L0 | 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.

Search Frictions and Product Design in the Municipal Bond Market

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

Layer 1 — Overview

Research Question

This paper investigates whether intermediaries in the U.S. municipal bond market strategically exploit product design to increase search frictions and, through that channel, capture rents. Specifically, it asks: do underwriters who negotiate bond design with local governments have an incentive to add nonstandard provisions that raise their own competitive advantage in subsequent secondary-market intermediation, even at the expense of issuing governments and their taxpayers?

Setting and Data

The study focuses on tax-exempt general obligation and revenue bonds issued via negotiated sales by local governments (counties, cities, school districts, and other special-purpose governments) from 2010 to 2013, tracking all secondary-market transactions through 2014. The final sample comprises 13,118 bond issues with a total face value of $266.9 billion. Bond attribute data come from Mergent; transaction data come from the Municipal Securities Rulemaking Board (MSRB). Issuer financial health, demographics, and economic conditions are drawn from the Census and American Community Survey; state revolving-door regulations are compiled from the National Conference of State Legislatures database. Structural estimation uses a subsample of 927 bonds concentrated in the five states that enacted revolving-door regulations during the study period and neighboring border counties.

Identification Strategy

A core empirical challenge is that unobserved factors may jointly determine bond complexity and market outcomes. The authors exploit panel variation in state-level revolving-door regulations — laws that restrict former public officials from taking employment at firms regulated by their former agencies for a “cool-off” period — as an instrument for bond complexity. Between 2010 and 2013, three states (Arkansas 2011, Indiana 2010, Maine 2013) enacted new legislation covering state officials, and two states (New Mexico 2011, Virginia 2011) extended existing regulations to cover local officials. A difference-in-differences regression, with county and year-month fixed effects, shows that adopting revolving-door regulations covering local officials reduces bond complexity by 6% on average (coefficient −0.064, p < 0.01). Regulations targeting only state officials, who are not directly involved in bond negotiations, yield smaller and statistically fragile effects. Placebo checks on auctioned bonds, where underwriters cannot influence design, show no effect, and there is no evidence of pre-existing trends in complexity.

Main Findings

Flexibility vs. liquidity trade-off: A 1% increase in the bond complexity index lowers the number of negative credit-watch events (a proxy for default risk) by 0.002, a 3% decrease relative to the mean of 0.074, confirming that nonstandard provisions provide genuine financial flexibility. However, increasing the complexity index from its mean (1.46) to the 75th percentile (1.69) raises the intermediation spread — the cost for an investor to buy and immediately sell a bond — by 17 basis points (a 14% increase over the average of 120 basis points), confirming that complexity raises trading frictions. For context, the average intermediation spread of 120 basis points is large relative to the 30–60 basis point bid-ask spread of corporate bonds in 2010–2013.
Underwriter incentive to complicate: Increasing complexity from the mean to the 75th percentile raises the underwriter’s market share in secondary-market intermediation by 1.4 percentage points, an 11% increase over the average underwriter share of 12.2%. The underwriter’s gross profits from intermediation also increase with complexity.
Structural estimates — search costs: For a median bond, average dealer search costs amount to 10% of monthly gross profits ($2,625 per month). The underwriter’s exclusive initial sales generate a client network that lowers its effective search costs by 21% relative to an average dealer, more than offsetting its initial geographical disadvantage (for 72% of bonds, the underwriter’s baseline search cost exceeds the median dealer’s). Nonstandard provisions increase both the initial search cost parameter (φ₀) and the network-effect parameter (φ₁): a 1% increase in the complexity index increases φ₀ by 3.79% and φ₁ by 1.66%, implying complex bonds raise search costs broadly but amplify the advantage of a large client network — a position the underwriter occupies via exclusive primary-market sales.
Investor demand: Nonstandard provisions do not substantially change the average investor valuation but substantially increase the dispersion: the standard deviation of investor valuations is 0.003 for simple bonds and 0.013 for complex bonds, consistent with complex bonds being niche products that investors “either love or loathe.”
Government cost: The marginal cost of paying debt obligations is convex in complexity, reaching a minimum at an interior level of provisions; the government’s marginal financial cost increases by 42% when a median bond is stripped of all nonstandard provisions, reflecting the value of payment flexibility.
Conflict of interest: The estimated weight that government officials place on underwriter payoffs in the absence of revolving-door regulations (ψ₀) is 0.34, implying the underwriter’s value accounts for 6.7% of the government official’s payoff under the median unregulated issuer. With revolving-door regulations in place, ψ₁ is essentially zero.

Counterfactual Policies (on representative bond: face value $6.45 million, maturity 7.7 years)

Standardization mandate (ban on all nonstandard provisions): The coupon rate falls from 2.81% to 2.16% (−23%), average dealer search costs fall 47%, and investor surplus rises 13.3%. However, the marginal financial cost (c₀) rises by 41% (from 0.615 to 0.871), so the issuer’s total debt payment cost — principal plus interest, weighted by c₀ — rises by 35%, from $5.13 million to $6.96 million. The standardization policy harms issuers even while saving 7.8% of raw principal-and-interest payments ($8,349K to $7,997K), because the loss of flexibility more than offsets the liquidity gain.
Issuer-driven design (issuer sets complexity to minimize its own debt payment cost, then negotiates the coupon): Complexity falls 19% to 1.14, the interest rate falls to 2.37%, total issuer cost falls 1.5%, investor surplus rises 6%, and the underwriter’s secondary-market payoff falls 19.9%.
Underwriter intermediation ban (underwriter excluded from trading after six months): Complexity falls 5.7% to 1.33, the coupon falls to 2.59%, issuer cost falls 1.5%, but investor surplus falls 1.84% and even other dealers are worse off by 3.97%, because the underwriter’s information on primary-market buyers is lost, offsetting the liquidity gains from lower complexity.

In depth

Q1. What are the five nonstandard bond features tracked as proxies for complexity, and how are they combined into a single index?

Following Harris and Piwowar (2006), the paper focuses on five features that are particularly difficult for investors to price: (i) multiple or serial bonds per issue (as opposed to a single bond), (ii) call provisions allowing early redemption, (iii) sinking fund provisions requiring periodic debt retirement, (iv) nonstandard interest payment frequencies (other than semiannual), and (v) variable or floating interest rates. The complexity index is constructed as the simple average of the latter four provisions across bonds within an issue, plus a dummy for whether the issue contains multiple bonds.

Q2. Why do revolving-door regulations that target local officials reduce complexity more than those targeting state officials?

State officials are not directly involved in bond origination negotiations — they can only indirectly influence local governments through budget allocations. Local officials negotiate directly with underwriters and are thus the proximate counterparties whose incentives the regulations alter. Accordingly, revolving-door regulations covering local officials reduce complexity by 6% (coefficient −0.064, p < 0.01 with full controls), whereas regulations targeting only state officials produce a smaller effect (approximately 2%) that loses statistical significance once issuer financial health controls are added.

Q3. How does the paper validate that revolving-door regulations are a valid instrument for bond complexity?

The paper provides three pieces of evidence. First, the regulations have no effect on the credit ratings of bonds issued prior to their enactment, on the annual amount of bond issuance, or on the maturity length and sale method conditional on issuance — confirming the regulations do not alter governments’ risk management or underlying financing needs. Second, the regulations have no effect on complexity for competitively auctioned bonds, where underwriters cannot influence design — a direct placebo test. Third, a pre-trend analysis (Figure A1) finds no differential trend in complexity in states that subsequently adopted regulations.

Q4. What is the mechanism by which underwriters benefit from adding nonstandard provisions, and why does this advantage not diminish over time?

Underwriters purchase and distribute the entire bond issue at origination, giving them an exclusive network of investors who initially purchased the bonds. In the secondary market, knowing who owns a bond allows the underwriter to locate buyers and sellers with lower search effort. For complex bonds, this advantage is amplified: nonstandard provisions make investor education and persuasion more costly, increasing the value of pre-existing client relationships. The network-effect parameter φ₁ — which governs how rapidly search costs fall as a dealer’s cumulative trades grow — itself rises with complexity (by 1.66% per 1% increase in the complexity index), so the underwriter’s head start in client network accumulation translates into a persistently larger cost advantage precisely for the most complex bonds.

Q5. How large is the underwriter’s search cost advantage in equilibrium, and what drives it?

At the equilibrium meeting rate, the underwriter’s effective search cost of maintaining a given meeting rate is 21% lower than that of an average dealer. This advantage arises despite the underwriter having a higher initial search cost type (φ₀ of $3,609 vs. $3,216 for the average dealer at λ = 1), because for 72% of bonds the underwriter has less local trading experience than the median dealer. The advantage is entirely driven by the underwriter’s network: its exp(−φ₁ log(b)) cost discount factor averages 0.34, 32% lower than the average dealer’s 0.50. The underwriter meets investors 20% more frequently than the average dealer (0.23 vs. 0.19 per month), despite higher absolute search expenditures ($3,045 vs. $2,625 per month).

Q6. How does bond complexity affect investor demand — mean or dispersion of valuations?

Structural estimates show that increasing the complexity index by 1% increases the standard deviation of investor valuations (γ₂) by 4.60% but has no statistically significant effect on the mean valuation (coefficient −0.085, standard error 0.561). This pattern is consistent with complex bonds being niche products — they attract a subset of investors with specific preferences for the embedded features (e.g., certain tax or cash-flow attributes), while being unappealing to most investors. The standard deviation of valuations is 0.003 for a low-complexity bond (25th percentile) and 0.013 for a high-complexity bond (75th percentile).

Q7. What does the structural estimate of ψ₀ imply about the degree of collusion between government officials and underwriters?

The estimated collusion parameter without revolving-door regulations (ψ₀ = 0.34) implies that, for the median unregulated issuing government, the underwriter’s value from secondary-market trading accounts for 6.7% of the government official’s objective function. This is a substantial weight: it means officials act partly as agents for the underwriter rather than purely for taxpayers. With revolving-door regulations (ψ₁ ≈ 0), this collusive weight is essentially eliminated, explaining the empirical reduction in complexity found in Table 2.

Q8. What are the effects of a full standardization mandate on each class of market participant, and why does the issuer lose overall despite paying a lower coupon?

Under standardization, the coupon falls 23% (from 2.81% to 2.16%) and the raw principal-plus-interest payment falls 7.8% (from $8,349K to $7,997K). However, the marginal financial cost c₀ rises 41% (from 0.615 to 0.871), reflecting the loss of payment flexibility previously provided by call provisions and other features; the total issuer cost — c₀A(1 + rT) — rises by 35% (from $5.13 million to $6.96 million). Investors gain 13.3% in surplus because they value liquidity and, on average, do not value nonstandard features. The underwriter loses 36.6% of its secondary-market value while other dealers gain 36.1%, as standardization erodes the underwriter’s network advantage.

Q9. Why does the issuer-driven design scenario outperform standardization in terms of total issuer cost, even though complexity does not fall to zero?

Under issuer-driven design, the government minimizes its total cost of debt payment c₀A(1 + rT), accounting for both the flexibility value of provisions and their effect on the negotiated coupon. The optimal complexity index is 1.14 — positive, but 19% below the current baseline of 1.41 — because some provisions genuinely lower c₀ by allowing flexible debt service. The cost of search frictions (and hence the liquidity premium embedded in the coupon) falls 32% and the negotiated coupon falls to 2.37%, sufficient to reduce total issuer cost by 1.5%. By contrast, full standardization imposes a complexity of zero, which overshoots: c₀ rises more than the coupon savings compensate, increasing total costs by 35%.

Q10. What are the net welfare effects of the underwriter intermediation ban, and why is investor surplus negative despite lower complexity?

The ban reduces complexity by 5.7%, lowering the coupon to 2.59% and reducing issuer costs by 1.5%. However, the underwriter’s client network — built during exclusive initial sales — is a productive resource that improves match quality in the secondary market; banning the underwriter from trading after six months wastes this information. Average dealer search costs rise 1.2% and the meeting rate falls 1.7%, net of the complexity reduction. Investors face bonds with lower coupons and higher effective search frictions, so their surplus falls 1.84%. Non-underwriter dealers also lose 3.97% because lower coupons reduce the rents extractable from intermediation.

Q11. How is the structural model estimated, and what role do revolving-door regulations play in the estimation?

Estimation proceeds in three steps. In Step 1, bond-specific trading market parameters (investor demand, dealer search costs, meeting rates, bargaining parameters) are recovered separately for each bond by minimizing squared differences between observed and simulated trading prices, quantities, and transaction timing. In Step 2, IV regressions using revolving-door regulations and their interactions with county/state attributes as instruments for endogenous complexity map Step 1 parameters to bond attributes, addressing the endogeneity of complexity in determining search costs and investor demand. In Step 3, GMM moment conditions derived from Nash bargaining first-order conditions for the equilibrium complexity and coupon rate identify government preference parameters (θ_c, ψ₀, ψ₁), using the orthogonality condition that unobserved financing cost shocks are mean-zero conditional on observed attributes, regulations, and bond supply from neighboring counties.

Q12. Does the underwriting market show signs of concentration that might amplify the conflict-of-interest problem?

Yes. The mean state-level Herfindahl-Hirschman Index (HHI) for underwriting is 0.12, with the top three firms covering 45% of the market on average. For smaller deals (under $10 million), concentration is markedly higher: mean HHI of 0.24 and top three firms covering 64% of the market. Repeat relationships are common — 41% of bonds issued in 2011–2017 were underwritten by a firm that had underwritten a prior bond for the same issuer within five years — reflecting both informational advantages of local presence and potentially entrenched relationships that may increase government officials’ susceptibility to underwriter influence.

Key Concepts

Complexity index (nonstandard provisions): A bond-level measure computed as the simple average, across bonds within an issue, of four nonstandard features — call provisions, sinking fund provisions, nonstandard interest payment frequency, and variable/floating interest rates — plus a dummy for whether the issue contains multiple bonds. Used as the primary measure of bond complexity in all regressions and the structural model.

Revolving-door regulation: A state-level law restricting former public officials or employees from engaging in lobbying or taking employment at regulated firms for a specified “cool-off” period (typically one to two years) after leaving office. The paper uses the presence and scope of such regulations (whether they cover state officials, local officials, or both) as a source of exogenous variation in government officials’ incentives to align with underwriter interests.

Intermediation spread: The logarithm of the average dealer-to-investor sale price minus the logarithm of the average dealer-from-investor purchase price for a given bond. Used as the empirical measure of trading frictions; the sample average is 120 basis points.

Network effect in search (φ₁): The parameter governing how a dealer’s cumulative prior trades with investors in a given bond reduce its cost of meeting new investors for that bond. A higher φ₁ means a larger client network translates into steeper cost savings. The paper estimates that φ₁ itself increases with bond complexity, so complex bonds amplify the advantage of dealers (especially the underwriter) who accumulate large client networks.

Marginal cost of debt payment (c₀): A bond- and issuer-specific parameter capturing the effective cost to the government of repaying each dollar of principal and interest, net of the flexibility benefits provided by nonstandard provisions. Normalized to one for a bond with zero nonstandard provisions at average issuer characteristics; estimated to be convex in complexity with an interior minimum, implying some nonstandard provisions are beneficial from the government’s perspective.

Collusion weight (ψ): The weight a government official places on the underwriter’s secondary-market value from trading when negotiating bond design. Estimated at ψ₀ = 0.34 in the absence of revolving-door regulations (implying the underwriter’s interest accounts for 6.7% of the official’s objective) and at ψ₁ ≈ 0 when such regulations are present.

Underwriter dual role: The institutional arrangement in which the same investment bank (i) negotiates and purchases the entire bond from the issuing government at origination, and (ii) subsequently acts as a dealer in the bond’s secondary market. This dual role creates an incentive to design complex bonds that strengthen the underwriter’s competitive advantage in secondary intermediation via network effects in search.

Issuer-driven design: A counterfactual policy scenario in which the government sets the complexity level to minimize its total cost of debt payment — accounting for both the flexibility value of provisions and the anticipated effect on the negotiated coupon rate — before bargaining with the underwriter only over the coupon. This policy allows some nonstandard provisions (complexity index 1.14 vs. baseline 1.41) and reduces total issuer cost by 1.5% relative to the baseline.

Why Is Intermediating Houses So Difficult? Evidence from iBuyers

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

This paper examines frictions in dealer intermediation in durable consumer goods markets, using iBuyers — technology-driven real estate companies such as Opendoor and Offerpad — as a lens. The central research question is why dealer intermediation, which provides immediate liquidity by purchasing assets onto a balance sheet and reselling, is so limited in the U.S. housing market (valued at $50 trillion and representing roughly 70% of the median household’s net worth) relative to other durable goods markets such as automobiles.

The authors use CoreLogic deed transaction data and MLS listing data from five markets with substantial iBuyer presence (Phoenix, Las Vegas, Dallas, Orlando, and Gwinnett County, Georgia) over 2013–2018, covering arm’s-length, non-foreclosure single-family home and condominium transactions. They supplement this with Redfin ZIP-level data on listing speed and American Community Survey demographics. iBuyers are identified as Opendoor, Offerpad, Knock, Zillow, and Redfin.

The empirical analysis documents that iBuyers grew from roughly 1% market share in Phoenix in 2015 to about 6% by 2018, acting as balance-sheet intermediaries who hold properties for a median of 105 days. iBuyers purchase homes at a 3.1 percentage point (pp) discount relative to comparable homes sold in the same ZIP-quarter, and sell at a 2.2 pp premium relative to other institutional sellers, for a combined gross spread of approximately 5.3 pp (reported in the abstract and body as ~5%). Sellers to iBuyers show a 6.8 pp higher rate of market exit post-sale and a 4.0 pp higher probability of purchasing before selling, consistent with demand for immediacy from impatient, relocating households.

Two key frictions constrain intermediation. First, adverse selection: iBuyers rely on algorithmic valuation models (AVMs) that explain over 80% of price variation in iBuyer transactions versus only 68% in non-iBuyer transactions, leaving a residual of soft information (odor, neighbor quality) that sellers know but algorithms cannot capture. iBuyer presence is over three times greater in the lowest pricing-uncertainty tercile versus the highest, and a one standard deviation increase in pricing uncertainty reduces iBuyer presence by 1.23 pp within a ZIP and reduces gross spread per transaction by 1.5 pp. Second, underlying illiquidity: iBuyers are almost entirely absent in market segments where the probability of sale within three months (PSALE) falls below 50%, despite strong seller demand.

To quantify these frictions, the authors build and calibrate a continuous-time directed search equilibrium model with a dealer intermediary subject to adverse selection. Six parameters are calibrated to match empirical moments: iBuyer market share (5%), purchase discount (3.1 pp), sale premium (2.2 pp), iBuyer concentration in the most versus least liquid PSALE quartiles, impatient seller fraction, and median iBuyer holding time. The calibrated adverse selection parameter (α = 0.35) means the intermediary correctly identifies 35% of low-quality homes as such; the impatient seller share (μ = 0.18) means 18% of unmatched sellers are highly impatient; and the vacancy depreciation rate (d = 0.02) means 2% per period for unoccupied homes. External validation via a difference-in-differences comparison of Phoenix against other markets yields model-consistent predictions of a 0.5 pp reduction in time on market and a 0.8 pp increase in house prices.

Counterfactual experiments reveal that introducing a 30-day acquisition delay (rather than near-instantaneous) reduces iBuyer market share from 5% to below 2%; eliminating the signal entirely (α = 0) drops market share to just above 1%; and enabling iBuyers to rent vacant properties during the holding period could raise market share above 7.5 pp. A 50% reduction in PSALE reduces iBuyer market share roughly proportionally.

The calibrated model is then applied to other durable goods markets by varying informational asymmetry, liquidity, and depreciation parameters. Cars — more homogeneous (year/make/model/mileage fully characterizes value), mobile (transportable across markets), and depreciating primarily through use — are predicted to support dealer intermediary market shares of 40–55%, consistent with observed U.S. car dealer market share of ~50%. Reducing the depreciation rate from the housing level (d = 0.02) to a car-like level (d = 0.005) alone increases intermediary market share by about 5 pp. Houses — heterogeneous, immobile, and depreciating through time rather than use — are predicted to support near-zero intermediation under pre-iBuyer technology. The authors also explain COVID-19 iBuyer suspensions (reduced market liquidity made resale untenable) and Zillow’s November 2021 exit (very liquid markets eroded the iBuyer speed premium, worsening adverse selection while rapid price appreciation degraded AVM accuracy).

Q: What discount do iBuyers pay when purchasing homes, and what premium do they earn when selling? A: iBuyers purchase homes at a 3.1 pp discount relative to comparable homes sold in the same ZIP code and quarter, with a t-statistic of 8.55. They sell at a 2.2 pp premium relative to other institutional sellers. The combined gross spread is approximately 5.3 pp (referred to throughout the paper as roughly 5%).

Q: How large is the iBuyer market share, and in which markets did they operate? A: iBuyer market share grew from approximately 1% in Phoenix in 2015 to roughly 6% by 2018. In Gwinnett County, Las Vegas, and Dallas/Orlando, shares reached approximately 4%, 4%, and 2% respectively by 2018. The analysis covers five markets: Phoenix, Las Vegas, Dallas, Orlando, and Gwinnett County (suburban Atlanta).

Q: What is the evidence that iBuyer sellers are impatient rather than simply lower-quality-house owners? A: Sellers to iBuyers exhibit a 6.8 pp higher rate of market exit (defined as purchasing a home outside the county or making no subsequent real estate purchase within 12 months), consistent with relocation-driven impatience. They also have a 4.0 pp higher probability of purchasing a new home before completing the sale of their current home, which is enabled by the iBuyer transaction’s speed facilitating mortgage approval conditional on the existing property’s sale.

Q: How do the authors measure adverse selection risk and what is its relationship to iBuyer presence? A: Adverse selection is proxied by the squared residual from a hedonic pricing regression — the variation in transaction prices unexplained by observable characteristics — computed at the ZIP-year level for non-iBuyer transactions. iBuyer presence is over three times greater in the lowest pricing-uncertainty tercile than in the highest. A one standard deviation increase in pricing uncertainty reduces iBuyer presence by 1.23 pp within a ZIP (controlling for ZIP fixed effects, local prices, house age, and square footage), and reduces gross spread per transaction by 1.5 pp.

Q: What role does underlying asset liquidity play in constraining iBuyer intermediation? A: iBuyers concentrate almost entirely in market segments where the ex ante probability of selling within three months (PSALE) exceeds 50%, and are essentially absent where PSALE falls below 50%. This holds even though sellers in low-PSALE segments have strong demand for immediacy, implying that illiquidity raises intermediation costs above the demand-side willingness to pay a discount.

Q: What does the model’s calibration reveal about the share of impatient sellers and the accuracy of iBuyer signals? A: The calibrated adverse selection parameter α = 0.35 means the intermediary correctly identifies 35% of low-quality homes as low quality (the signal is moderately but imperfectly informative). The calibrated impatient seller share μ = 0.18 means approximately 18% of unmatched sellers are highly impatient and willing to accept a significant price discount for immediacy. The vacancy depreciation rate d = 0.02 implies a 2% per period cost for unoccupied properties.

Q: How important is transaction speed to the iBuyer model? A: Introducing a 30-day acquisition delay (rather than near-instantaneous purchase) reduces iBuyer market share from 5% to below 2% — a reduction of more than 60%. The model mechanism is that the primary iBuyer customers are highly impatient sellers who place extreme value on immediate transactions; even a moderate delay substantially reduces their willingness to accept a price discount.

Q: What happens if iBuyers lose their ability to distinguish between high- and low-quality homes? A: Setting the signal accuracy to zero (α = 0, the “naive intermediary” case) causes iBuyer market share to fall from 5% to just above 1%. Without any quality signal, severe adverse selection forces the intermediary to offer substantially lower prices to break even, which in turn reduces the number of sellers willing to transact.

Q: How much would enabling iBuyers to rent vacant properties during the holding period affect market share? A: The rental-enabled iBuyer counterfactual shows that market share could increase above 7.5 pp from the baseline 5%, because rental income would allow iBuyers to offer higher purchase prices while offsetting carrying costs. This suggests that rental infrastructure or policy changes permitting temporary rentals would substantially expand the scope of dealer intermediation in housing.

Q: How does the model validate itself externally? A: The authors use a difference-in-differences design comparing Phoenix (earlier and larger iBuyer entry) to the other four markets. The model predicts iBuyer entry should reduce average time on market and increase house prices; the DiD results show a 0.5 pp reduction in time on market and a 0.8 pp increase in house prices in Phoenix relative to comparison markets post-entry, consistent with model predictions.

Q: Why did iBuyers suspend operations during the COVID-19 pandemic despite having a contactless technological advantage? A: The model explains the suspension through the liquidity channel: iBuyers’ value proposition depends on quickly reselling acquired properties, not merely on contactless buying. When market liquidity collapsed during lockdowns (transaction volumes fell sharply), iBuyers could not resell properties quickly, making intermediation unprofitable regardless of their purchasing-side technological advantage. As liquidity recovered, iBuyers resumed operations.

Q: What does the model say about Zillow’s exit from iBuying in November 2021? A: In very liquid markets, the iBuyer speed advantage shrinks because homeowners can sell quickly in the traditional market anyway, reducing the discount sellers accept when selling to an iBuyer. With a smaller discount, adverse selection worsens because only sellers with unfavorable private information (knowing their house has problems the algorithm overvalued) choose the iBuyer route. The pandemic-era housing market also featured rapid price appreciation that degraded AVM accuracy trained on historical data, compounding adverse selection. Zillow reported having significantly overpaid for homes, consistent with this mechanism.

Q: Why is dealer intermediation approximately 50% in car markets but near-zero historically in housing? A: The model, applied to car-market parameters, predicts 40–55% dealer intermediation, consistent with observed U.S. car market shares. Three structural differences explain the gap: (i) cars are more homogeneous (year/make/model/mileage sufficiently characterizes value), reducing adverse selection; (ii) cars are mobile and can be transported across markets, increasing effective liquidity; and (iii) cars depreciate primarily through use, so holding a car on a dealer lot incurs lower value loss than leaving a house vacant. Reducing the depreciation rate from the housing calibration (d = 0.02) to a car-like level (d = 0.005) alone raises predicted intermediary market share by about 5 pp.

Q: Does subjective value dispersion (heterogeneity in buyer preferences) play a large role in limiting intermediation? A: While subjective value dispersion plays a significant role in shaping search market equilibrium (affecting match quality and the gains from household-to-household search), the model finds its effect on the overall level of intermediation is comparatively less pronounced than informational asymmetry, market liquidity, or the opportunity cost of vacancy.

Q: What evidence supports the claim that iBuyers use algorithmic pricing? A: Observable property characteristics and ZIP-quarter fixed effects explain over 80% of price variation in iBuyer transactions, compared to only 68% in non-iBuyer transactions. The higher R-squared for iBuyer transactions is consistent with iBuyers relying on measurable, formalizable characteristics rather than soft information (such as odors or neighbor property conditions) that traditional buyers gather through physical visits.

Q: What are the structural limits on iBuyer expansion even with improved technology? A: Even with enhanced pricing technology (lower α), the scope for dealer intermediation remains narrow because strong incentives persist for iBuyers to avoid markets where algorithmic valuation is difficult, such as older and less homogeneous housing stock. The fundamental barriers — heterogeneity, immobility, and high vacancy opportunity cost — cannot be overcome by technology alone, meaning iBuyers are unlikely to reach the ~50% market share seen in automobile dealer markets.

iBuyers: Technology-driven real estate companies (principally Opendoor and Offerpad) that use automated valuation models and online platforms to make near-instantaneous cash offers on homes, functioning as dealer intermediaries who purchase properties onto their balance sheet and resell after a short holding period, thereby providing immediate liquidity to sellers who would otherwise wait 90+ days in the traditional listing process.

Dealer (Balance Sheet) Intermediation: A form of market-making in which an intermediary purchases an asset outright and holds it on its own balance sheet while finding a subsequent buyer, as distinct from matchmaking intermediaries (brokers) who connect buyers and sellers without taking ownership. The intermediary earns a gross spread between purchase and sale prices.

Adverse Selection (in iBuyer context): The problem arising because sellers possess soft private information about their property (odors, hidden defects, neighbor quality) that algorithmic valuation models cannot capture, while traditional buyers can acquire this information through physical visits. Because iBuyers price quickly without visits, they disproportionately attract sellers of unobservably lower-quality homes, as measured in the paper by the calibrated parameter α = 0.35 (the fraction of low-quality homes the intermediary correctly identifies).

Algorithmic Valuation Model (AVM): The pricing technology used by iBuyers to value homes near-instantaneously using observable property characteristics. The paper measures AVM performance by the R-squared of a hedonic regression: over 80% for iBuyer transactions versus 68% for non-iBuyer transactions, with the residual representing information the algorithm misses and traditional buyers discover through visits.

PSALE (Probability of Sale within 3 Months): An ex ante measure of a property’s underlying liquidity, estimated from a probit model on non-iBuyer listings, capturing the probability that a given home sells within three months of listing. The paper uses PSALE as the key liquidity variable; iBuyers are almost entirely absent where PSALE falls below 50%.

Occupancy Cost: The value loss incurred when a house is held vacant on an intermediary’s balance sheet — encompassing both foregone housing service flows (which continue to benefit occupants under traditional listing but are lost under iBuyer ownership) and ongoing maintenance and depreciation costs (calibrated at d = 0.02 per period). This cost distinguishes housing from goods like cars that depreciate primarily through use rather than time.

Gross Spread: The difference between the price at which an iBuyer sells a property and the price at which it purchased that property, expressed as a percentage of the acquisition price. The paper documents a gross spread of approximately 5% (combining the 3.1 pp purchase discount and the 2.2 pp sale premium), which is persistently positive over the sample period.