I11 | Macro Paper Warehouse

Demand Analysis under Latent Choice Constraints

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

Agarwal and Somaini study demand estimation in markets where consumers face latent choice constraints — situations where a consumer’s effective choice set is determined not only by her preferences but also by supply-side rationing or information frictions that restrict which options are actually available to her. Standard discrete choice methods assume consumers pick freely from the full product set, but this assumption fails in school and college admissions, entry-level labor markets, healthcare with selective admissions, and consumer markets with incomplete consideration sets. The paper provides a unified non-parametric identification framework for this class of models, proves necessity of the identifying instruments, proposes a computationally tractable estimator, and applies the framework to the California kidney dialysis market.

The model combines a general random utility specification — accommodating multi-dimensional unobserved heterogeneity and product-level unobservables correlated with observed characteristics as in Berry (1994) and BLP (1995) — with a reduced-form acceptance policy function that governs which products accept which consumers. The consumer’s latent choice set is the set of products that accept her, and she picks her most preferred option within that set. Crucially, the acceptance decision may be arbitrarily correlated with consumer preferences, ruling out the independence assumptions common in the consideration-set literature.

Identification rests on two sets of instruments. The first is a preference shifter, a consumer-product observable that affects utility but is excluded from the acceptance policy — distance to facility in the application. The second is a choice-set shifter, an observable that affects the acceptance decision but is excluded from consumer utility — short-term deviation of a facility’s caseload from its estimated target in the application. The main result (Theorem 1) establishes non-parametric point identification of the joint distribution of indirect utilities and acceptance decisions given both instruments. Proposition 1 establishes that the model is not identified when the choice-set shifter is absent — even when the preference shifter has full support — making both instruments necessary rather than merely sufficient.

The application uses USRDS data on 41,913 new dialysis patients treated at 552 California facilities between 2015 and 2018. Most facilities are owned by Fresenius or DaVita. The choice-set shifter is the facility’s caseload deviation from target when a patient enters the market; facility and quarter fixed effects are included so that only short-term caseload variation drives identification. A reduced-form regression shows that higher caseload deviation significantly reduces the inflow of new patients to a facility, consistent with supply-side rationing. Patients also choose more distant facilities when nearby facilities have above-normal caseloads, providing further reduced-form evidence that rationing shapes allocations.

A Gibbs sampler with data augmentation — drawing alternately from the distribution of latent choice sets conditional on utilities and from utility parameters conditional on choice sets — circumvents the curse of dimensionality that makes direct likelihood maximization over all possible choice sets infeasible.

Estimation results show that the probability a patient is accepted at her first-choice facility is only 73.0%, with variation across facilities. Standard discrete choice models that ignore rationing misestimate facility quality, systematically assigning high desirability to low-caseload facilities in a manner that conflates easy access with genuine patient preference. A naive correction that includes the caseload measure in the utility function mischaracterizes the diversion pattern: rationed patients are marginal for the facility but strictly prefer it, so they divert differently from patients who voluntarily switch because of quality changes. Fresenius and DaVita facilities are estimated to be more selective than independent facilities, consistent with chain networks enabling coordinated patient-flow management across locations.

Q: What is the core empirical problem the paper addresses? A: Standard demand estimation inverts market shares to recover preference parameters under the assumption that consumers choose freely from the full product set. When choice sets are constrained by supply-side rationing or information frictions, the largest market share product need not be the one most preferred — it may simply be the one that accepts the most consumers. This makes the standard inversion inapplicable, and ignoring constraints yields biased preference estimates.

Q: What does the paper’s model consist of? A: The model has two components: (1) a random utility model for consumer preferences with rich observed and unobserved heterogeneity, allowing product-level unobservables correlated with observed characteristics; and (2) a reduced-form acceptance policy function sigma_jt taking values in {0,1} that determines whether product j accepts consumer i. The consumer’s latent choice set is the set of products that accept her; she picks her most preferred option within it. Utilities and acceptance decisions may be arbitrarily correlated.

Q: What examples of latent choice constraints are covered by the framework? A: The reduced form encompasses: selective admissions in healthcare (facility accepts patient if profitability exceeds a caseload-dependent threshold); two-sided matching markets where a pairwise stable allocation is described by cutoff scores (school admissions, entry-level labor markets); consideration set models where brand awareness advertising or inattention determines which products a consumer sees; fixed-sample consumer search; and product stock-outs. Each of these implies an acceptance policy function of the form specified in the paper’s reduced-form model.

Q: What are the two identifying instruments and the intuition behind each? A: The preference shifter yij is a consumer-product observable that affects the consumer’s indirect utility for product j but is excluded from that product’s acceptance decision. In the application this is distance: dialysis requires multiple weekly visits, so distance affects patient utility, but a facility’s decision to accept a patient does not depend on how far the patient lives. The choice-set shifter zij is an observable that affects the acceptance decision but is excluded from consumer preferences. In the application this is the deviation of facility caseload from its estimated target: short-term caseload swings affect whether a facility can take a new patient but, conditional on facility fixed effects, do not reflect facility quality as perceived by patients.

Q: What does Theorem 1 establish and under what conditions? A: Theorem 1 establishes non-parametric point identification of (i) the function gj mapping the preference shifter to its utility contribution, and (ii) the joint distribution of indirect utilities and acceptance indicators, for every consumer attribute vector and every value in the interior of the joint support of the instruments. Conditions required include: monotonicity of the acceptance policy in the choice-set shifter (higher z makes acceptance weakly less likely, with sigma=1 as z approaches negative infinity and sigma=0 as z approaches positive infinity); conditional independence of unobservables from the instruments given observed consumer attributes; and at least two products available.

Q: What does Proposition 1 establish about necessity of the choice-set shifter? A: Proposition 1 shows that if the choice-set shifter z has singleton support (no variation), then even when the preference shifter g has full support on R^|J|, the distribution of preferences is not identified wherever a choice set strictly smaller than the full product set has positive probability. The non-identification result applies on any open set where a constrained choice set has positive probability — it is not a knife-edge case. This makes the choice-set shifter a necessary condition for identification, not merely a convenient one.

Q: How does the paper handle endogeneity of product characteristics? A: Corollary 2 extends the baseline identification result to allow product-level unobservables that may be correlated with observed product characteristics, as in Berry (1994) and BLP (1995). Identification in this case requires an additional instrument that shifts product characteristics but is excluded from both preferences and choice sets — analogous to BLP supply-side instruments — alongside the two shifters already required. This extends Berry and Haile (2010) to settings with constrained choice sets.

Q: What is the Gibbs sampler estimator and why is it needed? A: With J products per market, the number of possible choice sets is 2^J, making direct likelihood computation infeasible for even moderate J. The Gibbs sampler uses data augmentation to alternate between: (a) drawing latent choice sets conditional on current utility parameters and observed choices; and (b) drawing utility parameters conditional on the augmented choice sets. Each conditional draw reduces to a standard problem, avoiding the curse of dimensionality. The Bernstein-von Mises theorem implies that the posterior mean of the sampling chain is asymptotically equivalent to the maximum likelihood estimator.

Q: What is the reduced-form evidence for supply-side rationing in dialysis? A: The regression of log(1 + new patient inflows to facility j in quarter q) on facility fixed effects, quarter fixed effects, and the caseload deviation z_jq yields a statistically significant negative coefficient on caseload deviation: above-target caseloads reduce new patient admissions even after controlling for facility-level and time-level averages. Additionally, patients whose nearest facilities have above-normal caseloads travel to more distant facilities, providing complementary evidence that rationing displaces patients geographically.

Q: What is the estimated probability of acceptance at a first-choice facility? A: The structural estimates imply that a patient is accepted at her first-choice facility with probability only 73.0%, with variation across facilities. The implied 27.0% rejection rate is economically substantial, meaning a large share of observed allocations do not reflect unconstrained patient preference.

Q: How do estimates from the constrained model differ from a standard discrete choice model? A: The standard model, which ignores selective admissions, assigns higher utility to facilities with lower caseloads — a bias that conflates easy access with genuine patient preference. The constrained model separately identifies the facility’s acceptance propensity from the patient’s underlying preference, yielding different facility quality rankings. The largest facilities are not necessarily the most desirable once selective admissions are accounted for.

Q: Why is the naive correction — including caseload in the utility function — insufficient? A: The naive correction treats caseload as a quality attribute, implying that a patient turned away because of high caseload and a patient who voluntarily avoids a high-caseload facility are pulled from the same margin. In the constrained model, a rationed patient is marginal for the facility but strictly prefers it, so she diverts to a different set of alternatives than a patient who voluntarily switches. Not capturing this distinction produces quantitatively different diversion ratios.

Q: What do the estimates say about chain versus independent facilities? A: Fresenius and DaVita facilities are estimated to be more selective in their admissions than independent facilities. The paper interprets this as consistent with large chains having better ability to coordinate patient flows across their network of facilities, potentially directing turned-away patients to other chain locations.

Q: What is the scope of the identification results? A: Identification is established within each market, for consumer attribute vectors in the interior of support, and for utility-acceptance pairs in the interior of the joint support of the instruments. The results are non-parametric in that they do not restrict the functional form of preferences or acceptance policies beyond monotonicity and support conditions, and they allow unobservables affecting choice sets to be arbitrarily correlated with preference unobservables. The empirical application implements a parametric version for tractability.

Latent choice constraint: A restriction on a consumer’s effective choice set arising from supply-side rationing or information frictions, such that the consumer can only choose among the products that accept her rather than freely among all products in the market. Distinct from price-based market clearing.

Acceptance policy function: A reduced-form function mapping consumer attributes, consumer unobservables, and the choice-set shifter to a binary accept/reject decision by product j. Indexed by product and market, allowing arbitrary variation in selectivity across products and time. The consumer’s latent choice set is defined as the set of products whose acceptance policy equals 1.

Choice-set shifter: A consumer-product observable that shifts the acceptance probability — making product j more or less likely to accept consumer i — while being excluded from consumer indirect utility. In the application: short-term deviation of facility caseload from its estimated target. Necessary (not merely sufficient) for non-parametric identification of the model.

Preference shifter: A consumer-product observable that shifts consumer utility for product j and is separable from consumer-specific unobservables, but is excluded from that product’s acceptance policy function. In the application: distance from patient’s residence to the facility. Also necessary for identification.

Curse of dimensionality in constrained choice: The computational problem that the number of possible latent choice sets grows as 2^J with the number of products J, making direct likelihood integration over choice sets infeasible for even moderate J. Resolved in this paper by a Gibbs sampler with data augmentation that conditions alternately on latent choice sets or utility parameters.

Diversion ratio under selective admissions: The share of patients lost by a facility who are captured by each alternative facility. In a model with selective admissions, rationed patients (marginal for the facility) divert differently from patients who voluntarily switch (marginal for the consumer), because rationed patients strictly prefer the rejecting facility. The naive correction conflates these two margins, yielding quantitatively different and biased diversion ratio estimates.

Non-parametric necessity of instruments: The property that both the preference shifter and the choice-set shifter are individually necessary conditions for point identification of the joint distribution of preferences and acceptance decisions, not merely convenient sufficient conditions. Absence of either instrument leaves the model non-identified on any open set where a constrained choice set has positive probability.

The Productivity of Professions: Evidence from the Emergency Department

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

This paper studies the productivity of nurse practitioners (NPs) versus physicians performing overlapping tasks in Veterans Health Administration (VHA) emergency departments (EDs), exploiting a quasi-experiment created by the VHA’s December 2016 grant of full practice authority to NPs. The identification strategy instruments patient assignment to NPs versus physicians using quasi-random variation in the number of NPs on duty on a given ED-day, conditional on ED-by-time-category fixed effects. The sample covers 1.1 million ED visits across 44 VHA EDs from January 2017 to January 2020, seen by 1,348 physicians and 156 NPs. The instrument is validated by demonstrating balance in patient observable characteristics across values of the instrument, stability of IV estimates across 256 combinations of patient covariate controls, and absence of spillover effects from NP presence onto physician performance.

On average in the ED setting, NPs increase patient length of stay by 11 percent (approximately 18 additional minutes) and raise the cost of the ED visit by 7 percent (approximately $66 per visit). NPs raise the 30-day preventable hospitalization rate by 0.25 percentage points, a 20 percent increase relative to the mean. No statistically significant effect on 30-day mortality is detected (95 percent confidence interval: -0.34 to 0.11 percentage points). OLS estimates carry the opposite sign because NPs are assigned healthier patients in observational data; the IV design corrects for this selection.

The average NP-physician performance gap varies systematically by case complexity and severity. For the highest-complexity quartile of cases (by Elixhauser comorbidities), NPs increase ED costs by 12 percent and length of stay by 28 percent. For cases at or above the 95th percentile of severity (based on 30-day mortality by diagnosis), NPs increase ED costs by 25 percent, length of stay by 99 percent, and admissions by 26 percentage points (42 percent relative to the mean), while reducing 30-day preventable hospitalization by 3 percentage points — suggesting that NPs’ higher care intensity partially offsets worse intrinsic skill for the most severe cases. For lower-complexity cases, the cost and length-of-stay gaps are smaller, but NPs still significantly raise preventable hospitalizations.

NPs exhibit clinical decision-making patterns consistent with lower diagnostic skill: they are more likely to order consults (2.6 percentage points, or 11 percent of the mean), CT scans (1.2 percentage points, or 8.3 percent), and X-rays (2.0 percentage points, or 6.9 percent). NPs lower opioid prescriptions by 1.8 percentage points (20 percent of the mean) and raise antibiotic prescriptions by 4.0 percentage points (6.3 percent of the mean), consistent with threshold adjustment under lower diagnostic skill with asymmetric error costs. Downstream, patients treated by NPs incur similar opioid use disorder rates despite lower opioid prescribing, and higher infection-related return visit rates despite higher antibiotic prescribing.

Counterfactual analysis finds that allocating one quarter of ED patients to NPs increases net spending by $129 million per year to the VHA after accounting for NPs’ lower wages (approximately half of physicians’). However, deploying NPs exclusively to the least-complex quarter of cases reduces net spending to approximately one-fifth of this amount.

A distributional analysis deconvolving provider-specific IV estimates reveals that within-profession productivity variation substantially exceeds the average between-profession gap. The interquartile range in annual spending attributable to provider productivity within each profession is approximately $900,000, roughly three times the mean annual spending difference between the average NP and the average physician. A randomly chosen NP outperforms a randomly chosen physician in up to 38 percent of pairs. Within professions, individual provider productivity shows essentially no relationship with wages or case complexity assigned, whereas between professions, case assignment and wages are strongly sorted by professional class.

Q: What is the core research question? A: The paper asks whether NPs and physicians, who perform overlapping tasks in the ED but differ sharply in training, selectivity, and pay, differ in productivity, and how that average between-profession difference compares to productivity variation within each profession. It also asks what mechanisms drive any observed gap and how case assignment responds to provider skill differences.

Q: What is the identification strategy and why is it credible? A: The authors instrument patient assignment to NPs with the number of NPs on duty on the ED-day, conditional on ED-by-year, ED-by-month, ED-by-day-of-week, and ED-by-hour fixed effects. Credibility rests on: provider schedules being set months in advance, decoupling NP availability from arriving patient characteristics; patient characteristics being well balanced across values of the instrument conditional on fixed effects; IV estimates being stable across all 256 covariate-control combinations; and on-duty physician and NP characteristics also being balanced across the instrument.

Q: What are the main average effects of NPs on resource use? A: IV estimates show NPs increase patient length of stay by 11 percent (approximately 18 minutes) and ED cost by 7 percent (approximately $66 per visit). There is no significant average effect on inpatient admissions in the overall sample, though NPs significantly raise admissions for high-severity cases.

Q: What is the effect of NPs on patient health outcomes? A: NPs raise 30-day preventable hospitalizations by 0.25 percentage points, a 20 percent increase relative to the mean. The 95 percent confidence interval for 30-day mortality is -0.34 to 0.11 percentage points, implying no statistically significant mortality effect in the overall sample.

Q: Why do OLS and IV estimates have opposite signs? A: In observational data, NPs treat healthier patients than physicians: NP patients are younger (60.7 versus 62.5 years), have fewer Elixhauser comorbidities (3.2 versus 3.7), and have fewer prior inpatient stays (0.4 versus 0.7). This selection causes OLS estimates of NP effects to be negative. The IV corrects for this by exploiting quasi-random variation in NP availability; IV estimates are stable across all combinations of patient controls, consistent with the instrument being orthogonal to unobservable patient health.

Q: How does the NP-physician performance gap vary with case complexity and severity? A: For the highest-complexity quartile, NPs increase length of stay by 28 percent and ED costs by 12 percent without a significant preventable hospitalization effect. For cases at or above the 95th severity percentile, NPs increase length of stay by 99 percent, ED costs by 25 percent, and admissions by 26 percentage points (42 percent relative to the mean), while reducing 30-day preventable hospitalization by 3 percentage points. For lower-complexity quartiles, NPs show smaller cost and length-of-stay effects but significantly raise preventable hospitalizations, suggesting the higher care intensity at high severity compensates for lower skill.

Q: What does the heterogeneity by severity imply for optimal case assignment? A: The pattern is consistent with skill-task matching: NPs have a comparative and absolute disadvantage in complex cases, so optimal assignment directs less complex cases to NPs and fewer patients to NPs when physicians are more available. Empirically, NPs are indeed assigned healthier patients from the available pool, and are assigned a modestly smaller share when the ED is less busy.

Q: What mechanisms explain the average NP-physician gap? A: Three mechanisms are examined. First, experience: a one-standard-deviation increase in specific experience is associated with a 5.8 percent decline in the NP-physician length-of-stay gap, and general experience with a 10 percent decline; however, experience does not significantly narrow the preventable hospitalization gap. Second, information acquisition: NPs order more consults, CT scans, and X-rays, consistent with compensating for lower diagnostic skill. Third, prescription thresholds: NPs reduce opioid prescribing by 20 percent and raise antibiotic prescribing by 6.3 percent, consistent with threshold adjustment under asymmetric error costs, but downstream outcomes are not improved correspondingly.

Q: What do prescription patterns and downstream outcomes reveal about NP diagnostic skill? A: NPs prescribe fewer opioids yet patients treated by NPs obtain similar downstream opioid use disorder rates; NPs prescribe more antibiotics yet patients treated by NPs have higher rates of return visits with infections. This pattern is consistent with NPs exhibiting higher rates of both false positives and false negatives, not merely adjusted thresholds, suggesting genuinely lower diagnostic skill rather than threshold differences alone.

Q: What do counterfactual cost calculations show? A: Allocating one quarter of ED patients to NPs raises non-wage spending by $197 million per year to the VHA; after accounting for NP wages being half of physician wages (approximately $120,000 versus $240,000 per year), net cost is still $129 million per year. Restricting NP deployment to the least-complex quarter of cases reduces net spending to approximately one-fifth of this amount, illustrating that targeted case assignment substantially improves NP cost-effectiveness.

Q: How large is within-profession productivity variation relative to between-profession differences? A: The interquartile range in annual spending attributable to provider productivity within each profession is approximately $900,000, roughly three times the mean annual spending difference between the average NP and the average physician. A randomly chosen NP outperforms a randomly chosen physician in up to 38 percent of random pairs. The authors conclude that, despite stark differences in training and selection between professions, within-profession variation dominates.

Q: Is individual provider productivity reflected in wages or case assignment within professions? A: Within each profession, provider productivity shows essentially no relationship with wages or with the complexity of assigned cases. This contrasts sharply with between-profession patterns, where professional class strongly predicts both wages (NPs earn approximately $120,000 per year versus $240,000 for physicians) and assigned case complexity. The authors interpret this as evidence of informational and organizational frictions in recognizing individual productivity within professional classes, and note that professional class is a far stronger predictor of pay and case assignment than is individual productivity.

Q: How do complier characteristics relate to the broader patient population? A: Compliers — cases whose provider type is determined by the instrument — are healthier than the average case: younger, with fewer comorbidities, fewer prior inpatient stays, and lower predicted mortality. Never-takers are riskier than the average case. There are no always-takers since patients cannot be assigned to NPs on days when no NPs are on duty.

Q: How does this paper relate to the literature on NP scope-of-practice laws? A: The scope-of-practice literature estimates general-equilibrium effects of allowing NPs greater autonomy, including labor reallocation between professions. This paper instead estimates the partial-equilibrium causal effect of assigning a patient to an NP versus a physician, holding the broader labor market fixed. The two literatures are complementary: the heterogeneity findings here suggest that scope-of-practice expansions may be more beneficial in lower-complexity primary care settings where the NP-physician performance gap is smaller.

Q: What are the policy implications of the findings? A: Three implications are highlighted. First, the efficiency of using NPs depends critically on case assignment: deploying NPs on the least-complex cases reduces net costs to approximately one-fifth of indiscriminate deployment. Second, the substantial overlap between NP and physician productivity distributions provides support for NP use in less complex settings even within the ED context. Third, within-profession productivity variation far exceeding between-profession differences suggests that individual-level productivity assessment, rather than professional class, may be a more accurate guide to case assignment and compensation.

Quasi-experimental variation in NP availability: The identification strategy exploits day-to-day variation in the number of NPs scheduled to work in a given VHA ED, conditional on ED-by-time-category fixed effects, as an instrument for whether a patient is assigned to an NP versus a physician. Schedules are set months in advance, rendering the NP count orthogonal to arriving patient characteristics conditional on those fixed effects.

30-day preventable hospitalization: A standardized quality-of-care outcome defined by the Agency for Healthcare Research and Quality, measuring hospitalizations occurring within 30 days of ED discharge that are classified as preventable given adequate prior outpatient management. Used by the paper as the primary downstream health outcome beyond the ED visit itself.

Elixhauser comorbidities: A set of 31 binary indicators for chronic conditions (e.g., cancer, diabetes) based on medical histories in the prior 365 days, used in this paper to measure and stratify case complexity into quartiles for heterogeneity analysis.

Productivity distributions within professions: Provider-specific productivity estimates derived from a just-identified IV model that instruments assignment to individual providers by indicators for on-duty providers, then deconvolved into underlying distributions using the Efron (2016) and Kline-Rose-Walters (2022) method. These distributions characterize the spread of productivity within each professional class, separate from measurement error.

Prescription threshold adjustment: The mechanism, formalized in Chan, Gentzkow, and Yu (2022), by which providers with lower diagnostic skill optimally adjust treatment thresholds in response to asymmetric costs of false-positive versus false-negative errors. In this paper’s application, NPs lower the opioid prescription rate (where false positives carry higher costs: addiction and overdose) and raise the antibiotic prescription rate (where false negatives carry higher costs: untreated infection), but downstream outcomes do not improve correspondingly.

Skill-task matching: The organizational economics principle (Acemoglu and Autor 2011) that efficiency requires assigning more complex tasks to higher-skilled workers. The paper documents that between professions, case assignment broadly follows this principle (NPs receive less complex patients on average), but within professions, essentially no matching between individual provider productivity and case complexity is observed.

Full practice authority (VHA, December 2016): The VHA policy that allowed NPs to treat patients independently without physician supervision at VHA facilities, superseding state-level restrictions. This policy change defines the start of the paper’s sample period and establishes the institutional context in which the quasi-experiment occurs, as it removed the requirement for physician oversight that previously constrained NP independence.