diff --git a/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-bellman-excerpt.md b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-bellman-excerpt.md new file mode 100644 index 00000000..7fada638 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-bellman-excerpt.md @@ -0,0 +1,180 @@ +# Household Bellman Problem — Excerpt from Gornemann, Kuester, Nakajima (2012) + +Faithful summary of the household dynamic program in Section 2 of the paper. + +## States + +**Aggregate state** (post labor-market transitions): + +\[ +X = (K,\; N,\; Z,\; D,\; \mu), +\] + +where \(K\) is capital, \(N\) is employment, \(Z\) is TFP, \(D\) is the monetary-policy shock, and \(\mu\) is the cross-sectional distribution of households. + +**Individual state:** \((e,\, s,\, a)\) — employment status \(e \in \{0,1\}\), skill level \(s \in S\), and mutual-fund shares \(a \in A \subseteq \mathbb{R}\). + +The paper also defines a **pre-transition** aggregate state \(\tilde{X} = (K, \tilde{N}, Z, D, \tilde{\mu})\), measured at the start of the period before separations and matching occur. + +## Timing + +1. Households enter the period with state \((\tilde{e}, s, a)\) and observe \(\tilde{X}\). +2. Employed households are separated with probability \(\lambda\). +3. All jobless households (including newly separated) search; matches form with probability \(f(\tilde{X})\). The aggregate state updates to \(X = \hat{G}(\tilde{X})\). +4. Households choose consumption \(c\) and next-period shares \(a'\). Production occurs. +5. New shocks \((Z', D', s')\) are drawn; the economy enters next period at \(\tilde{X}'\). + +## Employment Transitions + +For a household that is **employed** at the consumption stage, next-period employment probabilities are: + +- Stays employed: \(1 - \lambda + \lambda\, f(\tilde{X}')\) — keeps job, or separates but re-matches immediately. +- Becomes unemployed: \(\lambda\bigl(1 - f(\tilde{X}')\bigr)\) — separates and fails to match. + +For an **unemployed** household: + +- Becomes employed: \(f(\tilde{X}')\). +- Stays unemployed: \(1 - f(\tilde{X}')\). + +## Employed Household Bellman (eq. 1) + +\[ +W(X, 1, s, a) = +\max_{c,\; a' \geq 0} +\left\{ +u(c) + \beta\,\mathbb{E}\!\left[ + \bigl(1 - \lambda + \lambda\, f(\tilde{X}')\bigr)\, W(X', 1, s', a') + + \lambda\bigl(1 - f(\tilde{X}')\bigr)\, W(X', 0, s', a') +\right] +\right\} +\] + +subject to the budget constraint + +\[ +c + p_a(X)\,a' = \bigl(p_a(X) + d_a(X)\bigr)\,a \;+\; w(X)\,s\,\bigl(1 - \tau(X)\bigr). +\] + +## Unemployed Household Bellman (eq. 3) + +\[ +W(X, 0, s, a) = +\max_{c,\; a' \geq 0} +\left\{ +u(c) + \beta\,\mathbb{E}\!\left[ + f(\tilde{X}')\, W(X', 1, s', a') + + \bigl(1 - f(\tilde{X}')\bigr)\, W(X', 0, s', a') +\right] +\right\} +\] + +subject to + +\[ +c + p_a(X)\,a' = \bigl(p_a(X) + d_a(X)\bigr)\,a \;+\; b\,s. +\] + +## Preferences + +Period utility is CRRA: + +\[ +u(c) = \frac{c^{1-\sigma}}{1-\sigma}, \qquad \sigma = 1.5. +\] + +Labor supply is inelastic: a household works full-time (\(e=1\)) or not at all (\(e=0\)). The time-discount factor is \(\beta = 0.966\). + +## Skill Process + +There are four discrete skill levels, \(s \in S = \{s_1, s_2, s_3, s_4\}\): + +| Level | Value | Interpretation | +|---|---|---| +| \(s_1\) | 0.123 | Low | +| \(s_2\) | 0.421 | Medium | +| \(s_3\) | 1.435 | High | +| \(s_4\) | 34.65 | Super-skilled | + +Skills evolve according to a Markov chain with transition matrix \(\pi_{s,s'}\) (Table 2 of the paper): + +\[ +\pi = \begin{pmatrix} +0.9719 & 0.0275 & 0.0000 & 0.0006 \\ +0.0275 & 0.9444 & 0.0275 & 0.0006 \\ +0.0000 & 0.0275 & 0.9719 & 0.0006 \\ +0.0183 & 0.0183 & 0.0183 & 0.9450 +\end{pmatrix}. +\] + +The lower three levels are obtained by discretizing an AR(1) for log productivity (Tauchen method). The super-skilled state is calibrated to match U.S. wealth concentration. Skill transitions are drawn at the end of each period; they do not depend on employment status or aggregate state. + +## Wage Function + +The wage per efficiency unit is a reduced-form function of aggregate output (eq. 39): + +\[ +\log w(X) - \log \bar{w} = \varepsilon_w \bigl(\log y(X) - \log \bar{y}\bigr), \qquad \varepsilon_w = 0.45, +\] + +where \(\bar{w}\) and \(\bar{y}\) are steady-state values. Values of \(\varepsilon_w < 1\) capture wage stickiness. + +## Budget Constraint Notation + +| Symbol | Meaning | +|---|---| +| \(p_a(X)\) | Ex-dividend mutual-fund share price | +| \(d_a(X)\) | Dividends per share | +| \(w(X)\) | Wage per efficiency unit | +| \(\tau(X)\) | Proportional payroll tax | +| \(b\) | Unemployment benefit per efficiency unit | + +The short-sale constraint \(a' \geq 0\) rules out borrowing. The expectation \(\mathbb{E}\) is over \((Z', D', s')\); the household takes as given the laws of motion \(\tilde{X}' = \tilde{G}(X)\) and \(X' = G(X)\). + +## Job-Finding Probability and Aggregate Law of Motion + +Matches are created by a Cobb–Douglas matching function: + +\[ +M(\tilde{X}, V) = \gamma\bigl(U(\tilde{X}) + \lambda\, N(\tilde{X})\bigr)^{\alpha}\, V^{1-\alpha}, +\] + +so the job-finding rate is + +\[ +f(\tilde{X}) = \frac{M\bigl(\tilde{X},\, V(\tilde{X})\bigr)}{U(\tilde{X}) + \lambda\, N(\tilde{X})}, +\] + +where vacancies \(V(\tilde{X})\) satisfy a free-entry condition. Three aggregate mappings link the within- and across-period states: + +- \(X = \hat{G}(\tilde{X})\): pre-transition to post-transition (within period). +- \(\tilde{X}' = \tilde{G}(X)\): post-transition to start of next period. +- \(X' = G(X) = \hat{G}\bigl(\tilde{G}(X)\bigr)\): composite law of motion. + +Employment evolves as \(N = (1-\lambda)\,\tilde{N} + M(\tilde{X}, V)\), and the type distribution \(\mu\) updates through employment transitions and household saving decisions (equations 28–30 of the paper). + +## Perceived Law of Motion + +The household takes the aggregate laws of motion \(\tilde{X}' = \tilde{G}(X)\) and \(X' = G(X)\) as given. In practice these are approximated numerically using the method of Krusell and Smith (1998): the infinite-dimensional distribution \(\mu\) is summarized by a finite set of moments, and log-linear forecasting rules are estimated from simulated data. The paper does not specify the forecasting-rule functional form in the main text; details are in Appendix B. + +## Key Calibration Parameters + +From Tables 1–2 of the paper (one period = one quarter): + +| Parameter | Value | Description | +|---|---|---| +| \(\sigma\) | 1.5 | Relative risk aversion | +| \(\beta\) | 0.966 | Time-discount factor | +| \(\lambda\) | 0.10 | Exogenous separation rate | +| \(b\) | 0.446 | UI benefit per efficiency unit | +| \(\alpha\) | 0.60 | Matching elasticity (searchers) | +| \(\gamma\) | 0.645 | Matching efficiency | +| \(\bar{w}\) | 0.637 | Steady-state wage per eff. unit | +| \(\varepsilon_w\) | 0.45 | Wage elasticity w.r.t. output | +| \(\rho_D\) | 0.70 | Monetary-shock persistence | +| \(\sigma_D\) | 6.25e-4 | Monetary-shock std. dev. | +| \(\rho_Z\) | 0.95 | TFP persistence | +| \(\sigma_Z\) | 0.006 | TFP std. dev. | +| \(\rho_\Pi\) | 1.20 | Taylor-rule inflation response | +| \(\bar{\Pi}\) | 1.005 | Inflation target (quarterly gross) | + +Borrowing constraint: \(a' \geq 0\) (no borrowing). diff --git a/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-bellman-improved.md b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-bellman-improved.md new file mode 100644 index 00000000..46a24c6f --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-bellman-improved.md @@ -0,0 +1,252 @@ +# GKN Household Problem: A Stage-Oriented Decomposition + +Source: Gornemann, Kuester, and Nakajima (2012), Section 2. + +## 1. The Full Problem + +A household with employment status \(e \in \{0,1\}\), skill \(s \in S\), and mutual-fund shares \(a \geq 0\) solves + +\[ +W(X, e, s, a) = +\max_{c,\; a' \geq 0} +\left\{ +\frac{c^{1-\sigma}}{1-\sigma} ++ \beta\,\mathbb{E}\!\left[ + \pi^e_{1}(\tilde{X}')\, W(X', 1, s', a') + + \pi^e_{0}(\tilde{X}')\, W(X', 0, s', a') +\right] +\right\} +\] + +subject to + +\[ +c + p_a(X)\,a' = \bigl(p_a(X) + d_a(X)\bigr)\,a + y(e, s, X), +\] + +where \(\pi^e_1, \pi^e_0\) are the employment transition probabilities (defined in Section 4 below) and the expectation is over \((Z', D', s')\). + +The aggregate state is \(X = (K, N, Z, D, \mu)\). The paper distinguishes a pre-transition state \(\tilde{X}\) from the post-transition state \(X\); see Section 3. + +This section decomposes \(W\) into three sub-value functions — one at each perch — following a backward stage structure analogous to SolvingMicroDSOPs §12–13. + +--- + +## 2. Stage Decomposition: Overview + +Working backward from the end of the period: + +\[ +\boxed{v_{\succ}(e,s,a',X')} +\;\xrightarrow{\;\mathbb{B}\;}\; +\boxed{v(e,s,m,X')} +\;\xrightarrow{\;\mathbb{I}\;}\; +\boxed{v_{\prec}(e_{\text{old}},s_{\text{old}},a,X)} +\] + +| Stage | Perch | State | Operation | +|---|---|---|---| +| 3 → 2 | Continuation → Decision | \((e,s,a',X') \to (e,s,m,X')\) | \(\mathbb{B}\): optimize over \(c\) | +| 2 → 1 | Decision → Arrival | \((e,s,m,X') \to (e_{\text{old}},s_{\text{old}},a,X)\) | \(\mathbb{I}\): integrate over shocks | + +The full-period operator is \(\mathbb{T} = \mathbb{I} \circ \mathbb{B}\), closed by the identity \(v_{\succ} = v_{\prec}^{\text{next period}}\). + +--- + +## 3. Continuation Perch — \(v_{\succ}(e, s, a', X')\) + +**State:** \((e, s, a', X')\) — post-decision employment, skill, chosen shares, and next-period aggregate state. + +The continuation value is defined as the value of entering the next period: + +\[ +v_{\succ}(e, s, a', X') \;\equiv\; v_{\prec}^{\text{next}}(e, s, a', X'). +\] + +This is the "end-of-period" value function. At this perch the household has already chosen \(a'\) and all current-period actions are complete. The mapping to the next period's arrival is a rename: \(a' \to a\), \(X' \to X\), \(e \to e_{\text{old}}\), \(s \to s_{\text{old}}\). + +--- + +## 4. Decision Perch — \(v(e, s, m, X')\) + +**State:** \((e, s, m, X')\) — realized employment, skill, market resources, and (post-transition) aggregate state. + +**Mover \(\mathbb{B}\)** (backward, from continuation to decision): a pure optimization, no integration. + +\[ +v(e, s, m, X') = \max_{c \in [0,\, m]} +\left\{ +\frac{c^{1-\sigma}}{1-\sigma} + \beta\, v_{\succ}(e, s, m - c, X') +\right\} +\] + +**Transition** (decision → continuation): + +\[ +a' = m - c, \qquad e_{\text{post}} = e, \qquad s_{\text{post}} = s, \qquad X_{\text{post}} = X'. +\] + +Employment and skill pass through unchanged — they are not chosen at this stage. + +### Solution via EGM + +The first-order condition \(c^{-\sigma} = \beta\, v'_{\succ}(e, s, a', X')\) can be inverted: + +\[ +c^{*}(a') = \bigl(\beta\, v'_{\succ}(e, s, a', X')\bigr)^{-1/\sigma}. +\] + +The endogenous grid point for \(m\) is recovered from the budget identity: + +\[ +m^{*}(a') = a' + c^{*}(a'). +\] + +The envelope condition delivers the marginal value of resources: + +\[ +v'(e, s, m, X') = c^{-\sigma}. +\] + +--- + +## 5. Arrival Perch — \(v_{\prec}(e_{\text{old}}, s_{\text{old}}, a, X)\) + +**State:** \((e_{\text{old}}, s_{\text{old}}, a, X)\) — beginning-of-period employment, skill, share holdings, and pre-transition aggregate state. + +**Mover \(\mathbb{I}\)** (integration, from decision to arrival): expectation over all pre-decision shocks. + +\[ +v_{\prec}(e_{\text{old}}, s_{\text{old}}, a, X) += \mathbb{E}_{e, s, Z', D'}\!\Big[\, +v\!\bigl(e,\; s,\; m(e, s, a, X'),\; X'\bigr) +\Big] +\] + +### 5.1 Shock draws + +| Variable | Draw | Distribution | +|---|---|---| +| \(e\) | Employment status | \(P_e(\cdot \mid e_{\text{old}}, \tilde{X}')\) — see below | +| \(s\) | Skill level | \(\pi_{s_{\text{old}}, \cdot}\) — Markov chain, independent of \(e, X\) | +| \(Z'\) | TFP | AR(1): \(\log Z' = (1-\rho_Z)\log\bar{Z} + \rho_Z\log Z + \varepsilon_Z\) | +| \(D'\) | Monetary shock | AR(1): \(\log D' = \rho_D \log D + \varepsilon_D\) | + +### 5.2 Aggregate state transition + +After shocks draw, the aggregate state updates: + +\[ +X' = H(X, Z', D'). +\] + +In practice \(H\) is the Krusell-Smith log-linear forecasting rule approximating the full law of motion. + +### 5.3 Resource formation + +Market resources depend on employment status: + +\[ +m = \bigl(p_a(X') + d_a(X')\bigr)\,a + y(e, s, X'), +\] + +where + +\[ +y(e, s, X') = +\begin{cases} +w(X')\,s\,\bigl(1 - \tau(X')\bigr) & \text{if } e = 1 \text{ (employed)}, \\ +b\,s & \text{if } e = 0 \text{ (unemployed)}. +\end{cases} +\] + +### 5.4 Shadow marginal value + +For EGM in a prior (or outer) problem, the marginal value of shares at the arrival perch is: + +\[ +v'_{\prec}(e_{\text{old}}, s_{\text{old}}, a, X) += \mathbb{E}_{e, s, Z', D'}\!\Big[ +\bigl(p_a(X') + d_a(X')\bigr)\, v'(e, s, m, X') +\Big]. +\] + +The return factor \((p_a + d_a)\) enters via the chain rule on the budget constraint. + +--- + +## 6. Employment Transitions + +The paper's within-period timing (Figure 1) generates the following transition probabilities, evaluated at the pre-transition aggregate state \(\tilde{X}'\) of the next period. + +**From employed** (\(e_{\text{old}} = 1\)): + +\[ +\Pr(e = 1 \mid e_{\text{old}}=1) = 1 - \lambda + \lambda\,f(\tilde{X}'), \qquad +\Pr(e = 0 \mid e_{\text{old}}=1) = \lambda\bigl(1 - f(\tilde{X}')\bigr). +\] + +An employed household is separated with probability \(\lambda\), but a separated household can immediately re-match with probability \(f(\tilde{X}')\). + +**From unemployed** (\(e_{\text{old}} = 0\)): + +\[ +\Pr(e = 1 \mid e_{\text{old}}=0) = f(\tilde{X}'), \qquad +\Pr(e = 0 \mid e_{\text{old}}=0) = 1 - f(\tilde{X}'). +\] + +### Job-finding rate + +\[ +f(\tilde{X}) = \frac{\gamma\bigl(U(\tilde{X}) + \lambda N(\tilde{X})\bigr)^{\alpha}\, V(\tilde{X})^{1-\alpha}}{U(\tilde{X}) + \lambda N(\tilde{X})}, +\] + +where vacancies \(V(\tilde{X})\) satisfy a free-entry condition from the firm side. + +--- + +## 7. Functional Forms and Calibration + +### Preferences + +\[ +u(c) = \frac{c^{1-\sigma}}{1-\sigma}, \qquad \sigma = 1.5, \quad \beta = 0.966. +\] + +Labor supply is inelastic. + +### Skill grid and transition matrix + +Four levels \(s \in \{0.123,\; 0.421,\; 1.435,\; 34.65\}\). Transition matrix (Table 2): + +\[ +\pi = \begin{pmatrix} +0.9719 & 0.0275 & 0.0000 & 0.0006 \\ +0.0275 & 0.9444 & 0.0275 & 0.0006 \\ +0.0000 & 0.0275 & 0.9719 & 0.0006 \\ +0.0183 & 0.0183 & 0.0183 & 0.9450 +\end{pmatrix}. +\] + +### Wage function + +\[ +\log w(X) - \log \bar{w} = \varepsilon_w\bigl(\log y(X) - \log\bar{y}\bigr), \qquad \varepsilon_w = 0.45,\; \bar{w} = 0.637. +\] + +### Other parameters + +| Symbol | Value | Description | +|---|---|---| +| \(\lambda\) | 0.10 | Separation rate | +| \(b\) | 0.446 | UI benefit per efficiency unit | +| \(\alpha\) | 0.60 | Matching elasticity | +| \(\gamma\) | 0.645 | Matching efficiency | +| \(\rho_Z\) | 0.95 | TFP persistence | +| \(\sigma_Z\) | 0.006 | TFP std. dev. | +| \(\rho_D\) | 0.70 | Monetary-shock persistence | +| \(\sigma_D\) | 6.25e-4 | Monetary-shock std. dev. | +| \(\rho_\Pi\) | 1.20 | Taylor-rule inflation response | +| \(\bar{\Pi}\) | 1.005 | Inflation target (quarterly gross) | + +Borrowing constraint: \(a' \geq 0\). diff --git a/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-dolo.yaml b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-dolo.yaml new file mode 100644 index 00000000..2d7f6c35 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-dolo.yaml @@ -0,0 +1,100 @@ +# GKN (2012) Household Problem — Dolo-Plus YAML +# Gornemann, Kuester, Nakajima: Monetary Policy with Heterogeneous Agents +# Generated via Matsya session topics2026-mon-policy + +name: gkn_household +model_type: adc-stage + +symbols: + spaces: + E: '@def {0, 1}' + S: '@def {1, ..., n_s}' + Xa: '@def R+' + Xm: '@def R+' + XAgg: '@def R^n_X' + + prestate: + e_old: '@in E' + s_old: '@in S' + a: '@in Xa' + X: '@in XAgg' + + states: + e: '@in E' + s: '@in S' + m: '@in Xm' + X_prime: '@in XAgg' + + poststates: + e_post: '@in E' + s_post: '@in S' + a_prime: '@in Xa' + X_post: '@in XAgg' + +equations: + arvl_to_dcsn_transition: | + e ~ P_e(e_old, X) + s ~ P_s(s_old) + X_prime = H(X, Z_prime, D_prime) + y = e * w(X_prime) * s * (1 - tau(X_prime)) + (1 - e) * b_unemp * s + m = (p_a(X_prime) + d_a(X_prime)) * a + y + + dcsn_to_cntn_transition: | + a_prime = m - c + e_post = e + s_post = s + X_post = X_prime + + cntn_to_dcsn_mover: + Bellman: | + V = max_{c}{c^(1 - sigma) / (1 - sigma) + beta * V[>]} + InvEuler: | + c[>] = (beta * dV[>])^(-1/sigma) + MarginalBellman: | + dV = c^(-sigma) + cntn_to_dcsn_transition: | + m[>] = a_prime + c[>] + + dcsn_to_arvl_mover: + Bellman: | + V[<] = E_{e, s, Z_prime, D_prime}(V) + ShadowBellman: | + dV[<] = E_{e, s, Z_prime, D_prime}{(p_a(X_prime) + d_a(X_prime)) * dV} + + # Employment transition probabilities (Section 2.3 of the paper) + # Employed: P(e'=1 | e=1) = 1 - lambda + lambda * f(X_tilde') + # P(e'=0 | e=1) = lambda * (1 - f(X_tilde')) + # Unemployed: P(e'=1 | e=0) = f(X_tilde') + # P(e'=0 | e=0) = 1 - f(X_tilde') + +calibration: + parameters: + sigma: 1.5 + beta: 0.966 + lambda: 0.10 + b_unemp: 0.446 + alpha: 0.60 + gamma_match: 0.645 + w_bar: 0.637 + eps_w: 0.45 + rho_D: 0.70 + sigma_D: 6.25e-4 + rho_Z: 0.95 + sigma_Z: 0.006 + rho_Pi: 1.20 + Pi_bar: 1.005 + n_s: 4 + s_grid: [0.123, 0.421, 1.435, 34.65] + P_s: + - [0.9719, 0.0275, 0.0000, 0.0006] + - [0.0275, 0.9444, 0.0275, 0.0006] + - [0.0000, 0.0275, 0.9719, 0.0006] + - [0.0183, 0.0183, 0.0183, 0.9450] + + settings: + n_a: 200 + a_min: 0.0 + a_max: 500.0 + n_X: 3 + tol: 1.0e-6 + max_iter: 1000 diff --git a/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-verification.md b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-verification.md new file mode 100644 index 00000000..8b93c035 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/gkn-verification.md @@ -0,0 +1,31 @@ +# Verification: Matsya Outputs vs. Source Paper + +Reference: Gornemann, Kuester, and Nakajima (2012), Section 2, equations (1)–(4), Tables 1–2. + +## What we accepted + +**Three-perch ADC decomposition.** Matsya's split into arrival \((e_\text{old}, s_\text{old}, a, X)\), decision \((e, s, m, X')\), and continuation \((e, s, a', X')\) is structurally sound. The paper's Bellman equations (1) and (3) separate cleanly into a pure optimization over \(c\) (the backward mover \(\mathbb{B}\)) and an expectation over next-period shocks (the integration mover \(\mathbb{I}\)). We accepted this decomposition without modification. + +**Mover placement.** Matsya correctly placed all stochastic transitions — employment, skill, TFP, monetary shock — in the arrival mover \(\mathbb{I}\), leaving the decision mover \(\mathbb{B}\) as a deterministic \(\max_c\). This matches the paper: consumption and saving are chosen *after* the household knows its employment status and the aggregate state (Section 2.2, Figure 1). + +**EGM structure.** The inverse Euler equation, endogenous grid recovery, and envelope condition in the YAML's `cntn_to_dcsn_mover` follow directly from the CRRA first-order condition in equation (1) and are standard. + +**Calibration block.** All parameter values (\(\sigma, \beta, \lambda, b, \alpha, \gamma, \rho_Z, \sigma_Z, \rho_D, \sigma_D, \rho_\Pi, \bar{\Pi}\)), the skill grid, and the \(4 \times 4\) transition matrix were verified against Tables 1 and 2 of the paper. However, **Matsya returned the skill transition matrix as a zero placeholder** — it could not retrieve the values from piped input — so we filled in the actual matrix from Table 2 by hand. + +## What we edited + +**Resource formation notation.** Matsya's first decomposition used the generic expression \(m = R(X')a + y(e,s,X')\). The paper uses mutual-fund shares, not a risk-free return. We corrected this to \(m = (p_a(X') + d_a(X'))a + y(e,s,X')\), matching the budget constraints in equations (2) and (4). Matsya's YAML draft (produced in a later call) used the correct notation. + +**Shadow marginal value.** The `dcsn_to_arvl_mover` ShadowBellman carries the factor \((p_a + d_a)\) through the expectation. Matsya produced this correctly in the YAML, but it was absent from the initial plain-text decomposition. We added it to the improved markdown (Section 5.4). + +**Timing of \(f(\tilde{X}')\).** Matsya's initial decomposition was ambiguous about whether the job-finding rate is evaluated at the pre-transition or post-transition aggregate state. The paper is explicit: \(f\) is a function of \(\tilde{X}'\) (the pre-transition state of the next period), not \(X'\). The YAML records the employment transition as `P_e(e_old, X)`, which conflates the two. The improved markdown and the YAML comments clarify that the argument is \(\tilde{X}'\). + +**Wage and tax in income function.** The YAML's `arvl_to_dcsn_transition` correctly uses `w(X_prime) * s * (1 - tau(X_prime))` for employed income. We verified this against equation (2): \(y(1,s,X) = w(X)s(1-\tau(X))\). The use of `X_prime` in the YAML (vs. \(X\) in the paper) reflects the stage decomposition's timing convention, where the decision-stage aggregate state has already been relabeled as \(X'\). + +## What we rejected or flagged + +**Piped-content retrieval.** Matsya's vector-store retrieval never ingested the piped excerpt. Across three attempts it returned only internal dolo-plus spec documents. This means Matsya's equations were reconstructed from conversation context and its training data, not directly from the paper. All equations were therefore cross-checked against the source before acceptance. + +**Generic `H(X, Z', D')` law of motion.** The YAML uses a black-box `H` for the aggregate transition. The paper solves this via Krusell-Smith log-linear forecasting rules (Appendix B), but does not give a closed-form \(H\) in the main text. We accepted `H` as a placeholder and noted the approximation method. + +**Grid settings.** Matsya proposed `n_a = 200`, `a_max = 500.0`, `n_X = 3` as computational settings. These are reasonable defaults but are not from the paper (which does not report grid sizes in the main text). We kept them as placeholders in the YAML `settings` block. diff --git a/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/matsya-session.txt b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/matsya-session.txt new file mode 100644 index 00000000..6cfaff49 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/GKNMonetaryPolicyHA/docs/matsya-session.txt @@ -0,0 +1 @@ +topics2026-mon-policy diff --git a/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/HKMOHousingChannelMP.ipynb b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/HKMOHousingChannelMP.ipynb index e63643a1..bcf28c31 100644 --- a/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/HKMOHousingChannelMP.ipynb +++ b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/HKMOHousingChannelMP.ipynb @@ -1,295 +1,318 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "slide" + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "

Paper 1: \"Monetary Policy, Heterogeneity, and the Housing Channel\"
\n", + "

\n", + "
Hedlund, Karahan, Mitman, Ozkan (2017)
\n", + "

\n", + "
Nino Kodua
\n", + "

\n", + "
Johns Hopkins University
\n", + "

\n", + "
February 16, 2020
" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Overview\n", + "\n", + "* **Research Question: What is the extent to which housing and mortgage debt affect the transmission and effectiveness of monetary policy?**\n", + "* **Contribution:** First structural HA-NK model that jointly has heterogeneous households, a frictional housing market and mortgages, and nominal rigidities, to analyze how monetary policy transmits through the housing channel.\n", + "* **Channels to consider:** \n", + " * **Direct intertemporal substitution effect**\n", + " * **House price channel**\n", + " * **Liquidity channel**\n", + " * **Cash-flow channel**\n", + " * **Redistribution channel**\n", + "* **HANK model with nominal rigidities and a frictional housing market** \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Prior Literature\n", + "\n", + "The HKM&O (2017) paper sits on several strands of prior work. **Housing, wealth, and consumption:** Micro evidence showed that house prices affect spending in different ways for different households—e.g. Campbell and Cocco (2007) and Case, Quigley, and Shiller (2011) found important housing-wealth or collateral effects, while Attanasio et al. (2009) and Browning et al. (2013) stressed collateral/credit and common factors rather than a pure wealth effect. That heterogeneity in who responds to house prices and why is central to a \"housing channel\" of policy. **Heterogeneity and monetary transmission:** Work on hand-to-mouth and \"wealthy hand-to-mouth\" (Kaplan, Violante, and Weidner 2014), partial consumption insurance (Blundell, Pistaferri, and Preston 2008; Kaplan and Violante 2010), and the redistribution channel of monetary policy (Di Maggio, Kermani, and Ramcharan 2014; Gornemann, Kuester, and Nakajima 2014) showed that differences in marginal propensities to consume and in exposure to interest rates and inflation are key for how monetary policy affects aggregate demand. **Housing and mortgages in general equilibrium:** Models with heterogeneous households, illiquid housing, default, and foreclosures—e.g. Jeske, Krueger, and Mitman (2013), Hedlund (2016), Corbae and Quintin (2015), and Favilukis (2010)—and \"balance sheet recession\" ideas (Huo and Ríos-Rull 2013) provided the tools to embed a frictional housing market and mortgage contracts in a macro model. Together, this literature gave the ingredients HKM&O use: a heterogeneous-agent framework where housing is illiquid and collateral matters, and where monetary policy works partly through the housing channel and redistribution, which their paper then formalizes in a single model.\n", + "\n", + "**Key foundational papers:** Jeske, Krueger & Mitman (2013); Hedlund (2016); Kaplan & Violante (2010, 2014); Blundell, Pistaferri & Preston (2008); Campbell & Cocco (2007); Favilukis (2010); Di Maggio, Kermani & Ramcharan (2014). See `prior-literature.md` in this folder for details." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Households\n", + "\n", + "* **Infinitely lived households with uninsurable idiosyncratic labor productivity risk**\n", + "
" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "## Selling decision of a household: \n", + "
\n", + "\n", + " \n", + " \\begin{aligned}\n", + "V_{O W N}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right)=\\max _{\\varsigma_{t} \\in\\{0,1\\}} \\varsigma_{t} V_{S E L L}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right)+\\left(1-\\varsigma_{t}\\right) V_{N S e l l}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right)\n", + " \\end{aligned}\n", + " \n", + "\n", + "\n", + "* ***$\\varsigma_{t}$ - Mortgage initiation cost;*** \n", + "* ***$M_{t}$ - Mortgage size;*** \n", + "* ***$h_{t}$ - House size;*** \n", + "* ***$z_{t}$ - Idiosyncratic labor productivity;***\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "## A household wanting to sell the house chooses a list price ${x_{s}}$\n", + "
\n", + "\n", + " \n", + "\\begin{aligned} \n", + " V_{S E L L}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right) &=\\max _{x_{s t}}-\\xi+\\tilde{p}_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right) V_{N O w n}^{t}\\left(a_{t}+x_{s t}-M_{t}, z_{t}\\right) \\\\ &+\\tilde{p}_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right) V_{N S e l l}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right) \n", + " \\end{aligned}\n", + " \n", + " \n", + "\n", + "* ***$\\tilde{p}_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right)$ - Probability of a meeting between a real estate broker and a seller;***\n", + "* ***$\\theta_{t}\\left(x_{s}, h\\right)$ - tightness of the submarket for house size $h$ and a price ${x_{s}}$***\n", + "* ***$\\xi$ - utility cost if homeowner tries but fails to sell the house***\n", + "
\n", + "\n", + "* **Free entry condition for brokers:**\n", + "\n", + " \n", + "\\begin{aligned} \\kappa h=\\overbrace{\\alpha_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right)}^{\\text {prob of match }} \\overbrace{\\left(p_{t}^{H} h-x_{s}\\right)}^{\\text {broker revenue }}\\end{aligned}\n", + " \n", + " \n", + "\n", + "\n", + "## Buying decision of a household who does not own a house (recently sold or never owned)\n", + "
\n", + "\n", + " \n", + "\\begin{aligned} \n", + "V_{N O w n}^{t}\\left(a_{t}, z_{t}\\right)=\\max _{B u y_{t} \\in\\{0,1\\}} B u y_{t} V_{B u y}^{t}\\left(a_{t}, z_{t}\\right)+\\left(1-B u y_{t}\\right) V_{R e n t}^{t}\\left(a_{t}, z_{t}\\right)\n", + "\\end{aligned}\n", + " \n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "## Household who buys a house\n", + "
\n", + "\n", + " \n", + "\\begin{aligned} \n", + " V_{B u y}^{t}\\left(a_{t}, z_{t}\\right)=\\max _{h_t, M_{t+1}, b_{t+1}, c_{t}, l_{t} \\geq 0} u\\left(c_{t}, h_{t}, l_{t}\\right)+\\beta_{L} \\mathbb{E}\\left[V_{o w n}^{t+1}\\left(a_{t+1}, M_{t+1}, h_{t+1}, z_{t+1}\\right)\\right]\\end{aligned} \n", + "\\begin{aligned} s.t. P_{t} c_{t}+q_{t}^{B} b_{t+1}+p_{t}^{H} h_{t} & \\leq a_{t}+q_{m t}^{0} M_{t+1} \\\\ a_{t+1} &=P_{t+1} w_{t+1} z_{t+1} l_{t+1}+b_{t+1} \\end{aligned} \n", + " \n", + " \n", + "\n", + "\n", + "* **involves decisions of house price, mortgage debt payment, bond holdings, consumption and labor supply** \n", + "* **Banks issue long-term, adjustable rate mortgage contracts.** \n", + " * **Borrower received nominal resources $q_{m t}^{0} M_{t+1}$ ($q_{m t}^{0}$ - mortgage price at origination).**\n", + " * **Interest rate on the loan $r_{m t}$ adjusts each period:** \n", + " \n", + " \\begin{aligned}1+r_{m t}=\\underbrace{(1+\\phi)}_{\\text {spread }} \\underbrace{\\left(1+r_{t}\\right)\\left(1+\\pi_{t}\\right)}_{\\text {nominal risk-free rate }}\\end{aligned} \n", + " \n", + "\n", + "\n", + "## Household who rents a house\n", + "
\n", + "\n", + " \n", + "\\begin{aligned} \n", + "V_{\\text {Rent }}^{t}\\left(a_{t}, z_{t}\\right)=\\max _{b_{t+1}, s_{t}, c_{t}, l_{t} \\geq 0} u\\left(c_{t}, h_{t}, l_{t}\\right)+\\beta_{L} \\mathbb{E}\\left[V_{N O w n}^{t+1}\\left(a_{t+1}, z_{t+1}\\right)\\right]\n", + "\\end{aligned} \n", + "\\begin{aligned} s.t. P_{t} c+q_{t}^{B} b_{t+1}+P_{t} r_{s} s_{t} & \\leq a_{t} \\\\ s_{t} & \\leq \\bar{s} \\\\ a_{t+1} &=P_{t+1} w_{t+1} z_{t+1} l_{t+1}+b_{t+1} \\end{aligned}\n", + " \n", + " \n", + "
\n", + "\n", + "* **$s_t$ - service flow from renting a house**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Mortgages and Banks - two types of risks when issuing loans\n", + "\n", + "**1. Borrowers default - foreclosure**\n", + " * **Bank sells the repossessed house (REO)** \n", + " * **in a frictional decentralized housing market as individual sellers to**\n", + " * **incurs a loss $\\gamma^{ROE}$**\n", + " * **Value to banks of repossessing a house size $h$:** \n", + " \n", + " \n", + " \n", + " \\begin{aligned} J_{R E O}^{t}(h)=R_{R E O}^{t}(h)-\\eta h+\\frac{1}{1+r_{t+1}} J_{R E O}^{t+1}(h)\n", + " \\end{aligned}\n", + " \n", + " \n", + " \n", + "\n", + " \n", + "\\begin{aligned} R_{R E O}^{t}(h)=\\max \\left\\{0, \\max _{x_{s} \\geq 0} \\tilde{p}_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right)\\left[\\left(1-\\gamma^{R E O}\\right) x_{s}-\\left(-\\eta h+\\frac{1}{1+r_{t+1}} J_{R E O}^{t+1}(h)\\right)\\right]\\right\\}\n", + " \\end{aligned}\n", + " \n", + " \n", + " \n", + "* ***$\\eta$ - the cost of holding onto the house (maintenance, property taxes, etc.)*** \n", + "* ***$R_{R E O}^{t}(h)$ - the option value of trying to sell the house in period $t$***\n", + "\n", + "\n", + " \n", + "**2. Prepayment and refinancing the loan by households**\n", + " \n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "## Mortgages and Banks - two types of risks when issuing loans\n", + "
\n", + "\n", + "* **Banks take these risks into account and determine the mortgage price $q_{m t}^{0}$ accordingly:**\n", + "\n", + "
\n", + " \n", + " \n", + " \\begin{aligned} q_{m t}\\left(M_{t+1}, b_{t+1}, h_{t}, z_{t}\\right) M_{t+1}=\\frac{1}{\\left(1+r_{m t}\\right)} \\mathbb{E}\\{\\overbrace{\\tilde{p}_{t+1}\\left(\\theta_{t+1}\\left(x_{s t+1}, h_{t}\\right)\\right) M_{t+1}}^{\\text {sell }+\\text { repay }}+\\overbrace{\\left[1-\\tilde{p}_{t+1}\\left(\\theta_{t+1}\\left(x_{s t+1}, h_{t}\\right)\\right)\\right]}^{\\text {no sale (do not try } / \\text { fail })}\n", + "\\times[\\underbrace{d_{t+1} \\min \\left\\{P_{t+1} J_{R E O}(h), M_{t+1}\\right\\}}_{\\text {default + repossession }}+\\operatorname{Refi}_{t+1} M_{t+1}\n", + "\\left.\\left.+\\left(1-d_{t+1}-\\operatorname{Refi}_{t+1}\\right)(\\underbrace{M_{t+1}-\\frac{M_{t+2}}{\\left(1+r_{m t+1}\\right)}}_{\\text {borrower payment net of servicing costs }}+\\underbrace{q_{m t+1}\\left(M_{t+2}, b_{t+2}, h_{t}, z_{t+1}\\right) M_{t+2}}_{\\text {continuation value of new } M^{\\prime \\prime}})\\right]\\right\\}\n", + " \\end{aligned}\n", + " \n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "## Additional Ingredients: \n", + "
\n", + "\n", + " \n", + "* **To close the model:**\n", + " * **Government sponsored enterprises**\n", + " * **provide insurance to the banks against the default risk of mortgages**\n", + " * **Intermediate goods produces - monopolistically competitive**\n", + " * **A representative final goods produce**\n", + " * **intermediate goods into the final consumption good**\n", + " * **Government - sets fiscal policy**\n", + " * **Monetary authority - sets the nominal interest rate**\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Results:\n", + "\n", + "* **The calibrated steady state of the model** \n", + " * **matches heterogeneity in home ownership, leverage and MPC across households**\n", + " * **MPC differs between low- and high-loan-to-value (LTV) households)**\n", + " * **the US microeconomic & macroeconomic data over the past 20 years**\n", + "* **Effectiveness of the monetary policy depends on mortgage debt distribution:**\n", + " * **In a high-LTV economy expansionary monetary policy is more effective**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Subsequent Literature\n", + "\n", + "Work that cites HKM&O has taken several directions. The **refinancing and cash-flow channel** has been tested with regional and micro data: Beraja, Fuster, Hurst, and Vavra (QJE) use regional variation in mortgage structure and refinancing exposure; Wong ties the mechanism to population aging; and Cloyne, Ferreira, and Surico (REStud) provide direct evidence on how household debt alters the transmission of monetary policy. The literature has also embraced **micro heterogeneity for macro policy**—Kaplan and Violante (JEP) synthesize how heterogeneity in liquidity, debt, and MPC shapes the effects of monetary and other shocks—and **housing, credit, and macroprudential policy** (Funke et al., Koeniger et al., Pidkuyko). Central banks (Sveriges Riksbank, IMF) have framed the open question of whether higher household indebtedness has weakened monetary policy transmission. Open gaps remain: optimal monetary policy and welfare in HA-housing models; behavior at the ZLB and under unconventional policy; renters and tenure choice; structural estimation; and long-run distributional effects.\n", + "\n", + "**Most important subsequent papers:** Beraja et al. (QJE), \"Regional Heterogeneity and the Refinancing Channel of Monetary Policy\"; Cloyne et al. (REStud), \"Monetary Policy when Households have Debt\"; Kaplan & Violante (JEP), \"Microeconomic Heterogeneity and Macroeconomic Shocks.\" See `subsequent-literature-analysis.md` in this folder for the full analysis." + ] } - }, - "source": [ - "

Paper 1: \"Monetary Policy, Heterogeneity, and the Housing Channel\"
\n", - "

\n", - "
Hedlund, Karahan, Mitman, Ozkan (2017)
\n", - "

\n", - "
Nino Kodua
\n", - "

\n", - "
Johns Hopkins University
\n", - "

\n", - "
February 16, 2020
" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "slide" - } - }, - "source": [ - "# Overview\n", - "\n", - "* **Research Question: What is the extent to which housing and mortgage debt affect the transmission and effectiveness of monetary policy?** \n", - "* **Channels to consider:** \n", - " * **Direct intertemporal substitution effect**\n", - " * **House price channel**\n", - " * **Liquidity channel**\n", - " * **Cash-flow channel**\n", - " * **Redistribution channel**\n", - "* **HANK model with nominal rigidities and a frictional housing market** \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "slide" - } - }, - "source": [ - "# Households\n", - "\n", - "* **Infinitely lived households with uninsurable idiosyncratic labor productivity risk**\n", - "
" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "subslide" - } - }, - "source": [ - "## Selling decision of a household: \n", - "
\n", - "\n", - " \n", - " \\begin{aligned}\n", - "V_{O W N}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right)=\\max _{\\varsigma_{t} \\in\\{0,1\\}} \\varsigma_{t} V_{S E L L}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right)+\\left(1-\\varsigma_{t}\\right) V_{N S e l l}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right)\n", - " \\end{aligned}\n", - " \n", - "\n", - "\n", - "* ***$\\varsigma_{t}$ - Mortgage initiation cost;*** \n", - "* ***$M_{t}$ - Mortgage size;*** \n", - "* ***$h_{t}$ - House size;*** \n", - "* ***$z_{t}$ - Idiosyncratic labor productivity;***\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "subslide" - } - }, - "source": [ - "## A household wanting to sell the house chooses a list price ${x_{s}}$\n", - "
\n", - "\n", - " \n", - "\\begin{aligned} \n", - " V_{S E L L}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right) &=\\max _{x_{s t}}-\\xi+\\tilde{p}_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right) V_{N O w n}^{t}\\left(a_{t}+x_{s t}-M_{t}, z_{t}\\right) \\\\ &+\\tilde{p}_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right) V_{N S e l l}\\left(a_{t}, M_{t}, h_{t}, z_{t}\\right) \n", - " \\end{aligned}\n", - " \n", - " \n", - "\n", - "* ***$\\tilde{p}_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right)$ - Probability of a meeting between a real estate broker and a seller;***\n", - "* ***$\\theta_{t}\\left(x_{s}, h\\right)$ - tightness of the submarket for house size $h$ and a price ${x_{s}}$***\n", - "* ***$\\xi$ - utility cost if homeowner tries but fails to sell the house***\n", - "
\n", - "\n", - "* **Free entry condition for brokers:**\n", - "\n", - " \n", - "\\begin{aligned} \\kappa h=\\overbrace{\\alpha_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right)}^{\\text {prob of match }} \\overbrace{\\left(p_{t}^{H} h-x_{s}\\right)}^{\\text {broker revenue }}\\end{aligned}\n", - " \n", - " \n", - "\n", - "\n", - "## Buying decision of a household who does not own a house (recently sold or never owned)\n", - "
\n", - "\n", - " \n", - "\\begin{aligned} \n", - "V_{N O w n}^{t}\\left(a_{t}, z_{t}\\right)=\\max _{B u y_{t} \\in\\{0,1\\}} B u y_{t} V_{B u y}^{t}\\left(a_{t}, z_{t}\\right)+\\left(1-B u y_{t}\\right) V_{R e n t}^{t}\\left(a_{t}, z_{t}\\right)\n", - "\\end{aligned}\n", - " \n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "subslide" - } - }, - "source": [ - "## Household who buys a house\n", - "
\n", - "\n", - " \n", - "\\begin{aligned} \n", - " V_{B u y}^{t}\\left(a_{t}, z_{t}\\right)=\\max _{h_t, M_{t+1}, b_{t+1}, c_{t}, l_{t} \\geq 0} u\\left(c_{t}, h_{t}, l_{t}\\right)+\\beta_{L} \\mathbb{E}\\left[V_{o w n}^{t+1}\\left(a_{t+1}, M_{t+1}, h_{t+1}, z_{t+1}\\right)\\right]\\end{aligned} \n", - "\\begin{aligned} s.t. P_{t} c_{t}+q_{t}^{B} b_{t+1}+p_{t}^{H} h_{t} & \\leq a_{t}+q_{m t}^{0} M_{t+1} \\\\ a_{t+1} &=P_{t+1} w_{t+1} z_{t+1} l_{t+1}+b_{t+1} \\end{aligned} \n", - " \n", - " \n", - "\n", - "\n", - "* **involves decisions of house price, mortgage debt payment, bond holdings, consumption and labor supply** \n", - "* **Banks issue long-term, adjustable rate mortgage contracts.** \n", - " * **Borrower received nominal resources $q_{m t}^{0} M_{t+1}$ ($q_{m t}^{0}$ - mortgage price at origination).**\n", - " * **Interest rate on the loan $r_{m t}$ adjusts each period:** \n", - " \n", - " \\begin{aligned}1+r_{m t}=\\underbrace{(1+\\phi)}_{\\text {spread }} \\underbrace{\\left(1+r_{t}\\right)\\left(1+\\pi_{t}\\right)}_{\\text {nominal risk-free rate }}\\end{aligned} \n", - " \n", - "\n", - "\n", - "## Household who rents a house\n", - "
\n", - "\n", - " \n", - "\\begin{aligned} \n", - "V_{\\text {Rent }}^{t}\\left(a_{t}, z_{t}\\right)=\\max _{b_{t+1}, s_{t}, c_{t}, l_{t} \\geq 0} u\\left(c_{t}, h_{t}, l_{t}\\right)+\\beta_{L} \\mathbb{E}\\left[V_{N O w n}^{t+1}\\left(a_{t+1}, z_{t+1}\\right)\\right]\n", - "\\end{aligned} \n", - "\\begin{aligned} s.t. P_{t} c+q_{t}^{B} b_{t+1}+P_{t} r_{s} s_{t} & \\leq a_{t} \\\\ s_{t} & \\leq \\bar{s} \\\\ a_{t+1} &=P_{t+1} w_{t+1} z_{t+1} l_{t+1}+b_{t+1} \\end{aligned}\n", - " \n", - " \n", - "
\n", - "\n", - "* **$s_t$ - service flow from renting a house**" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "slide" - } - }, - "source": [ - "## Mortgages and Banks - two types of risks when issuing loans\n", - "\n", - "**1. Borrowers default - foreclosure**\n", - " * **Bank sells the repossessed house (REO)** \n", - " * **in a frictional decentralized housing market as individual sellers to**\n", - " * **incurs a loss $\\gamma^{ROE}$**\n", - " * **Value to banks of repossessing a house size $h$:** \n", - " \n", - " \n", - " \n", - " \\begin{aligned} J_{R E O}^{t}(h)=R_{R E O}^{t}(h)-\\eta h+\\frac{1}{1+r_{t+1}} J_{R E O}^{t+1}(h)\n", - " \\end{aligned}\n", - " \n", - " \n", - " \n", - "\n", - " \n", - "\\begin{aligned} R_{R E O}^{t}(h)=\\max \\left\\{0, \\max _{x_{s} \\geq 0} \\tilde{p}_{t}\\left(\\theta_{t}\\left(x_{s}, h\\right)\\right)\\left[\\left(1-\\gamma^{R E O}\\right) x_{s}-\\left(-\\eta h+\\frac{1}{1+r_{t+1}} J_{R E O}^{t+1}(h)\\right)\\right]\\right\\}\n", - " \\end{aligned}\n", - " \n", - " \n", - " \n", - "* ***$\\eta$ - the cost of holding onto the house (maintenance, property taxes, etc.)*** \n", - "* ***$R_{R E O}^{t}(h)$ - the option value of trying to sell the house in period $t$***\n", - "\n", - "\n", - " \n", - "**2. Prepayment and refinancing the loan by households**\n", - " \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "subslide" - } - }, - "source": [ - "## Mortgages and Banks - two types of risks when issuing loans\n", - "
\n", - "\n", - "* **Banks take these risks into account and determine the mortgage price $q_{m t}^{0}$ accordingly:**\n", - "\n", - "
\n", - " \n", - " \n", - " \\begin{aligned} q_{m t}\\left(M_{t+1}, b_{t+1}, h_{t}, z_{t}\\right) M_{t+1}=\\frac{1}{\\left(1+r_{m t}\\right)} \\mathbb{E}\\{\\overbrace{\\tilde{p}_{t+1}\\left(\\theta_{t+1}\\left(x_{s t+1}, h_{t}\\right)\\right) M_{t+1}}^{\\text {sell }+\\text { repay }}+\\overbrace{\\left[1-\\tilde{p}_{t+1}\\left(\\theta_{t+1}\\left(x_{s t+1}, h_{t}\\right)\\right)\\right]}^{\\text {no sale (do not try } / \\text { fail })}\n", - "\\times[\\underbrace{d_{t+1} \\min \\left\\{P_{t+1} J_{R E O}(h), M_{t+1}\\right\\}}_{\\text {default + repossession }}+\\operatorname{Refi}_{t+1} M_{t+1}\n", - "\\left.\\left.+\\left(1-d_{t+1}-\\operatorname{Refi}_{t+1}\\right)(\\underbrace{M_{t+1}-\\frac{M_{t+2}}{\\left(1+r_{m t+1}\\right)}}_{\\text {borrower payment net of servicing costs }}+\\underbrace{q_{m t+1}\\left(M_{t+2}, b_{t+2}, h_{t}, z_{t+1}\\right) M_{t+2}}_{\\text {continuation value of new } M^{\\prime \\prime}})\\right]\\right\\}\n", - " \\end{aligned}\n", - " \n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "subslide" - } - }, - "source": [ - "## Additional Ingredients: \n", - "
\n", - "\n", - " \n", - "* **To close the model:**\n", - " * **Government sponsored enterprises**\n", - " * **provide insurance to the banks against the default risk of mortgages**\n", - " * **Intermediate goods produces - monopolistically competitive**\n", - " * **A representative final goods produce**\n", - " * **intermediate goods into the final consumption good**\n", - " * **Government - sets fiscal policy**\n", - " * **Monetary authority - sets the nominal interest rate**\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "slideshow": { - "slide_type": "slide" + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": ".venv-darwin-arm64", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.7" } - }, - "source": [ - "## Results:\n", - "\n", - "* **The calibrated steady state of the model** \n", - " * **matches heterogeneity in home ownership, leverage and MPC across households**\n", - " * **MPC differs between low- and high-loan-to-value (LTV) households)**\n", - " * **the US microeconomic & macroeconomic data over the past 20 years**\n", - "* **Effectiveness of the monetary policy depends on mortgage debt distribution:**\n", - " * **In a high-LTV economy expansionary monetary policy is more effective**" - ] - } - ], - "metadata": { - "celltoolbar": "Slideshow", - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} + "nbformat": 4, + "nbformat_minor": 2 +} \ No newline at end of file diff --git a/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/MP-Housing-Channel.bib b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/MP-Housing-Channel.bib new file mode 100644 index 00000000..12f97df8 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/MP-Housing-Channel.bib @@ -0,0 +1,316 @@ +@ARTICLE{Auclert2019-ch, + title = "Monetary policy and the redistribution channel", + author = "Auclert, Adrien", + journal = "Am. Econ. Rev.", + publisher = "American Economic Association", + volume = 109, + number = 6, + pages = "2333--2367", + abstract = "This paper evaluates the role of redistribution in the + transmission mechanism of monetary policy to consumption. Three + channels affect aggregate spending when winners and losers have + different marginal propensities to consume: an earnings + heterogeneity channel from unequal income gains, a Fisher channel + from unexpected inflation, and an interest rate exposure channel + from real interest rate changes. Sufficient statistics from + Italian and US data suggest that all three channels are likely to + amplify the effects of monetary policy. (JEL E21, E31, E43, E52)", + month = jun, + year = 2019, + language = "en" +} + +@ARTICLE{Attanasio2009-tp, + title = "Booms and busts: Consumption, house prices and expectations", + author = "Attanasio, Orazio P and Blow, Laura and Hamilton, Robert and + Leicester, Andrew", + journal = "Economica", + publisher = "Wiley", + volume = 76, + number = 301, + pages = "20--50", + abstract = "Over much of the past 25 years, house price and consumption + growth have been closely synchronized. Three main hypotheses for + this have been proposed: increases in house prices raise + household wealth and so their consumption; house price growth + reduces credit constraints by increasing the collateral available + to homeowners; and house prices and consumption are together + influenced by common factors. Using microeconomic data, we find + that the relationship between house prices and consumption is + stronger for younger than older households, contradicting the + wealth channel. We suggest that common causality has been the + most important factor linking house prices and consumption.", + month = feb, + year = 2009, + language = "en" +} + +@ARTICLE{Bansal2004-uo, + title = "Risks for the Long Run: A potential resolution of asset pricing + puzzles", + author = "Bansal, Ravi and Yaron, Amir", + journal = "J. Finance", + publisher = "Wiley", + volume = 59, + number = 4, + pages = "1481--1509", + abstract = "ABSTRACTWe model consumption and dividend growth rates as + containing (1) a small long‐run predictable component, and (2) + fluctuating economic uncertainty (consumption volatility). These + dynamics, for which we provide empirical support, in conjunction + with Epstein and Zin's (1989) preferences, can explain key asset + markets phenomena. In our economy, financial markets dislike + economic uncertainty and better long‐run growth prospects raise + equity prices. The model can justify the equity premium, the + risk‐free rate, and the volatility of the market return, + risk‐free rate, and the price–dividend ratio. As in the data, + dividend yields predict returns and the volatility of returns is + time‐varying.", + month = aug, + year = 2004, + language = "en" +} + +@ARTICLE{Corbae2015-xj, + title = "Leverage and the foreclosure crisis", + author = "Corbae, Dean and Quintin, Erwan", + journal = "J. Polit. Econ.", + publisher = "University of Chicago Press", + volume = 123, + number = 1, + pages = "1--65", + abstract = "How much of the recent rise in foreclosures can be explained by + the large number of high-leverage mortgage contracts originated + during the housing boom? We present a model where heterogeneous + households select from a set of mortgage contracts and choose + whether to default on their payments given realizations of income + and housing price shocks. The set of mortgage contracts consists + of loans with high downpayments and loans with low downpayments. + We run an experiment where the use of low downpayment loans is + initially limited by payment-to-income requirements but then + becomes unrestricted for 8 years. The relaxation of approval + standards causes homeownership rates, high-leverage originations + and the frequency of high interest rate loans to rise much like + they did in the US between 1998-2006. When home values fall by + the magnitude observed in the US from 2007-08, default rates + increase by over 180\% as they do in the data. Two distinct + counterfactual experiments where approval standards remain the + same throughout suggest that the increased availability of + high-leverage loans prior to the crisis can explain between 40\% + to 65\% of the initial rise in foreclosure rates. Furthermore, we + run policy experiments which suggest that recourse could have had + significant dampening effects during the crisis.", + month = feb, + year = 2015, + language = "en" +} + +@ARTICLE{Di-Maggio2014-xm, + title = "Monetary policy pass-through: Household consumption and voluntary + deleveraging", + author = "Di Maggio, Marco and Kermani, Amir and Ramcharan, Rodney", + journal = "SSRN Electron. J.", + publisher = "Elsevier BV", + abstract = "Do households bene…t from expansionary monetary policy? We + investigate how indebted households'consumption and saving + decisions are aected by anticipated changes in monthly interest + payments. We focus on borrowers with adjustable rate mortgages + originated between 2005 and 2007 featuring an automatic reset of + the interest rate after …ve years. The monthly payment due from + the average borrower falls by 52 percent ($900) upon reset, + resulting in an increase in disposable income totaling tens of + thousands of dollars over the remaining life of the mortgage. We + uncover three patterns. First, the average household increases + monthly car purchases by 40 percent ($150) upon reset. Second, + this expansionary eect is attenuated by the borrowers'voluntary + deleveraging, as a signi…cant fraction of the increased income is + deployed to accelerate debt repayment. Third, the marginal + propensity to consume is signi…cantly higher for low income and + underwater borrowers. To complement these household-level + …ndings, we employ county-level data to provide evidence that + consumption responded more to a reduction in short-term interest + rates in counties with a larger fraction of adjustable rate + mortgage debt. Our results shed light on the income channel of + monetary policy as well as the role of debt rigidity in reducing + the eectiveness of monetary policy.", + year = 2014, + language = "en" +} + +@INPROCEEDINGS{Hedlund2017-lb, + title = "Monetary policy, heterogeneity, and the housing channel", + author = "Hedlund, Aaron and Karahan, Fatih and Mitman, Kurt and Ozkan, + Serdar", + booktitle = "2017 Meeting Papers", + volume = 1610, + pages = 6, + abstract = "In this section, we develop a heterogeneous agents New of the + housing channel in the transmission of monetary policy, we + include the following key ingredients: (1) a frictional housing", + year = 2017, + language = "en" +} + +@ARTICLE{Blundell2008-qj, + title = "Consumption inequality and partial insurance", + author = "Blundell, Richard and Pistaferri, Luigi and Preston, Ian", + journal = "Am. Econ. Rev.", + publisher = "American Economic Association", + volume = 98, + number = 5, + pages = "1887--1921", + month = nov, + year = 2008 +} + +@ARTICLE{Browning2013-wo, + title = "Housing wealth and consumption: A micro panel study", + author = "Browning, Martin and Gørtz, Mette and Leth-Petersen, Søren", + journal = "Econ. J. (London)", + publisher = "Oxford University Press (OUP)", + volume = 123, + number = 568, + pages = "401--428", + abstract = "There is strong evidence that house prices and consumption are + synchronised. There is, however, disagreement over the causes of + this link. This study examines if there is a wealth effect of + house prices on consumption. Using a household‐level panel data + set with information about house ownership, income, wealth and + demographics for a large sample of the Danish population in the + period 1987–96, we model the dependence of the growth rate of + total household expenditure with unanticipated innovations to + house prices. Controlling for factors related to competing + explanations, we find little evidence of a housing wealth effect.", + month = may, + year = 2013, + language = "en" +} + +@ARTICLE{Campbell2007-qe, + title = "How do house prices affect consumption? Evidence from micro data", + author = "Campbell, John Y and Cocco, João F", + journal = "J. Monet. Econ.", + publisher = "Elsevier BV", + volume = 54, + number = 3, + pages = "591--621", + abstract = "Housing is a major component of wealth. Since house prices + fluctuate considerably over time, it is important to understand + how these fluctuations affect households’ consumption decisions. + Rising house prices may stimulate consumption by increasing + households’ perceived wealth, or by relaxing borrowing + constraints. This paper investigates the response of household + consumption to house prices using UK micro data. We estimate the + largest effect of house prices on consumption for older + homeowners, and the smallest effect, insignificantly different + from zero, for younger renters. This finding is consistent with + heterogeneity in the wealth effect across these groups. In + addition, we find that regional house prices affect regional + consumption growth. Predictable changes in house prices are + correlated with predictable changes in consumption, particularly + for households that are more likely to be borrowing constrained, + but this effect is driven by national rather than regional house + prices and is important for renters as well as homeowners, + suggesting that UK house prices are correlated with aggregate + financial market conditions.", + month = apr, + year = 2007, + language = "en" +} + +@ARTICLE{Carroll2011-jc, + title = "How large are housing and financial wealth effects? A new + approach", + author = "Carroll, Christopher D and Otsuka, Misuzu and Slacalek, Jiri", + journal = "J. Money Credit Bank.", + publisher = "Wiley", + volume = 43, + number = 1, + pages = "55--79", + month = feb, + year = 2011, + language = "en" +} + +@ARTICLE{Case2011-bd, + title = "Wealth effects revisited 1978-2009", + author = "Case, Karl E and Quigley, John M and Shiller, Robert J", + journal = "SSRN Electron. J.", + publisher = "Elsevier BV", + abstract = "We re-examine the link between changes in housing wealth, + financial wealth, and consumer spending. We extend a panel of + U.S. states observed quarterly during the seventeen-year period, + 1982 through 1999, to the thirty-one year period, 1978 through + 2009. Using techniques reported previously, we impute the + aggregate value of owner-occupied housing, the value of financial + assets, and measures of aggregate consumption for each of the + geographic units over time. We estimate regression models in + levels, first differences and in error-correction form, relating + per capita consumption to per capita income and wealth. We find a + statistically significant and rather large effect of housing + wealth upon household consumption. This effect is consistently + larger than the effect of stock market wealth upon consumption. + This reinforces the conclusions reported in our previous + analysis. In contrast to our previous analysis, however, we do + find -- based on data which include the recent volatility in + asset markets -- that the effects of declines in housing wealth + in reducing consumption are at least as large as the effects of + increases in housing wealth in increasing the course of household + consumption.", + year = 2011, + language = "en" +} + +@ARTICLE{Challe2015-dq, + title = "Precautionary saving and aggregate demand", + author = "Challe, Edouard and Matheron, Julien and Ragot, Xavier and + Rubio-Ramirez, Juan Francisco", + journal = "SSRN Electron. J.", + publisher = "Elsevier BV", + abstract = "We formulate and estimate a tractable macroeconomic model with + time-varying precautionary savings. We argue that the latter + affect aggregate fluctuations via two main channels: a + stabilizing aggregate supply effect working through the supply of + capital; and a destabilizing aggregate demand effect generated by + a feedback loop between unemployment risk and consumption demand. + Using the estimated model to measure the contribution of + precautionary savings to the propagation of recent recessions, we + find strong aggregate demand effects during the Great Recession + and the 1990–1991 recession. In contrast, the supply effect at + least offset the demand effect during the 2001 recession.", + year = 2015, + language = "en" +} + +@ARTICLE{Blundell2016-he, + title = "Consumption inequality and family labor supply", + author = "Blundell, Richard and Pistaferri, Luigi and Saporta-Eksten, Itay", + journal = "Am. Econ. Rev.", + publisher = "American Economic Association", + volume = 106, + number = 2, + pages = "387--435", + abstract = "We examine the link between wage and consumption inequality using + a life-cycle model incorporating consumption and family labor + supply decisions. We derive analytical expressions for the + dynamics of consumption, hours, and earnings of two earners in + the presence of correlated wage shocks, nonseparability, + progressive taxation, and asset accumulation. The model is + estimated using panel data for hours, earnings, assets, and + consumption. We focus on family labor supply as an insurance + mechanism and find strong evidence of smoothing of permanent wage + shocks. Once family labor supply, assets, and taxes are properly + accounted for there is little evidence of additional insurance. + (JEL D12, D14, D91, J22, J31)", + month = feb, + year = 2016, + language = "en" +} + +@ARTICLE{Calomiris2009-pt, + title = "The (mythical?) housing wealth effect", + author = "Calomiris, Charles W and Longhofer, Stanley D and Miles, William", + journal = "SSRN Electron. J.", + publisher = "Elsevier BV", + year = 2009 +} diff --git a/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/prior-literature.md b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/prior-literature.md new file mode 100644 index 00000000..b0f6e614 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/prior-literature.md @@ -0,0 +1,15 @@ +# Prior Literature Summary: Monetary Policy, Heterogeneity, and the Housing Channel + +## The papers my ballpark paper cites + +The HKM&O (2017) paper sits on several strands of prior work. **Housing, wealth, and consumption:** Micro evidence showed that house prices affect spending in different ways for different households—e.g. Campbell and Cocco (2007) and Case, Quigley, and Shiller (2011) found important housing-wealth or collateral effects, while Attanasio et al. (2009) and Browning et al. (2013) stressed collateral/credit and common factors rather than a pure wealth effect. That heterogeneity in who responds to house prices and why is central to a “housing channel” of policy. **Heterogeneity and monetary transmission:** Work on hand-to-mouth and “wealthy hand-to-mouth” (Kaplan, Violante, and Weidner 2014), partial consumption insurance (Blundell, Pistaferri, and Preston 2008; Kaplan and Violante 2010), and the redistribution channel of monetary policy (Auclert 2019; Di Maggio, Kermani, and Ramcharan 2014; Gornemann, Kuester, and Nakajima 2014) showed that differences in marginal propensities to consume and in exposure to interest rates and inflation are key for how monetary policy affects aggregate demand. **Housing and mortgages in general equilibrium:** Models with heterogeneous households, illiquid housing, default, and foreclosures—e.g. Jeske, Krueger, and Mitman (2013), Hedlund (2016), Corbae and Quintin (2015), and Favilukis (2010)—and “balance sheet recession” ideas (Huo and Ríos-Rull 2013) provided the tools to embed a frictional housing market and mortgage contracts in a macro model. Together, this literature gave the ingredients HKM&O use: a heterogeneous-agent framework where housing is illiquid and collateral matters, and where monetary policy works partly through the housing channel and redistribution, which their paper then formalizes in a single model of “monetary policy, heterogeneity, and the housing channel.” + +## Key foundational papers + +- **Jeske, Krueger & Mitman (2013)**: Same author (Mitman), same theme—heterogeneous-agent model with housing, mortgages, and default; direct methodological and topical precursor. +- **Hedlund (2016)**: Same author (Hedlund)—illiquid housing, debt, and foreclosures; supplies the “frictional housing” block and cyclical housing/debt dynamics that HKM&O build on. +- **Kaplan & Violante (2010, 2014)**: Consumption insurance and “wealthy hand-to-mouth”; establish that MPC heterogeneity is central for aggregate consumption and policy, so the housing channel matters precisely because of this heterogeneity. +- **Blundell, Pistaferri & Preston (2008)**: BPP partial-insurance framework; empirical and conceptual base for the consumption-insurance/heterogeneity literature that Kaplan–Violante and HKM&O build on. +- **Campbell & Cocco (2007)**: Micro evidence on how house prices affect consumption by age/tenure; canonical support for a housing channel and for heterogeneity in that response. +- **Favilukis (2010)**: Early heterogeneous-agent GE model with housing wealth, housing finance, and limited risk-sharing; methodological precedent for putting housing in a macro model. +- **Di Maggio, Kermani & Ramcharan (2014)**: Direct evidence on monetary policy pass-through to consumption via mortgages (e.g. ARM resets) and higher MPC for constrained borrowers; empirical counterpart to the mechanism in HKM&O. diff --git a/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/proposed-revisions.md b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/proposed-revisions.md new file mode 100644 index 00000000..08ce8dd9 --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/proposed-revisions.md @@ -0,0 +1,31 @@ +# Proposed Revisions: Monetary Policy, Heterogeneity, and the Housing Channel + +## Prior Literature section to add + +**Place after the Overview slide and before the Households slide.** + +# Prior Literature + +The HKM&O (2017) paper sits on several strands of prior work. **Housing, wealth, and consumption:** Micro evidence showed that house prices affect spending in different ways for different households—e.g. Campbell and Cocco (2007) and Case, Quigley, and Shiller (2011) found important housing-wealth or collateral effects, while Attanasio et al. (2009) and Browning et al. (2013) stressed collateral/credit and common factors rather than a pure wealth effect. That heterogeneity in who responds to house prices and why is central to a "housing channel" of policy. **Heterogeneity and monetary transmission:** Work on hand-to-mouth and "wealthy hand-to-mouth" (Kaplan, Violante, and Weidner 2014), partial consumption insurance (Blundell, Pistaferri, and Preston 2008; Kaplan and Violante 2010), and the redistribution channel of monetary policy (Di Maggio, Kermani, and Ramcharan 2014; Gornemann, Kuester, and Nakajima 2014) showed that differences in marginal propensities to consume and in exposure to interest rates and inflation are key for how monetary policy affects aggregate demand. **Housing and mortgages in general equilibrium:** Models with heterogeneous households, illiquid housing, default, and foreclosures—e.g. Jeske, Krueger, and Mitman (2013), Hedlund (2016), Corbae and Quintin (2015), and Favilukis (2010)—and "balance sheet recession" ideas (Huo and Ríos-Rull 2013) provided the tools to embed a frictional housing market and mortgage contracts in a macro model. Together, this literature gave the ingredients HKM&O use: a heterogeneous-agent framework where housing is illiquid and collateral matters, and where monetary policy works partly through the housing channel and redistribution, which their paper then formalizes in a single model. + +**Key foundational papers:** Jeske, Krueger & Mitman (2013); Hedlund (2016); Kaplan & Violante (2010, 2014); Blundell, Pistaferri & Preston (2008); Campbell & Cocco (2007); Favilukis (2010); Di Maggio, Kermani & Ramcharan (2014). See `prior-literature.md` in this folder for details. + +--- + +## Subsequent Literature section to add + +**Place after the Results slide (at the end of the notebook).** + +# Subsequent Literature + +Work that cites HKM&O has taken several directions. The **refinancing and cash-flow channel** has been tested with regional and micro data: Beraja, Fuster, Hurst, and Vavra (QJE) use regional variation in mortgage structure and refinancing exposure; Wong ties the mechanism to population aging; and Cloyne, Ferreira, and Surico (REStud) provide direct evidence on how household debt alters the transmission of monetary policy. The literature has also embraced **micro heterogeneity for macro policy**—Kaplan and Violante (JEP) synthesize how heterogeneity in liquidity, debt, and MPC shapes the effects of monetary and other shocks—and **housing, credit, and macroprudential policy** (Funke et al., Koeniger et al., Pidkuyko). Central banks (Sveriges Riksbank, IMF) have framed the open question of whether higher household indebtedness has weakened monetary policy transmission. Open gaps remain: optimal monetary policy and welfare in HA-housing models; behavior at the ZLB and under unconventional policy; renters and tenure choice; structural estimation; and long-run distributional effects. + +**Most important subsequent papers:** Beraja et al. (QJE), "Regional Heterogeneity and the Refinancing Channel of Monetary Policy"; Cloyne et al. (REStud), "Monetary Policy when Households have Debt"; Kaplan & Violante (JEP), "Microeconomic Heterogeneity and Macroeconomic Shocks." See `subsequent-literature-analysis.md` in this folder for the full analysis. + +--- + +## Other improvements + +- **Overview:** Add a **Contribution** bullet: *"First structural HA-NK model that jointly has heterogeneous households, a frictional housing market and mortgages, and nominal rigidities, to analyze how monetary policy transmits through the housing channel."* +- **Slideshow:** If using Jupyter slideshow, set `slide_type: "slide"` (or equivalent) on the Prior Literature and Subsequent Literature cells so they appear as distinct slides. +- **See also (optional):** At the end of the notebook, add a short line pointing to `prior-literature.md`, `subsequent-literature-analysis.md`, and `MP-Housing-Channel.bib` for full references and analysis. diff --git a/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/subsequent-literature-analysis.md b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/subsequent-literature-analysis.md new file mode 100644 index 00000000..ca7de39b --- /dev/null +++ b/models/We-Would-Like-In-Econ-ARK/HKMOHousingChannelMP/subsequent-literature-analysis.md @@ -0,0 +1,19 @@ +# Subsequent Literature Analysis: Monetary Policy, Heterogeneity, and the Housing Channel + +## Papers that cite my ballpark paper + +I found 18 papers in LitMaps (16 unique after removing duplicate entries). + +## What the subsequent literature tells us + +Several clear research directions emerged from work that cites HKM&O. First, the **refinancing and cash-flow channel** was taken to data: Beraja, Fuster, Hurst, and Vavra (QJE) use regional variation in mortgage structure and refinancing exposure to test the channel; Wong ties the same mechanism to population aging; and Cloyne, Ferreira, and Surico (REStud) provide direct evidence on how household debt alters the transmission of monetary policy. So one major direction is **empirical validation and cross-sectional (regional, demographic) testing** of the mechanism. Second, the literature has embraced **micro heterogeneity for macro policy**: Kaplan and Violante (JEP) synthesize how heterogeneity in liquidity, debt, and MPC shapes the aggregate effects of monetary and other shocks; Bunn et al. document asymmetric consumption responses to income shocks. A third direction is **housing, credit, and macroprudential policy**—Funke et al., Koeniger et al., and Pidkuyko connect the housing channel to financial stability and macroprudential tools. Central banks (Sveriges Riksbank, IMF) have framed the open question of whether **higher household indebtedness has weakened** monetary policy transmission, and Hendry and Muellbauer discuss the place of HA models in policy institutions. + +Cutting-edge topics include regional and micro identification of the cash-flow channel, the interaction of the housing channel with macroprudential and credit policy, and the debate over whether high debt dampens or redistributes the effects of monetary policy. Open gaps remain: **optimal monetary policy** and welfare in HA-housing models; behavior at the **ZLB** and under **unconventional policy**; **renters** and tenure choice; **housing supply** and geography; **structural estimation** of HA-housing models; and **long-run distributional** effects of policy that works through the housing channel. + +## Most important subsequent papers + +1. **Beraja, Fuster, Hurst & Vavra (QJE 2018/2019), "Regional Heterogeneity and the Refinancing Channel of Monetary Policy"**: Brings HKM&O’s refinancing channel to regional data and shows differential consumption responses by mortgage exposure; sets the template for empirical work on the housing/refinancing channel and for regional heterogeneity in transmission. + +2. **Cloyne, Ferreira & Surico (REStud 2020), "Monetary Policy when Households have Debt: New Evidence on the Transmission Mechanism"**: Provides direct micro/aggregate evidence on how household debt changes the transmission of monetary policy; central to the “debt and transmission” debate and policy relevance. + +3. **Kaplan & Violante (JEP 2018), "Microeconomic Heterogeneity and Macroeconomic Shocks"**: Canonical synthesis of why micro heterogeneity (liquidity, debt, MPC) matters for macro shocks and policy; frames how the field thinks about HA models and the housing/debt channel in a broader agenda.