, σc 2, γ) g SRH λ g t, t = 1,..., 4 y i1 = x i1β g 1 + ε i1 y i2 = x i2β g 2 + ε i2 y i3 = x i3β g 3 + ε i3 y i4 = x i4β g 4 + ε i4, G = 5

155 ε i = (ε i1, ε i2, ε i3, ε i4 ) x i = (x i1, x i2, x i3, x i4 ) 0 1 ρ g 21 ρ g 31 ρ g 41 ε i x i NID 0 0, ρ g 21 1 ρ g 32 ρ g 42 ρ g 31 ρ g 32 1 ρ g ρ g 31 ρ g 32 ρ g 43 1 g ξ g = (η g 1,..., ηg 4, ) ρg η g t = (β g t, λ g t ), t = 1,..., 4 ρ g = (ρ g 21, ρg 31, ρg 41, ρg 32, ρg 42, ρg 43 ) η g 1 =... = ηg 4 = ηg = (β g, λ g ) θ g = (β g, λ g, ρ g ) β g = β ρ g = ρ ε it c i u it ρ σ 2 c γ ρ 21 = ρ 32 = ρ 43 = (1 γ)σ 2 c + γ ρ 31 = ρ 42 = (1 γ 2 )σ 2 c + γ 2 ρ 41 = (1 γ 3 )σ 2 c + γ 3. γ σ 2 c β ŷ it = x it ˆβ + c i + ũ it. x ˆβ it SRH

156 c i + ũ it x ˆβ it c i ˆσ c 2 ũ i1 1 ˆσ c 2 ζ it, t = 2,, T (1 ˆγ 2 )(1 ˆσ c 2 ) ũ it u it SRH

157 SRH SRH SRH SRH SRH SRH SRH SRH SRH

158 SRH SRH SRH

159

160 SRH β γ σc 2

161 SRH SRH yit β σ 2 c γ y it y it 1 (1 γ) σ 2 c + γ = 0.70 σ 2 c γ ˆσ 2 c = ˆγ = yit SRH SRH β SRH

162 Pr (SRH it = l SRH it 1 = k, x it, x it 1 ) = Pr (ˆλg l 1 x ˆβ it < ε it < ˆλ g l x ˆβ ˆλ g it k 1 x ˆβ it 1 < ε it 1 < ˆλ g k x ˆβ ) it 1 = P (ˆλ g l 1 x ˆβ it < ε it < ˆλ g l x ˆβ, ˆλ g it k 1 x ˆβ it 1 < ε it 1 < ˆλ g k x ˆβ, it 1 ˆρ 12 ) P (ˆλ g k 1 x ˆβ it 1 < ε it 1 < ˆλ g k x ˆβ), it 1 k, l = 1,..., 5 ˆρ 12 = (1 ˆγ) ˆσ 2 c + ˆγ

163

164 SRH

165 SRH SRH SRH SRH SRH N = 24, 486 N = 16, 720

166 N = 16, 720 t 1 \ t t 1 \ t N = 163, 695

167

168 N = 16, 720 λ g1,1 λ g1,2 λ g1,3 λ g1,4 λ g2,1 λ g2,2 λ g2,3 λ g2,4 λ g3,1 λ g3,2 λ g3,3 λ g3,4 λ g4,1 λ g4,2 λ g4,3 λ g4,4 λ g5,1 λ g5,2 λ g5,3 λ g5,4 γ σc 2 G = 5

169 N = 16, 720 λ g1,1 λ g1,2 λ g1,3 λ g1,4 λ g2,1 λ g2,2 λ g2,3 λ g2,4 λ g3,1 λ g3,2 λ g3,3 λ g3,4 λ g4,1 λ g4,2 λ g4,3 λ g4,4 λ g5,1 λ g5,2 λ g5,3 λ g5,4 γ σc 2 G = 5

170 SRH N = 16, 720 t \ t + 1 t \ t + 1

171 t \ t + 1

172 t \ t + 1

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174 Males Females Age

175 Males Higher Lower Intermediate Age Females Higher Lower Intermediate Age

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184 [28, 41] [22, 511; 40, 000]

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187 R 2

188 t t λ D (t X, v) = λ D 0 (t) exp(x β D + v), X K D D β D λ D 0 ( ) v t t λ R (t Z, w) = λ R 0 (t) exp(z β R + w), Z K R R X β R λ R 0 ( ) w

189 m λ C m(t X, u) = λ m 0 (t) exp(x β m C + u), βc m K D λ m 0 ( ) u (v = v i ) = p i N i=1 p i = 1 N N

190 β D β R λ D 0 ( ) λ R 0 ( ) f(v) g(w) βc m λm 0 ( ) h m (u) m k(v, w)

191

192 exp(β D ) n + 1 n

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206 survivor function duration until 1st claim disability duration 95% conf.interval duration in days

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209 exp(βd) exp(β C m ) m = 1, 2, 3 p βd β C m (u = u 1) = 1 (u = u2) = p γ p p p p u1 u2 p γ exp (βd) p exp (β C 1 ) p exp (β2 C ) p exp (β3 C ) p 2

210 exp (β D ) p exp (β D ) p 2 p p v 1 v 2 p γ exp(β D ) p β D (v = v 1 ) = 1 (v = v 2 ) = p γ

211 exp(βd) p βd (v = v1) = 1 (v = v2) = p γ p p p p v1 v2 p γ exp (βd) p exp (βd) p exp (βd) p exp (βd) p 2

212 exp (β D ) p exp (β D ) p 2 p p v 1 v 2 p γ exp(β D ) p β D (v = v 1 ) = 1 (v = v 2 ) = p γ

213 β C m p β C m m = 1, 2, 3 (u = u1) = 1 (u = u2) = p γ p p p u1 u2 p γ exp (β C 1 ) p exp (β2 C ) p exp (β3 C ) p 2

214 exp (β R ) p exp (β R ) p exp (β R ) p exp (β R ) p exp (β R ) p 2 p p p p p w 1 w 2 w 3 p 1 p 2 γ exp(β R ) p β R (w = w i ) = p i γ

215 exp (β R ) p exp (β R ) p 2 p p w 1 w 2 w 3 p 1 p 2 γ exp(β R ) p β R (w = w i ) = p i γ

216 λ D (t X, v) = λ D 0 (t) exp(x β D + v), S D (t X, v) = ( t 0 ) λ D (s X, v)ds. D k k = 1,..., n D X k v v N D v {v 1,..., v N D} δk D = 0 D k L = n D k=1 (N D p l S D (D k X k, v l )λ D (D k X k, v l ) δd k l=1 p l = (v = v l ) l = 1,..., N D ), λ R (t Z, w) = λ R 0 (t) exp(z β R + w), S R (t Z, w) = ( t 0 ) λ R (s Z, w)ds. R jk j k = 1,..., n R Z jk w w N R w {w 1,..., w N R} k j k δjk R = 0 R jk

217 L = n R k=1 (N R j k ) p l S R (R jk Z jk, w l )λ R (R jk Z jk, w l ) δr jk, l=1 j=1 p l = (w = w l ) l = 1,..., N R λ C m(t X, u) = λ m 0 (t) exp(x β m C +u), S C m(t X, u) = ( t 0 ) λ C m(s X, u)ds. C km k = 1,..., n D m X k u m u m N C m u m {u m 1,..., u m N C } m = 1 m = 2 m = 3 δ C km = 1 k m δkm C = 0 m L = n D k=1 ( N m C ) p lm Sm(C C km X k, u m l )λ C m(c km X k, u m l ) δc km, l=1 p lm = (u m = u m l ) l = 1,..., N C m

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University of Groningen. Enantioselective liquid-liquid extraction in microreactors Susanti, Susanti

University of Groningen. Enantioselective liquid-liquid extraction in microreactors Susanti, Susanti University of Groningen Enantioselective liquid-liquid extraction in microreactors Susanti, Susanti IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite