Inferring Labor Income Risk and Partial Insurance From Economic Choices

Picture a grocery receipt and a pay stub sitting side by side on a kitchen table. Economists have known for decades that if you watch both of those documents change over time — not just the paycheck, but what someone actually spends — you can infer things about economic life that neither document reveals alone. However, for most of the history of macroeconomics, models of income risk have looked only at the pay stub. Guvenen and Smith decided to examine both. What they found reshapes a foundational assumption inherent in decades of economic modeling. The assumption in question is this: people face large, uninsurable idiosyncratic income risk. This assumption drives predictions about how much households save as a precaution, how inequality evolves within a generation, and how badly people need insurance mechanisms. The problem is that this assumption comes almost entirely from patterns in earnings data, and earnings data cannot tell you whether a given income fluctuation was anticipated by the worker or already absorbed through informal insurance. Raw income volatility conflates genuine unanticipated shocks, predictable differences in lifetime earnings trajectories, and measurement noise. If you cannot separate those three elements, you will overstate how much risk people are actually exposed to. The core insight of Guvenen and Smith's paper is that consumption helps solve this problem. How spending responds to an income innovation reveals how much of that innovation is effectively insured. A shock that consumption fully absorbs has been insured. A shock that consumption mirrors one-for-one has not. And a movement in income that consumption ignores entirely was probably anticipated — it wasn't a shock to the person living through it at all. To exploit this, Guvenen and Smith build a life-cycle consumption-savings model where individuals have constant relative risk aversion utility, face possibly binding borrowing constraints, and receive a realistic pension at retirement. Critically, the model allows individual labor income profiles to differ in their slopes — people sit on genuinely different lifetime earnings trajectories — but each person starts working with only an imperfect sense of which trajectory they're on. They update that belief over time using a Kalman filter, the same Bayesian updating algorithm used in signal processing and navigation. This tracks how new income observations each year sharpen a worker's estimate of their own long-run growth rate. Partial insurance enters the model explicitly as a transfer in the budget constraint, capturing informal mechanisms — family transfers, credit networks, and consumption smoothing outside of formal markets — that absorb part of any income surprise. Because the true structural equations of this model aren't directly estimable, the authors use a technique called indirect inference. They choose an auxiliary model — a reduced-form approximation of the joint dynamics of consumption and income. They estimate it on real data and on data simulated from the structural model, then select structural parameters so the two sets of auxiliary estimates match as closely as possible. One methodological point they emphasize is that using consumption levels, not only consumption changes, in the auxiliary model allows the estimation to separate advance information from partial insurance. Changes alone cannot do it. Levels can. Monte Carlo validation confirms the approach works. The indirect inference estimator delivers little bias and tight standard errors even under realistic complications — frequently binding borrowing constraints, missing observations, and imperfect auxiliary model approximation. That reliability matters because the results the method produces are striking. Start with what people know about themselves. Guvenen and Smith find that individuals enter working life with substantial information about their own income growth rates. Their estimate implies that by age 25, roughly eighty-eight percent of the cross-sectional dispersion in labor income is already predictable by the individual — not by the econometrician, but by the person. This is consistent with work by Cunha and colleagues, who found about sixty percent predictability by age eighteen. The implication is direct: a large fraction of what looks like income risk in population data isn't experienced as risk by the people inside it. If you already know which trajectory you're on, fluctuations around that trajectory don't feel like uncertainty about your future. This connects to a key distinction the paper makes between two models of income dynamics. Under heterogeneous income profiles — calling it HIP — individuals genuinely differ in their underlying long-run growth rates. Under restricted income profiles — calling it RIP — everyone has the same underlying trend and dispersion comes only from transitory or permanent shocks affecting identically situated people. Guvenen and Smith find that the data favor HIP. The standard deviation of individual income growth rates is one point seventy-six percent per year, estimated precisely. That's a meaningful spread: two people with the same starting salary at age twenty-five can expect substantially different earnings by age fifty-five for reasons that have nothing to do with luck and everything to do with who they are. Now layer in the insurance. The paper estimates that roughly half of income surprises — the shocks people didn't anticipate — are smoothed through informal channels before they reach consumption. The partial insurance parameter theta is estimated at zero point four hundred fifty-one. That means about forty-five cents of every unexpected income dollar gets absorbed by something other than the individual's own saving and dissaving. This is consistent with findings from Blundell, Pistaferri, and Preston, whose work on consumption insurance reached a similar ballpark. However, Guvenen and Smith arrive there through a richer framework that simultaneously estimates the income process itself rather than taking it as given. The income shocks that do pass through are moderately persistent — not permanent. The autoregressive persistence parameter rho is zero point seven hundred fifty-six, with a standard error of zero point zero twenty-three, and the innovation standard deviation is twenty-two point seven percent annually. This rules out a unit root, which had been a common modeling choice. Shocks fade. They're real, but they don't last forever. Borrowing constraints add a further wrinkle. The estimated tightness parameter implies individuals can borrow against roughly sixty cents of each dollar of future minimum income, which translates to a maximum debt of about eight percent of average income at age twenty-five. The fraction of households who are actually constrained peaks at seventeen point four percent around age twenty-nine, then falls. That's a meaningful share — but not a majority, and not one that overwhelms the other results. Measurement error also receives explicit attention, because failing to account for it would distort everything else. The transitory measurement error in income has a standard deviation of about fourteen point seven percent annually — larger than the standard deviation of true transitory income shocks, which sits near ten percent annually. Consumption measurement error is even larger, partly reflecting imputation noise in the Panel Study of Income Dynamics data the paper uses. Separating signal from noise is not merely a technicality here. It's load-bearing. The model fit is good where it matters. It reproduces the within-cohort rise in income variance — about a thirty log-point increase from age twenty-five to fifty-five — and closely matches the lifecycle pattern of consumption inequality from the mid-twenties through the mid-forties. Put all of this together and the headline finding comes into focus. The amount of uninsurable lifetime income risk that individuals actually perceive is substantially smaller than what standard incomplete-markets models have assumed. Guvenen and Smith report that the uncertainty a twenty-five-year-old perceives about their income at age fifty-five is about one-third of what Guvenen's earlier twenty-oh-seven work estimated. Three reasons drive that compression: income shocks are less persistent than assumed, individuals know more about their own trajectories than the data suggest, and informal insurance absorbs roughly half of what does arrive unexpectedly. The implications for macroeconomics are direct. Models calibrated on the old assumptions may overstate precautionary saving motives, misread the sources of within-cohort consumption inequality, and overstate the demand for formal insurance mechanisms. Guvenen and Smith are explicit: analysts should revisit calibrations that embed large uninsurable lifetime risk. The methodology they demonstrate — indirect inference using the joint dynamics of consumption and income — is a blueprint for doing exactly that across different institutional settings and populations. The pay stub alone was never enough. What people spend, season after season, year after year, is a record of what they believed about their futures and what they managed to insure against. Reading that record carefully turns out to tell a quieter story about income risk than the one economists had been telling themselves. This lecture was created by ennepō. Go to https://ennepo.ai to Discover, Create and Follow the latest research in your field. Read when you can. Listen when you want to.