Distributional Dynamics — Data

Quarterly estimates of the joint distribution of consumption, income, and wealth for U.S. households, 1962-Q3 to 2024-Q1, with posterior uncertainty — plus small scripts that turn them into whatever moment or micro dataset you need.

This is the data product of:

Bayer, Christian, Luis Calderon, and Moritz Kuhn. "Distributional Dynamics." CEPR Discussion Paper 19829, 2026.

Please cite the paper when using the data (CITATION.cff). Methodology, estimation code, and the full replication package live in DD_replication.

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The data (data/)

File	What it is
smoothed_factors.csv	Latent states $\hat F_t$ (43 columns × 248 quarters, point estimate / posterior mode). The first 8 columns (x1–x8) are the distributional factors — the main objects. x9–x32 are their lags (the model conditions annual surveys on 4-quarter averages), x33–x43 the aggregate block.
smoothed_factor_draws.csv	400 posterior draws of the states (parameter + state uncertainty), same column layout — again, x1–x8 are the factors that matter. The basis for credible bands on any moment.
smoothed_factors_bands.csv	Ready-made per-quarter 5/50/95 percentiles of each factor.
{PSID,SCF,CEX}_coefficients_{normal,average}.csv	Model-implied Legendre coefficients of the joint distribution, dense across all quarters. _normal = HP trend re-added (use in-sample); _average = time-averaged trend (use for extrapolation).
{PSID,SCF}_functional_data{,_detrended}.csv	The raw survey-based coefficient estimates that enter the model (NaN where no survey).
PSID_synthetic_microdata.csv	Synthetic micro data: one weighted cross-section per quarter (1000 rows = 10³ decile-copula cells) — cell weight, decile-average consumption/income/wealth (relative to per-HH mean), cell indices.
aggregate_anchors.csv	Per-household aggregates (consum/income/wealth_per_hh, tot_hhs) — multiply relative values by these for dollar levels.

Units: distributional values are relative to the quarter's per-household mean (e.g. 0.80 = 80% of mean consumption). Levels = value × <measure>_per_hh from aggregate_anchors.csv.

The scripts (julia/, python/)

Named for the pipeline stage they implement — same API in both languages, agreeing to machine precision:

factors  →  coefficients  →  moments / micro data

Script	In → Out
factors_to_coefficients	factors → coefficient rows (FactorMap; perturb a factor for counterfactuals). _average trend convention only — the map is re-estimated from the published files (exact, R² = 1.0) since the model's own loadings/means/trend are not shipped; the _normal HP trend is not a function of the factors.
coefficients_to_moments	coefficients → decile cuts & averages, levels, shares, robust Ginis, copula density (DATE=all for full time series)
coefficients_to_micro_data	coefficients → weighted synthetic cross-sections
posterior_bands	factor draws → credible band on any moment
plot_factor_bands	factor draws → factor paths with bands
reconstruct	the core library both languages share (Reconstruction, quantile_at, copula_density_at, copula_pmf_grid, FactorMap, …)

Quick start

Julia (deps pinned in Project.toml):

julia --project=. -e 'using Pkg; Pkg.instantiate()'   # once
julia --project=. julia/coefficients_to_moments.jl    # deciles + copula density
DATE=2008-Q3 julia --project=. julia/coefficients_to_micro_data.jl
julia --project=. julia/plot_factor_bands.jl          # factors with 5–95% bands

Python (needs numpy, pandas, matplotlib):

python python/coefficients_to_moments.py
python python/posterior_bands.py --measure wealth --date 2008-Q3

As a library:

import sys; sys.path.insert(0, "python")
from reconstruct import Reconstruction, FactorMap

r = Reconstruction("data/PSID_coefficients_normal.csv")
r.quantile_at("2008-Q3", "consum", [0.1, 0.5, 0.9])   # → [0.325, 0.802, 1.874]
r.copula_density_at("2008-Q3", 0.5, 0.5, 0.5)          # → 1.754
r.copula_pmf_grid("2008-Q3")                           # 10³ cell masses

include("julia/reconstruct.jl"); using .DistributionalReconstruction
r = Reconstruction("data/PSID_coefficients_normal.csv")
quantile_at(r, "2008-Q3", :consum, [0.1, 0.5, 0.9])

Posterior uncertainty

smoothed_factors.csv is the posterior mode. For bands, push each row-group of smoothed_factor_draws.csv through FactorMap — posterior_bands does this for you. Each draw combines parameter uncertainty (posterior θ) with the Kalman smoother's state uncertainty; draws are marginal per quarter (exact for pointwise bands and per-date moments; joint cross-date statistics would need a joint simulation smoother).

Technical notes

• Marginal coefficients are stored on an asinh scale; the helpers apply the sinh back-transform, so returned values are already in natural (relative) units. The copula block is stored as-is.
• Basis: orthonormal Legendre on [0,1], $Q_o(u) = \sqrt{2o+1},P_o(2u-1)$; 12 orders per margin, 12³ copula tensor (34 immutable entries reconstructed by the helpers).
• The synthetic micro data reproduces the replication pipeline's construct_micro_dataset layout; the degree-11 basis truncates the extreme wealth tail (weighted mean ≈ 0.93 of the true mean for wealth — the Forbes-type top is not representable in this basis).

License

See LICENSE. Data are model-generated estimates; underlying surveys (PSID, SCF, CEX, CPS, SIPP) are public — see DD_replication for sources and the full data availability statement.