D91 | Macro Paper Warehouse

A Cognitive Theory of Reasoning and Choice

Mon, 01 Jan 0001 00:00:00 +0000

Bordalo, Gennaioli, Lanzani, and Shleifer develop a cognitive theory of choice in which a decision maker’s attention to the features of options is determined by her categorization of the current problem against a memory database of problems she solved in the past. The core claim is that before solving a problem, the decision maker asks “what kind of problem is this?” and resolves it by selecting the category — indexed by a prototype attention-plus-context vector and a time-discounted frequency — whose similarity to the current problem is maximized. This problem recognition step then pins down which features (price, quality, probabilities) receive attention, which in turn shapes valuation and choice.

The model formalizes two-step choice. In step one (recognition), the decision maker jointly chooses an attention vector alpha_P and a category c* to maximize a separable similarity function S[(alpha_P, kappa_P), (alpha_c, kappa_c)] weighted by category frequency F_c, plus a Type I extreme-value shock that yields a logit probability over categories. In step two, she maximizes perceived value over the menu using the endogenously determined weights. Perceived hedonic value of feature i shrinks toward the menu average when alpha_{P,i} < 1; perceived probabilities compress toward uniform when the event-attention weight falls below 1, producing probability overweighting of unlikely events. Full attention recovers expected utility.

The model yields three structural predictions that hold without changing tastes or information. First, within-person multi-modal attention: because categorization is stochastic, the same person can cluster on entirely different features (e.g., the base rate vs. the likelihood in an inference problem) across otherwise identical choice occasions. Second, systematic context-driven instability: when an irrelevant context feature kappa_{P,i} drifts away from a category’s diagnostic kappa_{c,i}, the probability of that category falls discontinuously, causing a discrete switch in the attention profile and hence in valuation. Third, experience-driven heterogeneity: people more frequently exposed to a category (higher F_c) are more likely to use it, producing persistent differences in price elasticities or probability weighting at constant income and tastes.

Applied to riskless consumer choice, the paper introduces two categories — “buying” (full attention to price, partial to quality: alpha_{M_g}=1 > alpha_{Q_g}=alpha) and “consuming” (full attention to quality, partial to price: alpha_{Q_g}=1 > alpha_{M_g}=alpha). A jam problem categorized as buying yields valuation v = alphaq - etap; categorized as consuming, v = q - alphaetap. The valuation jumps discontinuously as context crosses a threshold kappa*, which shifts when relative category frequency F_{buy}/F_{con} changes. This framework accounts for context-dependent price elasticities (Wakefield and Inman 2003), poverty-driven excess price focus (Shah et al. 2018), de-commoditization through advertising, and mental accounting anomalies including opportunity cost neglect and the sunk cost fallacy — both arising because con neglects capital gains (alpha_{con,Delta_M}=0) and buy neglects quality shocks (alpha_{buy,Delta_Q}=0).

Applied to statistical judgment, the paper introduces two categories — “frequency estimation” (attention alpha_1=1 to a single i.i.d. draw from a known DGP) and “agnostic inference” (attention alpha_S=1 to the share of heads as a sufficient statistic). The threshold N* separates recognition: for sequence length N_P < N*(F_{freq}/F_{inf}), the decision maker categorizes as frequency and correctly assesses odds; for N_P >= N*, she switches to inference and overweights balanced sequences, producing the Gambler’s Fallacy. The same competition between categories also accounts for base rate neglect, conjunction fallacy, and correlation neglect, with the bias strengthening as sequences grow longer.

Applied to risky choice, bottom-up salience — sensory prominence and contrast — interacts with categorization. A publicity shock drawing attention to a low-probability contamination risk raises similarity to “consuming,” triggering a category switch that amplifies attention to quality broadly and reduces attention to price, producing large valuation drops disproportionate to the actual probability shift. This mechanism generates the framing effects of prospect theory without a stable S-shaped utility function: gains and losses frames correspond to different contexts activating different categories.

Scope conditions: the theory applies when features and their values are fully known to the decision maker (no uncertainty about attributes), so the distortions take the form of altered sensitivity to known features rather than missing information. The set of categories C is taken as given in the formal analysis, though the authors discuss endogenization as future work.

Q: What is the paper’s central departure from standard rational inattention and noisy-perception models?

A: Standard models (Sims 2003, Woodford 2012, Enke and Graeber 2023) produce unimodal, stably weighted valuations — the decision maker’s weighting of features is a smooth function of payoff-relevant costs or priors. In this paper, the weighting is determined by problem recognition, which is discrete and stochastic, producing within-person multi-modal attention: the same person can cluster on entirely different features across identical problems. The authors cite direct evidence from Bordalo, Conlon, Gennaioli, Kwon, and Shleifer [20] showing bimodal clustering on base rates vs. likelihoods in statistical problems, a pattern inconsistent with stable-weighting models.

Q: How is perceived value distorted when the attention weight on a hedonic feature is below 1?

A: The perceived value of hedonic feature i is u_i(alpha_P) = alpha_{P,i} * u_i + (1 - alpha_{P,i}) * u_bar_i, where u_bar_i is the average value of that feature across options in the menu. An attention weight of zero collapses perceived variation in that feature to zero; full attention recovers the true value. The implication is that under-attention shrinks the decision maker’s effective sensitivity to a known attribute, causing systematic under- or over-valuation relative to a rational benchmark while tastes (marginal utilities) are held fixed.

Q: How is perceived probability distorted?

A: With attention weight alpha_{P,W} on event W, the perceived probability of event e is P(e)^{alpha_{P,W}} / sum_{e’} P(e’)^{alpha_{P,W}}, which compresses the distribution toward uniform as alpha_{P,W} falls toward 0 and recovers the true distribution at alpha_{P,W}=1. In the jam example, under-attention to the small probability of spoilage causes the decision maker to overestimate the risk of contamination. For multi-dimensional event vectors the formula generalizes multiplicatively, allowing “editing out” of entire event dimensions (e.g., urn selection in a balls-and-urns problem) when their attention weight hits zero.

Q: What is the mechanism for context-dependent price elasticity?

A: When context kappa_P is below threshold kappa*(F_{buy}/F_{con}), the decision maker categorizes the problem as “buying” and her valuation is v = alphaq - etap, giving a high price sensitivity (coefficient eta) and attenuated quality sensitivity (coefficient alpha < 1). Above kappa*, she categorizes as “consuming” and valuation is v = q - alphaetap, reversing the emphasis. Because the threshold kappa* is increasing in relative frequency F_{buy}/F_{con}, a decision maker with more buying experience has a higher threshold and thus acts as more price-elastic at any given context level. These elasticity differences arise without any change in the true marginal utility of money eta or quality q.

Q: How does the model generate the sunk cost fallacy and opportunity cost neglect as a unified phenomenon?

A: Both anomalies arise because buying and consuming categories selectively neglect shocks. In the football example, recognizing the problem as “buying” activates alpha_{buy,Delta_Q}=0, so the blizzard quality shock Delta_q<0 is ignored and the decision maker drives to the game as if the shock did not occur — the sunk cost fallacy. In the wine example, recognizing the problem as “consuming” activates alpha_{con,Delta_M}=0, so the capital gain Delta_p is ignored and the decision maker reports a zero or purchase-price cost — opportunity cost neglect. The unifying mechanism is that each category attends only to the features diagnostic of its prototypical experiences: buying attends to price paid and normal quality; consuming attends to realized quality and partly to price, but not to capital gains.

Q: What comparative static does the model predict for sunk cost susceptibility based on experience?

A: People with higher F_{buy} (more buying experiences, e.g. poverty experiences or having recently purchased but not yet consumed the good) exhibit more sunk cost fallacy and less opportunity cost neglect. Conversely, season ticket holders face many consuming experiences relative to one buying event, raising F_{con} and thus reducing susceptibility to the sunk cost fallacy for sports events. Making the blizzard more salient in the description shifts similarity toward “consuming,” also reducing the sunk cost fallacy through a different channel (bottom-up salience rather than experience).

Q: What is the paper’s explanation for the Gambler’s Fallacy, and what distinguishes it from prior accounts?

A: The Gambler’s Fallacy arises when sequence length N_P exceeds threshold N*(F_{freq}/F_{inf}), causing the decision maker to switch from the frequency category (which attends to the 50:50 fairness of the coin) to the inference category (which attends to the share of heads). Under inference, the decision maker treats balanced and unbalanced sequences as representatives of their “share of heads equivalence class,” and the class of balanced sequences is larger, so balanced sequences receive higher estimated probability — the Gambler’s Fallacy. This differs from Rabin and Vayanos (2010), where the bias stems from a belief that the coin is drawn from a pool; here the decision maker knows the coin is fair (kappa_{P,U}=0.5) but the inference representation causes question substitution rather than a wrong model of the DGP.

Q: How does the model make the Gambler’s Fallacy testable beyond length effects?

A: The model predicts the bias is stronger for decision makers who recently solved many inference problems (lower F_{freq}/F_{inf}), and weaker when the 50:50 nature of flips is made bottom-up salient in the choice context (because salience raises similarity to the frequency category, hindering recognition of inference). These cognitive proxies — experience frequencies and bottom-up salience — are orthogonal to the statistical content of the problem and thus allow identification of the mechanism separately from changes in information or incentives.

Q: How does the model produce framing effects in risky choice without a stable S-shaped utility function?

A: Gains and losses frames are modeled as different context vectors kappa_P that differentially increase similarity to a “safe outcome” category or a “risk” category. Recognizing the problem as the safe-outcome category shifts attention toward the certain option; recognizing it as the risk category shifts attention toward variance. The reversal of preferences between gain and loss frames (the Asian Disease problem, Tversky and Kahneman 1981) thus emerges from context-driven re-categorization rather than from a fixed probability weighting function. The novel prediction is that framing effects should be stronger for decision makers with more experience with the category activated by each frame, and weaker when bottom-up salience of the alternative frame’s features is raised.

Q: How does bottom-up salience interact with top-down categorization in the contamination example?

A: A publicity shock alpha_{delta,Q_b}>0 raises baseline attention to the spoiled-jam quality feature, increasing the similarity of the current problem to the “consuming” category (where quality is focal). This triggers a category switch for marginal agents, activating the full consuming attention profile — which attends to quality broadly, not just to contamination specifically, and reduces attention to price. The resulting valuation drop is therefore disproportionate to the actual probability of contamination and exhibits price insensitivity, because re-categorization shifts the entire attention profile rather than just updating a single probability.

Q: How does the model relate to and distinguish itself from case-based decision theory (Gilboa and Schmeidler 1995) and analogical reasoning (Mullainathan 2002, Fryer and Jackson 2008)?

A: In Gilboa-Schmeidler and related models, the decision maker uses past cases to resolve uncertainty about unknown attributes of current options; attention is full and the mechanism is extrapolation of payoffs from similar cases. In Mullainathan (2002) memory-based model, categories again serve to fill in missing information. In this paper, there is no uncertainty about attributes — features and their values are fully known — and the distortion instead takes the form of altered sensitivity to known features through selective attention. This allows the model to produce biases even in simple problems with full data disclosure, and to explain phenomena like base rate neglect and price insensitivity that are not primarily about missing information.

Q: What does the model predict about within-person versus across-person distributions of valuations?

A: Within a person, attention is multi-modal (bimodal in the two-category case) because categorization is stochastic. However, if many categories are possible across the population, the aggregate distribution of valuations can appear approximately unimodal even though each individual’s distribution is not. This distinction is empirically important: a researcher observing average choices may incorrectly infer smooth preference heterogeneity when the underlying mechanism is discrete category switching.

Q: What cognitive proxies does the model propose for empirical identification?

A: The theory links endogenous attention and choice to three observable (or measurable) proxies: (1) past experience frequencies F_c, measurable from administrative histories, surveys about past exposure, or experimental manipulation of training; (2) contextual similarity, measurable from field or experimental variation in irrelevant context features; and (3) bottom-up salience, experimentally controllable via prominence or contrast manipulations. The key identification logic is that these proxies are payoff-irrelevant — they do not change tastes, information, or the objective choice problem — yet predict systematic shifts in choice through their effect on recognition.

Problem Recognition: The first step in the decision maker’s choice process, in which she jointly selects an attention vector alpha_P and a category c* by maximizing weighted similarity between the current problem (characterized by its context vector kappa_P) and the prototype of a past category (alpha_c, kappa_c), multiplied by the category’s time-discounted frequency F_c. Recognition is not about resolving uncertainty over attributes but about selecting which known attributes to attend to.

Category: A partition element of the decision maker’s memory database, indexed by a prototype attention-plus-context vector (alpha_c, kappa_c) and a frequency scalar F_c. The prototype encodes both the context features diagnostic of experiences in that category (binary alpha_{c,i} for i in Phi_K) and the attention to hedonic and event features (alpha_{c,i} for i in Phi_H union Phi_E) used when solving problems in that category. Examples in the paper: “buying” and “consuming” for riskless choice; “frequency estimation” and “agnostic inference” for statistical judgment.

Attention Weight (alpha_{P,i}): A scalar in [0,1] assigned to feature i of the current problem P. For hedonic features, alpha_{P,i}<1 collapses perceived variation toward the menu average; for event features, alpha_{P,i}<1 compresses perceived probabilities toward uniform. Full attention alpha_{P,i}=1 recovers expected utility. Attention weights are the endogenous output of the recognition step, not fixed preference parameters.

Contextual Similarity S: A separable function measuring how close the current problem (alpha_P, kappa_P) is to a category prototype (alpha_c, kappa_c). It decreases in discrepancies in the attention vector (measured by a strictly increasing, convex function d) and in discrepancies in the values of context features diagnostic of the category (d_i(kappa_{P,i}, kappa_{c,i}) * alpha_{c,i}). Endogenous attention to context is set to reduce sensitivity to discrepancies, not to eliminate them.

Mental Accounting (as categorization): In the paper’s account, non-fungibility, sunk cost fallacy, and opportunity cost neglect all arise because buying and consuming categories selectively attend to different monetary and quality features. The sunk cost effect is alpha_{buy,Delta_Q}=0; opportunity cost neglect is alpha_{con,Delta_M}=0. Mental accounts are not separate budget constraints but the by-product of category-specific attention profiles that were calibrated to normal-state experiences and do not generalize to shocks.

Bottom-up Salience: Exogenous attention to a feature driven by sensory prominence (described by alpha_{delta,i} in the problem’s presentation vector) or payoff contrast (the DM attends more to features where her option’s value deviates more from the menu average relative to total menu variance). Bottom-up salience raises baseline attention to a feature before top-down categorization acts, and can trigger a category switch by raising similarity to the category for which that feature is focal.

Gambler’s Fallacy via Question Substitution: In the model, the Gambler’s Fallacy arises when a long sequence length kappa_{P,N} causes recognition of the “agnostic inference” category, which focuses attention on the share of heads alpha_S=1. The decision maker then treats sequences as representatives of a “share of heads equivalence class,” and since the balanced class is larger than the unbalanced class, balanced sequences are assigned higher estimated probability. This is not a belief that the coin is unfair; it is question substitution induced by the inference representation.

Growth Experiences and Trust in Government

Mon, 01 Jan 0001 00:00:00 +0000

This paper investigates whether individuals who have experienced stronger GDP growth over their lifetimes are more likely to trust their national government. The authors — Besley, Dann, and Dray — assemble a newly harmonized global dataset comprising approximately 3.3 million respondents across 166 countries since 1990, drawn from 11 major opinion surveys (Afrobarometer, Americasbarometer, Arabarometer, Asiabarometer, European Social Survey, Gallup World Poll, Integrated Values Survey, Latinobarometer, Life in Transition Survey, South Asia Barometer, and World Justice Project). They supplement this with longer-run U.S. evidence from the American National Election Studies (ANES) going back to 1958, covering respondents born as early as the 1880s, and longitudinal Swiss evidence from the Swiss Household Panel (SHP) which allows individual fixed-effects estimation.

The core methodological contribution is the exploitation of country-cohort variation in lifetime GDP growth experiences. Following Malmendier and Nagel (2011), the authors construct a weighted average of past growth realizations across an individual’s lifetime, with weights decaying linearly over time (lambda = 1), so that more recent growth receives greater weight. The baseline specification includes country fixed effects, cohort-by-subcontinent fixed effects, survey-by-survey-year fixed effects, controls for log GDP per capita at year of birth, and individual characteristics (sex, marital status, education, religious denomination). More demanding specifications add country-by-survey-year and country-by-age fixed effects. For Switzerland, individual fixed effects are included, fully absorbing time-invariant personal characteristics.

The main finding is that a one standard deviation increase in lifetime GDP growth experience — corresponding to approximately 2 percentage points of additional growth — is associated with a 2.1 percentage point increase in the probability of trusting the national government, significant at the 1 percent level. This corresponds to roughly 0.042 standard deviations of the trust outcome and approximately 5 percent of the global mean trust in government. The effect is quantitatively meaningful: it approximates between one-quarter and one-half of the difference in average trust between older and younger cohorts in India and Italy, respectively. For the U.S. ANES sample, a one standard deviation increase in growth experience (about 0.2 percentage points) increases trust in the federal government by 2.4 percentage points, explaining more than two-thirds of the average trust gap between Baby Boomers (born 1946–1964) and Millennials (born 1981–1996).

Several scope conditions and heterogeneity findings sharpen the interpretation. First, the growth-trust link is specific to government institutions: there is no statistically significant effect of growth experience on interpersonal trust or trust in religious organizations, indicating the channel runs through perceptions of state performance rather than generalized social capital. Second, a recency heuristic operates: the linearly decaying weighting function (lambda = 1) outperforms both an unweighted lifetime average (lambda = 0) and a formative-years weighting. Growth experienced during formative years (ages 18–25) or before birth has no detectable effect on trust in government; the pre-birth result serves as a placebo test. Third, the positive growth-trust relationship is stronger in democracies than in autocracies, which the authors interpret as democracies producing citizens more responsive to government performance signals. Fourth, a “trust paradox” emerges: unconditionally, average trust in government is lower in democracies than in autocracies, and longer democratic experience is associated with lower trust, which the authors attribute to democratic institutions generating greater citizen skepticism about government performance. Fifth, core results are robust to controlling for other lifetime politico-economic experiences including inflation, banking and currency crises, epidemics, political unrest, executive turnover, stock market returns, and income inequality. The Swiss evidence further shows that private income growth experience does not drive the result — only aggregate macroeconomic growth does.

Q: What is the paper’s core quantitative finding on the growth-trust relationship? A: Using the global harmonized dataset of 3.3 million respondents across 166 countries, a one standard deviation increase in lifetime GDP growth experience (corresponding to approximately 2 percentage points of additional growth) is associated with a 2.1 percentage point increase in the probability of trusting the national government, significant at the 1 percent level. Using only the Gallup World Poll subsample (roughly half the observations), the estimated effect is somewhat larger at 3.6 percentage points per standard deviation increase. These estimates remain statistically significant under more demanding specifications with country-by-survey-year and country-by-age fixed effects, though the magnitudes decrease as these interacted fixed effects absorb variation in recent growth experiences.

Q: How do the authors measure individual lifetime growth experience? A: The growth experience variable is a weighted average of all past annual GDP per capita growth rates since an individual’s birth, with weights that decay linearly over time (lambda = 1 in the Malmendier-Nagel framework). Under this parameterization, the measure simplifies to how much recent economic performance (in the year prior to the survey) exceeds the long-run mean over the respondent’s lifetime, scaled by the respondent’s midpoint of life. This implies younger individuals are more sensitive to recent growth outcomes because their shorter life histories give recent events relatively greater weight. The authors validate this lambda = 1 choice via a grid search over alternative weighting structures using minimum residual sum of squares as the criterion.

Q: How is reverse causality addressed? A: The empirical strategy identifies the relationship using past, cumulative growth experiences measured prior to the survey, so current trust in government cannot cause past growth. Survey-year fixed effects absorb all aggregate time trends simultaneously affecting trust and growth. The authors also conduct a placebo test showing that GDP growth occurring before an individual’s birth has a precisely estimated null effect on their trust in government, which would not be the case if unobserved societal trends were jointly driving both growth histories and political perceptions.

Q: Does growth experience affect interpersonal trust or trust in non-state institutions? A: No. The estimated coefficient on lifetime growth experience is statistically insignificant at conventional levels when interpersonal trust replaces trust in government as the dependent variable, with narrow confidence intervals indicating a precisely estimated null. Similarly, growth experience has no systematic effect on trust in religious organizations such as churches or mosques. The authors interpret these null results as evidence against the alternative explanation that broad modernizing social changes are jointly driving both growth experiences and political trust.

Q: What do the U.S. ANES results add? A: The ANES data, which extends back to 1958 and captures cohorts born as early as the 1880s, provide a within-country test controlling for state fixed effects, generation dummies, and rich individual characteristics including partisan affiliation and partisan strength. A one standard deviation increase in U.S. growth experience (approximately 0.2 percentage points) raises trust in the federal government by 2.4 percentage points, significant at the 1 percent level. This estimate is quantitatively large enough to explain more than two-thirds of the average trust gap between Baby Boomers and Millennials. Results are robust to adding state-by-survey-year fixed effects and birth-state-by-generation fixed effects, and hold for a broader “trust in government index” covering beliefs about waste, corruption, and responsiveness of the federal government.

Q: What do the Swiss Household Panel results contribute? A: The SHP allows individual fixed-effects estimation, exploiting within-person changes in growth experience and trust over time from 1999 onward, which absorbs all time-invariant individual characteristics that could confound the global and U.S. cross-cohort results. The growth experience coefficient remains positive and significant, with a one standard deviation increase yielding a 1.9 percentage point increase in trust in the Swiss federal government (significant at the 1 percent level). The Swiss data also uniquely allow the authors to test whether personal income growth experience drives the result; they find no significant effect of private income growth experience on trust in government, only aggregate macroeconomic growth matters.

Q: Does the recency heuristic hold — does growth in formative years matter? A: No. The authors find no detectable effect of growth experienced specifically during formative years (ages 18–25) on trust in government. Additionally, in a grid-search exercise assessing model fit across different lambda values, the linearly decaying weighting scheme (lambda = 1, giving more weight to recent growth) outperforms both equal-weighted lifetime averages (lambda = 0) and weighting schemes that emphasize earlier life experiences (lambda less than 0). The pre-birth placebo result (null effect) and the absence of a formative-years effect together indicate that the operative mechanism is about evaluating current government performance based on recent macroeconomic experience, not the imprinting of long-lasting political dispositions during youth.

Q: What is the “trust paradox” and how is it documented? A: The trust paradox refers to the empirical finding that average trust in government is lower in democracies than in autocracies at the cross-country level, and that longer experience with democratic institutions within countries is associated with lower levels of trust in government in the micro data. This is counterintuitive given the standard view that good institutions should foster confidence in government. The authors suggest the paradox likely reflects democracies cultivating greater citizen skepticism and more critical judgment of government performance, rather than indicating that democratic governance actually performs worse. Importantly, the positive effect of growth experience on trust remains present in democracies, and the growth-trust relationship is actually stronger in democratic regimes, consistent with citizens in democracies being more responsive to government performance signals.

Q: How is the growth-trust finding related to corruption perceptions and living standards? A: Using the Gallup World Poll, the authors find that stronger lifetime growth experience is associated with lower perceived corruption in government, greater satisfaction with personal living standards, and higher likelihood of feeling one lives comfortably on one’s present income. These results are consistent with citizens attributing economic success to government competence and integrity, and with growth translating into perceptions of improved personal circumstances through both direct income effects and indirect public goods provision.

Q: Are the results robust to controlling for other lifetime politico-economic experiences? A: Yes. When the authors include lifetime experience measures for political unrest, executive turnover, epidemic exposure, banking crises, currency crises, and inflation (both levels and volatility) simultaneously in equation (3), the growth experience coefficient remains consistently positive, stable, and significant across all specifications. Among the other experience variables, only lifetime unrest and epidemic exposure are independently negative and statistically significant at conventional levels. F-tests reject the null hypothesis that the crisis and growth experience coefficients are equal in magnitude. The U.S. results are also robust to adding lifetime experiences with S&P 500 returns, unemployment, and top-income-share inequality measures.

Q: What are the policy implications of the findings? A: The authors note that sustained economic growth may itself be a mechanism for building political trust, with positive downstream effects for policy compliance — a connection they document has been relevant during the COVID-19 pandemic (where higher-trust societies showed lower mobility during lockdowns and higher vaccine acceptance). The growth-trust channel could have implications for increasing compliance across a range of policy domains including climate action and tax morale. Governments that deliver sustained economic growth can expect citizens to update their trust upward, particularly in democracies where citizens are more performance-responsive, while governments that preside over stagnation or contraction face predictable erosion of political legitimacy across cohorts.

Growth experience: A weighted average of all past annual GDP per capita growth realizations since an individual’s birth, with weights that decay linearly over time following Malmendier and Nagel (2011), so that more recent growth receives greater weight. Under the paper’s preferred parameterization (lambda = 1), the measure equals how much last year’s GDP per capita exceeds the respondent’s lifetime mean, scaled by the respondent’s midpoint of life.

Trust in government: A binary dummy variable equal to one if a survey respondent expresses “a great deal” or “quite a lot” of trust or confidence in the national government, constructed from harmonized responses across 11 major opinion surveys. The paper treats this as reflecting respondents’ perceptions of government performance rather than a deep interpersonal trust relationship.

Trust paradox: The empirical regularity documented in the paper whereby average trust in government is unconditionally lower in democracies than in autocracies at the cross-country level, and whereby longer democratic experience within countries is associated with lower individual trust in government. The authors attribute this to democratic institutions generating more critical citizen judgment of government performance.

Recency heuristic: The finding that more recent growth experiences carry greater weight in forming trust in government, as captured by the linear decay weighting scheme (lambda = 1) outperforming equal-weighted or early-life-weighted alternatives. Growth before birth and growth during formative years (ages 18–25) have no detectable effect, while recent macroeconomic performance is the operative signal.

Cohort-level variation: The within-country differences in lifetime growth experiences across birth cohorts that form the paper’s primary identification strategy. Because different cohorts in the same country have lived through different sequences of growth episodes, differences in trust across cohorts within a country can be attributed to differential growth exposure rather than time-invariant country characteristics.

Formative years effect: The hypothesis, tested and rejected in the paper, that economic experiences during ages 18–25 have a lasting imprint on political attitudes analogous to formative-years effects found in other political behavior literatures. The paper finds no statistically significant association between growth experienced during these years and trust in government.

Source text origin: In the pipeline context relevant to this paper’s acquisition, this refers to whether a summary was generated from full working paper text (“pdf” or “oa-html”) versus abstract only (which is hard-blocked). The working paper was obtained from LSE Research Online (eprint 129614), classified as published version under CC BY 4.0.

Health Shocks, Health Insurance, Human Capital, and the Dynamics of Earnings and Health

Mon, 01 Jan 0001 00:00:00 +0000

Capatina and Keane build and calibrate a life-cycle model of labor supply and savings for U.S. men that incorporates health shocks, endogenous human capital accumulation via learning-by-doing, employer-sponsored health insurance (ESHI), means-tested social insurance, and endogenous medical treatment decisions. The model is calibrated to White males using the Medical Expenditure Panel Survey (MEPS) for 2000–2013, supplemented by CPS, HRS, and PSID data; separate calibrations are presented for Black and Hispanic men with high school or less education.

The paper’s central research question is how health shocks affect labor supply, earnings, and earnings inequality over the life cycle, and through which mechanisms. Four channels are identified and quantified: (1) the direct labor supply effect — sick days and reduced tastes for work caused by health shocks; (2) the human capital effect — reduced work experience from health-shock-induced employment exits, which deteriorates future job and wage offers in a snowball dynamic; (3) the health-productivity effect — reduced functional health directly lowering wage offers; and (4) the behavioral effect — anticipation of health risk induces low-skill workers lacking ESHI to curtail labor supply to maintain means-tested transfer eligibility.

The key quantitative findings from eliminating serious health shocks for working-age men (ages 25–64) are: the expected present value of lifetime earnings (PVE) for White men rises by 11% on average, and inequality in PVE falls by 12% (coefficient of variation). For White men with high school or less education the increase in PVE is 17.9%. For the typical White male the four channels contribute 5.7%, 2.7%, 1.4%, and 0.8% respectively. For low-skill White high school men the same channels contribute 10.7%, 14.8%, 1.3%, and 9.8% — with the human capital and behavioral effects dramatically larger for the low-skill group. For comparison, a severe health shock at age 40 reduces the present value of remaining lifetime earnings by 5.6% (approximately $53.9k) for a typical college man and by 11.5% (approximately $55.0k) for a typical high school man.

Human capital amplification operates through employment persistence: a major health shock causes full-time employment to drop by 12 percentage points one year after the shock for the average man, and by 20 percentage points for high school men, with recovery still incomplete eight years later (employment remains 7.8 pp and 10 pp below baseline, respectively). Holding human capital fixed as in the pre-shock baseline causes employment to recover quickly, confirming that persistent wage-offer deterioration is the mechanism.

On health insurance policy, the model evaluates providing public insurance to all workers lacking ESHI. This substantially increases medical utilization, improves health and life expectancy (survival to age 65 rises from 82% to 87% when health shocks are eliminated, as a related benchmark), reduces Medicaid and free-care costs, and raises labor supply among low-skill workers by weakening means-tested transfer incentives. The net program cost in a balanced budget simulation is modest, and all agent types are ex ante better off. By contrast, expanding Medicaid access creates perverse labor supply disincentives — workers reduce labor supply to maintain eligibility — does little to improve health, and makes almost all agents worse off in a balanced budget scenario.

Scope conditions: the primary calibration covers non-institutionalized civilian White males; results for Blacks and Hispanics are presented only for the high school or less education group due to small samples. The model period ends at 2013, before ACA implementation.

Q: What is the model’s overall estimate of how much health shocks reduce lifetime earnings for White men? A: Eliminating serious health shocks at working ages (25–64) would increase the expected present value of lifetime earnings (PVE) for the average White male by 11% and reduce inequality in PVE by 12% as measured by the coefficient of variation. For White men with high school or less education the PVE gain is larger at 17.9%.

Q: What are the four channels through which health shocks affect earnings, and how large is each for the average White male versus a low-skill high school male? A: The four channels are (1) direct labor supply via sick days and reduced tastes for work, (2) human capital deterioration from lost work experience worsening future job/wage offers, (3) reduced health productivity lowering wage offers, and (4) behavioral responses to health risk reducing labor supply to preserve transfer eligibility. For the average White male the contributions to PVE are 5.7%, 2.7%, 1.4%, and 0.8%, respectively. For low-skill White high school men the same channels contribute 10.7%, 14.8%, 1.3%, and 9.8% — the human capital and behavioral effects are roughly five to twelve times larger for the low-skill group.

Q: Why is the human capital effect so much larger for low-skill high school men than for college men? A: Low-skill high school men are much more likely to exit full-time employment following a major health shock and are slow to return. Lifetime work years decline by 1.89 for the typical high school man versus only 0.84 for the typical college man following a major shock at age 40. Because job offer probabilities depend on lagged employment, absence from the labor market creates a snowball effect that persistently depresses offer quality; human capital accounts for 42% of the earnings decline for high school men versus 34% for college men.

Q: How does the paper characterize the persistent employment effects of a major health shock? A: For the average man, full-time employment drops by 12 percentage points one year after a severe shock and remains 7.8 pp below baseline after eight years. For high school men the initial drop is 20 pp, still 10 pp below baseline after eight years; for college men the figures are 7 pp and 3 pp. When human capital is held fixed at the pre-shock baseline — so wage and job offers do not deteriorate due to lost experience — employment recovers quickly for workers of all skill levels, confirming the human capital mechanism drives the persistence.

Q: How does the behavioral effect operate for low-skill workers? A: Workers without ESHI who face health risk have an incentive to maintain sufficiently low income and assets to qualify for means-tested social insurance, which provides a consumption floor approximating Medicaid, Food Stamps, SSDI, and SSI. This perverse incentive leads low-skill workers to curtail labor supply preemptively. When health risk is eliminated, this incentive disappears and labor supply rises, generating the behavioral effect of 9.8% of PVE for low-skill high school men versus only 0.8% for the average White male.

Q: How does the paper correct for under-reporting of health shocks among the uninsured? A: The measurement model assumes health shocks are correctly measured for the treated, but uninsured workers who do not seek treatment only record a shock with a shock-specific probability less than one. A key identifying assumption is that, conditional on health status, risk factors, age, and education, the true frequency of health shocks does not differ by insurance status per se — ruling out ex ante moral hazard. The measurement model parameters are calibrated to match observed frequencies of health shocks and high risk in MEPS for the uninsured.

Q: What does the model estimate regarding the effect of a severe health shock on cumulative earnings relative to existing reduced-form evidence? A: The model predicts an average cumulative (non-discounted) earnings loss of $42.8k over ten years following a severe shock for men aged 50, compared with Smith’s (2004) estimate of $37k from the HRS. The paper argues Smith’s estimate identifies effects on workers who actually experience shocks, who are a selected sample with low baseline earnings (as untreated shocks are more likely to be severe, and non-treaters tend to have low earnings). The model’s “average effect” — comparing a world where everyone experiences the shock to one where no one does — yields a substantially higher loss of $59.8k.

Q: What are the key findings from the public insurance experiment (providing insurance to the uninsured)? A: Providing public insurance to all workers lacking ESHI substantially increases medical utilization among the previously uninsured, who are intrinsically less healthy. This improves health and life expectancy, raising Social Security costs. However, it also generates positive labor supply incentives for low-skill workers (reducing their reliance on means-tested transfers), substantially reduces Medicaid and free-care costs, and increases tax revenue. On balance, the net program cost in a balanced budget simulation is modest, and all types of workers are ex ante better off.

Q: Why does expanding Medicaid access produce perverse results in contrast to providing public insurance? A: Medicaid is means-tested, so expanded access requires workers to maintain sufficiently low income and assets to remain eligible. This creates disincentives to work and save — workers reduce labor supply to preserve eligibility. The result is reduced earnings, lower tax revenue, little improvement in health (as access to care depends on maintaining low income), and almost all agents being worse off in a balanced budget scenario.

Q: What role does insurance play beyond consumption smoothing in this model? A: Beyond lowering out-of-pocket (OOP) costs and smoothing consumption, insurance grants access to care: in the US system, proof of insurance is often required before treatment, so uninsured workers may not have the option to treat at all. The model captures three distinct option sets for the uninsured — all options available, treatment not available, or default not available — each motivated by different real-world contexts. Non-treatment worsens health transition probabilities, so the access-granting role of insurance independently affects health trajectories beyond its cost-reducing role.

Q: What explains the observed positive association between education, income, insurance, and health transitions in the data, and how does the model generate this without education entering the health production function directly? A: The association between education and health is largely driven by the positive correlation between education and latent health types; controlling for latent health type in a descriptive logit largely eliminates the education coefficient. The association between insurance and health transitions is driven by the fact that the insured are more likely to receive treatment; controlling for treatment and true shocks eliminates the insurance coefficient. Education affects health indirectly through its effects on treatment decisions — via wages, job offers with ESHI, and consumption capacity — without appearing as a direct argument in the health production function.

Q: How large are the effects of health shocks on key population health statistics according to the model? A: Eliminating serious health shocks at working ages would increase the fraction of working-age men in good health from 60% to 75% and raise the probability of survival to age 65 from 82% to 87%. Average annual sick days of 16.42 would be eliminated, implying a 6% increase in work days for employed workers and an employment rate increase from 88% to 91%. Average annual medical costs would fall from $4,618 to $1,132.

Q: How do the results for Black and Hispanic men compare to White men? A: The results are qualitatively similar, but the magnitudes for Black men are somewhat larger. Eliminating health shocks would raise PVE for Whites, Blacks, and Hispanics with high school or less education by 17.9%, 23.7%, and 17.7%, respectively. Separate access-to-care probabilities are calibrated for each group, reflecting racial disparities in access that explain part of the observed differences in health outcomes and treatment rates.

Q: What is the role of the consumption floor (means-tested social insurance) in shaping equilibrium outcomes for low-skill workers? A: The consumption floor guarantees a minimum household consumption level approximating Medicaid, Food Stamps, SSDI, and SSI. It shields low-skill workers from the full cost of health shocks, reducing both the consumption-smoothing value of ESHI and precautionary saving incentives. However, it also creates a powerful disincentive for low-skill workers without ESHI to work, as earning above the eligibility threshold would eliminate benefits. This mechanism amplifies earnings inequality by generating perverse labor supply behavior concentrated among low-skill, uninsured workers.

Functional Health (H): A discrete stock variable (Poor, Fair, or Good) measuring aspects of health that directly affect worker productivity and tastes for work; distinguished from asymptomatic health risk. Transitions depend on lagged health, latent health type, age, persistent health shocks, and whether shocks are treated.

Asymptomatic Health Risk (R): A binary state (low or high) capturing risk factors such as obesity, high cholesterol, and hypertension that increase the probability of future health shocks but do not affect current productivity.

Human Capital Effect: The channel by which health shocks reduce lifetime earnings not directly but indirectly — by causing employment exits that slow work experience accumulation, which in turn deteriorates future job offer probabilities and wage offers in a persistent, self-reinforcing (snowball) dynamic.

Behavioral Effect: The reduction in labor supply — and associated earnings loss — that occurs because workers facing health risk and lacking ESHI have an incentive to keep income and assets low enough to maintain eligibility for means-tested social insurance, even absent any contemporaneous health shock.

Tied Wage-Hours-Insurance Offer: The model’s labor market structure in which employment offers jointly specify a wage rate, hours (no offer, part-time, or full-time), and whether the offer includes ESHI; workers accept or reject the bundle rather than choosing hours and insurance independently.

Source Text Origin: The paper’s own term distinguishing how the full text of a paper was obtained (PDF, OA-HTML, or abstract-only); used in the summarization pipeline. [Note: this concept is from the summarization pipeline metadata, not from the paper itself — omitting.]

Treatment/Payment Options: The set of decisions available to a worker after a health shock occurs — whether to seek treatment and, if treated, whether to pay the out-of-pocket cost or default on bills. The available choice set differs by insurance status and context: the uninsured may face denial of access (option to treat unavailable) or required prepayment (default unavailable), or may have all options including free care.

Latent Health Type: An unobserved permanent individual characteristic capturing innate biological resilience and pre-age-25 health investments; determines baseline transition probabilities for functional health conditional on shocks. Positively correlated with latent skill type within education groups.

Identifying Preference for Early Resolution from Asset Prices

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper develops a revealed-preference theory that uses asset-market data to identify whether investors have a preference for early resolution of uncertainty (PER), a property of non-expected utility preferences that is distinct from risk aversion. The central theorem shows that, under a condition called generalized risk sensitivity (GRS), the representative agent prefers early resolution if and only if claims to future stock market volatility earn a positive premium during the period in which the informativeness of upcoming macroeconomic announcements is resolved — a window the authors call the Resolution of Information Quality (ROIQ) period. Using S&P 500 index option data from 1996 to 2019, the paper identifies the ROIQ period as the five weekdays before FOMC announcements, demonstrates that the inverse slope of the implied-volatility term structure (9-day/90-day VIX ratio) significantly predicts the informativeness of upcoming announcements, and finds a statistically significant positive ROIQ premium on synthetic variance claims (beta = 1.085, t = 2.44) and on at-the-money straddles (beta = 0.428, t = 2.25). The evidence supports Epstein-Zin recursive utility with the intertemporal elasticity of substitution exceeding the reciprocal of risk aversion, and hence is consistent with the Bansal-Yaron long-run risk framework. Crucially, this identification requires no parametric calibration of the full asset pricing model.

Summary of a published paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is preference for early resolution (PER) and why is it hard to identify?

PER means that an agent with a given distribution over future outcomes strictly prefers to learn the outcome sooner rather than later, as formalized by Kreps and Porteus (1978); under Epstein-Zin recursive utility, PER is equivalent to risk aversion exceeding the reciprocal of the IES (or IES > 1/risk aversion). In standard applied asset pricing models with constant-elasticity recursive utility, PER is intertwined with risk aversion and the IES, so that the separate role of the timing of resolution is obscured. Existing papers either test joint implications of the full calibrated model (conflating PER with other preference properties) or use thought-experiment willingness-to-pay calculations without market-data grounding. The authors’ goal is to provide a necessary and sufficient condition for PER directly from asset prices, independent of a fully specified model.

Q2. What is the role of Generalized Risk Sensitivity (GRS) in the identification theorem?

GRS — the condition that the certainty-equivalent functional I is increasing in second-order stochastic dominance — provides the bridge between the unobservable ranking of utility levels across states and the observable ranking of marginal utilities (stochastic discount factors) across those states. The authors prove that under GRS (Theorem 1), the vector of partial derivatives of I with respect to continuation utility is strictly negatively comonotone with the level of continuation utility: higher utility states have lower marginal utility. This inversion is what allows asset prices to reveal the ordering of utility levels. GRS itself is empirically supported by the well-documented fact that assets earn positive announcement premia around scheduled macroeconomic releases (Savor and Wilson, 2013).

Q3. How does the main theorem (Theorem 2) identify PER from a single asset class?

Theorem 2 establishes that, under strict GRS, the premium earned by any asset comonotone with the informativeness of upcoming macroeconomic announcements during the ROIQ period is strictly positive if and only if the agent has PER; a negative ROIQ premium would indicate preference for late resolution. The intuition is that if the agent prefers early resolution, she assigns higher continuation utility to the early-resolution state (0E) than to the late-resolution state (0L); under strict GRS, higher continuation utility maps to lower marginal utility, meaning assets paying off more in the early-resolution state are negatively correlated with the SDF and therefore carry a positive risk premium. Claims to stock market return variance serve as the test asset because expected variance is high before informative announcements (early resolution) and low before uninformative ones (late resolution).

Q4. How do the authors operationalize the ROIQ period empirically?

The ROIQ period is identified as the five weekdays before FOMC announcements, during which market attention to the Fed (measured by RavenPack Fed-related news intensity) is significantly positively correlated with the change in the inverse slope of the implied-volatility term structure (coefficient = 1.076, t = 4.09), while no such correlation exists in the ten days 6–10 before or after the announcement. This correlation arises because, during those five days, investors regularly update their expectations about whether the upcoming FOMC statement will be informative; more expected informativeness raises the demand for short-dated options (driving up the 9-day VIX relative to the 90-day VIX) and simultaneously raises Fed-related news coverage. Outside the ROIQ window, the two series are uncorrelated (coefficient = −0.242, t = −1.13 unconditionally), confirming that the window is the correct testing period.

Q5. What is the empirical evidence for a positive ROIQ premium, and how is it constructed?

Synthetic variance claims constructed as option portfolios following Bakshi, Kapadia, and Madan (2003) earn a ROIQ premium (coefficient beta in the panel regression) of 1.085 percentage points per day (t = 2.44) above their average daily return; at-the-money straddles earn 0.428 pp/day (t = 2.25), both significantly positive. The panel regression controls for maturity fixed effects (11 dummies for weeks to expiration), FOMC-day effects, and day-of-week effects. Crucially, the market itself earns approximately 8 basis points lower than average during the ROIQ period, and the market loading on variance claims does not increase during the ROIQ window (Table 5), ruling out an interpretation in which the premium simply reflects a higher market beta at announcement times.

Q6. How does the paper rule out alternative explanations for the ROIQ premium?

A placebo test using VIX futures — which pay the forward-looking VIX level (expected volatility over the next 30 days after expiry) rather than realized variance over the announcement — shows no significant ROIQ premium, confirming that the effect operates specifically through exposure to volatility during the announcement itself rather than through general volatility-level exposure. The paper also shows that controlling for the Fama-French three factors does not appreciably change the ROIQ coefficient. An additional test using individual stock options (5 weekdays before earnings announcements) also yields positive ROIQ premiums, extending the result beyond FOMC to firm-level announcements.

Q7. What does the finding imply for macroeconomic preference modeling and policy?

The empirical finding that investors have a positive ROIQ premium — i.e., PER — without assuming any particular utility functional form confirms the central calibration assumption of Bansal-Yaron long-run risk models (risk aversion > 1/IES) and provides the market-based evidence that Epstein, Farhi, and Strzalecki (2014) stated was unavailable. The paper’s approach is significant for macro modeling because it establishes PER from minimal assumptions (GRS and monotonicity of preferences), meaning that the result holds across expected utility deviations including robust control, smooth ambiguity, and disappointment aversion preferences — as long as they satisfy GRS — making it a broadly applicable empirical anchor for calibrating non-expected utility models.

Q8. What are the identification limitations and scope conditions?

The identification relies on three maintained conditions: (i) GRS holds for the representative agent, (ii) FOMC announcements genuinely resolve macro uncertainty (so that the ROIQ window is correctly specified), and (iii) the pre-announcement period does not contain price-relevant news (so that market return premia during the ROIQ are not confounded with the news content of the announcement itself). The empirical support for condition (iii) comes from the fact that the market does not earn abnormal returns during the ROIQ (negative, not positive, as expected from the announcement drift literature), and from the lack of a ROIQ premium for VIX futures that expire after but not over the announcement. The framework abstracts from heterogeneous agents and assumes a representative-agent economy, which is standard but may not fully capture distributional effects.

Key Concepts

preference for early resolution of uncertainty (PER) : the property of a dynamic preference that the agent strictly prefers to learn the realization of a future uncertain outcome earlier rather than later, holding the distribution unchanged; equivalent in Epstein-Zin recursive utility to risk aversion exceeding the reciprocal of the IES.

generalized risk sensitivity (GRS) : the condition that the certainty-equivalent functional I is strictly increasing in second-order stochastic dominance; equivalent to the existence of strictly positive announcement premia for all assets comonotone with continuation utility; the paper’s key maintained assumption connecting utility levels to asset prices.

resolution of information quality (ROIQ) period : the period during which investors learn whether the upcoming macroeconomic announcement will be informative; empirically identified as the five weekdays before FOMC meetings, during which Fed-related news intensity co-moves with the inverse slope of the VIX term structure.

ROIQ premium : the excess return earned by a claim to market volatility (synthetic variance claim or straddle) during the ROIQ period over its average daily return on non-ROIQ days; the paper’s operational test for PER; estimated at 1.085 percentage points per day for variance claims.

inverse slope of the implied-volatility term structure : the ratio IV9/IV90 (9-day CBOE VIX divided by 90-day CBOE VIX); the paper’s market-based predictor of FOMC announcement informativeness; a higher ratio reflects investor anticipation of large announcement-day volatility relative to long-run baseline uncertainty.

Life-Cycle Wages and Human Capital Investments: Selection and Missing Data

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1 – Overview

Research Question

This paper asks how wage inequalities build up over the life cycle when individual wage trajectories are plagued by interruptions in private-sector participation, and when the standard Missing At Random (MAR) assumption used to handle those gaps may be violated. Specifically, it asks: what is the causal effect of career interruptions on both the level and the dispersion of wages after twenty years of potential experience, and does endogeneity of those interruptions matter for the dispersion result?

Data and Sample

The empirical analysis uses the 2011 DADS Grand Format-EDP panel, a French administrative dataset merging social security records (DADS) and census extracts (EDP). The working sample covers males who entered the private sector between 1985 and 1992, aged 16-30 at entry, and observed through 2011. The authors require at least 15 years of observed private-sector wages, yielding a working sample of 7,004 males and 137,315 person-year observations. Education is grouped into four levels (high-school dropouts, high-school graduates, some college, college graduates). Participation outside the private sector – including public-sector employment, self-employment, unemployment, and non-employment – constitutes the “alternative sector” and generates missing wage observations. On average, cumulative duration outside the private sector is 3.7 years, and the average number of interruptions is 1.44.

Model and Methodology

The paper builds on a structural Ben Porath (1967) human capital model extended to two sectors (private sector and an alternative sector), yielding a reduced-form log-wage equation with five individual-specific coefficients: an intercept (initial human capital), a linear trend in potential experience (growth rate), a curvature term in potential experience (Mincer concavity), the cumulative years of interruptions, and a curvature term in interruptions. Because parameters are individual-specific, the wage equation is a random-coefficient model estimated with a fixed-effects approach.

Selection into the private sector is addressed not by a standard MAR assumption but by a weaker “Missing At Random Conditionally On Factors” (MARCOF) assumption. Sector-preference shocks, human capital prices, and depreciation rates are each decomposed into a common factor (time-varying) and an individual factor loading, plus a residual that is mean-independent of factors and loadings. Conditional on factors and factor loadings, wage residuals and sector choices are independent, making covariates – including the interruption variables – exogenous. The preferred specification includes two unobserved factors, selected by four of six Bai-Ng (2002) information criteria.

Estimation proceeds via an Expectation-Maximization (EM) algorithm adapted from Bai (2009) and Song (2013), with initial values from Moon and Weidner (2018)’s nuclear-norm convex estimator. Because individual parameters converge at rate sqrt(T) and summary statistics of their distributions suffer from incidental-parameter bias, the authors use bias-correction methods from Jochmans and Weidner (2019) for quantiles and inter-decile ranges, and from Arellano and Bonhomme (2012) for variances. Monte Carlo experiments confirm that variances remain poorly corrected even when T > 20, so the paper focuses on inter-decile ranges as the dispersion measure.

Counterfactual “average structural functions” (Blundell and Powell, 2003) are constructed by holding individual parameters fixed and manipulating the history of interruptions. These compare four scenarios: the observed benchmark, the counterfactual with no interruptions (potential wage), the counterfactual with no current-period selection, and both combined.

Main Findings

Downward bias from omitting interruptions and factors. Omitting interruption variables and unobserved factors strongly downward biases estimated returns to experience after 20 years. Most of this bias is attributable to interruptions rather than to the interactive factor effects: selectivity is mainly captured through the interruption channel, not through residual factor structure.
Effect on mean wages. Potential experience increases log wages by approximately 65% over 20 years, consistent with cross-country evidence from homogeneous Mincer equations. The average cost of interruptions after 20 years is approximately 10% of log wages. Reassigning interruptions to the beginning of the working life has a persistent negative effect on mean log wages that never fully recovers over 20 years, while reassigning them to the end increases mean wages above the no-interruption benchmark at every experience level.
Effect on wage dispersion – a new stylized fact. Interruptions decrease, not increase, the inter-decile range of log wages after 20 years. After 20 years, with an average interruption duration of 2.47 years, interruptions decrease the inter-decile range by 0.52 log points (approximately 38%). This compression operates differentially: the 90th percentile falls by 0.34 and the 10th percentile rises by 0.18.
Endogeneity explains the dispersion compression. When years of interruption are randomly reassigned across time (holding total interruption years fixed), the inter-decile range diverges upward from the observed benchmark after about 5 years. This shows that the dispersion-reducing effect of actual interruptions is due to the endogenous timing of those interruptions – specifically to the negative correlation between the timing of interruptions and potential log wages – rather than to the correlation between the structural coefficients on interruptions and potential wages (which is also negative, with a Spearman rank correlation of -0.32 between eta_i1 and eta_i3). Endogenously chosen interruptions smooth inequality over time.
Current-period selection is negligible. Current-period selection into private-sector employment has no statistically significant effect on median, mean, variance, or inter-decile range of wages at any experience level, as confirmed by the small inter-decile range of the interactive factor component.

Scope Conditions

Results pertain to cohorts of French males entering the private sector between 1985 and 1992, restricted to those with at least 15 observed private-sector years. The French context is distinctive: wage inequality in the working population was stable over 1985-2011, driven in part by minimum wage policy and payroll tax exemptions for lower-skilled workers, in contrast to rising inequality in the United States and Germany. Results on timing of interruptions (eta_i3 and eta_i4) are identified only for individuals with at least two interruptions followed by re-entry (roughly those with K_T >= 2). The paper does not analyze female wages.

In depth

Q1. What is the structural model and how does it generate a reduced-form wage equation?

The model is a Ben Porath (1967) two-sector human capital model in which individuals divide time between investing in human capital and earning wages in either the private sector (e) or an alternative sector (n). Human capital accumulation in each sector has a sector-specific return rate (rho^s) and depreciation (lambda^s_t). Period utility is log income minus a quadratic investment cost, plus a sector preference shock. Solving the dynamic program backwards (because of log-linearity) yields closed-form optimal investments that are linear in the individual-specific terminal value of human capital (kappa). The resulting log-wage equation (Proposition 5) is a function of five terms: an intercept (eta_i0), a linear trend in potential experience t (eta_i1), a geometric curvature term beta^{-t} (eta_i2), cumulative years of interruptions x^(3)_it (eta_i3), and a curvature in interruptions x^(4)_it (eta_i4), all with individual-specific coefficients. This provides a tractable random-coefficient structure.

Q2. What is the MARCOF assumption and why is it weaker than MAR?

MARCOF – Missing At Random Conditionally On Factors – posits that sector-preference shocks, human capital prices, and depreciation rates each follow factor structures: a common time-varying factor (phi_t) multiplied by an individual loading (theta_i) plus an i.i.d. residual. The residuals are assumed mean-independent of factors and loadings, and independent over time. Under standard MAR, missingness is assumed independent of outcomes conditional on observables alone. Under MARCOF, residuals in the wage equation and the sector choice equation are independent conditional on (unobserved) factors and factor loadings. This is weaker than MAR because it allows the unobservable determinants of wages and participation to share common factors, accommodating the high persistence observed in human capital stocks (20-year lag correlation of 0.28, far above the geometric decay benchmark of 0.024).

Q3. How are the individual-specific parameters identified?

Under exogenous selection (or, under MARCOF, conditional on factors), identification of eta_i0, eta_i1, and eta_i2 requires variation in potential experience within the individual’s time series. Identification of eta_i3 and eta_i4 separately requires individuals to experience at least two spells out of the private sector each followed by re-entry (at least four transitions, so K_T >= 2). An individual with only one interruption spell generates proportional variation in x^(3) and x^(4), so only a linear combination of eta_i3 and eta_i4 is identified. The “flat spot” approach – using the observed fact that individuals aged 50-55 have stopped investing in human capital – separately identifies time, cohort, and age effects and provides the restriction that factors are orthogonal to the level, trend, and curvature in potential experience.

Q4. What do the distributions of estimated individual-specific coefficients look like?

Focusing on the main (two-factor) specification with bias correction: the median of the growth parameter eta_i1 is positive (consistent with rising wages with experience) and the median of the curvature parameter eta_i2 is negative (consistent with concavity). However, heterogeneity is substantial: the 90th percentile of eta_i1 is 6.2 times the median, and the first quartile of eta_i1 is negative (implying declining potential wages for a non-negligible share). For the interruption coefficients eta_i3 (year of interruptions) and eta_i4 (curvature), bias-corrected medians are close to zero in the sub-sample with >=2 interruptions, but dispersion is large and symmetric around zero. Bias correction reduces the 90th percentile of eta_i1 by approximately 20% and reduces the absolute 10th percentile of eta_i3 by approximately 27%.

Q5. How important are interruptions relative to potential experience and factors in explaining wage variation?

A wage decomposition using inter-decile ranges (preferred over variance due to bias) shows that the potential experience component is the largest contributor to wage dispersion, followed by the interruption component (described as “sizable”), while factors play a minor role. Crucially, the potential experience and interruption components are highly negatively rank-correlated: the Spearman rank correlation between the growth coefficient eta_i1 and the interruption coefficient eta_i3 is -0.32. This negative correlation is central to understanding why interruptions compress dispersion rather than expanding it.

Q6. What is the finding on the effect of interruptions on mean wages, and what does the timing experiment show?

After 20 years, the average cost of interruptions (relative to a counterfactual of no interruptions) is approximately 10% of log wages. The timing of interruptions matters: reassigning interruptions to the beginning of the working life causes a persistent loss in mean log wages that does not fully recover over the 20-year horizon, while reassigning them to the end raises mean log wages above the no-interruption level at every experience level. For median wages, the early-interruption loss is eventually recovered (median log wages do catch up), but the mean does not catch up. These asymmetries are consistent with early interruptions having a larger negative effect on human capital accumulation due to the geometric structure of investment returns.

Q7. What is the key finding on wage dispersion and what explains it?

Interruptions compress the inter-decile range of log wages by 0.52 log points (approximately 38%) after 20 years, with average interruption duration of 2.47 years. This compression is asymmetric: the 90th percentile of wages falls by 0.34 and the 10th percentile rises by 0.18. The dispersion-reducing effect is established by comparing the benchmark (observed interruptions) to the counterfactual of no interruptions. When interruptions are instead randomly reassigned across time (holding total interruption duration fixed), the inter-decile range diverges upward from the benchmark starting around 5 years of experience. This demonstrates that the compression is due to the endogenous timing of interruptions – individuals who have high potential wages tend to time their interruptions in ways that reduce the measured spread of actual wages – rather than to the negative structural coefficient (eta_i3 < 0 for high-wage workers on average).

Q8. How does the paper handle the incidental parameter problem for distributional statistics?

Because individual parameters are estimated at rate sqrt(T) and the panel is unbalanced (some individuals observed for as few as 15 years while the model has up to 7 individual parameters), standard distributional statistics like the variance suffer from substantial incidental parameter bias. Monte Carlo experiments show that bias-corrected variance estimates remain strongly biased even at T > 20. Inter-decile ranges are better behaved and the Jochmans and Weidner (2019) bias-correction procedure reduces their bias satisfactorily. This is why the paper reports inter-decile ranges as its primary dispersion measure rather than variances. The bias in corrected inter-decile ranges is at most approximately 10% of the uncorrected estimate.

Q9. What does the paper show about the MAR assumption in the context of this data?

The results directly challenge the MAR assumption that is standard in the life-cycle earnings literature. Under MAR, interruptions would be treated as random conditional on observables, and their endogeneity would be ignored. The paper shows that treating interruptions as endogenous (through the MARCOF + structural model approach) substantially changes estimated returns to experience (there is a strong downward bias when interruptions and factors are omitted) and reverses the sign of the effect of interruptions on dispersion (under exogenous interruptions, randomly reassigned, dispersion would be higher than observed; the actual compression is an artifact of endogenous timing). The conclusion is that MAR assumptions produce systematically misleading pictures of life-cycle wage inequality dynamics.

Q10. What are the robustness and external validity considerations?

The working sample excludes individuals observed fewer than 15 years. A robustness exercise compares the subsample observed 10-14 years to a censored version of the 20+ subsample with matched marginal distributions of observation counts. Median profiles for the uncensored and censored 20+ samples are similar, and inter-decile ranges are slightly more dispersed in the censored sample only for potential experience greater than 7. However, the 10-14 year sample shows substantially different patterns – larger median gaps between benchmark and no-interruption cases, and a larger inter-decile range – consistent with lower private-sector returns to human capital for that group. The authors conclude that selection into the 15+ working sample matters, and results are explicitly restricted to that working sample. The French context (stable aggregate wage inequality, minimum wage policy) limits direct comparability to countries with rising inequality.

Key Concepts

MARCOF (Missing At Random Conditionally On Factors): The paper’s central identifying assumption, weaker than standard MAR. It posits that sector-preference shocks, human capital prices, and depreciation rates follow factor structures (common time-varying factor x individual loading + i.i.d. residual), and that residuals are mean-independent of factors, loadings, and their own histories. Conditional on factors and loadings, wage residuals and sector-choice residuals are independent, making selection exogenous.

Interactive effects / factor structure for selection: An approach in which unobserved confounders are modeled as a bilinear product of time-varying common factors (phi_t) and individual factor loadings (theta_i). This allows flexible correlation between wage processes and participation choices without requiring exclusion restrictions or instrumental variables. The paper’s preferred specification uses two unobserved factors identified by Bai-Ng information criteria.

Average structural functions: Objects defined by Blundell and Powell (2003) that integrate counterfactual outcomes (wages evaluated at a manipulated interruption history) over the distribution of individual-specific parameters. They allow estimation of the causal impact of a change in interruption timing or presence while holding individual structural parameters fixed, under identification conditions analogous to those of Chernozhukov et al. (2013).

Individual-specific coefficients (random coefficients): The five parameters (eta_i0, eta_i1, eta_i2, eta_i3, eta_i4) governing each individual’s wage equation, with structural interpretations: initial log human capital, return to potential experience, curvature (Mincer concavity), effect of cumulative interruption years, and curvature in interruptions. Their individual-specificity is the source of the incidental parameter problem for distributional statistics.

Flat spot approach: An identification device (from Heckman, Lochner, and Taber, 1998; Bowlus and Robinson, 2012) that uses median wages of workers aged 50-55 – who are assumed to have stopped investing in human capital – as consistent estimates of human capital prices by education group and year. This separates the volume of human capital from its price, and provides the restriction identifying the level, trend, and curvature factors from the time-varying unobserved factors phi_t.

Interruption variables x^(3) and x^(4): Reduced-form variables derived from the structural model summarizing the history of private-sector participation gaps. x^(3)_it is the cumulative number of periods spent in the alternative sector prior to date t; x^(4)_it is a geometric-weighted version of those interruptions that reflects the timing (early vs. late) through the discount factor beta. They enter the wage equation with individual-specific coefficients that are identified only for workers with at least two complete interruption spells.

Mincer dip: A U-shaped profile in wage variance (or inter-decile range) over potential experience, predicted by the Ben Porath model because high-return workers invest more at the start of their careers (reducing current wages), causing their wage profile to cross below then above low-return workers. Estimated in this paper at approximately 5 years of potential experience under the main specification.

Incidental parameter bias in distributional statistics: The bias that arises when estimating moments or quantiles of the distribution of individual-specific parameters that converge at rate sqrt(T) rather than sqrt(N). The paper shows through Monte Carlo experiments that variance estimates remain substantially biased even after Arellano-Bonhomme (2012) correction when T >= 20, while inter-decile ranges corrected by Jochmans-Weidner (2019) are more reliable.

Organizational Change and Reference-Dependent Preferences

Mon, 01 Jan 0001 00:00:00 +0000

Schmidt and von Wangenheim develop a dynamic model of organizational change in which workers have reference-dependent preferences — specifically loss aversion and social comparisons — to explain several empirically observed patterns that standard models cannot easily account for: organizational inertia in normal times, sudden productivity jumps during crises, persistent total factor productivity (TFP) differences across firms in the same industry, and effort and wage compression within firms.

The motivating empirical puzzle is the early-1980s collapse of the Great Lakes iron ore and steel industry, which had been geographically shielded from foreign competition for over 100 years. When Brazilian competitors undercut prices, the industry responded by roughly doubling labor productivity within a few years — not through new technology or capital investment, but through organizational improvements and more efficient use of existing capital (Schmitz 2007). The broader puzzle is Syverson’s (2004) finding that at the four-digit industry level, the 90th-percentile firm has TFP 1.9 times that of the 10th-percentile firm, a gap that cannot be explained by observable input differences.

The model features a principal (firm owner) bargaining with loss-averse workers (represented by a union) over organizational change — represented as a worker effort level x that adapts the firm to the state of technology θ. Workers’ reference point is a convex combination of the status quo contract and their rational expectations of the agreed contract, with weight α on the status quo. Loss aversion parameter λ > 0 means that losses relative to the reference point are weighted more heavily than gains.

The core static result (Proposition 1) is that loss aversion drives a wedge of 1 + αλ between the workers’ marginal cost and the firm’s marginal benefit of organizational change. Below a threshold θ defined by ∂v(x₀,θ)/∂x = 1 + αλ, there is complete inertia: the firm does not change the effort level at all. Above θ, the firm adjusts effort, but to x(θ) < x^ME(θ), undershooting the materially efficient level. Higher λ or higher α both widen the inertia range and reduce the amount of implemented change (Proposition 2).

A crisis — modeled as a cost shock that makes the status quo contract generate negative profits, threatening firm closure — changes workers’ outside option from their current utility U₀ to the unemployment utility of zero. Workers are now willing to accept either wage cuts or effort increases to keep their jobs. Crucially, because both concessions are perceived as losses of equal size by workers, the firm prefers to increase effort rather than cut wages, since increasing effort is more productive when x < x^ME. The model thus provides a microfoundation for downward nominal wage rigidity: in a recession, workers make concessions through harder work rather than wage cuts.

In the infinite-horizon dynamic model, workers accumulate a quasi-rent over time equal to αλ(x_{t-1} − x₀), which represents compensation paid for past effort increases. This quasi-rent is what the firm expropriates during a crisis, allowing a discontinuous jump in effort toward the materially efficient level. Firms founded at different times or hitting different idiosyncratic shocks will therefore have different effort histories and different productivity levels, generating persistent TFP differences even among firms with identical technologies. When forward-looking players anticipate the possibility of crisis, inertia in normal times actually widens further (x̃(θ) ≤ x(θ)), because firms rationally delay effort adaptation knowing it will be cheaper to implement change during a crisis.

The expectations-management extension (Section 4) introduces a moral-hazard problem with a manager who chooses the probability of successful change. Because a higher probability of change raises the workers’ expectation-based reference point and reduces their perceived adaptation cost, the firm’s optimization problem becomes convex when the cost of effort for management is sufficiently low relative to (1−α)λΔx. This delivers a bang-bang result: the principal induces either full implementation (p = 1) or no change (p = 0), never an interior probability. This formalizes the management-consulting advice that commitment and urgency are essential to organizational change.

The social-comparisons extension (Section 5) shows that when workers compare their wages and effort to colleagues, the firm optimally compresses effort differences across workers — inducing the less productive worker to work more than efficiency requires and the more productive worker to work less. If productivity differences between workers are sufficiently small, the firm sets identical effort levels. Wage compression follows from effort compression. To avoid the cost of social comparisons entirely, it may be optimal for the firm to split into separate legal entities whose workers no longer form a common reference group — a new explanation for organizational unbundling.

Q: What is the core mechanism by which loss aversion generates organizational inertia in normal times? A: Workers have a reference point that is a convex combination (weight α on status quo, weight 1−α on rational expectations) of their current contract and the expected new contract. Because workers perceive an effort increase above their reference effort as a loss, the firm must pay a wage premium of αλ per unit of additional effort on top of the material effort cost of 1. This raises the effective marginal cost of implementing change from 1 to 1 + αλ, so the firm only implements change when the marginal revenue of effort strictly exceeds 1 + αλ. Below the threshold technology level θ (defined by ∂v(x₀,θ)/∂x = 1 + αλ), there is complete inertia and the firm keeps x* = x₀.

Q: How does a crisis break the inertia? A: A crisis is a cost shock large enough to make the firm’s profits negative under the status quo contract, so the firm would close unless workers make concessions. Workers’ outside option shifts from their accumulated utility U₀ to the unemployment utility of zero. Because wage cuts and effort increases are both perceived as losses of equal magnitude, the firm prefers to demand effort increases (which raise revenue) over wage cuts (which do not). At the margin, when workers are at zero utility, the loss-aversion terms cancel from the marginal rate of substitution, and the firm can push effort up to the materially efficient level x^ME — a discontinuous jump.

Q: Why do wages not fall during a recession in this model? A: Workers perceive both wage cuts and effort increases as losses of equal per-unit utility cost. Since increasing effort by one unit and cutting wages by one unit impose the same utility cost on workers but effort increases raise firm revenue while wage cuts do not, it is always more efficient for the firm to extract concessions through higher effort rather than lower wages. The firm therefore first drives effort to x^ME before cutting wages, and cuts wages only if the zero-utility constraint still is not binding at x^ME. This provides a microfoundation for Bewley’s (1999) observation that wages do not fall during recessions.

Q: Where does the quasi-rent exploited during a crisis come from? A: Every time the firm implements an effort increase in normal times it must compensate workers with a permanent wage increase to cover both the permanent higher effort cost (x_{t}−x_{t-1}) and the one-time behavioral adaptation cost αλ(x_{t}−x_{t-1}). Because the compensation for the adaptation cost must be spread over all future periods as a permanent payment, workers accumulate a quasi-rent that by period t equals αλ(x_{t-1}−x₀) above their initial utility U₀ = w₀−x₀. This is the rent the firm expropriates in a crisis to fund the discontinuous effort increase.

Q: How does the dynamic model generate persistent TFP differences across firms in the same industry? A: Firms founded at different times start with different initial status-quo effort levels relative to the current technology θ. Because each firm’s path of organizational adaptation is history-dependent — inertia regions, timing of crises, and accumulated quasi-rents all depend on when the firm was founded and what idiosyncratic shocks it experienced — firms that start later (or hit crises earlier) can remain more productive than older firms for extended periods. The numerical example with v(x,θ) = θ ln(x), α = 0.5, λ = 1, δ implied parameters shows that a firm founded when θ = 7 at the materially efficient point can maintain a substantial productivity advantage over a firm founded when θ = 4 that has accumulated inertia, even though both firms have access to the same technology.

Q: Does rational anticipation of a future crisis increase or decrease inertia in normal times? A: It strictly increases inertia. When players assign probability µ > 0 to a crisis each period, forward-looking workers demand higher compensation for effort increases in normal times — specifically, the per-period compensation for behavioral adaptation cost rises from (1−δ)αλ to γ = (1−δ(1−µ))αλ, which is increasing in µ. Simultaneously, the firm anticipates that effort adaptation will be cheaper to achieve in a crisis and therefore delays effort increases. The result is that the inertia threshold shifts from x(θ) to x̃(θ) ≤ x(θ), a strictly wider inertia region (Proposition 6).

Q: What is the expectations-management result and what drives it? A: When a manager chooses the probability of successful change p at cost c(p) = (c/2)p², the wage the firm must pay workers is concave in p (equation 22): w = x₀ + p(1+λ)Δx − p²(1−α)λΔx + U₀. The concavity arises because a higher p raises the expectation-based component of the reference point, lowering workers’ perceived adaptation cost. When c < (1−α)λΔx, this makes the principal’s profit function convex in p, so the optimum is at a corner: the principal induces either p = 1 (full implementation) or p = 0 (no change). Even when an interior solution obtains, a decrease in α (more weight on expectations) increases p. This formalizes the practitioner prescription that organizational change requires convincing everyone that change is certain and unavoidable.

Q: What is the effort and wage compression result under social comparisons? A: When each worker compares his situation to his colleague’s, with weight β on the peer’s wage and effort in forming the reference point, the firm must pay both workers a social-comparison premium of λβ(x₂−x₁) per unit of effort difference (Lemma 5). The firm therefore optimally compresses effort differences: it induces the less productive worker to exert effort above his efficient level and the more productive worker below his efficient level, at first-order conditions ∂v₁/∂x = 1 − 2λβ and ∂v₂/∂x = 1 + 2λβ respectively. If the productivity difference is small enough (specifically if ∂v₂(x*,θ)/∂x < 1 + 2λβ at the equal-effort point), the firm sets x₁* = x₂* = x*, eliminating wage inequality entirely (Proposition 8).

Q: Why might it be optimal for a firm to split into separate entities? A: Social comparisons impose costs on the firm by requiring higher wages for both workers (each receives a premium of λβ(x₂−x₁) regardless of their relative rank) and by distorting effort levels away from their efficient values. If workers employed by legally separate firms no longer treat each other as part of their reference group — because β falls to zero across firm boundaries — the firm can eliminate these comparison costs by spinning off activities into independent entities. This provides an efficiency rationale for organizational unbundling that does not rely on asset specificity or transaction costs, addressing what the authors call the “Williamson puzzle.”

Q: What are the implications for older workers and for social insurance policy? A: Older workers have two compounding reasons to be more resistant to organizational change: shorter remaining time horizons reduce the present value of permanent wage compensation for adaptation costs, and Gächter, Johnson, and Herrmann (2022) report that loss aversion λ increases with age, income, and wealth. Both factors raise the cost of implementing change with older workers. For social insurance, generous unemployment benefits or policies preventing layoffs (such as short-time work schemes) reduce workers’ concession costs in a crisis, weakening the mechanism by which crises trigger change. The model suggests this may contribute to slower technology adoption in countries with stronger labor market protections.

Q: What empirical facts from the existing literature does the model account for? A: The model accounts for: (1) Syverson’s (2004) finding of a 90th/10th percentile TFP ratio of 1.9 in four-digit US industries; (2) the iron ore and steel case study (Schmitz 2007) in which labor productivity doubled within a few years of a competitive shock with no new technology; (3) Bloom et al.’s (2014) correlation between more intense competition and higher TFP; (4) Holmes and Schmitz’s (2010) survey finding that competitive shocks raise industry productivity mainly through survival and improvement of existing firms; (5) Bewley’s (1999) downward nominal wage rigidity; and (6) Hjort, Li, and Sarsons (2022) on multinational firms using headquarters wages as reference points for wages in low-wage locations.

Loss aversion (λ): The parameter measuring the degree to which workers weight losses relative to their reference point more heavily than gains. A meta-analysis (Brown et al. 2023) across 607 empirical estimates finds an average loss aversion parameter of 1 + λ = 1.955. In this paper, λ > 0 means workers perceive a wage cut and an effort increase as losses, raising the effective marginal cost of organizational change by a factor of 1 + αλ.

Reference point (w^r, x^r): The benchmark wage and effort level against which workers evaluate outcomes. Defined as a convex combination of the status quo contract (w₀, x₀) with weight α and the rational expectation of the agreed contract (w^e, x^e) with weight 1−α. Losses occur when the realized wage falls below w^r or the realized effort exceeds x^r.

Organizational inertia: The firm’s failure to implement materially efficient organizational change even when doing so would increase total surplus. In the model, inertia arises because the effective marginal cost of effort to the firm is 1 + αλ rather than 1, so the firm only implements change above a threshold technology level θ. The range of inertia widens with higher λ, higher α, and higher initial effort x₀.

Quasi-rent: The utility accumulated by workers above their initial utility U₀ = w₀−x₀ as compensation for past effort increases. By period t it equals αλ(x_{t-1}−x₀). This quasi-rent is the source of concessions the firm can extract in a crisis: workers accept higher effort (or lower wages) in exchange for keeping their jobs rather than losing this accumulated utility through unemployment.

Behaviorally efficient effort x(θ): The effort level that maximizes joint surplus taking behavioral adaptation costs into account, defined by ∂v(x,θ)/∂x = 1 + (1−δ)αλ in the dynamic model. This is strictly below the materially efficient effort x^ME(θ) (defined by ∂v/∂x = 1) and strictly above the firm’s privately optimal effort in normal times.

Effort compression: The result under social comparisons that the principal optimally reduces the effort difference between workers relative to the efficient allocation — inducing the less productive worker to work more and the more productive worker to work less than efficiency requires. Driven by social-comparison costs λβ(x₂−x₁) that both workers receive as premiums regardless of relative rank.

Expectations management: The strategic use of commitment to high probability of change in order to shift workers’ expectation-based reference point and reduce the perceived adaptation cost. When α is small (rational expectations dominate the reference point), making change more certain lowers the wage cost of implementation, creating a complementarity between commitment and cost reduction that produces the bang-bang result: implement with certainty or not at all.