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Published one-asset HANK equilibrium

calibrate_one_asset_hank and solve_one_asset_hank implement the one-asset model in the authors' HANK notebook, associated with Auclert, Bardóczy, Rognlie and Straub (2021). The implementation is NumPy/SciPy. The authors' package is used only in a separate environment to generate independent comparison arrays.

from puremacro.models import calibrate_one_asset_hank, solve_one_asset_hank

steady = calibrate_one_asset_hank()  # 500 asset nodes, 7 income states
linear = solve_one_asset_hank(steady, horizon=300)
nonlinear = solve_one_asset_hank(steady, horizon=300, nonlinear=True)
assert steady.converged and linear.converged and nonlinear.converged
print(steady.summary())
print(nonlinear.diagnostics)
print(nonlinear.to_dataframe().head())

The shock reduces the Taylor-rule intercept by 0.0025 * 0.61**t. Set magnitude=0.0025 for the opposite shock. Paths are level deviations, with rates and inflation in decimal units. A consumption response of 0.001 is 0.1% of steady consumption, which is normalized to one. Results also provide summary, to_markdown, to_latex and to_typst.

Equations and timing

Households choose consumption, hours and saving:

\[c_t+a_{t+1}=(1+r_t)a_t+w_t e_t n_t+(Div_t-Tax_t)e_t,\quad a_{t+1}\ge0.\]

Marginal utility is \(c^{-1/\mathrm{EIS}}\); the labor first-order condition is \(v_\phi n^{1/\mathrm{Frisch}}=wec^{-1/\mathrm{EIS}}\). EGM solves the interior problem and a constrained budget/FOC solve handles the borrowing limit. Transfers and dividends are proportional to skill, whose stationary mean is one.

Output and steady productivity are one. Firms hire \(L_t=Y_t\), pay dividends \(Div_t=Y_t-w_tL_t-Adj_t\), and incur

\[Adj_t=\frac{\mu}{\mu-1}\frac{\log(1+\pi_t)^2}{2\kappa}Y_t.\]

Government debt is fixed at \(B=5.6\) and \(Tax_t=r_tB\). Realized returns include the date-zero revaluation of previously issued nominal debt:

\[1+r_t=\frac{1+r^\star_{t-1}+\phi\pi_{t-1}}{1+\pi_t}.\]

The solver determines \((\pi_t,w_t,Y_t)\) from \(A_t=B\), \(NE_t=L_t\) and

\[0=\kappa(w_t-1/\mu)+\frac{Y_{t+1}}{Y_t} \frac{\log(1+\pi_{t+1})}{1+r_{t+1}}-\log(1+\pi_t).\]

Goods clearing \(Y_t=C_t+Adj_t\) and household budgets are separate checks. Initial nominal policy is predetermined. Terminal household values and future aggregate quantities equal their steady-state values; horizon refinement measures the effect of that terminal assumption.

Calibration and independent checks

Defaults are EIS = Frisch = 0.5, log-skill persistence 0.966, unconditional log-skill standard deviation 0.5, markup 1.2, Phillips coefficient 0.1, Taylor coefficient 1.5 and quarterly steady interest rate 0.005. Beta and labor disutility are calibrated to assets 5.6 and effective labor one. Matching those targets alone does not demonstrate numerical convergence.

The pinned author-code fixture compares saving, consumption, hours, the distribution, calibrated parameters, and nine aggregate paths. Linear paths must agree within 1e-6 per unit of the monetary shock; nonlinear paths for both signs must agree within 1e-7 in levels. Market residuals must be below 1e-8. The reference generator verifies the installed author sources against the pinned checkout and records array hashes and dependency versions.

python -m pytest tests/test_models/test_one_asset_hank.py -q
python -m tools.reference_validation.check_hank_equilibrium \
  --output /tmp/hank-equilibrium --convergence

The refinement protocol compares the first 40 quarters. Its criterion is 1% of the finer response's peak, with a level floor of 1e-6; changes in beta and labor disutility must be below 1e-4. Asset grids, income-state counts, the asset bound and transition horizons are checked separately. Richer income grids require a wider asset bound than the notebook's 150.

The frozen run in tests/fixtures/hank_equilibrium/convergence.json records:

Check	Result
Published 500 × 7 calibration	beta 0.9822435541; labor disutility 0.7864334303
Largest author-code linear path difference	9.23e-14
Largest nonlinear path difference, either sign	9.67e-10
Assets, 500 → 1,000 nodes	Passed
Income states, 11 → 15 and 15 → 21	Failed; retained in the record
Income states, 21 → 31	Passed; worst response change 0.614% of its peak
Assets, 500 → 1,000, at 31 income states	Passed
Horizon, 300 → 600, at 31 income states	Passed

The extended income study uses assets up to 600. The asset-bound check from 300 to 600 at 15 states passes; the largest terminal-grid mass across all reported transitions is 1.09e-29. The notebook calibration reproduces the authors' discretization; the extended grid establishes the stated refinement criterion. It does not certify every intermediate income grid.

This benchmark validates a deterministic perfect-foresight monetary transition around one published steady state. It does not establish accuracy for arbitrary large shocks, a binding lower bound on nominal rates, two assets, or aggregate stochastic welfare. The existing solve_hank_sequence_space and DAG examples have different closures; their results are not this benchmark.