§16.1Stochastic Bellman 도입
Stochastic Bellman Setup7 eq
(16.2) ★
Stochastic capital dyn
Stochastic Capital Dynamics
DRAFT
vc-passed
$$k(t+1) = f(k(t), z(t)) + (1-\delta)\, k(t) - c(t)$$
Intuition
DRAFT — ★ stochastic capital — z(t) 가 productivity shock.
3세 비유
DRAFT — ★ stochastic capital — z(t) 가 productivity shock.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ stochastic capital — z(t) 가 productivity shock.
(16.3)
History tilde k
History tilde k
DRAFT
vc-passed
$$\tilde k[z^t] = f(\tilde k[z^{t-1}], z(t)) + (1-\delta)\, \tilde k[z^{t-1}] - c[z^t]$$
Intuition
DRAFT — ★ z^t 의 함수로 capital path.
3세 비유
DRAFT — ★ z^t 의 함수로 capital path.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ z^t 의 함수로 capital path.
(16.4) ★
Sequence problem (stochastic)
Sequence Problem (Stochastic)
DRAFT
vc-passed
$$\max_{\{\tilde k[z^t]\}} \mathbb{E}_t \sum_{t=0}^{\infty} \beta^t\, U(\tilde k[z^{t-1}], \tilde k[z^t], z(t))$$
Intuition
DRAFT — ★ stochastic sequence problem.
3세 비유
DRAFT — ★ stochastic sequence problem.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ stochastic sequence problem.
(16.5)
Markov policy
Markov Policy
DRAFT
vc-passed
$$k(t+1) = \pi(k(t), z(t))$$
Intuition
DRAFT — ★ Markov policy — t-independent.
3세 비유
DRAFT — ★ Markov policy — t-independent.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ Markov policy — t-independent.
(16.6) ★
★ NGM Bellman
NGM Bellman (Stochastic)
DRAFT
vc-passed
$$V(k, z) = \sup_{y \in [0, f(k,z) + (1-\delta)k]} u(f(k, z) + (1-\delta)k - y) + \beta\, \mathbb{E}[V(y, z') \mid z]$$
Intuition
DRAFT — ★ ★ stochastic NGM Bellman func eq.
3세 비유
DRAFT — ★ ★ stochastic NGM Bellman func eq.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ stochastic NGM Bellman func eq.
(16.7) ★
★ ★ Stochastic Bellman general
★ ★ Stochastic Bellman General
DRAFT
vc-passed
$$V(x, z) = \sup_{y \in G(x, z)} U(x, y, z) + \beta\, \mathbb{E}[V(y, z') \mid z]$$
Intuition
DRAFT — ★ ★ ★ Bellman func eq with expectations — stochastic DP 정전.
3세 비유
DRAFT — ★ ★ ★ Bellman func eq with expectations — stochast
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ ★ Bellman func eq with expectations — stochastic DP 정전.
(16.8)
Bellman with policy
Bellman with Policy
DRAFT
vc-passed
$$V(x, z) = U(x, \pi(x, z), z) + \beta\, \mathbb{E}[V(\pi(x, z), z') \mid z]$$
Intuition
DRAFT — ★ optimal policy 형태.
3세 비유
DRAFT — ★ optimal policy 형태.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ optimal policy 형태.
§16.2Principle of Optimality (random)
Principle of Optimality (Random)8 eq
(16.9)
Principle of Optimality (header)
Principle of Optimality (Header)
DRAFT
vc-passed
$$\text{Theorem 16.2: V is unique fixed point of } T$$
Intuition
DRAFT — Theorem 16.2 statement.
3세 비유
DRAFT — Theorem 16.2 statement.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — Theorem 16.2 statement.
(16.10) ★
Envelope (stochastic)
Envelope (Stochastic)
DRAFT
vc-passed
$$D_x V(x', z) = D_x U(x', \pi(x', z), z)$$
Intuition
DRAFT — ★ Envelope theorem in stochastic DP.
3세 비유
DRAFT — ★ Envelope theorem in stochastic DP.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Envelope theorem in stochastic DP.
(16.11)
Assumption 16.6
Assumption 16.6
DRAFT
vc-passed
$$\text{(continuity, compactness, monotonicity)}$$
Intuition
DRAFT — Assumption 16.6 (Blackwell-style).
3세 비유
DRAFT — Assumption 16.6 (Blackwell-style).
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — Assumption 16.6 (Blackwell-style).
(16.12)
ε-supremum 1
ε-Supremum 1
DRAFT
vc-passed
$$\forall \varepsilon > 0,\ \exists x'\ s.t.\ V^*(x(0), z(0)) - V^*(x', z') < \varepsilon$$
Intuition
DRAFT — ε-suboptimality.
3세 비유
DRAFT — ε-suboptimality.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ε-suboptimality.
(16.14)
ε-supremum 2
ε-Supremum 2
DRAFT
vc-passed
$$\forall \varepsilon > 0,\ \exists y' \in G\ s.t.\ V(x(0), z(0)) - U(x(0), y') - \beta\, \mathbb{E}[V(y')] < \varepsilon$$
Intuition
DRAFT — ε-suboptimality on policy.
3세 비유
DRAFT — ε-suboptimality on policy.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ε-suboptimality on policy.
(16.15)
Optimality equation
Optimality Equation
DRAFT
vc-passed
$$\bar U(x^*_t \mid \tilde x^*[z^{t-1}], z(t)) = V^*(\tilde x^*[z^{t-1}], z(t))$$
Intuition
DRAFT — ★ optimality of plan.
3세 비유
DRAFT — ★ optimality of plan.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ optimality of plan.
(16.16)
Optimality recursion
Optimality Recursion
DRAFT
vc-passed
$$V^*(\tilde x^*[z^{t-1}], z(t)) = \bar U(x^*_t \mid \tilde x^*[z^{t-1}], z(t))$$
Intuition
DRAFT — ★ recursion preserved.
3세 비유
DRAFT — ★ recursion preserved.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ recursion preserved.
(16.17)
Sub-optimality elimination
Sub-optimality Elimination
DRAFT
vc-passed
$$\mathbb{E}[\bar U(x^*_{t+1} \mid \tilde x^*[z^t], z(t+1)) \mid z(t)] \geq \mathbb{E}[\bar U(x_{t+1} \mid \tilde x^*[z^t], z(t+1)) \mid z(t)]$$
Intuition
DRAFT — ★ optimality via expectation.
3세 비유
DRAFT — ★ optimality via expectation.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ optimality via expectation.
§16.3Stochastic Euler equations
Stochastic Euler Equations5 eq
(16.18)
Theorem 16.3 statement
Theorem 16.3 Statement
DRAFT
vc-passed
$$V^*(x, z) \leq V(x, z)\ \text{always}$$
Intuition
DRAFT — ★ V* upper bound.
3세 비유
DRAFT — ★ V* upper bound.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ V* upper bound.
(16.19) ★
★ ★ Stochastic Euler (FOC)
★ ★ Stochastic Euler (FOC)
DRAFT
vc-passed
$$D_y U(x, y^*, z) + \beta\, \mathbb{E}[D_x V(y^*, z') \mid z] = 0$$
Intuition
DRAFT — ★ ★ ★ stochastic FOC = expected marginal value 0.
3세 비유
DRAFT — ★ ★ ★ stochastic FOC = expected marginal value 0.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ ★ stochastic FOC = expected marginal value 0.
(16.20)
Envelope (FOC form)
Envelope (FOC Form)
DRAFT
vc-passed
$$D_x V(x, z) = D_x U(x, y^*, z)$$
Intuition
DRAFT — ★ Envelope.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ Envelope.
(16.21) ★
★ ★ Stochastic Euler (combined)
★ ★ Stochastic Euler (Combined)
DRAFT
vc-passed
$$D_y U(x, \pi(x, z), z) + \beta\, \mathbb{E}[D_x U(\pi(x, z), \pi(\pi(x, z), z'), z') \mid z] = 0$$
Intuition
DRAFT — ★ ★ stochastic Euler — discrete time.
3세 비유
DRAFT — ★ ★ stochastic Euler — discrete time.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ stochastic Euler — discrete time.
(16.22) ★
★ Stochastic TVC
★ Stochastic TVC
DRAFT
vc-passed
$$\lim_{t\to\infty} \beta^t\, \mathbb{E}[D_x U(\tilde x^*[z^{t-1}], \tilde x^*[z^t], z(t)) \cdot \tilde x^*[z^{t-1}] \mid z(0)] = 0$$
Intuition
DRAFT — ★ ★ stochastic transversality.
3세 비유
DRAFT — ★ ★ stochastic transversality.
Genealogy
| 인물 | 저작 | note |
|---|
| Richard Bellman (1957) | Dynamic Programming | DRAFT — DP 의 정전. 확정과 확률 모두. |
| David Blackwell (1965) | Discounted Dynamic Programming (Annals) | DRAFT — Blackwell theorem (compactness). |
| Stokey & Lucas with Prescott (1989) | Recursive Methods in Economic Dynamics | DRAFT — modern macro의 표준 DP textbook. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ stochastic transversality.
§16.5Hall Permanent Income Hypothesis
Hall Permanent Income Hypothesis5 eq
(16.23)
PIH header
PIH Header
DRAFT
vc-passed
$$\text{Permanent Income Hypothesis}$$
Intuition
DRAFT — PIH 섹션 헤더.
Genealogy
| 인물 | 저작 | note |
|---|
| Milton Friedman (1957) | A Theory of the Consumption Function | DRAFT — permanent income hypothesis. |
| Robert Hall (1978) | Stochastic Implications of the Life Cycle Permanent Income (JPE) | DRAFT — Hall PIH random walk consumption. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — PIH 섹션 헤더.
(16.24) ★
★ ★ Hall random-walk consumption
★ ★ Hall Random-Walk Consumption
DRAFT
vc-passed
$$\beta^t\, u'(\tilde c[w^t]) = \frac{1}{(1+r)^t}\, \tilde \lambda[w^t]$$
Intuition
DRAFT — ★ ★ Hall PIH 핵심 — u'(c) 가 martingale.
3세 비유
DRAFT — ★ ★ Hall PIH 핵심 — u'(c) 가 martingale.
Genealogy
| 인물 | 저작 | note |
|---|
| Milton Friedman (1957) | A Theory of the Consumption Function | DRAFT — permanent income hypothesis. |
| Robert Hall (1978) | Stochastic Implications of the Life Cycle Permanent Income (JPE) | DRAFT — Hall PIH random walk consumption. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ Hall PIH 핵심 — u'(c) 가 martingale.
(16.25) ★
★ Bellman PIH
★ Bellman PIH
DRAFT
vc-passed
$$u'(c(t)) = \beta\, \mathbb{E}_t\!\left[\frac{\partial V(a(t+1), w(t+1))}{\partial a}\right]$$
Intuition
DRAFT — ★ Hall stochastic Euler.
3세 비유
DRAFT — ★ Hall stochastic Euler.
Genealogy
| 인물 | 저작 | note |
|---|
| Milton Friedman (1957) | A Theory of the Consumption Function | DRAFT — permanent income hypothesis. |
| Robert Hall (1978) | Stochastic Implications of the Life Cycle Permanent Income (JPE) | DRAFT — Hall PIH random walk consumption. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ Hall stochastic Euler.
(16.26)
Envelope PIH
Envelope PIH
DRAFT
vc-passed
$$\frac{\partial V(a(t), w(t))}{\partial a} = u'(c(t))$$
Intuition
DRAFT — PIH envelope.
3세 비유
DRAFT — PIH envelope.
Genealogy
| 인물 | 저작 | note |
|---|
| Milton Friedman (1957) | A Theory of the Consumption Function | DRAFT — permanent income hypothesis. |
| Robert Hall (1978) | Stochastic Implications of the Life Cycle Permanent Income (JPE) | DRAFT — Hall PIH random walk consumption. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — PIH envelope.
(16.27) ★
★ Quadratic utility PIH
★ Quadratic Utility PIH
DRAFT
vc-passed
$$u(c) = \varphi c - \frac{1}{2}c^2,\quad c(t) = (1-\kappa)\, [a(t) + \mathbb{E}_t \sum w(t+s)/(1+r)^s]$$
Intuition
DRAFT — ★ ★ Hall quadratic PIH — 영구소득 = 소비.
3세 비유
DRAFT — ★ ★ Hall quadratic PIH — 영구소득 = 소비.
Genealogy
| 인물 | 저작 | note |
|---|
| Milton Friedman (1957) | A Theory of the Consumption Function | DRAFT — permanent income hypothesis. |
| Robert Hall (1978) | Stochastic Implications of the Life Cycle Permanent Income (JPE) | DRAFT — Hall PIH random walk consumption. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ Hall quadratic PIH — 영구소득 = 소비.
§16.6McCall job search reservation wage
McCall Job Search Reservation Wage6 eq
(16.28) ★
★ McCall accept-reject Bellman
★ McCall Accept-Reject Bellman
DRAFT
vc-passed
$$V(a') = \max\!\left\{V_{\text{accept}}(a'),\ \beta\, \mathbb{E}V\right\}$$
Intuition
DRAFT — ★ ★ McCall search 의 정전.
3세 비유
DRAFT — ★ ★ McCall search 의 정전.
Genealogy
| 인물 | 저작 | note |
|---|
| John McCall (1970) | Economics of Information and Job Search (QJE) | DRAFT — McCall job search 모형. |
| Mortensen & Pissarides (1994) | Job Creation and Job Destruction (RES) | DRAFT — search/matching 모형. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ McCall search 의 정전.
(16.29)
Expected V
Expected V
DRAFT
vc-passed
$$\mathbb{E}V = \int_0^{\bar a} V(a)\, dH(a)$$
Intuition
DRAFT — ★ expected value over wage distribution.
3세 비유
DRAFT — ★ expected value over wage distribution.
Genealogy
| 인물 | 저작 | note |
|---|
| John McCall (1970) | Economics of Information and Job Search (QJE) | DRAFT — McCall job search 모형. |
| Mortensen & Pissarides (1994) | Job Creation and Job Destruction (RES) | DRAFT — search/matching 모형. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ expected value over wage distribution.
(16.30) ★
★ McCall Bellman expanded
★ McCall Bellman Expanded
DRAFT
vc-passed
$$V(a') = \max\!\left\{\frac{a'}{1-\beta},\ \beta\, \int_0^{\bar a} V(a)\, dH(a)\right\}$$
Intuition
DRAFT — ★ McCall 분석적 형태.
3세 비유
DRAFT — ★ McCall 분석적 형태.
Genealogy
| 인물 | 저작 | note |
|---|
| John McCall (1970) | Economics of Information and Job Search (QJE) | DRAFT — McCall job search 모형. |
| Mortensen & Pissarides (1994) | Job Creation and Job Destruction (RES) | DRAFT — search/matching 모형. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ McCall 분석적 형태.
(16.31)
Reservation R = β E V
Reservation R = β E V
DRAFT
vc-passed
$$\frac{R}{1-\beta} = \int_0^{\bar a} \beta\, V(a)\, dH(a)$$
Intuition
DRAFT — ★ reservation wage 정의.
3세 비유
DRAFT — ★ reservation wage 정의.
Genealogy
| 인물 | 저작 | note |
|---|
| John McCall (1970) | Economics of Information and Job Search (QJE) | DRAFT — McCall job search 모형. |
| Mortensen & Pissarides (1994) | Job Creation and Job Destruction (RES) | DRAFT — search/matching 모형. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ reservation wage 정의.
(16.32) ★
★ Reservation wage equation
★ Reservation Wage Equation
DRAFT
vc-passed
$$\frac{R}{1-\beta} = \beta\, \frac{R\, H(R)}{1-\beta} + \int_R^{\bar a} \frac{a}{1-\beta}\, dH(a)$$
Intuition
DRAFT — ★ ★ McCall reservation wage equation.
3세 비유
DRAFT — ★ ★ McCall reservation wage equation.
Genealogy
| 인물 | 저작 | note |
|---|
| John McCall (1970) | Economics of Information and Job Search (QJE) | DRAFT — McCall job search 모형. |
| Mortensen & Pissarides (1994) | Job Creation and Job Destruction (RES) | DRAFT — search/matching 모형. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ McCall reservation wage equation.
(16.33) ★
★ R closed-form
★ R Closed-Form
DRAFT
vc-passed
$$\frac{R}{1-\beta} = \beta\!\left(\frac{R\, H(R)}{1-\beta} + \int_R^{\bar a} \frac{a}{1-\beta}\, dH(a)\right)$$
Intuition
DRAFT — ★ ★ McCall reservation wage 의 closed form.
3세 비유
DRAFT — ★ ★ McCall reservation wage 의 closed form.
Genealogy
| 인물 | 저작 | note |
|---|
| John McCall (1970) | Economics of Information and Job Search (QJE) | DRAFT — McCall job search 모형. |
| Mortensen & Pissarides (1994) | Job Creation and Job Destruction (RES) | DRAFT — search/matching 모형. |
Applications
- Bellman 1957 stochastic DP
- Brock-Mirman 1972 stochastic NGM
- Hall 1978 PIH
- McCall 1970 job search
- Mortensen-Pissarides search/matching
Civilizational Relevance
DRAFT — ★ canonical bridge — ★ ★ McCall reservation wage 의 closed form.