Earnings dynamics refers to the stochastic process governing how individual earnings evolve over the life cycle. The central empirical question is how to decompose earnings variation into permanent components (unobserved individual heterogeneity that persists indefinitely) and transitory components (shocks that dissipate over time), and how the shape of the shock distribution affects estimates of earnings mobility, the returns to education, and the sources of racial earnings gaps. The answer has direct implications for understanding poverty persistence, optimal insurance policy, and the long-run consequences of early-career labor market outcomes.
The canonical decomposition (Lillard and Willis 1978; MaCurdy 1982) models log earnings as the sum of a time-invariant individual effect plus an autoregressive transitory component. Geweke and Keane (2000) extend this to a nonstationary life-cycle model on Panel Study of Income Dynamics (PSID) data (male household heads, 1968–1989):
Key estimated parameters (full sample, mixture model): lagged earnings ; transitory shock autocorrelation ; individual heterogeneity .
In any given year, approximately – of unexplained log earnings variance is due to transitory shocks. Over a lifetime, transitory shocks average out; approximately of unexplained lifetime earnings variance is attributable to permanent individual characteristics () uncorrelated with race, education, or age. This permanent dominance at the lifetime horizon is why low earnings early in the career strongly predict low lifetime earnings.
Lillard and Willis noted that log earnings distributions are leptokurtic and left-skewed, but did not model this. Geweke and Keane parameterize each shock as a mixture of three normal distributions (seven free parameters: three means, three variances, three mixture probabilities). The resulting distributions are strongly leptokurtic and left-skewed — a large fat left tail (big earnings losses) combined with a mode to the right of zero (most years are slightly above average). This structure substantially improves the fit to observed earnings quintile transition probabilities.
The normal model's failure is specific: it overstates short-run persistence of poverty. This occurs because, under normality, the only way to generate observed fat-tail poverty sequences is to increase overall shock variance — which also inflates the predicted frequency of consecutive non-poverty years to levels that are too low. The mixture of normals sidesteps this by treating the left tail as a distinct distributional component.
For young black men, Geweke and Keane report:
| Sequence | Actual | Mixture | Normal |
|---|---|---|---|
−−− (poverty 3 yrs) |
|||
+++ (non-poverty 3 yrs) |
The mixture model achieves near-exact fit for all eight sequences for whites and for young black men; it performs somewhat less well for the full (ages 25–65) sample, particularly at age 45, where the constant shock-variance assumption may bind.
The shock distribution assumption materially changes structural estimates:
Education premium (full sample):
Racial earnings gap (ceteris paribus):
The mixture model implies more of the cross-sectional black-white earnings gap is mediated through education attainment differences, and less is a direct race effect.
Quintile position at age 30 is strongly predictive of future lifetime earnings even conditioning on race and education:
The normal model also predicts strong persistence but of a different character: more spells of shorter duration ( expected spells, years mean length) vs. mixture model's fewer but longer spells ( expected spells, years mean length) for low-education whites.
The model is explicitly nonstationary: the first-period earnings equation differs from subsequent periods, covariates include cubic age polynomials, and shock variances differ between the initial and subsequent periods. Earnings variance is highest at age 25, drops rapidly to a stable level by age 30, and remains constant thereafter. The fraction of variance due to permanent heterogeneity rises from roughly one-quarter at age 25 (before the career has revealed much) to approximately one-third by age 30 and beyond.
The model is estimated by Bayesian inference using a Gibbs sampling algorithm. Because the first-period model differs from subsequent periods and the life-cycle process is nonstationary, the distribution of the first observation for men who enter the sample after age 25 is intractably complex. Geweke and Keane address this via data augmentation: treating unobserved earnings and marital status before the first observed period as latent variables, then drawing them jointly with the model parameters in the Gibbs algorithm. This allows the full sample of men to be used (vs. the men observed at age 25), tripling the sample at the cost of 332 seconds per Gibbs iteration (on 1999 hardware).
The prior on the mixture components is weakly informative: mixture component means centered at (, 0, 0.1), with the second mean fixed at zero as a normalization; probability vector assigned a multivariate beta prior. The data dominate in determining the posterior cumulative distribution function (c.d.f.) of the shocks, while the prior matters more for the individual components of the mixture.
If the normal model is used, low-earnings spells appear more frequent and shorter-duration than they actually are. The mixture model reveals fewer but longer-duration poverty spells — implying that anti-poverty interventions need to target structural long-term low earners, not just transient shock victims. The distinction between a -year average spell and a -year spell compounds substantially over a 40-year career.
The substantially larger education premium under the mixture model ( vs. of mean PV lifetime earnings for college vs. HS) implies higher social returns to educational investment than the normal model suggests.
The smaller racial earnings gap in the mixture model ( vs. ) shifts the policy focus from addressing wage discrimination per se toward addressing differential access to education and the skill formation process.
The finding that early career earnings strongly predict lifetime earnings, conditioning on all observable characteristics, is a within-lifetime analogue of the intergenerational mobility finding (Chetty et al. 2014) that income rank at birth predicts adult outcomes. Both findings point to the importance of permanent heterogeneity — unobserved characteristics that are fixed early and persistent — as a primary driver of inequality. See Intergenerational Income Mobility.