Form Is Function: Bulk Restrictions, Not Design Review, as the Binding Constraint on Denser Housing in Conservation Overlay Districts

1. Introduction

Conservation overlay districts—known in Nashville as Neighborhood Conservation Zoning Overlays (NCZOs) and Historic Preservation Zoning Overlays (HPZOs)—bundle multiple regulatory instruments: design review for new construction, demolition controls, material standards, and height and bulk restrictions (the parameters governing the buildable envelope: maximum height, building width, and roof form). These overlays have proliferated nationally as municipalities seek to manage neighborhood change without the political costs of blanket downzoning (Bronin, 2012; Glaeser and Ward, 2009), often through participatory processes that amplify incumbent homeowner preferences (Einstein, Glick, and Palmer, 2020; Trounstine, 2020). Nashville's 27 NCZOs and 8 HPZOs are among the most extensively deployed in any US city.

The existing literature establishes that historic preservation and conservation overlays constrain housing supply (Glaeser and Gyourko, 2018; Listokin, Listokin, and Lahr, 1998; Waights, 2019) and may inflate prices through supply restriction and amenity capitalization (Coulson and Leichenko, 2001; Noonan, 2007; Ahlfeldt, Holman, and Wendland, 2017; Been, Ellen, Gedal, Glaeser, and McCabe, 2016). Zhou (2021) demonstrates that local historic designation with regulatory restrictions reduces new construction in Denver, while National Register listing without local restrictions does not, establishing that the regulatory content of designation drives supply effects. But the dominant measurement tool in the field, the Wharton Residential Land Use Regulatory Index (Gyourko, Saiz, and Summers, 2008; Gyourko, Hartley, and Krimmel, 2021), collapses multiple regulatory dimensions into a single score, making it difficult to isolate which specific regulation drives supply effects. As Gyourko and Molloy (2015) note, "the relative importance of different types of regulations is not well understood." What the literature has not addressed is which component of the overlay bundle constrains new housing on the land where development is feasible. Demolition controls obviously bind on contributing structures—nearly 70 percent of NCZO parcels in Nashville—but on the remaining 30 percent, where non-contributing or post-period structures sit on developable lots, the question is open. If design review or material mandates are binding on these eligible parcels, streamlining the review process or relaxing material standards unlocks supply. If bulk restrictions are binding, neither process reform nor material liberalization will matter—only the height standard determines whether denser housing is economically viable within the overlay.

This paper exploits variation in height standards across and within Nashville's overlay districts to test a specific claim: the height limitation, operating through the buildable floor area per unit, is the regulatory channel that determines whether conservation overlays suppress Horizontal Property Regime (HPR) two-on-one housing development on eligible land. HPR is a Tennessee state law that allows by-right two-unit development on duplex-zoned lots through a streamlined nonprofit corporate structure, avoiding subdivision regulations and condominium financing requirements (Gardner and Pemberton, 2024). Nashville's duplex zoning covers 58 percent of the city's zoned acreage (National Zoning Atlas, 2024), providing a large treatment-eligible population. The height limitation constrains two-unit development selectively because the floor area per unit drops below the minimum viable threshold for the for-sale product, while single-family development, which concentrates the full buildable envelope in one unit, remains unconstrained.

Nashville–Davidson County provides an unusually clean research setting. The HPR framework creates a uniform statewide mechanism for two-unit development, eliminating subdivision regulation as a confounder. Metro Nashville does not track HPR units in its administrative records, requiring inferential classification from parcel data, but this limitation is non-differential across overlay and non-overlay areas, so measurement error attenuates rather than biases the estimates. And the Lockeland Springs–East End NCZO contains a natural experiment—two adjacent groups of parcels within the same overlay, subject to the same design review, demolition controls, and material standards, but governed by different bulk standards adopted in the same year—with no parallel in the published literature.

We present four levels of evidence, each with different identification assumptions. The within-LSEE comparison (Level 1) holds all non-bulk regulatory channels constant and finds that the bulk relaxation increases HPR development ninefold relative to contextual-height parcels (odds ratio = 10.6, p = 0.0001). The cross-overlay boundary comparison (Level 4) generalizes the result across 22 overlays: the logit Inside × Stories interaction is +0.75 (p < 0.001) on 7,594 boundary parcels, and the combined-outcome specification confirms that overlays suppress total residential construction (Inside × Stories = +0.43, p = 0.025). The Salemtown replication (Level 2) provides external validation in a different overlay where a codified two-story standard preserved HPR production. The all-overlay panel (Level 3) documents a large average overlay suppression effect (Poisson: -0.89, p < 0.001) with the height interaction in the predicted direction, though underpowered with 33 clusters.

On eligible parcels—where the height standard rather than demolition controls is the binding constraint—contextual overlays cut HPR development rates nearly in half, suppressing approximately 560 units. Total overlay suppression, including demolition controls on contributing parcels, is substantially larger (approximately 1,500 units) but conflates regulatory channels the paper's design separates. The replacement fee-simple homes sell at a 15 percent premium over comparable HPR units outside the overlay.

The approach follows a mechanism-identification strategy analogous to Autor, Palmer, and Pathak (2014), who exploit within-district variation in rent control intensity, and to Turner, Haughwout, and van der Klaauw (2014) and Ganong and Shoag (2017), who demonstrate that aggregate regulatory indices obscure the channels through which specific regulations affect markets. The closest empirical precedent is Kulka, Sood, and Chiumenti (2024), who decompose bundled zoning regulations in Greater Boston and find that relaxing density restrictions is the most effective channel for increasing housing supply. Their finding that height restrictions alone have little effect in suburban settings is complementary rather than contradictory: in low-density suburbs where lots are large, lot-size minimums are the binding dimensional constraint; in urban conservation overlays where lots are small and fixed, the binding constraint shifts to the height envelope. The Minneapolis 2040 reform confirms the mechanism in reverse: the city legalized triplexes citywide in 2020 but retained height limits of 28 feet and FAR caps of 0.5, and only 20 new duplexes and triplexes were built on formerly single-family-only lots through 2024 (Hartley, 2025). International evidence confirms that dimensional relaxations produce supply responses: Büchler and Lutz (2024) find FAR increases in Zurich raise housing units by 9 percent within a decade, and Greenaway-McGrevy and Phillips (2023) document that Auckland's 2016 upzoning doubled the rate of housing construction. In the domestic context, Gray and Millsap (2023) show that Houston's 1998 minimum-lot-size reduction produced a large supply response concentrated in smaller, denser housing forms—the closest US analog to the dimensional-relaxation mechanism this paper documents.

We make three contributions. First, we decompose the overlay bundle using within-overlay, cross-overlay, and cross-regulatory-type variation to identify dimensional restrictions as the dominant channel through which overlays suppress denser housing on eligible land. Contextual Overlay Districts (CODs), which impose bulk standards without MHZC review, produce suppression of comparable magnitude to NCZOs and HPZOs—evidence that the preservation-review apparatus is not independently necessary for the supply effect.

Second, we show that the height standard determines whether overlay suppression is merely quantitative or also qualitative. Below approximately 1.5 stories, the height restriction eliminates two-unit development entirely and redirects construction to single-family forms on the same duplex-zoned land. This form-selection mechanism—one large single-family home where two ownership-oriented homes would otherwise stand—is the paper's central finding. The decomposition tells policymakers what to reform; the reversion finding tells them what the current design is actually producing.

Third, we document that even codified two-story height standards suppress HPR development substantially on high-value land, consistent with the minimum viable unit size A_min rising with land cost. The binary codified/contextual classification employed in the empirical analysis captures the physical-viability threshold—below which two-unit development is infeasible regardless of land cost—but not the financial-competitiveness threshold at which a two-story envelope cannot outbid the single-family alternative on expensive land.

2. Theoretical Framework

2.1 The Floor-Area Threshold

Consider a standard two-on-one HPR redevelopment project on a lot zoned for two dwelling units. The project is financially viable when total per-unit revenue exceeds total per-unit cost:

where P is the achievable sale price per square foot, A_unit is gross floor area per unit, C_land is total land acquisition cost (divided by two units), C_hard is construction hard cost per square foot, C_soft is soft costs per unit (design, permitting, legal, financing), and C_overlay is overlay-specific incremental costs (MHZC review, upgraded materials, demolition delay carrying costs).

The height standard constrains A_unit through the buildable envelope:

where F is the buildable footprint per unit (determined by lot geometry, setbacks, and coverage limits) and S is the number of stories achievable within the allowed height envelope. The project is viable only if A_unit exceeds a market-specific minimum viable unit size, A_min, determined by buyer preferences and the competitive product set. In Nashville's post-2014 urban core, A_min for a for-sale two-on-one is approximately 1,800 to 2,200 square feet, based on the distribution of observed unit sizes (Gardner and Pemberton, 2024).

The model predicts a threshold effect, consistent with the bunching behavior at regulatory caps documented by Anagol, Ferreira, and Rexer (2024). At S ≥ 2, the two-on-one delivers approximately 2,800 to 3,200 square feet per unit—well above A_min—and the project is viable. At S ≈ 1.5, per-unit area falls to 1,800–2,200 square feet, at or near A_min, and the project is marginal. At S ≤ 1.25, per-unit area drops to 1,400–1,800 square feet—below A_min—and the project is infeasible regardless of land cost or market price.

The threshold binds asymmetrically across housing forms. A single-family project concentrates the full buildable envelope in one unit: for an identical lot and height cap, the single-family unit achieves twice the floor area of each two-on-one unit. A 1.5-story cap produces 2,400 to 3,000 square feet for a single-family home on the same lot where it cannot deliver two viable HPR units. The height restriction therefore constrains two-unit development while leaving single-family development unconstrained—producing a selective, form-specific suppression of denser housing.

The minimum viable unit size A_min is not a physical constant. Rearranging the viability condition: A_min = (C_land/2 + C_soft + C_overlay) / (P - C_hard). As land cost rises, A_min rises with it. On a lot valued at $300,000, a two-story envelope delivering 2,800 square feet per unit comfortably exceeds A_min and the project is viable. On a lot valued at $700,000, the same envelope is marginal—the per-unit land cost absorbs most of the revenue, and the two-on-one HPR project may not generate a higher land bid than the single-family alternative. A two-story height standard that is physically sufficient for two-unit development may be financially insufficient on expensive land. This implies that the height standard operates at two thresholds: a physical-viability threshold (below approximately 1.5 stories, where the project cannot deliver a sellable product regardless of land cost) and a financial-competitiveness threshold (at two stories on high-value land, where the project delivers a viable product but cannot outbid single-family). The binary codified/contextual classification employed in the empirical analysis captures the first threshold; the codified-two-story overlay suppression documented in Section 4.2 is consistent with the second.

2.2 The Fee-Simple Premium and Land-Value Reversion

The viability condition in Section 2.1 is necessary but not sufficient. A two-on-one HPR project must generate more total residual land value than the single-family alternative competing for the same lot. Buyers consistently pay a per-square-foot premium for fee-simple single-family homes over HPR units in the same neighborhood. Define the fee-simple premium as φ = (P_sf - P_hpr) / P_sf.

The developer's land bid for a two-on-one HPR project is:

The developer's land bid for a single-family project on the same lot is:

The HPR project wins the lot when Bid_hpr > Bid_sf. Note that A_unit,sf is not exogenous to the neighborhood—developers in affluent markets build to the full envelope because the market absorbs larger homes, while developers in moderate markets may leave buildable area unused. The fee-simple revenue advantage therefore compounds across both the intensive margin (higher P_sf) and the extensive margin (larger A_unit,sf), widening the land-bid gap faster than φ alone predicts. As the height standard S decreases, A_unit,hpr falls faster in effective terms because the HPR project splits a shrinking envelope across two units. At some critical height S^*, the HPR bid falls below the single-family bid, and the developer reverts to building one large home. This is the land-value reversion point.

The reversion point varies with φ. In neighborhoods where the fee-simple premium is large, S^* is higher: the HPR project needs more stories to overcome the per-square-foot discount through volume. In neighborhoods where the premium is small, S^* is lower. This generates a testable prediction: the height standard's suppressive effect should interact with φ.

The two mechanisms compose a hierarchy. Section 2.1 determines a binary feasibility condition—whether the HPR project can deliver units above A_min—that operates independently of market conditions. Section 2.2 determines a competitive condition—whether the HPR bid exceeds the fee-simple bid—that operates only where feasibility is met. When the height standard is binding (contextual overlays), Section 2.1 dominates and φ is irrelevant. When the height standard is not binding (codified-two-story overlays), Section 2.2 governs and φ determines the outcome. This hierarchy generates two testable predictions: in the constrained regime, φ should have no effect on HPR development rates; in the unconstrained regime, HPR rates should decline monotonically with φ. We estimate φ by hedonic regression in Section 3.6 and test these predictions in Section 4.1.

2.3 Alternative Channels

Conservation overlays bundle multiple regulatory instruments. To claim that bulk is the binding constraint, the research design must distinguish it from four alternatives.

Channel B: Process costs and uncertainty. All overlays require MHZC design review for new construction, adding months to the entitlement timeline and introducing discretionary uncertainty. If process costs are binding, all overlays should suppress HPR equally regardless of height standard. Contextual Overlay Districts (CODs), which impose dimensional standards without MHZC review, provide a direct test of whether the preservation-review apparatus independently constrains development (Section 4.2).

Channel C: Demolition controls. Both NCZOs and HPZOs restrict demolition of contributing structures, and these controls are unambiguously binding—they effectively remove contributing parcels from the developable stock. This paper does not test whether demolition controls constrain development; they do. The question is whether the height standard additionally constrains development on the parcels where demolition is not an issue. Cross-overlay variation in contributing-structure share is addressed by the eligible-parcel denominator robustness check, which restricts the sample to non-contributing parcels.

Channel D: Design review stringency. HPZOs regulate all exterior work to federal preservation standards; NCZOs apply less stringent local guidelines. If stringency is binding, HPZOs should suppress HPR more than NCZOs after controlling for height. The HPZO indicator in the Level 3 panel tests this channel directly.

Channel E: Material and design standards. Overlay-mandated materials increase hard costs but do not reduce buildable area. If binding, the overlay should produce a price premium reflecting cost pass-through, with production declining only if the premium exceeds buyer willingness to pay.

The within-LSEE comparison (Level 1) holds Channels B through E constant by design. The cross-overlay boundary comparison (Level 4) controls for neighborhood-level confounders. The HPZO indicator in the panel (Level 3) tests Channel D. The eligible-parcel denominator controls for Channel C by restricting the sample to parcels where demolition protections do not apply. The convergent evidence across designs with different assumptions is the basis for concluding that Channel A—bulk restriction—is the regulatory channel that determines whether overlays suppress development on eligible land. The non-bulk channels (B, C, E) are held constant or controlled for rather than directly tested; the evidence shows that height is sufficient for suppression and that development continues under full non-height regulation when the height standard accommodates it.

3. Data and Institutional Context

3.1 Nashville's Overlay System

Nashville–Davidson County administers three types of conservation overlay districts through the Metropolitan Historic Zoning Commission (MHZC): 27 Neighborhood Conservation Zoning Overlays (NCZOs), 8 Historic Preservation Zoning Overlays (HPZOs), and 33 Contextual Overlay Districts (CODs).† NCZOs and HPZOs are the focus of this study; CODs impose separate, typically less restrictive design standards and are examined as a comparison group in Section 4.2.

Both NCZOs and HPZOs require MHZC design review for new construction, additions, and demolition. Both impose material standards and bulk guidelines specified in district-level design guideline documents. The regulatory difference between the two types lies in scope and stringency. HPZOs regulate all exterior work—including routine maintenance, window replacement, and repointing—and apply the Secretary of the Interior's Standards for Rehabilitation or equivalent local standards. NCZOs regulate new construction, additions, and demolition but exempt minor renovations and maintenance, applying locally developed guidelines that afford greater latitude. If design review stringency, rather than bulk, were the binding constraint, HPZOs should suppress HPR development more than NCZOs after controlling for height.

A critical feature of the contextual height standard is the reference population it uses. The NCZO design guidelines specify that the height of new construction "should be compatible with surrounding historic buildings of the same building type and on the same block face" (MHZC, 2025, Part I, Section V.A.1; emphasis added). Non-contributing structures—including contemporary new construction—are not the primary reference for the contextual baseline. The effective height limit is therefore a function of the historic building stock, not the current built environment. In a neighborhood where all surviving historic structures are one story but recent development has added two-story buildings on adjacent lots, the contextual standard remains one story. This practice creates a self-reinforcing constraint: as neighborhoods redevelop, the contextual baseline remains anchored to an increasingly unrepresentative historic stock, and the height restriction becomes more binding over time rather than less.

3.2 The LSEE NCZO and the Boscobel Carve-Out

The Lockeland Springs–East End NCZO was adopted in 1985 (Ordinance O85-896) and expanded in 2003 (BL2003-1369) and 2014 (BL2014-737 and BL2014-812). The 2014 expansion brought approximately 465 lots into the overlay. The MHZC staff report for BL2014-812 (MHZC, 2014) documents the rationale for block-specific provisions on the 1400–1600 blocks of Boscobel Street. Staff noted that these blocks "have characteristics that are unique to the Lockeland Springs–East End Neighborhood Conservation overlay district": very few historic structures (only eight with Boscobel frontage), a grade change of more than 20 feet across some parcels, one block face lacking an improved alley, and "significant new construction on these blocks since 2010, most of which is in a contemporary style and two-stories in height with a flat roof form." Because of these conditions, staff recommended—and the Commission adopted—additional guidelines permitting two-story height, 40-foot building widths, and flat or minimal-slope roofs on the Boscobel blocks. All other expansion parcels received the district's general contextual height standard. The applicant for the expansion was Councilmember Peter Westerholm; the staff report does not reference developer participation in the drafting of the block-specific provisions.

The Boscobel carve-out creates a natural experiment within a single overlay. The treatment assignment was not random—it was driven by the blocks' existing physical conditions—and the implications for identification are discussed in Section 4.1. The 59 treatment lots and the adjacent control lots entered the same regulatory system on the same date, subject to the same design review board, the same demolition standards, the same material requirements, and the same application process. The only difference is the bulk envelope. This is an unusually clean identification setting: the within-overlay comparison holds constant not only overlay status (the binary treatment in prior studies) but the specific regulatory institution administering it.

3.3 HPR Classification

Metro Nashville does not directly code HPR units in its administrative records. We classify HPR units inferentially from parcel, assessor, and building data following the methodology described in Gardner and Pemberton (2024). The classification merges 286,102 Davidson County parcel records with building improvement data from the Property Assessor's office (PADCTN), identifies multi-unit parcels, distinguishes HPR from condominium and fee-simple ownership structures, and assigns HPR subtypes (two-on-one, townhouse, detached cluster, duplex cluster, conversion, plus-one).

Validation against published benchmarks yields 20,717 HPR units and 8,770 two-on-ones in the 2010–2023 study period, deviations of 2.9 percent and 1.1 percent respectively from the 20,125 and 8,675 reported in Gardner and Pemberton (2024). The classifier identifies seven HPR subtypes: two-on-one (8,770), townhouse (7,063), detached cluster (2,484), duplex cluster (657), original (575), plus-one (487), unit split (236), and 445 units identified as HPR but not assigned to a specific subtype. The classification is conservative by design: parcels must satisfy multiple convergent indicators—ownership structure (HPR regime filing), physical form (building footprint, unit count), and parcel characteristics—before receiving an HPR classification. This approach minimizes false positives at the cost of potentially missing edge-case HPR developments (false negatives). Classification error is non-differential across overlay and non-overlay areas, attenuating rather than biasing the treatment effect estimates.

3.4 Overlay Height Standard Extraction

The 37 NCZO and HPZO design guideline documents are published by the MHZC on the Metro Nashville website. Nashville organizes its NCZO guidelines into umbrella documents—a "Turn-of-the-Century" volume (Parts I and II) covering 27 districts and a "Mid-Century" volume covering newer districts—with district-specific chapters. Each HPZO has its own guideline document. We retrieved all 14 source documents programmatically. The 14 documents collectively contain design guidelines for all 37 overlay districts; we extracted provisions at the district level from the relevant chapter of each umbrella document. Height and bulk provisions were extracted using a structured prompt submitted to the Claude API (Anthropic, model: claude-sonnet-4-20250514), with the extracted text from each PDF as input.

The extraction coded 36 overlay districts on 18 fields, including height standard type (codified absolute, codified stories, contextual, or hybrid), maximum height in feet and stories, verbatim contextual language, effective maximum stories for new residential construction, demolition standard, and material requirements. Thirty-six overlays were successfully coded.† Thirteen were classified as codified two-story (effective maximum of two or more codified stories) and 23 as contextual or restricted (below two stories). Thirty-two extractions achieved high confidence, three medium, and one low. The three medium-confidence and one low-confidence extractions (Marathon Village at 2.5 stories, LSEE at 1.5, Richland West End Addition at 1.5, South Music Row at 1.5) all fall clearly on one side of the binary threshold; none is borderline. The binary classification—codified two-story versus contextual—is robust to measurement error for two reasons: no overlay sits at exactly the 2.0-story threshold where reclassification would change its category, and contextual standards are functionally unpredictable regardless of their specific language (no NCZO defines a formula for computing contextual height; the effective maximum is set by MHZC staff on an application-by-application basis). The three medium-confidence and one low-confidence overlays (Marathon Village, LSEE, Richland West End Addition, South Music Row) do not contribute to the Level 4 boundary sample due to insufficient outside-buffer parcels, so the Level 4 interaction estimate is mechanically unaffected by their classification. Four overlays classified as codified two-story have contextual guideline language (Edgefield, Germantown, Woodland-in-Waverly, Belmont-Hillsboro); in each case, the contextual reference population includes two-story contributing structures, making the effective contextual standard two stories. Reclassifying all four as contextual and re-estimating the Level 4 specification yields Inside × Stories = +4.05 (p < 0.001, N = 7{,}594). The large increase from the primary coefficient (+0.75) reflects the mechanical effect of moving four high-suppression overlays (Belmont-Hillsboro: 17.7 pp suppression; Edgefield: 13.0 pp) from the codified-two-story category to the contextual category, concentrating more of the identified suppression in the height channel. In substantive terms, both specifications tell the same story: predicted HPR rates inside contextual overlays are 5–9 percent regardless of coding, compared to 24 percent outside. The primary specification, which codes these four overlays as codified two-story, is conservative: it attributes their suppression to non-height overlay channels rather than to the height standard.

3.5 Parcel Data Assembly

Parcel boundaries, assessor records, base zoning classification, and overlay boundary polygons are from Metro Nashville Open Data and the Metro Nashville GIS portal. All spatial operations use EPSG:2274 (Tennessee State Plane, NAD83, US Feet). Overlay membership is assigned by spatial join of parcel centroids to overlay polygons: 10,796 parcels fall within NCZOs and 2,057 within HPZOs, of which 6,263 are on duplex-zoned (R-classified) land permitting two-family development by right. Boundary distances are computed as Euclidean distance from parcel centroids to the nearest overlay boundary segment, yielding 8,090 parcels within 500 feet. Annual year-end GIS snapshots of overlay and building boundaries from 2010 through 2021 provide the time-varying overlay geography.

Contributing status is approximated by comparing each parcel's year built (from assessor records) to the overlay's designated period of significance (from the guideline extraction). This is a proxy for the MHZC's formal contributing-structure determination, which is not available in structured form. Structures built within the period of significance are coded as contributing; structures postdating it, structures with assessed improvement value of zero (vacant lots), and structures with improvement value below $25,000 (conditionally eligible) are coded as eligible for redevelopment. Of the 10,796 NCZO parcels, 10,142 can be classified using assessor year-built data matched to overlay-specific periods of significance: 7,082 (69.8 percent) are contributing and 3,060 (30.2 percent) are non-contributing. The share varies widely across overlays, from 97 percent in Haynes Manor (period of significance 1950–1980, nearly all original stock intact) to 28 percent in Salemtown (period of significance 1855–1945, extensive post-POS infill). The remaining 654 NCZO parcels lack year-built records and could not be classified.

3.6 Fee-Simple Premium Estimation

The neighborhood-level fee-simple premium φ is estimated by hedonic regression on post-2010 sales of HPR two-on-ones and fee-simple single-family homes built since 2000, restricted to census tracts with at least 30 transactions of each type. The specification includes unit square footage, year built, lot area, census-tract fixed effects, and sale-year fixed effects (annual; sale-quarter fixed effects would be preferable given Nashville's intra-year price variation but are not estimable for all tract-year cells at the minimum sample size). The sample comprises 8,244 transactions across 29 tracts.

The pooled HPR coefficient is -0.084 (p < 0.001), implying a hedonic fee-simple premium of 8.0 percent after controlling for physical characteristics and location. The tract-level median is 9.1 percent (IQR: -5.8 to 18.9 percent). Negative estimates (HPR trading at an apparent premium to fee simple) occur in three tracts and are uniformly insignificant at conventional levels; the largest positive estimates are significant (p < 0.05). The pooled estimate is consistent with the descriptive finding in Gardner and Pemberton (2024) that the HPR discount varies from near zero in working-class neighborhoods to substantial premiums in affluent areas, though the hedonic estimate is smaller than the raw median-price comparisons reported there because the hedonic controls absorb the mechanical contribution of unit size and lot area differences.

4. Empirical Strategy and Results

4.1 Within-Overlay Comparison: Lockeland Springs–East End

The Lockeland Springs–East End (LSEE) Neighborhood Conservation Zoning Overlay provides a natural experiment in which the only regulatory difference between two groups of parcels is the bulk envelope. The LSEE overlay was originally adopted in 1985 and expanded twice in 2014. Two ordinances enacted within two months of each other brought adjacent blocks into the same overlay under different bulk standards. BL2014-812 governs several hundred lots in the 2014 expansion but includes specific bulk provisions for the 59 lots on the 1400–1600 blocks of Boscobel Street, codifying a two-story height allowance, a 40-foot building width, and permission for flat or minimal-slope roofs. BL2014-737, governing 142 lots in the McEwen blocks, imposed the district's general contextual height standard, which the Metropolitan Historic Zoning Commission (MHZC) interprets as approximately one to one and a half stories based on surrounding contributing structures. The non-Boscobel portions of BL2014-812—an additional 188 lots on cross streets—received the same contextual standard.

The two groups share everything except bulk. Both are subject to the same MHZC design review for new construction. Both face the same demolition controls, the same material standards, the same application fees, and the same review timeline. The Boscobel carve-out relaxes only the buildable envelope—height, width, and roof form—while holding all non-bulk regulatory channels constant. The treatment is therefore a composite bulk relaxation, not an isolated height experiment. Because the theoretical model in Section 2.1 operates through total floor area per unit, which is a function of all three parameters, the composite treatment tests the mechanism the theory identifies.

The Boscobel carve-out was not randomly assigned. As documented in the MHZC staff report, the block-specific provisions were adopted because the 1400–1600 blocks of Boscobel already had extensive two-story contemporary construction and very few historic structures—conditions that made the general contextual standard inapplicable. The staff report identifies the ordinance applicant as Councilmember Peter Westerholm, not a developer; the documented record shows a council-initiated process rather than developer-driven lobbying. Because MHZC determines contextual height predominantly from contributing structures (Section 3.1), the effective standard on the Boscobel blocks—with only eight historic structures amid extensive contemporary two-story construction—would have been set by those eight one-story buildings, not by the surrounding two-story infill. The carve-out therefore permits height that the contextual standard would have prohibited, not merely codifies height that the contextual standard would have allowed. The treatment is a genuine bulk relaxation, not a reduction in regulatory uncertainty about the same effective height. We confirm this empirically by coding all 73 MHZC staff recommendations for primary new construction on R-zoned parcels in LSEE from 2012 through 2024 (excluding the Boscobel carve-out blocks). In at least 74 percent of cases (54 of 73), staff recommended a contextual height of 1.5 stories or below. The remaining cases include projects described as "two-story" in staff reports that are architecturally one-and-a-half-story gabled forms—steep-pitched roofs with dormered attic space—consistent with the contextual standard. The median recommended height is 1.5 stories, confirming that the contextual standard in LSEE typically defaults to heights incompatible with two-unit development.

The pre-trend evidence directly addresses whether the Boscobel blocks were on a divergent trajectory before the carve-out. The change in HPR rates from the pre-period to the post-period was 10.1 percentage points on Boscobel and 0.6 percentage points on McEwen—a difference-in-differences of 9.5 percentage points. McEwen barely changed; Boscobel accelerated sharply. All eight pre-2014 HPR units on Boscobel were built in 2013, before BL2014-812 brought these blocks into the overlay—consistent with the county-wide pre-adoption development surge (Figure 4) rather than a sustained Boscobel-specific trend. Entity ownership rates do not differ significantly between the groups in the pre-period (p = 0.199).

The endogeneity concern also cannot explain the form-specificity of the result. Pre-existing development pressure on duplex-zoned land predicts more development of all types—both HPR and single-family—on the higher-pressure blocks. But the post-period divergence is exclusively HPR on Boscobel and exclusively single-family on McEwen. A pure momentum story cannot generate this form-specific pattern; only the bulk standard can, because only the bulk standard differentially constrains two-unit development while leaving single-family feasible. We list the non-random assignment as a limitation in Section 5.3, and note that the Level 4 boundary comparison—which exploits cross-overlay variation in height standards rather than within-overlay carve-outs—does not share this concern.

We estimate a linear probability model at the lot level:

where i indexes lots in the 2014 expansion area, BulkRelaxation_i equals one for Boscobel lots and zero otherwise, and X_i includes lot area, pre-overlay assessed value, and year built. We supplement this with Fisher's exact test, which requires no distributional assumptions and is appropriate for the small treatment group. Standard errors in the LPM are heteroskedasticity-robust.

HPR Suppression

Of the 59 Boscobel lots, 11 (18.6 percent) were redeveloped as HPR two-on-ones after the 2014 overlay adoption. Of the 142 McEwen lots under contextual height restrictions, 3 (2.1 percent) were similarly redeveloped (N = 201). The odds ratio is 10.6 (p = 0.0001, Fisher's exact). The LPM estimates β̂₁ = 0.165 (t = 3.16, p = 0.002), implying that the bulk relaxation increased the probability of HPR redevelopment by 16.5 percentage points.

The result is robust to the control-group definition. Using the full set of non-Boscobel 2014 expansion parcels (330 lots, N = 389) as the comparison group yields an odds ratio of 2.9 (p = 0.011) and β̂₁ = 0.114 (p = 0.031). The attenuation is expected: some non-Boscobel parcels within the BL2014-812 polygon lie on cross streets (Lillian, Shelby, 14th through 17th) that may benefit from proximity to the Boscobel carve-out without being formally subject to it. Both control-group definitions produce significant effects; the McEwen-only comparison is the cleaner design, and the all-expansion comparison demonstrates that the finding is not an artifact of sample restriction.

Pre-Trend Validation

The Boscobel and McEwen blocks differ on observable parcel characteristics. Boscobel lots are smaller (mean lot area 4,489 sq ft versus 7,660 sq ft, p < 0.001), have lower pre-overlay assessed values ($654,000 versus $759,000, p = 0.010), and carry newer structures (mean year built 1986 versus 1946, p < 0.001). These differences reflect the Boscobel corridor's position within the neighborhood—closer to Shelby Avenue and the commercial redevelopment frontier, with smaller lots from older subdivision plats that were already experiencing development pressure by 2014.

The more informative pre-trend test examines pre-overlay outcomes rather than parcel characteristics. Entity ownership rates—a proxy for speculative acquisition—do not differ significantly between the two groups (p = 0.199). Pre-2014 HPR activity was modestly higher on Boscobel lots (8.5 percent versus 1.5 percent, p = 0.060). All eight pre-2014 HPR units on Boscobel were built in 2013, before BL2014-812 brought these blocks into the overlay—this is pre-treatment activity on pre-treatment land. The concentration in the year immediately before adoption is consistent with the pre-adoption development surges visible in the event-study figure (Figure 4), where HPR production typically peaks in the years just before overlay adoption across all overlay types. The Boscobel pre-trend reflects a county-wide pattern rather than a corridor-specific anomaly.

The pre-period gap nonetheless requires assessment. The change in HPR rates from the pre-period to the post-period was 10.1 percentage points on Boscobel (8.5 to 18.6 percent) and 0.6 percentage points on McEwen (1.5 to 2.1 percent). An informal difference-in-differences estimate is 10.1 - 0.6 = 9.5 percentage points. McEwen barely changed; Boscobel accelerated sharply after the carve-out. The post-period divergence also operates in the specific direction the theory predicts: concentrated in HPR two-on-ones, absent in single-family development, and consistent with the floor-area threshold mechanism. A pre-existing trend in general development activity would not produce this form-specific pattern.

Including lot area, assessed value, and year built as LPM controls reduces β̂₁ from 0.165 to 0.065 (p = 0.250). This attenuation is expected: lot size and HPR feasibility are mechanically correlated in Nashville, where smaller lots are more common in the denser, HPR-prone neighborhoods regardless of overlay status. The controlled estimate is a conservative lower bound that absorbs some of the treatment effect through this correlation. Fisher's exact test—which requires no functional-form assumptions and is designed for exactly this sample structure—remains the primary test. The odds ratio of 10.6 (p = 0.0001) on an 11-out-of-59 versus 3-out-of-142 comparison is not a fragile result.

Reversion

The theoretical framework predicts that where the bulk envelope kills the HPR project, developers should revert to building one fee-simple single-family home on duplex-zoned lots—the only viable for-sale product within the constrained envelope. We test this directly by estimating the same LPM with an indicator for fee-simple single-family new construction as the dependent variable.

No Boscobel lot received fee-simple single-family new construction after 2014. Four McEwen lots (2.8 percent) did. The reversion coefficient is β̂₁ = -0.028 (p = 0.044, LPM; p = 0.32, Fisher's exact). Fisher's exact test—the primary test for the HPR comparison—does not reject at conventional levels, reflecting limited power with only 4 events on 142 control lots. The LPM, which imposes stronger distributional assumptions but has more power at small event counts, detects the effect at the 5 percent level. The Level 1 reversion finding is suggestive but underpowered. The stronger evidence for the form-selection mechanism comes from the Salemtown/Waverly-Belmont replication (Section 4.3), where the SF/HPR ratio diverges sharply between codified-two-story and contextual overlays, and from the cross-overlay combined-outcome specification (Section 4.2), which confirms that overlays suppress total residential construction.

This reversion finding extends the quantity-quality tradeoff documented by Noonan and Krupka (2011), who show that preservation designations affect the composition of housing investment. Kulka, Sood, and Chiumenti (2024) find a parallel compositional effect in Greater Boston: restrictive zoning shifts housing toward larger, more expensive units. Prior studies measure the aggregate supply effect of overlay adoption; none have shown that overlays selectively suppress one housing form while permitting another on the same land. The finding connects directly to the policy implication: the overlay is not form-neutral. A contextual height standard applied to a neighborhood of one-story buildings makes two-unit development physically impossible while leaving single-family development unconstrained, redirecting market activity toward a less dense, more expensive product.

The Two-Regime Structure

The theoretical model in Section 2 predicts a regime-switching mechanism: the height standard determines feasibility (Section 2.1), while the fee-simple premium determines selection conditional on feasibility (Section 2.2). We examine this prediction by cross-tabulating HPR and single-family development rates against the tract-level fee-simple premium, separately for parcels in contextual-height and codified-two-story overlays.

In contextual-height overlays (effective maximum below two stories), the fee-simple premium has no systematic relationship with the HPR development rate or the SF/HPR ratio (Spearman ρ = -0.20, p = 0.80). The height restriction kills HPR development across all values of φ, in neighborhoods where HPR trades near parity with fee simple and in neighborhoods where the premium is large. Section 2.1 dominates: the floor-area threshold binds absolutely, not relatively.

In codified-two-story overlays (effective maximum of two stories or more), the pattern reverses. HPR development declines monotonically from 19.8 percent in the lowest φ quartile to zero in the highest (Spearman ρ = 1.0, exact permutation p = 0.042, n = 4 quartile bins). Where the height standard permits HPR, the fee-simple premium determines whether developers exercise the option. In affluent neighborhoods where fee-simple homes command a large per-square-foot premium, developers build one large house even where zoning and height would permit two.

The two regimes compose a sequential filter. Height is the gate; the fee-simple premium is the switch on the other side. This structure explains the insignificance of the linear Post × EffectiveStories interaction in the Level 3 panel: a linear interaction term imposes the wrong functional form on a mechanism that operates in discrete regimes, with φ irrelevant when height is binding and dominant when it is not.

The tabulation tests pre-specified theoretical predictions, not an atheoretical data exploration. The theory predicts two specific patterns: in the constrained regime, φ should have no effect (because the project is infeasible regardless of market conditions), and in the unconstrained regime, HPR rates should decline monotonically with φ. Both are confirmed. For the pattern to be spurious, a neighborhood-level confounder would need to correlate with φ, independently suppress HPR development, and do so only in codified-two-story overlays while having no effect in contextual overlays. The most plausible candidates—land price and lot size—are absorbed by the hedonic controls that produce the φ estimates. The conditional tabulation is nonetheless descriptive and does not control for unobserved neighborhood characteristics that may independently affect development patterns. We present it as evidence consistent with the theoretical mechanism, not as a causally identified test of the fee-simple premium channel.

4.2 Cross-Overlay Boundary Comparison

The within-LSEE comparison provides clean identification but is limited to a single overlay. To generalize across Nashville's overlay districts, we exploit the spatial discontinuities created by overlay boundaries, following the boundary-based comparison framework discussed by Keele and Titiunik (2015) and applied to land-use boundaries by Black (1999), Turner, Haughwout, and van der Klaauw (2014), and Koster, van Ommeren, and Rietveld (2012, 2016). Parcels on opposite sides of a boundary street share the same base zoning, lot characteristics, and housing market but face different overlay regulations. Nashville's overlay boundaries do not coincide with base zoning boundaries (which predate the overlays) or with census-tract boundaries, mitigating the compound treatment concern that Keele and Titiunik (2015) identify as the primary threat to boundary-based designs.

The boundary sample includes all duplex-zoned residential parcels within 500 feet of NCZO and HPZO overlay boundaries. The expanded sample contains 7,594 duplex-zoned parcels matched to overlay height data across 22 overlays, of which 4,821 lie inside an overlay and 2,773 outside. Median assessed values are comparable across the boundary ($824,000 inside vs $724,000 outside at 0–100 feet), confirming that the boundary provides a valid comparison of similar land under different regulatory regimes.

We estimate:

where i indexes parcels, k indexes the nearest overlay, Distance_i is the signed distance to the overlay boundary (positive inside, negative outside), and EffectiveStories_k is the coded height standard of the overlay. The outcome is a binary indicator for HPR development after the overlay adoption date. Because the HPR development rate on duplex-zoned parcels outside overlay boundaries is 23.8 percent, we estimate by logit to avoid the out-of-range fitted values that a linear probability model produces at low base rates with large treatment effects (Angrist and Pischke, 2009). We report average marginal effects (AMEs) for interpretability.

The boundary comparison rests on the assumption that parcels on opposite sides share similar market conditions. Median assessed values at 0–100 feet from the boundary are $824,000 inside and $724,000 outside—a 14 percent gap that narrows to 9 percent at 100–250 feet ($804,000 vs. $737,000). The gradient is smooth across the boundary with no discontinuous jump in land value, consistent with the overlays delineating regulatory zones within otherwise comparable neighborhoods rather than separating fundamentally different markets. The distance control absorbs any remaining spatial trend.

The logit estimates on the expanded sample with Boscobel parcels coded at effective stories of 2.0 yield β̂₁ = -2.34 (p < 0.001) and β̂₃ = +0.75 (p = 0.0004), N = 7{,}594. All overlays suppress HPR development, and the suppression varies with the height standard. Predicted HPR rates from the logit are 23.8 percent outside overlay boundaries, 8.5 percent inside contextual overlays, and 11.9 percent inside codified-two-story overlays—a suppression of 15.3 percentage points in contextual overlays and 11.9 percentage points in codified-two-story overlays. The interaction is significant: contextual overlays suppress more than codified-two-story overlays, with a differential of 3.4 percentage points attributable to the height channel. But codified-two-story overlay suppression is substantial—nearly half the HPR development that occurs outside overlay boundaries is eliminated even when the height standard accommodates two stories.

The LPM produces coefficients in the predicted direction: Inside = -0.249 (p < 0.001), Inside × Stories = +0.062 (p = 0.0006), confirming the logit findings.†

Figure 3 presents HPR development rates by distance from the overlay boundary, faceted by height standard type. In the contextual-height panel, inside-overlay parcels show lower HPR rates than comparable parcels outside. In the codified-two-story panel, the differential narrows but does not vanish. The visual confirms the regression finding: the same regulatory institution produces different outcomes depending on the height standard.

Results are consistent at the 250-foot bandwidth: Inside × Stories = +0.61 (p = 0.020), N = 4{,}451, indicating that the finding is not sensitive to bandwidth choice.

A scope note on the identification: because the non-bulk regulatory channels (design review, material standards, process costs) are present in all overlays, the cross-overlay variation isolates height as the channel that explains which overlays suppress development more. It does not identify whether the non-height channels independently reduce the level of development uniformly across all overlays, since these channels do not vary in the research design. The paper identifies height as sufficient for suppression—when height is contextual, development collapses—and as necessary for the variation in outcomes across overlays. The Salemtown evidence (Section 4.3) provides the most direct test of the non-height bundle: full design review, demolition controls, and material standards are present, and HPR development increased nearly sevenfold after adoption. If the non-height channels were independently sufficient to suppress development, Salemtown should show suppression, and it does not.

Eligible-Parcel Denominator

The primary specification measures HPR rates against the full population of R-zoned parcels, but not all parcels in an overlay are realistically eligible for redevelopment. Structures classified as contributing to the district's period of significance face demolition controls that effectively remove them from the redevelopable stock. We re-estimate the logit boundary specification restricting the sample to parcels built after 1945 or with missing construction dates, a proxy for non-contributing status since most overlay periods of significance end before 1945. The Inside × Stories coefficient is +0.59 (p = 0.013, N = 4{,}161). The height-standard effect persists when the denominator excludes parcels where demolition protections effectively prohibit redevelopment.

Because the 77 Boscobel parcels appear in both the Level 1 treatment group and the Level 4 boundary sample (coded at their actual effective height of 2.0 stories), we verify that the Level 4 result does not depend on recycling the Level 1 treatment. Excluding Boscobel entirely yields Inside × Stories = +0.49 (p = 0.027, N = 7{,}517). The interaction remains significant, confirming that the cross-overlay height gradient is not driven by the within-overlay carve-out.

Reversion

The theoretical model predicts that height restrictions redirect development from two-unit to single-family forms. We test this at the boundary by estimating the same specification with single-family new construction on duplex-zoned parcels as the dependent variable, then with any residential new construction (HPR or single-family combined) as the outcome.

Single-family rates are flat inside and outside overlays (2.28 percent inside versus 2.38 percent outside). The SF logit yields Inside = +1.38 (p = 0.08) and Inside × Stories = -0.90 (p = 0.047)—marginal evidence that contextual overlays produce modestly higher single-family rates conditional on the height standard, but the effect is small.

The combined-outcome specification provides the more informative test. Any residential new construction (HPR or SF) on a duplex-zoned parcel post-adoption yields: Inside = -1.70 (p < 0.001), Inside × Stories = +0.43 (p = 0.025). Overlays suppress total residential construction on duplex-zoned land, and the suppression is concentrated in contextual-height overlays.

The reversion mechanism is documented in the Level 1 within-overlay comparison (zero SF on Boscobel, 2.8 percent on McEwen) and the Level 2 Salemtown replication. The cross-overlay combined-outcome specification confirms overlays suppress total residential construction. The form-selection effect is concentrated in high-pressure markets; in lower-pressure settings, the height restriction suppresses total development without form substitution.

Placebo

Randomly assigning inside/outside status across all boundary parcels in 100 iterations produces no coefficient exceeding the observed +0.75 (permutation p < 0.01), confirming that the interaction reflects the regulatory treatment rather than spatial confounders.

Pre-Adoption Falsification

If the Inside × EffectiveStories interaction reflects pre-existing neighborhood characteristics rather than the overlay treatment, it should appear in pre-adoption HPR rates. We test this by replacing the outcome with an indicator for HPR development in the pre-adoption period (2005 through the year before each overlay's adoption). On the subsample of overlays adopted in 2008 or later—where a meaningful pre-adoption window exists—Inside × Stories is -0.15 (p = 0.77, N = 2{,}759). The height gradient is absent before overlays were adopted. On the full sample, the pre-adoption coefficient is negative (-1.53, p = 0.001), indicating that areas later assigned higher height limits actually had lower pre-adoption HPR rates—the opposite of the confounding pattern the test is designed to detect. The post-adoption reversal from negative to positive is consistent with the overlay treatment, not pre-existing trends, driving the observed height gradient.†

Contextual Overlay Districts

Contextual Overlay Districts (CODs) impose dimensional standards—height limited to 125 percent of the average height of the principal structures on the two abutting lots (maximum 35 feet) and footprint limited to 150 percent of the average building coverage of the two abutting lots—through standard Metro Codes permitting. CODs do not require MHZC review, commission hearings, or preservation-specific material mandates. The reference population for dimensional standards is all adjacent structures, including contemporary construction, unlike NCZOs which reference contributing (historic) structures only.

The COD boundary sample applies the same 500-foot bandwidth to COD boundaries, restricted to duplex-zoned parcels. The logit estimate yields Inside = -1.003 (p < 0.001). HPR rates drop from 17.6 percent outside to 7.3 percent inside (-10.3 percentage points), N = 5{,}697.

Comparing across overlay types, NCZOs suppress HPR by 12.5 percentage points while CODs suppress by 6.7 percentage points on average. But this comparison is confounded by at least four differences between CODs and NCZOs: the height formula (125 percent of adjacent vs. contextual match to historic), the footprint allowance (150 percent of adjacent vs. overlay-specific), the reference population (all adjacent structures vs. contributing structures only), and lot geometry (COD median lot area of 10,890 square feet vs. NCZO median of 8,276 square feet). The cross-type comparison cannot cleanly isolate the independent effect of the MHZC review process from these dimensional-formula differences.

The COD combined-outcome specification yields Inside = -0.910 (p < 0.001). Single-family rates are flat inside and outside CODs (0.42 percent inside, 0.39 percent outside). CODs suppress HPR development without redirecting to single-family forms—consistent with a quantitative suppression effect operating through dimensional restrictions alone, without the form-selection mechanism that operates in contextual-height NCZOs. This finding does not rule out an independent role for process costs and approval uncertainty, which Gabriel and Kung (2024) document as quantitatively important for multifamily supply in Los Angeles. The COD-NCZO comparison identifies the dimensional channel as sufficient for suppression; it cannot establish that the NCZO review process adds zero cost, because the two regulatory types differ on dimensions other than process (Section 5.3).

4.3 External Replication: Salemtown

The Salemtown NCZO, adopted in 2013, codifies a two-story, 35-foot height standard without contextual limitations. Its design guidelines note that "although there is only one historic two-story building in the overlay, two-story infill is appropriate because of the larger context of the neighborhood." Salemtown is the only post-2010 overlay in Nashville's urban core with a codified two-story standard.

HPR production in Salemtown increased nearly sevenfold after overlay adoption, from 0.47 to 3.15 units per 100 R-zoned parcels per year. The nearest-time contextual-height NCZO with a comparable R-zoned parcel base is Waverly-Belmont (737 R-zoned parcels, adopted 2016, effective maximum of 1.5 stories under a contextual standard requiring new construction to be "compatible with surrounding historic buildings of the same building type and on the same block face"). Waverly-Belmont's HPR rate declined 51 percent after adoption, from 0.91 to 0.45 per 100 parcels per year.

The reversion pattern replicates in the same comparison. After adoption, Salemtown's single-family new construction rate on R-zoned parcels fell to zero, while Waverly-Belmont's increased from 0.09 to 0.17 per 100 parcels per year. The SF/HPR ratio is 0.00 in Salemtown and 0.38 in Waverly-Belmont. Developers in the contextual-height overlay substituted single-family for two-unit construction on the same duplex-zoned land.

The expanded boundary analysis (Section 4.2) reveals that codified-two-story overlays suppress HPR by approximately 11.9 percentage points on average—less than contextual overlays, but not zero. Salemtown's post-adoption HPR increase demonstrates that a codified two-story standard permits housing production to continue—not that it imposes no cost.

The contrast replicates Level 1 in a different overlay, neighborhood, building stock, and adoption year. The mechanism is the same: a codified two-story standard preserves the HPR development option; a contextual standard destroys it and redirects development to less dense forms.

4.4 All-Overlay Panel: Descriptive Context

We construct an overlay-year panel covering 33 NCZO and HPZO districts over 2005–2023 (N = 627 overlay-years, 33 overlay districts comprising 32 unique overlay_name values due to Whitland Area and Whitland Ave mapping to the same extraction), with annual HPR two-on-one counts on R-zoned parcels as the outcome variable. The preferred specification includes overlay and year fixed effects:

Standard errors are clustered at the overlay level.

The average overlay effect is large and significant in the Poisson count specification (β̂₁ = -0.89, p < 0.001): overlays reduce HPR production substantially. The height interaction in the preferred log-linear specification has the correct sign (β̂₂ = +0.049) but does not reach significance (p = 0.43) with 33 clusters. The binary height specification (CodifiedTwoStory_j ≥ 2 stories) produces a larger point estimate (+0.143) but remains insignificant (p = 0.36). Adding the HPZO indicator to test Channel D (design review stringency) yields a near-zero, insignificant coefficient (-0.037, p = 0.76), conditional on height, providing evidence against the hypothesis that the HPZO/NCZO distinction independently constrains HPR development beyond what the height standard explains.

Wild cluster bootstrap p-values (Cameron, Gelbach, and Miller, 2008; 999 replications) for the height interaction are 0.30 in the continuous specification and 0.48 in the binary specification, confirming that the panel lacks power to detect the interaction with 33 clusters.

The panel does not detect the height interaction—the coefficient is positive but insignificant under both asymptotic and bootstrap inference, as expected with 33 clusters. The panel's contribution is not to the height mechanism but to two other findings: the large average overlay suppression effect (-0.89, p < 0.001 in the Poisson specification), and the null on design review stringency (the HPZO indicator is insignificant conditional on height, though the null is itself underpowered with only 8 HPZOs among 33 clusters and should be interpreted cautiously).

5. Discussion and Policy Implications

5.1 The Counterfactual

The counterfactual addresses two distinct policy questions. The first—reforming the height standard while keeping the overlay—corresponds to the politically feasible intervention: no overlay is getting repealed, but height-standard reform is achievable, as the Salemtown and Boscobel precedents demonstrate. The second—total overlay suppression—provides context for the housing-supply literature. The two estimates are nested, not additive: the height-channel estimate is a subset of the total.

Component 1: Height-Standard Reform on Eligible Land

On eligible parcels—where the height standard rather than demolition controls is the binding constraint—we compute overlay-specific suppression rates from the boundary comparison. We restrict the boundary sample to parcels built after 1945 or with missing construction dates (a proxy for non-contributing status) and apply a 10 percent outside-buffer filter, excluding overlays where fewer than 10 percent of boundary parcels lie outside the overlay (LSEE, Edgefield, and Woodland-in-Waverly). For excluded overlays, we substitute the pooled eligible-parcel rate for their height category.

On eligible parcels outside overlay boundaries, the HPR rate is 34.3 percent in contextual neighborhoods and 30.3 percent in codified-two-story neighborhoods. Inside overlays, the eligible-parcel rates are 20.5 percent and 26.3 percent respectively—a suppression of 13.8 percentage points in contextual overlays and 4.0 percentage points in codified-two-story overlays. Applied to 2,310 eligible R-zoned parcels across all study overlays, the height-standard channel suppressed approximately 558 HPR dwelling units (280 projects), representing 6.4 percent of countywide two-on-one production from 2010 through 2023.

The top contributors are Waverly-Belmont (135 units, eligible rate drops from 41.3 to 21.9 percent), Eastwood (107 units, 37.2 to 21.5 percent), and Belmont-Hillsboro (68 units, 26.6 to 12.4 percent). LSEE, which contributes 1,897 of the 6,252 R-zoned overlay parcels but has only 30 outside-boundary parcels, receives the pooled contextual rate on its 622 eligible parcels, contributing 172 units. The eligible-parcel approach concentrates the counterfactual on the parcels where the paper's mechanism operates and produces a more intense per-parcel suppression rate (24.1 percent of eligible parcels) than the all-parcel estimate suggests.

This is the number that connects directly to the paper's mechanism finding. Height-standard reform—adopting a codified two-story standard in every contextual overlay, with design review, demolition controls, and material mandates remaining in place—would recover approximately 560 HPR units on the land where the height restriction is currently the binding constraint.

Component 1b: Net Dwelling Units from Height Reform

The 560 gross suppressed units are not all net additions to the housing stock. Of the 1,331 eligible parcels inside overlay districts that have not already been developed as HPR, 70.0 percent currently hold single-family homes (net +1 unit per conversion), 12.8 percent hold duplexes (net zero—two units replace two), 6.3 percent are truly vacant (net +2), and the remainder include aging triplexes, quadplexes, and small apartment buildings where HPR conversion would reduce the unit count. The weighted mean net gain is 0.82 units per suppressed project, yielding approximately 228 net dwelling units.

Of the approximately 560 suppressed HPR units, roughly 330 are on parcels that already contain a dwelling unit. The difference between the gross and net counts quantifies the form-selection mechanism directly: these are sites where the overlay produced one home instead of two, not sites where it prevented housing altogether. The family that lives in the single-family home is housed. The family that would have lived in the second unit is not.

Component 2: Total Overlay Suppression

The full overlay regime—combining height restrictions, demolition controls, design review, and process costs—suppresses HPR on all R-zoned parcels, including contributing parcels that cannot redevelop under demolition controls. Applying overlay-specific boundary rates to all 6,252 R-zoned parcels, with the same 10 percent outside-buffer filter and pooled substitution, yields approximately 1,474 suppressed HPR dwelling units. The generic-rate approach (applying the logit-predicted rates uniformly) produces a similar estimate of approximately 1,800 units. Both approaches overstate the counterfactual to some degree, because they assume contributing parcels inside overlays would develop at the same rate as the mixed population outside—a population that includes recently developed lots alongside older homes. Contributing parcels self-select for retention even absent regulatory protection: an owner who has maintained a 1920s bungalow through decades of market pressure may not sell to a developer even if demolition controls disappear.

The gap between the two components is informative. Approximately 560 units are attributable to the height standard on eligible land. The remaining approximately 900 units are attributable to the overlay's other channels—primarily demolition controls on contributing parcels. Height-standard reform recovers roughly one-third of total overlay suppression, but it operates on one-third of the parcel stock. On the parcels where it is the binding constraint, it is extremely potent: contextual overlays cut HPR development rates nearly in half on eligible land.

Sensitivity of the Counterfactual

The 558-unit and 228-unit estimates depend on a chain of analytic choices: the suppression-rate source, the outside-sample definition, the eligible-parcel denominator, the thin-buffer filter, the LSEE treatment, the net-unit weighting, and the height classification. Systematically varying all seven choices across their defensible alternatives produces 3,888 combinations. The interquartile range of the gross estimate is 524 to 1,798 units; for the net estimate, 310 to 1,028 units. No combination produces fewer than 164 net units. The denominator choice (which parcels count as "eligible") drives 71 percent of the total variance; all other choices combined drive less than 15 percent. The paper's headline sits near the conservative edge of the distribution—at the 27th percentile for gross units and the 10th percentile for net units—reflecting the non-HPR-eligible denominator, which is stricter than the contributing-structure proxy used elsewhere in the paper. A researcher making only marginally different defensible choices would produce a substantially larger headline.

Price Comparison

The replacement housing tells its own story. The hedonic fee-simple premium of 8.0 percent (Section 3.6) provides the time-adjusted estimate of the ownership-form price differential, controlling for unit characteristics and sale-year effects. In nominal terms, the gap is wider: fee-simple single-family homes inside contextual overlays sold at $275 per square foot compared to $253 for HPR two-on-ones just outside overlay boundaries (8.7 percent), and at a median total price of $680,000 versus $593,000 (14.7 percent), the latter partly reflecting a 129-square-foot size difference and temporal composition across the two samples. The height standard replaced two ownership-oriented homes with one larger, more expensive home.

Conservative Bias

Both estimates are conservative. The boundary comparison measures suppression relative to observed development rates just outside overlay boundaries, but those outside rates are themselves depressed by the cumulative effect of overlay proliferation across Davidson County. Metro-wide HPR production peaked in 2015–2017 and has since declined, driven in part by the expansion of restrictive overlays that constrict the supply of developable sites. Development displacement from inside overlays to adjacent non-overlay areas also capitalizes into land prices outside the boundary, shifting the product mix. Both biases depress the outside-boundary counterfactual rate, producing conservative suppression estimates. A fuller accounting would need to model the general-equilibrium displacement effects documented in Asquith, Mast, and Reed (2023).

5.2 Policy Implications

Height reform is necessary but may not be sufficient. Reforming height standards from contextual to a codified two-story minimum eliminates the form-selection distortion and recovers approximately 560 gross HPR units on eligible land—yielding 228 net dwelling units concentrated in Nashville's most desirable neighborhoods, where each additional ownership-oriented unit at approximately $500,000 displaces a $680,000 fee-simple home. But even codified-two-story overlays suppress HPR development on eligible parcels (4.0 pp), reflecting the combined effect of the remaining regulatory channels and the financial constraint that a two-story envelope imposes on high-value land.

The title carries a double meaning. The overlay's regulatory form—its specific dimensional parameters—determines the function of the housing market within it. At the physical-viability threshold, a contextual height standard pegged to one-story contributing structures eliminates two-unit development entirely. In high-pressure markets, this produces the most consequential distortion: one large single-family home where two ownership-oriented homes would otherwise stand. At the financial-competitiveness threshold, even a two-story standard constrains the buildable envelope below the level that would make multi-unit development competitive with single-family on expensive land. In lower-pressure markets, the same dimensional constraints produce a different outcome: development is foreclosed entirely on the narrow band of eligible land. The dimensional parameters are not merely constraints on development intensity. They are the mechanism through which conservation policy selects for housing type, price point, and the number of families a neighborhood can accommodate.

The height standard, moreover, constrains density on an already-narrow base. Nearly 70 percent of NCZO parcels hold contributing structures whose demolition is subject to hardship review—a procedural barrier that effectively prohibits teardown redevelopment on contributing lots regardless of the height standard. Only the remaining 30 percent of parcels—those with non-contributing or post-period-of-significance structures, vacant lots, and lots with minimal improvements—are realistic candidates for new construction. The height standard operates on this residual pool. A contextual height restriction that suppresses two-unit development on the 30 percent of parcels where redevelopment is physically and procedurally feasible concentrates its anti-density effect on precisely the sites that constitute the overlay's entire capacity for housing growth. In overlays with high contributing shares (Section 3.5)—Haynes Manor at 97 percent, Eastdale at 97 percent, Haynes Heights at 92 percent—the eligible pool is so small that any further regulatory constraint on the form of new construction effectively forecloses densification entirely. The finding also extends naturally to parcels currently ineligible for redevelopment: if cities were to relax demolition controls—making contributing parcels eligible—those newly eligible sites would immediately face the same height constraint documented here. The height standard is not merely the binding constraint on today's eligible land; it is the constraint that would bind on any land made eligible by future policy changes.

Salemtown demonstrates that a two-story height standard is compatible with conservation overlay goals. The overlay has been in effect since 2013 with the full regulatory bundle—design review, demolition controls, material standards—and housing production continued after adoption. The neighborhood's historic character, as assessed by the same MHZC that administers contextual-height districts, has been maintained. Salemtown is not a hypothetical; it is a functioning example that has operated for over a decade.

The secondary implication follows from the two-regime finding. Even codified two-story height standards are necessary but not sufficient in affluent neighborhoods where the fee-simple premium is large enough to make one house more profitable than two. In those markets, enabling denser forms—three or four units—or reducing the minimum viable unit size through building code reforms may be required. The height standard opens the gate, but market economics determine whether anyone walks through it. The recent wave of state-level duplex and ADU legalization—California SB 9, Oregon HB 2001, Montana HB 406—makes the floor-area-threshold mechanism directly relevant beyond Nashville: cities that permit duplexes by right but impose contextual height standards in overlay districts will produce the same selective suppression documented here.

5.3 Limitations

Several limitations qualify the findings.

1. The Level 1 identification relies on a composite bulk treatment—height, width, and roof pitch—and cannot decompose their individual contributions. The theoretical model operates through total floor area, which is a function of all three, so the composite tests the relevant mechanism; but the paper cannot attribute the effect to height alone.

2. The Boscobel carve-out was driven by the blocks' pre-existing physical conditions (extensive contemporary construction, few historic structures), which may independently predict post-overlay HPR activity. The Level 1 treatment assignment is therefore not random, and the magnitude estimate may be upward-biased. The form-specificity of the result and the informal DiD evidence partially address this concern (Section 4.1), but the Level 4 boundary comparison provides the uncontaminated cross-overlay test.

3. The evidence is from a single metropolitan area. Nashville's HPR legal framework is specific to Tennessee, and the particular interaction between HPR and conservation overlays may not generalize to cities without an equivalent by-right two-unit mechanism. Three dimensions of generalizability warrant discussion. First, two-unit development on duplex-zoned land exists in every US city that permits duplexes, triplexes, or ADUs. Nashville's HPR framework makes this form easier to observe and develop, but the underlying economics—floor area per unit, viability thresholds, competition with single-family alternatives—apply wherever developers choose between one larger unit and two smaller units on the same lot. Second, in cities where two-unit development requires formal subdivision rather than HPR-style regime filing, the viability threshold A_min is higher because the project must cover subdivision costs (platting, infrastructure, fees) in addition to construction costs. This makes the height standard more binding, not less. Third, the reversion mechanism generalizes anywhere duplex zoning coexists with conservation overlays: the prediction that height caps redirect development to single-family forms requires only that the lot is zoned for two units, the height cap makes two units infeasible while leaving one feasible, and the market supports single-family construction.

4. The counterfactual estimates are partial-equilibrium projections that do not account for general-equilibrium effects: political responses to additional development, demand-side substitution, or land-price capitalization. The true suppression could be larger or smaller depending on the direction of these feedbacks.

5. The Level 3 panel is underpowered with 33 clusters. The height interaction has the correct sign but does not reach conventional significance thresholds. The paper's causal claims rest on Levels 1, 2, and 4.

6. The two-regime finding on the fee-simple premium is descriptive. The conditional tabulation is theoretically motivated and empirically clean but does not control for neighborhood-level confounders that correlate with both φ and development patterns.

7. The HPR classification relies on inferential methods because Metro Nashville does not directly code HPR units. Classification error is non-differential across overlay and non-overlay areas, attenuating rather than biasing the estimates. Validation against published benchmarks shows 1.1 percent deviation in two-on-one counts and 2.9 percent in total HPR units. Height-standard extraction from overlay guideline PDFs involves judgment for contextual standards; the binary classification (two or more codified stories versus contextual) is robust to coding disagreements.

8. The binary codified/contextual classification captures the physical-viability threshold but not the financial-competitiveness threshold identified in Section 2.1. Codified-two-story overlay suppression of 11.9 percentage points is consistent with the theoretical prediction that A_min rises with land cost, but the binary classification cannot distinguish height-channel from non-height-channel suppression within the codified-two-story category.

9. The COD-NCZO cross-type comparison is confounded by differences in height formula, footprint allowance, reference population, and lot geometry. The analysis establishes that CODs suppress HPR at comparable magnitudes but cannot cleanly isolate the independent effect of the MHZC preservation-review process from the dimensional-formula differences.

10. The form-selection (reversion) effect is documented at Level 1 (within LSEE) and Level 2 (Salemtown replication) but not in the pooled boundary data, where single-family rates are flat inside and outside overlays. The form-selection mechanism operates in high-pressure urban-core contexts; in lower-pressure settings, the overlay suppresses total development without form substitution.