--- title: "Asset Pricing and Risk-Sharing under DB vs DC Pensions: Coimbra, Gomes, Michaelides & Shen (2026)" description: >- Distilled: a general equilibrium model with an explicit defined-benefit pension fund matches the historical equity premium and riskless rate better than a standard PPG model; a shift to defined-contribution plans raises the riskless rate, lowers the Sharpe ratio, increases retiree consumption volatility and decreases worker consumption volatility. J. Finance 2026, CC BY 4.0. Eight core results with source locators, datasets used, and the model equations and method. sidebar: label: Coimbra-Gomes-Michaelides-Shen 2026 order: 1 tags: [paper-summary, asset-pricing, pensions, risk-sharing, equity-premium, open-access, cc-by, peer-reviewed, unreplicated, data:wrds, data:fred, data:flow-of-funds, data:nipa, data:scf, data:nber-cycles] paper: authors: Nuno Coimbra, Francisco Gomes, Alexander Michaelides, Jialu Shen authorList: - { family: Coimbra, given: Nuno, affiliation: "Banque de France and CEPR" } - { family: Gomes, given: Francisco, affiliation: "London Business School and CEPR" } - { family: Michaelides, given: Alexander, affiliation: "Imperial College London and CEPR" } - { family: Shen, given: Jialu, affiliation: "Fudan University" } year: 2026 venue: The Journal of Finance 81(1), February 2026, 143-188 venueShort: J. Finance 2026 licenseShort: CC BY 4.0 resultsCount: 8 citedByCount: 0 jel: codes: [G12, J32, E21] assignedBy: claude-opus-4-8 date: 2026-06-05 topics: ['Financial Literacy, Pension, Retirement Analysis', 'Insurance, Mortality, Demography, Risk Management'] dataAccess: licensed-commercial outcome: - equity premium and Sharpe ratio - riskless rate - consumption volatility by age group outcomeClass: [macro-aggregates] doi: 10.1111/jofi.13507 license: 'CC BY 4.0 (confirmed via Crossref DOI metadata: content-version vor, URL creativecommons.org/licenses/by/4.0/, delay-in-days 0, start 2025-10-07; corroborated by artifact p.143 Creative Commons Attribution License notice)' access: open machineAccess: 'blocked-paywall (Wiley site wrapper; DOI landing page tested 2026-05-31; VOR CC-BY licence in publisher DOI metadata overrides the wrapper)' redistribution: extract-only (CC BY 4.0 permits mirroring; PDF not hosted in this batch) methods: role: theory family: structural buildsFrom: [overlapping-generations, epstein-zin-weil, krusell-smith, incomplete-markets-olg] contributionType: [new-theory, new-fact] mechanisms: [demand-elasticity, risk-sharing] scope: region: US assetClass: US equities and government bonds period: 1929-01..2023-12 frequency: annual dataType: [market, administrative, survey] granularity: [aggregate] n: "U.S. aggregate moments 1929-2023; pension fund data 1970-2023" relatesTo: - { cite: 'Gomes & Michaelides (2008)', relation: extends, note: 'adds an explicit DB pension fund endowment and stochastic contribution rates to their OLG asset pricing framework with limited participation (p. 147)' } - { cite: 'Constantinides & Duffie (1996)', doi: '10.1086/262023', relation: builds-on, note: 'cross-sectional consumption volatility channel: stochastic contribution rates raise idiosyncratic income risk for workers and firms, raising the equity premium (p. 146)' } - { cite: 'Storesletten, Telmer & Yaron (2007)', doi: '10.1016/j.red.2007.02.004', relation: builds-on, note: 'OLG incomplete-markets production economy framework used as a benchmark (p. 147)' } - { cite: 'Favilukis, Ludvigson & Van Nieuwerburgh (2017)', doi: '10.1086/689606', relation: builds-on, note: 'OLG macro-housing general-equilibrium framework; paper shares the stochastic depreciation device for tractability (p. 149)' } - { cite: 'Guvenen, Ozkan & Song (2014)', doi: '10.1086/675535', relation: builds-on, note: 'countercyclical labor income risk process adopted for the earnings shock mixture distribution (pp. 153, 162)' } - { cite: 'Krusell & Smith (1998)', doi: '10.1086/250034', relation: builds-on, note: 'aggregate-capital forecasting rule used to solve the heterogeneous-agent general equilibrium (p. 158)' } openQuestions: - 'Further cross-sectional heterogeneity in pension scheme enrollment among households; comparative statics on adjustment rates suggest interesting risk-sharing implications (p. 185).' - 'Endogenous government bond supply process; current model treats the bond supply (debt-to-GDP ratio) as exogenous (p. 186).' - 'Transition dynamics from DB to DC are omitted because they require at least one additional state variable for the pension fund size and assumptions about phaseout rules (p. 179).' findings: - ref: R1 outcome: equity premium and Sharpe ratio metric: return-spread value: "equity premium 7.46% (data 7.55%), riskless rate 1.16% (data 0.86%), Sharpe ratio 0.39 (data 0.36)" direction: positive vsBenchmark: "matches empirical US moments (CRSP/NIPA 1929-2023)" - ref: R2 outcome: equity premium and Sharpe ratio metric: return-spread value: "equity premium 7.46% vs PPG 5.53%; Sharpe ratio 0.39 vs PPG 0.31; riskless rate 1.16% vs PPG 4.04%" direction: positive vsBenchmark: "beats PPG pure-pass-through model at same calibration" - ref: R3 outcome: equity premium and Sharpe ratio metric: return-spread value: "equity premium 10.60% to 5.48%; Sharpe ratio 0.55 to 0.28 as risky share moves 42% to 72%" direction: negative vsBenchmark: "increasing fund risky share lowers equity premium below baseline" - ref: R4 outcome: consumption volatility by age group metric: coefficient value: "SD consumption growth ages 20-35: 10.7% (baseline) vs 10.0% (rPPG1); ages 36-65: 8.4% vs 7.6%; retirees 66+: 2.2% vs 2.6%" direction: mixed vsBenchmark: "workers above rPPG1, retirees below rPPG1" - ref: R5 outcome: equity premium and Sharpe ratio metric: return-spread value: "equity premium 7.46%, 7.58%, 7.39%; Sharpe ratio 0.39, 0.39, 0.38 across three portfolio rules" direction: none vsBenchmark: "no meaningful difference across fixed, elastic, and reaching-for-yield rules" - ref: R6 outcome: equity premium and Sharpe ratio metric: return-spread value: "riskless rate 3.34% vs 1.16%; equity premium 4.96% vs 7.46%; Sharpe ratio 0.27 vs 0.39" direction: negative vsBenchmark: "DC-only economy below DB baseline on equity premium and Sharpe ratio" - ref: R7 outcome: consumption volatility by age group metric: coefficient value: "SD cons. growth ages 20-35: 10.1% vs 10.7%; ages 36-65: 7.4% vs 8.4%; retirees 66+: 2.8% vs 2.2%" direction: mixed vsBenchmark: "workers below DB baseline, retirees above DB baseline" - ref: R8 outcome: equity premium and Sharpe ratio metric: return-spread value: "participation 79.7% vs 57.2%; equity premium 4.60%, riskless rate 3.44%" direction: mixed vsBenchmark: "participation rises substantially but aggregate price effects modest vs base DC scenario" resultType: new-finding replicationCode: status: available licenceVerification: - source: Crossref REST API works/10.1111/jofi.13507 checked: 2026-05-31 by: paper-distiller (claude-sonnet-4-6) found: 'license[].content-version=vor, URL=http://creativecommons.org/licenses/by/4.0/, delay-in-days=0, start=2025-10-07' extraction: - by: paper-distiller (claude-sonnet-4-6) date: 2026-05-31 role: extracted note: Full text read (pp. 143-188 of the PDF on disk); all eight results extracted from figures and tables in the CC-BY PDF. Not human-verified. Not reproduced. Replication code not run. - by: paper-verifier (claude-sonnet-4-6) date: 2026-05-31 role: verified note: Locators and reported magnitudes re-checked against the source PDF; 7 of 8 rows confirmed exact, R4 corrected (rPPG1 ages 20-35 was 9.9%, Table IV reads 10.0%). - by: paper-distiller (claude-sonnet-4-6) date: 2026-06-01 role: extracted note: >- Augment pass: added methods, scope, relatesTo, openQuestions, replicationCode, and proposedVocab frontmatter; replaced the old Theory tested section with the three formal body sections (Theory / model, Method, Empirical specifications) with equations transcribed from the source PDF read this session (eqs. 1-39, pp. 149-178). Core results table and verifier attestation are unchanged. New formal sections are extracted, not yet re-verified. - by: paper-verifier (claude-sonnet-4-6) date: 2026-06-01 role: verified note: "All 8 result rows re-checked against Tables II-V, VIII-IX (pp. 164-182): every locator, magnitude, sign, and significance confirmed correct. Equations 1-39 verified term-by-term against pp. 149-178: subscripts, signs, summation indices, and equality conditions all match the PDF. No errors found; no corrections required." - by: paper-distiller (claude-sonnet-4-6) date: 2026-06-03 role: extracted note: >- Added classification axes (identification, contributionType, mechanisms, introducesData, data-scope) from a fresh PDF read; existing results and sections unchanged. - by: paper-verifier (claude-sonnet-4-6) date: 2026-06-03 role: verified note: >- Classification axes (identification, contributionType, mechanisms, introducesData, data-scope) re-checked against the source PDF; removed erroneous identification field (theory paper; field must be omitted per template rules) and removed accounting from dataType (paper uses only CRSP market data, Flow of Funds and NIPA administrative aggregates, and SCF survey data - no firm-level accounting data used). - by: paper-distiller (claude-sonnet-4-6) date: 2026-06-04 role: extracted note: >- Added the effectiveness axis (findings[] per Core-results row, resultType) built from the page's already-verified Core-results table and relatesTo edges; existing results and sections unchanged. - by: paper-verifier (claude-sonnet-4-6) date: 2026-06-04 role: verified note: >- Effectiveness axis (findings[] values/direction, resultType) re-checked against the source PDF; all 8 values confirmed against Tables II-V, VIII-IX (pp. 164-182); corrected R1 and R5 metric from alpha to return-spread (both rows report equity-premium and Sharpe-ratio moments, not regression alphas). rightsSignalConflict: false --- **What this is.** The paper's core results, model equations, solution method, and datasets: enough to know what it found and how without reading all 46 pages. To replicate or extend it, read the full source at the [original](https://doi.org/10.1111/jofi.13507). ## TL;DR The paper builds a general equilibrium incomplete-markets model with an explicit defined-benefit (DB) pension fund. Calibrated to U.S. data, the model matches the historical equity premium (7.46% vs. 7.55% in data), the riskless rate (1.16% vs. 0.86%), and the Sharpe ratio (0.39 vs. 0.36) better than a standard pass-through model that ignores the fund's endowment and asset demands. The DB fund's relatively conservative portfolio lowers the riskless rate and raises the equity premium; stochastic contribution rates create a new risk channel that raises consumption volatility for workers and firms. A shift to a DC-only economy produces a higher riskless rate (3.34% vs. 1.16%), a lower equity premium (4.96% vs. 7.46%), a lower Sharpe ratio (0.27 vs. 0.39), higher consumption volatility for retirees, and lower consumption volatility for workers. ## Core results Magnitudes and significance are as reported. Locators point into the source PDF (page numbers match the journal pagination printed on each page). | # | Result | Locator | Magnitude | |---|---|---|---| | R1 | Baseline DB model closely matches key asset pricing moments | Table II, p. 164 | Equity premium 7.46% (data 7.55%); riskless rate 1.16% (data 0.86%); Sharpe ratio 0.39 (data 0.36); stock market participation 59.1% (data 51.1%) | | R2 | DB model dominates pure-pass-through (PPG) model at same calibration: much higher equity premium and Sharpe ratio | Table III, p. 167 | Baseline: equity premium 7.46%, Sharpe 0.39 vs. PPG: 5.53%, 0.31; PPG riskless rate 4.04% vs. baseline 1.16% | | R3 | DB pension fund's conservative bond demand is the first pricing channel: raising equity premium and lowering riskless rate | Table V, p. 171 | Varying risky share from 42% to 72% moves equity premium from 10.60% to 5.48% and Sharpe ratio from 0.55 to 0.28 | | R4 | Stochastic DB contribution rates create a new risk channel: higher cross-sectional consumption volatility for workers | Table IV, p. 170 | SD consumption growth ages 20-35: 10.7% (baseline) vs. 10.0% (rPPG1); ages 36-65: 8.4% vs. 7.6%; retirees (66+): 2.2% vs. 2.6% | | R5 | Asset pricing results are robust across alternative DB fund portfolio allocation rules | Table II cols (1)-(3), p. 164 | Fixed vs. elastic vs. reaching-for-yield: equity premium 7.46%, 7.58%, 7.39%; Sharpe ratio 0.39, 0.39, 0.38 | | R6 | DC-only economy (DB phased out) has a substantially higher riskless rate and lower equity premium | Table IX col (2), p. 182 | Riskless rate 3.34% vs. 1.16%; equity premium 4.96% vs. 7.46%; Sharpe ratio 0.27 vs. 0.39 | | R7 | In the DC-only economy, retiree consumption volatility increases while worker consumption volatility decreases | Table IX col (2), p. 182 | SD cons. growth ages 20-35: 10.1% vs. 10.7%; ages 36-65: 7.4% vs. 8.4%; retirees (66+): 2.8% vs. 2.2% | | R8 | Lower stock market participation costs in DC economy raise participation but have modest aggregate price effects | Table IX col (3), p. 182 | Participation rises to 79.7% (vs. 57.2% at baseline DC costs); equity premium 4.60% and riskless rate 3.44%, both close to base DC scenario | **Overall (paper's conclusion).** The endowment and asset demands of DB pension funds matter for asset pricing and risk sharing in ways that purely PPG models miss. The shift toward DC plans is characterized by a higher riskless rate, a lower equity premium and Sharpe ratio, and a redistribution of consumption risk from retirees to workers. ## Theory / model The model is an incomplete-markets overlapping-generations (OLG) production economy, using the framework of Storesletten, Telmer, and Yaron (2007) as a benchmark. Households live from age 20 (adult age 1) to 100 (adult age 81), working until age 65 and retiring thereafter. Two household types (*A* and *B*) have heterogeneous discount factors and EIS but the same risk aversion. **Production technology (eq. 1, p. 149).** $$ Y_t = Z_t K_t^{\alpha} L_t^{1-\alpha} $$ where $$Z_t = G_t U_t$$ is aggregate productivity ($$G_t = (1+g)^t$$ is deterministic growth; $$U_t$$ is a two-state Markov business-cycle shock), $$K$$ is the beginning-of-period capital stock, and $$L$$ is labor supply (eq. 2, p. 149). **Stochastic depreciation (eq. 3, p. 149).** $$ \delta_t = \bar{\delta}(U_t) + \sigma^{\delta}(U_t) \cdot \eta_t $$ where $$\eta_t$$ is i.i.d. standard normal and both the conditional mean and standard deviation of depreciation are correlated with $$U_t$$. This device avoids explicit adjustment costs while generating return volatility in the incomplete-markets setting, sharing the stochastic depreciation device for tractability with Favilukis, Ludvigson, and Van Nieuwerburgh (2017). **Household preferences: Epstein-Zin-Weil (eq. 9, p. 151).** $$ V_{a,t} = \left\{ (1-\beta)(C^i_{a,t})^{1-1/\psi} + \beta\left( \mathbb{E}_t\!\left(p_a V^{1-\gamma}_{a+1,t+1}\right) \right)^{(1-1/\psi)/(1-\gamma)} \right\}^{1/(1-1/\psi)} $$ where $$\beta$$ is the discount factor, $$\gamma$$ is relative risk aversion, and $$\psi$$ is the elasticity of intertemporal substitution (EIS). Type-*B* households: $$\beta^B = 0.965$$, $$\psi^B = 0.65$$; type-*A*: $$\beta^A = 0.83$$, $$\psi^A = 0.25$$; both have $$\gamma = 6$$ (Table I, p. 160). **Labor income (eqs. 13-16, pp. 152-153).** Individual labor income is $$H^i_{a,t} = W_t L^i_{a,t}$$, with individual productivity $$L^i_{a,t} = P^i_{a,t} \epsilon^i_t$$ (permanent component times transitory shock). The permanent component follows: $$ P^i_{a,t} = \exp(f(a))\, P^i_{a-1,t-1}\, \xi^i_t $$ where $$f(a)$$ is a deterministic age profile (hump-shaped). Following Guvenen, Ozkan, and Song (2014), $$\ln \xi^i_t$$ is a mixture of two normals conditional on the aggregate state $$U_t$$, capturing countercyclical earnings risk. **Retirement income (eq. 17, p. 153).** Retired households receive: $$ H^i_{a,t} = (\lambda^{ss} + \lambda^{db})\, P^i_{a^R, t^R}\, W_t, \qquad a > a^R $$ where $$\lambda^{ss}$$ and $$\lambda^{db}$$ are the social security and DB pension replacement ratios, calibrated to 0.4596 and 0.2225 respectively (Table I). **Pension fund endowment and return (eq. 19, p. 155).** $$ R^P_t = \alpha^P R^K_t + (1 - \alpha^P) R^B_t $$ where $$\alpha^P$$ is the risky (equity) share of the pension fund portfolio, calibrated to 52% to match the historical Flow of Funds average. **Pension fund budget constraint and contribution rates.** The fund keeps endowment $$\omega^P$$ constant and adjusts contribution rates each year. In the general case (eq. 22-24, pp. 156-157), the shortfall before adjustments is: $$ \tilde{\omega}^P_t = (1 + R^P_t)\, \omega^P + \sum_{a=20}^{65} \int_{i \in I^a} \bar{\tau}^{db} L^i_{a,t}\, w_t\, di - \sum_{a=66}^{100} \int_{i \in I^a} \left[\lambda^{db} \exp(f(a^R))\, w_t\, P^i_{a^R, t^R}\right] di $$ The fraction $$\theta^P$$ of the shortfall is absorbed by employer contributions: $$ \tau^{kdb}_t = \theta^P \cdot \frac{\omega^P - \tilde{\omega}^P_t}{k_t - \alpha^P \omega^P} $$ and the remainder $$(1 - \theta^P)$$ by employee contributions: $$ \tau^{db}_t - \bar{\tau}^{db} = (1 - \theta^P) \cdot \frac{\omega^P - \tilde{\omega}^P_t}{\displaystyle\sum_{a=20}^{65} \int_{i \in I^a} L^i_{a,t}\, w_t\, di} $$ Baseline calibration: $$\theta^P = 0.5$$ (equal split). This stochastic adjustment is the new risk channel: return shocks feed into net wages and firm profits, raising cross-sectional consumption volatility. Building on Constantinides and Duffie (1996), stochastic contribution rates raise idiosyncratic income risk for workers and firms, which raises the equity premium. **Government budget constraint (eq. 8, p. 151).** $$ C^G_t + (1 + R^B_t)\, B_t = B_{t+1} + T_t $$ Bond supply is calibrated to a debt-to-GDP ratio of 42% (average U.S. Treasury holdings by the public). Interest payments are financed by taxes on capital income (rate $$\tau^K = 40\%$$), bond interest ($$\tau^B = 20\%$$), wages ($$\tau^W$$), and bequests. **Equilibrium conditions (eqs. 34-36, p. 160).** Markets clear in capital, bonds, and the consumption good: $$ k_{t+1} = \int \int P^i_{a,t}\, k^i_{a,t+1}\, da\, di $$ $$ b_{t+1} = \int \int P^i_{a,t}\, b^i_{a,t+1}\, da\, di $$ $$ U_t k_t^{\alpha} L_t^{1-\alpha} = \frac{C^G_t}{G_t^{1/(1-\alpha)}} + (1+g)^{1/(1-\alpha)} k_{t+1} - (1-\delta_t) k_t + \int \int P^i_{a,t}\, c^i_{a,t}\, da\, di $$ ## Method The paper contributes a calibrated structural model, not a new econometric method. The solution follows the `krusell-smith` approximate-aggregation approach, building on `overlapping-generations`, `epstein-zin-weil` preferences, and `incomplete-markets-olg` techniques. **Household optimization (eq. 30, pp. 158-159).** Households solve the Bellman equation: $$ V_a(x^i_{a,t}, E^i_a, k_t, U_t, \eta_t, P^B_t) = \max_{k^i_{a+1,t+1},\, b^i_{a+1,t+1}} \left\{ (1-\beta) (c^i_{a,t})^{1-1/\psi} + \beta \left( \mathbb{E}_t \left[ \left(\frac{P^i_{a+1,t+1}}{P^i_{a,t}} (1+g)\right)^{1-\rho} p_a V^{1-\rho}(x^i_{a+1,t+1}, E^i_{a+1}; k_{t+1}, U_{t+1}, \eta_{t+1}, P^B_{t+1}) \right] \right)^{(1-1/\psi)/(1-\rho)} \right\}^{1/(1-1/\psi)} $$ subject to: $$k^i \geq 0$$, $$b^i \geq 0$$, budget constraint $$c + b' + k' = x$$ (eq. 32), and the wealth transition (eqs. 26-27) that includes after-tax capital and bond income, net labor income (less social security and DB contribution taxes for workers), and retirement income (for retirees). State variables: age $$a$$, normalized cash-on-hand $$x^i_{a,t}$$, entry-cost dummy $$E^i_a$$, plus four aggregate variables $$(k_t, U_t, \eta_t, P^B_t)$$. **Aggregate forecasting rules (eqs. 28-29, p. 158).** $$ k_{t+1} = \Gamma_K(k_t, U_t, \eta_t) $$ $$ P^B_{t+1} = \Gamma_P(P^B_t, k_t, U_t, \eta_t) $$ These log-linear rules are estimated on simulated data and iterated to convergence (following Krusell and Smith 1998, and Gomes and Michaelides 2008). **Calibration procedure.** Aggregate parameters are calibrated to NBER business cycle frequencies (Markov chain $$\pi_r = 16/37$$), capital share $$\alpha = 34\%$$, depreciation $$\text{mean}(\delta) = 10\%$$, $$\text{vol}(\delta) = 10\%$$. Household parameters are chosen to jointly match: the standard deviation of consumption growth, the riskless rate level, and limited stock market participation. The pension fund risky share ($$\alpha^P = 52\%$$) is calibrated to the 1970-2023 Flow of Funds average (Table I, p. 160; Section I.H.3, p. 162). **Alternative DB pension fund portfolio rules (eqs. 37-38, p. 166).** The baseline uses a constant $$\alpha^P$$. Two alternatives are also studied: elastic allocation proportional to the equity premium: $$ \alpha^P_t = a^P + c^P \bigl(\mathbb{E}[R^K_t] - R^B_t\bigr), \qquad c^P = 0.25 $$ and reaching-for-yield allocation varying with the riskless rate: $$ \alpha^P_t = a^P + b^P R^B_t, \qquad b^P = -2 $$ Both deliver nearly identical asset pricing moments (Table II, cols 1-3), so the results are insensitive to the precise specification. **DC-only counterfactual (eq. 39, p. 178).** Setting $$\lambda^{db} = 0$$ and $$\omega^P = 0$$ removes the DB pension fund entirely; households finance retirement from private savings and social security only. The DC economy incorporates tax benefits via a reduced capital gains tax rate scaled to the increase in private household wealth, and a 10% early-withdrawal penalty (Sections V.B.1-V.B.2, pp. 179-180). The numerical solution adds an outer loop to find the fixed point for the implied capital gains tax adjustment. ## Empirical specifications The paper does not estimate regression equations. All quantitative results are steady-state moments from the calibrated structural model, compared against empirical counterparts. The "specifications" are the alternative calibrated economies: **Baseline DB economy (R1, R5):** $$\alpha^P = 52\%$$, $$\theta^P = 0.5$$, two household types (A and B), calibrated to match riskless rate SD, participation rate, and equity premium. Key moments computed at the stationary distribution of the model (Table II, p. 164). Asset pricing data from CRSP; real risk-free rate from Croce et al. (2012); participation from SCF; consumption/GDP from NIPA 1929-2023. **Comparison with PPG model (R2):** same parameter values, but $$\omega^P = 0$$ so the fund is a pure pass-through with no endowment and constant contribution rates (Table III, p. 167). Two recalibrations (rPPG1, rPPG2) additionally match the riskless rate or consumption growth SD of the baseline. **Risk channel decomposition (R3):** the pension fund risky share $$\alpha^P$$ is varied from 42% to 72% (Table V, p. 171) to isolate the bond-demand channel; all other parameters are held at the baseline. **Consumption risk sharing by age group (R4):** cross-sectional standard deviation of consumption growth reported by cohort (ages 20-35, 36-65, 66+) for the baseline and rPPG1 economy (Table IV, p. 170). **Adjustment rule robustness (R5):** $$\theta^P$$ is varied from 0.2 (mostly employee adjustment) to 0.8 (mostly employer adjustment) with the same aggregate parameters (Table VIII, p. 177). **DC-only counterfactual (R6-R8):** the DB fund is shut down ($$\lambda^{db} = 0$$, $$\omega^P = 0$$) and the model is solved for the new stationary equilibrium. Three scenarios: (1) same participation costs, (2) lower participation costs ($$F^0 = 3\%$$, $$F^1 = 0.1\%$$), (3) higher debt-to-GDP (0.6). Asset pricing and macro moments from Table IX (p. 182) are compared to the baseline. ## Datasets used | Dataset | Role in paper | Wiki page | |---|---|---| | CRSP (Center for Research in Security Prices) | Asset pricing moments: equity return mean and SD, riskless rate (via Croce et al. 2012 for real rate) | [WRDS / CRSP](/wiki/commercial/wrds/) (licensed) | | NIPA tables (BEA / Federal Reserve Bank of St. Louis) | Real consumption growth mean and SD; capital-output ratio (tables 1.1.3 and 1.1.5, 1929-2023) | [FRED](/wiki/datasets/fred/), free | | Flow of Funds (Federal Reserve) | DB pension fund total financial assets and endowment-to-GDP ratio (1970-2023) | [FRED](/wiki/datasets/fred/), free | | Survey of Consumer Finances (SCF, Federal Reserve) | Historical stock market participation rate (used as calibration target) | no page yet | | NBER business cycle dates | Calibration of productivity shock Markov chain (recession/expansion probabilities) | [NBER cycles](/wiki/datasets/nber-cycles/) | | Public Plans Data / Social Security Administration data | Decomposition of DB replacement ratio vs. social security replacement ratio | no page yet | Sample: U.S. aggregate, 1929-2023 for returns and consumption; 1970-2023 for pension fund data. ## When to read the full paper Use the [original article](https://doi.org/10.1111/jofi.13507) if you are: replicating or extending the quantitative model; examining Internet Appendix robustness checks (bequest motives, alternative bond supply, transition dynamics); doing a literature review of intermediary asset pricing or pension finance; or auditing a specific parameter value from the calibration (Table I, p. 160). The locators in the table above point to the exact figures and tables. For "what did this paper find," the table above is the intended default. ## Attribution and rights Source: peer-reviewed, *The Journal of Finance* 81(1), February 2026. This distillation was extracted by an LLM on 2026-05-31 and augmented on 2026-06-01; it is **not human-verified or independently reproduced**. > **Attribution (CC BY 4.0).** Coimbra, Nuno, Francisco Gomes, Alexander > Michaelides, and Jialu Shen. "Asset Pricing and Risk-Sharing Implications > of Alternative Pension Plan Systems." *The Journal of Finance* 81, no. 1 > (February 2026): 143-188. DOI: 10.1111/jofi.13507. (c) 2025 The Author(s). > Published by Wiley Periodicals LLC on behalf of the American Finance > Association. Licensed under [CC BY 4.0](https://creativecommons.org/licenses/by/4.0/). > This page is an **adaptation** by the Institute for Automated Research: > core results extracted and re-expressed; **changes were made**. CC BY 4.0 > permits mirroring; the PDF is not hosted in this batch.