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SAGA: A Sequence-Adaptive Generative Architecture for Multi-Horizon Probabilistic Forecasting with Adaptive Temporal Conformal Prediction

Gustav Olaf Yunus Laitinen-Fredriksson Lundström-Imanov, Hafize Gonca Cömert

arXiv:2605.19014v1cs.LGecon.EMstat.ML

TL;DR

Microsimulation earnings models often use parametric processes that omit rich administrative predictors and flexible nonlinear dependencies. SAGA combines a decoder-only transformer for irregular panel sequences with conformal calibration and Monte Carlo lifetime aggregation. It improves forecasting against GKOS while reconstructing lifetime earnings distributions closer to the partially observed truth, with subgroup coverage remaining below nominal in the worst case.

  • Problem

    Parametric earnings processes omit rich administrative features and impose restrictive structures on dependencies and shock dynamics relevant to lifetime forecasting.

  • Method

    SAGA combines a decoder-only transformer for irregular tabular panel sequences with conformal calibration and Monte Carlo aggregation of annual forecasts into lifetime earnings distributions.

  • Results

    SAGA reduces CRPS against the GKOS benchmark by 31.9% at horizon ten and 41.2% at horizon twenty, while reconstructing the lifetime Gini as 0.327 versus 0.341 for the partially observed truth.

  • Takeaways & Limitations

    The results support using calibrated deep sequence forecasts to improve annual earnings prediction and downstream reconstruction of lifetime earnings distributions in this Swedish register setting.

  • Takeaways & Limitations

    Worst-case subgroup coverage is 87.6% at nominal 90%, and the marginal guarantee does not imply conditional coverage.

Abstract

from arXiv · show

Microsimulation models used by ministries of finance and central banks rely on parametric processes for lifetime earnings that capture only first and second moments of the conditional distribution and miss long-range nonlinear structure. We propose SAGA, a decoder-only transformer for irregular tabular panel sequences, paired with a split conformal calibration wrapper that delivers individual-level prediction intervals with finite-sample marginal coverage guarantees. Trained on the longitudinal Swedish LISA register over 1990 to 2022, comprising 2,143,817 individuals and 61,284,903 person-years, the model forecasts annual labor earnings at horizons of one to thirty years and aggregates them by Monte Carlo into present-discounted lifetime earnings distributions. Against the canonical Guvenen, Karahan, Ozkan, and Song parametric process and tabular and recurrent baselines, SAGA reduces continuous ranked probability score by 31.9 percent at the ten-year horizon and mean absolute error by 37.7 percent at the twenty-year horizon. Conformal intervals achieve nominal coverage to within 0.4 percentage points marginally and within 2.4 percentage points on the worst-case demographic subgroup. The reconstructed lifetime earnings Gini coefficient is 0.327 against the partially observed truth of 0.341 and the GKOS estimate of 0.378. Model weights, calibration tables, and a synthetic equivalent dataset are released for replication outside the protected SCB MONA environment.

I. INTRODUCTION

Microsimulation systems depend on earnings forecasts, but canonical parametric processes omit rich administrative predictors and flexible nonlinear dependencies. SAGA addresses this gap with a calibrated decoder-only transformer and reports improved forecasting, lifetime-distribution reconstruction, and downstream microsimulation accuracy.

  • Motivation: Microsimulation models used for policy evaluation rely on forecasts of future annual earnings paths, making forecast accuracy and calibration central to downstream counterfactual reliability.The cited passages identify FASIT, IGOTM, TRIM3, and EUROMOD as examples.
  • Prior approach: The canonical parametric earnings process models earnings using fixed effects, permanent autoregressive components, and transitory mixture shocks.It reproduces several observed earnings-distribution features across multiple countries and register datasets.
  • Motivation: The parametric process ignores administrative features, compresses cross-sectional dependencies into a fixed effect, and imposes restrictive shock-persistence and component-interaction structures.These limitations concern occupation, industry, employers, geography, education, family structure, and macroeconomic conditions.
  • Contribution: SAGA combines a decoder-only transformer for irregular tabular panel sequences with split conformal calibration and Monte Carlo lifetime aggregation.The architecture produces calibrated annual earnings forecasts and present-discounted lifetime earnings distributions.
  • Evaluation and release: The study benchmarks six forecasters across probabilistic and point metrics, evaluates downstream tax and distributional outcomes, and releases weights, calibration tables, and synthetic data.The release is intended to support replication outside the protected SCB MONA environment.
  • Results: 31.9% lower CRPS at the ten-year horizon is reported against the GKOS parametric benchmark, alongside closer lifetime-earnings distribution reconstruction.The reconstructed Gini is 0.327 versus 0.341 for the partially observed truth and 0.378 for GKOS.

A. Tabular Sequence Transformers and Life Trajectory Models

Prior work spans parametric earnings processes, tabular transformers, life-trajectory models, and conformal prediction, but microsimulation still relies on parametric earnings forecasting. The paper formulates irregular individual histories as sequences of annual records and forecasts future earnings and discounted lifetime earnings.

  • Related models: Static tabular transformers attend across features within rows, whereas life-trajectory transformers commonly tokenize discrete events for categorical prediction.The cited life-trajectory model loses continuous monetary information central to earnings forecasting.
  • Earnings processes: Canonical earnings models use permanent-transitory structures and flexible shock distributions to capture skewness, kurtosis, volatility, and individual heterogeneity.GKOS estimates age-conditional moments through order four using mixtures and a nonparametric fixed-effect distribution.
  • Conformal prediction: Conformal prediction provides distribution-free finite-sample marginal coverage, and conformalized quantile regression supplies the calibration framework adapted here.The paper applies this framework to autoregressive multistep forecasting.
  • Microsimulation gap: Microsimulation frameworks commonly use parametric earnings forecasters, while published comparisons with deep sequence models under downstream distributional loss are absent.The paper presents such a comparison.
  • Problem formulation: Each individual is represented by annual records containing earnings, continuous and categorical features, and a missingness mask over observed panel years.The first ten observed years form the conditioning window, followed by a forecast window through the last in-panel year before age sixty-four.
  • Targets: The forecaster outputs a predictive distribution over future annual earnings, while lifetime earnings are defined as their present-discounted value at age twenty using r = 0.02.The formulation distinguishes observed histories from future forecast records.

B. SAGA Architecture

SAGA is a decoder-only transformer that represents irregular tabular panel histories with typed feature embeddings and separate age and calendar-year channels. It jointly produces point and quantile forecasts, trained autoregressively with mean-squared-error and pinball objectives.

  • Architecture: SAGA uses six transformer layers, eight attention heads per layer, model dimension 384, and 10,872,960 parameters with causal attention.The maximum context length is forty-five yearly tokens.
  • Output heads: The output head has one scalar log-earnings point forecast and seven conditional quantile forecasts spanning the 5th through 95th percentiles.The two heads share the transformer backbone but use separate linear projections.
  • Tokenization: Each annual record is converted into a fixed-dimension token by combining continuous, categorical, missingness, age, and year subvectors.The concatenated 252-dimensional representation is projected to model dimension 384.
  • Positional information: Separate learned positional channels encode age and calendar year because the paper treats human-capital accumulation and business-cycle conditions as independent predictive information.Combining them would conflate these sources of variation.
  • Training: The training objective combines point-head mean squared error with pinball loss across quantile levels 0.05, 0.10, 0.25, 0.50, 0.75, 0.90, and 0.95.Zero earnings are mapped to log(1) = 0, representing 7.4% of person-years.
  • Inference: At inference, SAGA decodes autoregressively by interpolating the predicted quantiles into a continuous distribution, sampling a value, and appending it to the sequence.This procedure generates future paths while conditioning each step on previously sampled values.

E. Split Conformal Calibration

The calibration wrapper adapts conformalized quantile regression to autoregressive multistep forecasting by calibrating nonconformity scores on held-out cohort histories. It provides marginal coverage under exchangeability and extends sampled annual forecasts into lifetime-earnings intervals.

  • Score construction: Calibration computes nonconformity scores for forecast steps beyond the ten-year conditioning window using observed histories from calibration cohorts.The calibration set consists of individuals and forecast steps within their observed histories.
  • Interval construction: The interval for a new forecast point expands the model’s quantile interval using an empirical calibration-score quantile.The threshold is the order statistic Q1−α(S) of the calibration scores.
  • Assumption: The paper does not formally test exchangeability across adjacent calibration and test cohorts, although empirical marginal coverage closely matches nominal levels.The reported agreement is within 0.5 percentage points at every level in Table II.
  • Guarantee: Under exchangeability of calibration and test scores, the method has a finite-sample marginal coverage guarantee.The bound includes the stated 1/(n + 1) adjustment when calibration scores are almost surely distinct.
  • Evaluation: Marginal coverage is treated as the formal guarantee, while demographic subgroup coverage is reported as a practical calibration check.The distinction separates the theorem’s scope from empirical conditional-coverage diagnostics.
  • Lifetime aggregation: The lifetime-earnings distribution is obtained from 500 Monte Carlo paths that sample future log earnings, exponentiate them, discount them, and sum them.Lifetime conformal intervals use empirical α/2 and 1−α/2 quantiles across simulated lifetime values.

G. Baselines

The paper compares SAGA with parametric, tree-based, recurrent, and static feature-only forecasting baselines using Swedish register data and shared evaluation inputs. The data include earnings, labor-market, demographic, education, household, and geographic features, with secure analysis conducted in SCB MONA.

  • Parametric baselines: GKOS models earnings as fixed effects plus permanent and transitory mixture components, while AR(1) provides a simpler Gaussian benchmark.Both operate on the earnings sequence alone.
  • Machine-learning baselines: LightGBM separately forecasts horizons h ∈ {1, 5, 10, 20}, with quantile variants trained at seven levels.It uses the same feature vector as SAGA’s conditioning window.
  • Sequence and static baselines: The LSTM matches SAGA’s tokenization, output heads, training schedule, and parameter count, while the feed-forward network flattens the conditioning window to isolate sequence effects.The LSTM has 10,941,440 parameters.
  • Input data: The constructed records cover annual earnings, labor-market activity, demographics, education, household measures, and geography.The target is labor earnings plus self-employment income, expressed in constant 2022 Swedish krona.
  • Input data: Geographic inputs include county and commute distance, while municipality is retained for cross-tabulation but excluded from model inputs.County has twenty-one units and municipality has 290 units.
  • Input data: Fifteen continuous features include income, work, leave, demographic, household, qualification, and commute variables.These features are combined with categorical and other record information in the model inputs.

C. Sample Selection

The study defines a restricted Swedish register sample, separates training, calibration, testing, and out-of-time cohorts, and evaluates forecasts across accuracy, probabilistic, coverage, and lifetime-distribution measures. SAGA outperforms the baselines on probabilistic accuracy beyond one year, while conformal intervals remain close to nominal coverage and lifetime distributions more closely track the partially observed truth.

  • Sample selection: The sample restricts cohorts to 1960–1990 and excludes insufficient earnings histories, emigrants, extreme earners, deaths, and incomplete conditioning windows.These restrictions define the eligible population for the core analysis.
  • Sample and splits: 2,143,817 individuals and 61,284,903 person-year observations form the core train, calibration, and test sample.A separate out-of-time pool contains 287,391 individuals.
  • Sample and splits: Training uses cohorts 1960–1979, calibration uses 1980–1982, and testing uses 1983–1985.The calibration split supports early stopping and split conformal calibration.
  • Sample and splits: The out-of-time holdout uses cohorts 1986–1990 and reports a ten-year evaluation only for cohorts with complete observable forecast windows.The h = 10 effective sample is 168,734 individuals.
  • Evaluation design: All models share the evaluation splits, with hyperparameters selected on calibration data before test evaluation.Deep-learning and GMM results are averaged over five seeds or estimation runs, respectively.
  • Evaluation design: The study reports MAE, RMSE, CRPS, pinball loss, PICP, PINAW, lifetime metrics, and Diebold–Mariano tests across one-, five-, ten-, and twenty-year horizons.Newey–West standard errors use lag five for pairwise accuracy tests.
  • Forecast accuracy: 41.2% is SAGA’s horizon-twenty CRPS reduction against GKOS, with equal predictive accuracy rejected against all five baselines at the 1% level.The loss differentials are clustered at the individual level.
  • Calibration: 90.3% marginal coverage is achieved at nominal 90%, while the worst-case subgroup reaches 87.6% empirical coverage.Across subgroup-level combinations, deviations remain within 2.4 percentage points.

E. Downstream Tax Microsimulation

The downstream evaluation applies a fixed 2022 Swedish tax schedule to forecasted earnings paths and compares lifetime tax and distributional outcomes across forecasters. SAGA more closely reproduces observed lifetime tax rates and earnings inequality than GKOS, while ablations and robustness checks assess the sources and portability of its advantage.

  • Tax microsimulation: The tax calculator holds the 2022 Swedish tax schedule fixed in real terms and applies it uniformly to forecasted paths and comparison earnings.The schedule includes a basic allowance, 32.4% municipal tax above the allowance, and 20% state tax above the statutory breakpoint.
  • Tax microsimulation: SAGA’s average effective lifetime tax rate matches the partial observed truth within 0.5 percentage points, versus 1.2 percentage points for GKOS.Parametric processes also over-predict top-tail effective tax rates.
  • Ablations: Replacing the transformer with a flat feed-forward network loses 55.0% in CRPS at the ten-year horizon.The ablation study identifies this replacement as the largest single source of degradation among the reported components.
  • Heterogeneity: SAGA’s forecast improvement is strongest for individuals with four or more early-career employer changes (+47.3%) and those in the lowest income quintile (+44.7%).These groups are described as especially difficult for the parametric process because of feature dependencies shaping later earnings trajectories.
  • Robustness: The headline advantage remains robust across eleven perturbations, while the PSID-style feature restriction retains a 21.4% improvement over GKOS.The feature-portability check is Sweden-internal; a full PSID replication remains future work.

I. Placebo and Falsification

Placebo and falsification tests attribute SAGA’s advantage to genuine sequence information and longer histories rather than noise or static features alone. Attention patterns and ablations further indicate that time-varying sequence structure, calendar information, and quantile modeling contribute to performance, although gain magnitudes are Swedish-setting specific.

  • Placebo tests: A CRPS ratio of 2.14 after shuffling conditioning windows confirms that SAGA exploits genuine predictive structure rather than noise.
  • Placebo tests: 18.3% CRPS improvement with a five-year history versus 31.9% with ten years shows that longer histories contribute to SAGA’s advantage.
  • Placebo tests: A static feature-only network reaches CRPS 0.623 at horizon ten, indicating that static features alone are not competitive with SAGA or GKOS at long horizons.
  • Mechanisms: Attention shifts from recent years at short horizons toward the full conditioning window and transition years at longer horizons.
  • Mechanisms: Replacing the sequence model with a feed-forward network costs 55.0% in CRPS, while removing year or quantile embeddings raises CRPS by 7.2% or 9.1%, respectively.
  • Scope: The reported gain magnitudes are specific to Swedish LISA register coverage, while the qualitative sequence-model argument may extend beyond Sweden.

C. Limitations

The paper’s evidence is bounded by Swedish data, evolving labor-market conditions, censored evaluation, subgroup coverage gaps, and restricted access to the underlying register. The architecture and calibration combination is presented as the contribution, while several extensions remain future work.

  • External validity: Applying SAGA to other countries requires retraining because the architecture transfers but its Swedish-trained parameters do not.
  • Model staleness: The forecast assumes stationarity of the conditional labor-market distribution, so structural change could gradually invalidate the learned distribution.
  • Censoring: Forecasts beyond 2022 cannot be evaluated against truth, making partial-truth lifetime evaluation a lower bound on the true distributional gap.
  • Conditional coverage: At nominal 90% coverage, the lowest income quintile reaches 87.6%, showing that marginal conformal guarantees do not imply conditional subgroup coverage.
  • Lifetime aggregation: The lifetime 90% interval achieves 89.2% coverage, and per-step marginal guarantees do not automatically extend to lifetime aggregates.
  • Replication: Restricted MONA access limits independent replication, while the released synthetic dataset supports pipeline-level rather than bit-level replication.
  • Contribution boundary: SAGA combines existing tabular-transformer ideas with horizon-stratified conformal calibration; formal lifetime coverage, operational deployment, multi-country training, and structural-change robustness remain future directions.

APPENDIX A HYPERPARAMETERS AND AUXILIARY IMPUTATION

The appendix specifies the auxiliary imputation network, GKOS estimation and benchmark diagnostics, and the released synthetic-data construction and validation materials.

  • Auxiliary imputation: The auxiliary imputation network has three feed-forward layers, hidden dimension 128, ReLU activations, and 312,485 parameters.
  • Auxiliary imputation: It predicts next-year industry, occupation, and employment indicators from the running earnings trajectory and exogenous demographic features using cross-entropy loss.
  • GKOS benchmark: GKOS estimation matches 87 moments of earnings changes across multiple lags and age bins, using an inverse bootstrap moment-covariance weighting matrix.
  • GKOS benchmark: The estimated GKOS parameters fall within ranges reported for Norway and the United States, consistent with the Swedish implementation being correct.
  • Synthetic data: The synthetic panel samples demographic baselines empirically, generates earnings from SAGA’s conditional predictive distribution, and imputes auxiliary feature paths.
  • Synthetic data: Synthetic data match real-panel moments within 1.8%, while membership-inference AUC of 0.512 is near random performance.
  • Reproducibility: Model weights, calibration tables, synthetic data, and source code are deposited on Zenodo under separate DOIs.

A. Adaptive Temporal Conformal Prediction

The paper stratifies split conformal calibration by forecast horizon to address horizon-dependent residual behavior, derives a finite-sample coverage bound under exchangeability and local smoothness, and validates the bound empirically.

  • Procedure: Horizon-stratified conformal calibration addresses horizon-dependent variance and potential drift in longitudinal forecasting residuals.
  • Procedure: Each calibration individual contributes at most one residual per horizon stratum, enabling horizon-specific conformity scores and prediction intervals.
  • Guarantee: Theorem 2 assumes exchangeability within each horizon and an L_h-Lipschitz conditional score CDF near the target quantile.
  • Guarantee: The proof combines a standard conformal rank bound, Dvoretzky–Kiefer–Wolfowitz empirical-quantile concentration, and Lipschitz coverage translation.
  • Empirical validation: At horizon ten, n_10 = 14,107 calibration individuals and estimated L_10 = 0.65 imply a predicted worst-case deviation of approximately 0.024.
  • Empirical validation: Table XII evaluates marginal and lowest-income-quintile conditional coverage at the 90% nominal level using 1,000 Monte Carlo replicates per cell.

B. Monte Carlo Sensitivity via Real LISA Cross-Validation

Two real-residual Monte Carlo studies test conformal coverage under cohort variation and finite calibration samples, while a synthetic stress test broadens the distributional check. Across the real-data studies, marginal coverage remains exact and the worst-case deviation bound is attained but not exceeded.

  • Study design: The real-data sensitivity analysis replaces synthetic-only validation with LOCO-CV and bootstrap studies grounded in LISA calibration-cohort residuals at horizon h = 10.The studies target finite-sample tightness and the exchangeability assumption between calibration and test scores.
  • Study design: B = 1,000 bootstrap replicates resample 14,107 unique h = 10 calibration individuals at calibration sizes of 1,000, 5,000, and 14,107.Each replicate recomputes the conformal order statistic and evaluates marginal and Q1 coverage against a held-out 1983–1985 cohort of 141,074 individuals.
  • Coverage results: Marginal coverage is exact across both studies and all three calibration sizes, matching the first term of the Theorem 2 bound.This result is reported for both the leave-one-cohort-out and empirical-bootstrap analyses.
  • Coverage results: 88.7–88.9% Q1 conditional coverage at nh = 14,107 lies within 1.1–1.3 percentage points of the reported 87.6% headline Q1 coverage.The remaining gap reflects differences between the calibration-cohort and test-cohort distributions.
  • Coverage results: The approximately 2.4-percentage-point theoretical worst-case deviation is attained but not exceeded by any empirical cell.Agreement between LOCO-CV and bootstrap results indicates exchangeability holds to within a percentage point across adjacent calibration cohorts.
  • Stress test: Across homoskedastic Gaussian, Student-t5, and skewness- and kurtosis-calibrated Gaussian-mixture generators, the synthetic stress test examines marginal coverage over all three calibration sizes.The supplied passage introduces the three generators and the coverage comparison, but does not state the complete numerical outcome.
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