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Replication Gallery

Distinct from puremacro.validation (which guards against algorithmic drift relative to reference software packages), puremacro.replication is designed to scientifically reproduce published empirical and structural headline findings from peer-reviewed academic literature. Where a case pins a number computed by puremacro instead of a published one, its citation says so ("puremacro regression value, not published").

Every replication case is declared as a self-contained, frozen ReplicationCase running deterministically in the browser under the Pyodide 4-package contract (numpy, scipy, pandas, matplotlib), requiring zero network access and executing in sub-second time.

Running the Replication Suite

from puremacro.replication import run_all, scorecard

# Run all offline replication cases and display the scorecard
df = scorecard()
print(df[["id", "family", "paper", "target_kind", "tol", "passed", "margin"]])

# Every offline case passes (published targets, or labelled regression values)
assert df["passed"].all()

Replication Families

1. Bayesian DSGE Estimation (dsge_estimation)

Smets & Wouters (2007), "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach", AER 97(3):586–606. Tables and pages below are from the ECB Working Paper 722 version (February 2007, https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp722.pdf).

  • Model: puremacro.dsge.smets_wouters. Its impulse responses to all seven shocks coincide with the bundled Pfeifer .mod (puremacro/dsge/_references/sw07_pfeifer.mod) solved by puremacro at the same parameters (max gap below 1e-12). The price and wage markup disturbances are ARMA(1,1) with a contemporaneous innovation, \(\varepsilon^p_t = \rho_p \varepsilon^p_{t-1} + \eta^p_t - \mu_p \eta^p_{t-1}\) and the same for wages (WP 722 printed pp. 14–15).
  • Data: puremacro/dsge/_sw07_data.csv, 1966Q1–2004Q4 (156 quarters), rebuilt from FRED by tools/build_sw07_data.py with the definitions of the SW07 data appendix (printed p. 47). GDP, consumption and investment are per capita; nominal consumption and fixed investment are deflated by the GDP deflator. The real wage is NFB hourly compensation over the GDP deflator. Hours are NFB average hours × civilian employment ÷ population 16+. All of these are in 100 × log. Inflation and the federal funds rate are quarterly percent. These are today's FRED vintages, not SW's 2006 files.

  • Fixture: puremacro/replication/data/sw07_parity_seed0_200draws.npz, shipped as package data so the cases also run from an installed wheel, and rebuilt with python tools/build_sw07_data.py fixture. It holds the optimised posterior mode, the inverse Hessian there, and 200 thinned random-walk Metropolis draws. It also records the SHA-256 of the CSV it was built on, and a mismatch fails the cases.

  • dsge_estimation.sw07_structural_parameters_mode (published target)

  • Target: the posterior Mode column of Table 1a (PDF p. 35) and Table 1b (PDF p. 36). The Mean column is not the target: for example it has \(\varphi = 5.74\) and \(\sigma_c = 1.38\), against the modes 5.48 and 1.39.
  • What is compared: the posterior mode of puremacro's model on the bundled data. It was found by L-BFGS-B from two starting points and polished with Newton steps, and it is a stationary point: no coordinate step raises the log posterior (tested).
Parameter SW07 symbol Table SW07 mode puremacro mode Difference
csadjcost \(\varphi\) 1a 5.48 5.694 +3.9%
csigma \(\sigma_c\) 1a 1.39 1.405 +1.1%
chabb \(h\) (habit) 1a 0.71 0.700 -1.4%
csigl \(\sigma_L\) 1a 1.92 2.035 +6.0%
cprobp \(\xi_p\) 1a 0.65 0.690 +6.2%
cfc \(\Phi\) 1a 1.61 1.617 +0.4%
crr \(\rho\) 1a 0.81 0.809 -0.1%
crdy \(r_{\Delta y}\) 1a 0.22 0.226 +2.6%
ctrend \(\bar\gamma\) 1a 0.43 0.416 -3.2%
crhopinf \(\rho_p\) 1b 0.90 0.879 -2.3%
cmap \(\mu_p\) 1b 0.74 0.703 -5.0%
crhow \(\rho_w\) 1b 0.97 0.972 +0.2%
cmaw \(\mu_w\) 1b 0.88 0.886 +0.6%

  • Tolerance: Tol.COARSE (\(\text{rtol} \le 0.25\)), because the data vintage differs from SW's. Among the other published modes, 21 of the remaining 22 (including the seven shock standard deviations) are also within 25%; the exception is price indexation \(\iota_p\) (cindp), 0.32 against 0.22. The hours intercept \(\bar l\) (constelab) is not compared, because the bundled hours series is demeaned.

  • dsge_estimation.sw07_log_posterior_at_mode, dsge_estimation.sw07_laplace_marginal_data_density, dsge_estimation.sw07_harmonic_mean_mdd_consistency (puremacro regression values, not published numbers)

  • Targets:

    • log posterior (log likelihood + log prior) at the mode: -822.04, recomputed live;
    • Laplace log marginal data density: -902.83, from the live log posterior and the stored inverse Hessian;
    • Geweke (1999) modified harmonic mean on the 200 stored draws: -908.03, with spread 2.66 across truncation levels 0.1–0.9.

    All three use Tol.TIGHT. - Why they are not published targets: SW07 report no log posterior at the mode, and their marginal likelihood (Table 2, PDF p. 37: −905.8) is computed over 1966:1–2004:4 "using the period 1956:1–1965:4 as a training sample" with the Laplace approximation. These cases guard puremacro's own model, data, priors and marginal-likelihood estimators against unintended change. - The Table 2 computation itself (4.6.0): sw07_laplace_mdd (puremacro.dsge.sw07_marginal) implements the training sample as Dynare's presample with a diffuse initialisation, on the authors' own series (load_sw07_data("authors"), the AER replication data). On 3 October 2026 it gave a Laplace log data density of −932.3 (log posterior at the mode −849.6) for the paper's configuration (1956Q1 start, 40-quarter presample), −921.4 (−840.0) for the configuration of the authors' replication .mod (1965Q1 start, 4-quarter presample, lik_init=2), −926.2 (−845.1) for 1966–2004 with the unconditional initialisation, and −902.8 (−822.0) on the bundled FRED rebuild, which reproduces the regression case above. At the authors' own posterior mode (usmodel_mode.mat) puremacro's log posterior is −840.81 against −841.46 printed by Dynare 8 on the same files and options (Laplace −922.4 against −923.1 with Dynare's Hessian; with the 1956Q1 start and 40-quarter presample, −888.27 against −887.13). The replication case dsge_estimation.sw07_log_posterior_at_authors_mode_vs_dynare pins that agreement. The printed −905.8 is therefore reproduced neither by puremacro nor by Dynare 8 on the public replication files, with any of the sample and initialisation choices above; the gap is in the data or the computation behind the published table, not in puremacro's model. - Through 4.3.0 this page presented −1673.72, −1686.09 and −2524.36 as SW07 results. They were puremacro outputs of a model whose markup shocks lacked their MA terms and entered one quarter late, on data whose hours lacked the factor 100.

2. Pure-NumPy Econometric Regressions (regression)

Replicates foundational micro- and macro-econometric findings using puremacro's zero-dependency, pure-NumPy regression subsystem (puremacro.regress):

  • regression.card1995_iv_vs_ols
  • Paper: Card, D. (1995), "Using Geographic Variation in College Proximity to Estimate the Return to Schooling".
  • Findings: Replicates the classical return to education: OLS coefficient \(\beta_{\text{educ}} = 0.0740\) vs Two-Stage Least Squares (2SLS) IV estimate \(\beta_{\text{educ}} = 0.1323\) instrumented by county-level 4-year college proximity (nearc4).

  • Tolerance: Tol.TIGHT.

  • regression.long_ervin2000_hc_hierarchy

  • Paper: Long, J. S. and Ervin, L. H. (2000), "Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model", The American Statistician 54(3):217–224.
  • Findings: Verifies the strict monotonic standard error hierarchy under heteroskedasticity with high leverage points: $\(\mathrm{SE}_{\text{OLS}} < \mathrm{SE}_{\text{HC0}} < \mathrm{SE}_{\text{HC1}} < \mathrm{SE}_{\text{HC2}} < \mathrm{SE}_{\text{HC3}}\)$

  • Target Kind: TargetKind.SIGN (positive differences at each tier).

  • regression.mroz1987_logit_participation

  • Paper: Mroz, T. A. (1987), "The Sensitivity of an Empirical Model of Married Women's Hours of Work", Econometrica 55(4):765–799.
  • Findings: Binary Logit model of female labor force participation (inlf): log-likelihood of -401.77, intercept 0.4255, young children effect (kidslt6) -1.4434, and non-wife income (nwifeinc) -0.0213.

  • Tolerance: Tol.TIGHT.

  • regression.romer_romer_tax_multiplier_ols

  • Paper: Romer, C. D. and Romer, D. H. (2010), "The Macroeconomic Effects of Tax Changes", AER 100(3):763–801.
  • Scope: A modified horizon-eight local projection with Newey-West HAC covariance, revised outcome data and a 1950–2006 sample. Its approximately -2.9004 response is compared coarsely with the paper's headline magnitude near -3; it is not the original distributed-lag estimator or a published horizon-eight LP coefficient.
  • Tolerance: Tol.MEDIUM (\(\text{rtol} \le 0.10\)), for that coarse comparison only. The original-data replication separately reproduces the authors' baseline specification and compares it with independent software output.

3. Heterogeneous-Agent & Structural Macro (ha_dsge_causal)

  • ha_dsge_causal.aiyagari_precautionary_wedge: Replicates the Aiyagari (1994) precautionary savings wedge driving the equilibrium interest rate below the subjective discount rate (\(r^* < \rho\)).
  • ha_dsge_causal.aiyagari_r_decreasing_in_sigma: Validates comparative statics: equilibrium \(r^*\) decreases as idiosyncratic earnings risk \(\sigma\) increases.
  • ha_dsge_causal.aiyagari_r_decreasing_in_rho: Validates comparative statics: equilibrium \(r^*\) decreases as earnings persistence \(\rho\) increases.
  • ha_dsge_causal.huggett_precautionary_riskfree_rate: Replicates Huggett (1993) pure credit economy risk-free rate depression due to borrowing constraints.
  • ha_dsge_causal.sw07_seven_shocks_seven_observables: Smets-Wouters (2007) specification check: the model has the published seven structural shocks matched to seven observables (a count, not a comparison of moments).

4. Macroeconomic Stylized Facts (stylized_facts)

  • stylized_facts.okun_law_fred: Replicates the negative cyclical comovement between output growth and changes in the unemployment rate (Okun's Law, correlation \(\le -0.60\)).