2.1 Expansion and localized competitive pressure

Competitive proximity increases with expected demand-side and strategic overlap between actors in the same market; competitive distance decreases as that overlap rises. Chen (1996) links competitor analysis to market commonality and resource similarity, emphasizing that competitive relationships can be pair-specific and asymmetric. Peteraf and Bergen (2003) similarly argue that competitor identification should consider functional similarities in products and resources rather than common market membership alone. Localized-competition research shows that rivalry can be strongest among organizations with comparable positions and resource requirements (Baum and Mezias, 1992). These arguments imply that a focal market action can impose greater competitive pressure on more proximate rivals.

The same focal activity may also expand attention to the broader market. With advertising directly observed, Shapiro (2018) finds positive demand spillovers from prescription-drug advertising to competing products through market expansion. Localized displacement and market expansion need not be competing explanations chosen after observing a coefficient; they may operate simultaneously. Let $a$ denote attributes of the focal action, $P_{im}$ competitor $i$’s relational proximity to the focal actor in market $m$, and $R_{im}(a)$ its response:

Here, $E_{m}(a)$ is an arena-wide expansion component and $C_{m}(P_{im}, a)$ is localized competitive pressure. Expansion can arise when an action increases category attention, legitimacy, information, or access that other actors can share. Localized pressure rises when the focal action appropriates demand or scarce resources from actors with greater substitution, market commonality, or resource overlap. The focal action and market context can therefore affect both components rather than merely adding a common shock to otherwise fixed rivals.

2.2 Distance gradient and endogenous threshold

Assume $C_{p} > 0$, so localized pressure increases with relational proximity. Then the response is strictly decreasing in proximity.

Proposition 1 ― Distance gradient. For a fixed focal action and market, a more competitively proximate actor has a less favorable response: if $P_{jm} > P_{km}$, then $R_{jm}(a) < R_{km}(a)$.

This relative prediction does not require both signs to appear. If expansion is below localized pressure even for the most distant actor, all observed responses occupy the shadow region. If expansion exceeds localized pressure even for the most proximate actor, all occupy the spotlight region. Mixed signs require an interior crossing.

Proposition 2 ― Shadow–spotlight threshold and boundary shift.

If $C_{m}(P_{\min}, a) < E_{m}(a) < C_{m}(P_{\max}, a)$ and $C_{m}$ is continuous and strictly increasing in $P$, a unique threshold $P_{m}^{*}$ satisfies $C_{m}(P_{m}^{*}, a) = E_{m}(a)$. Actors with $P < P_{m}^{*}$ occupy the spotlight region, and actors with $P > P_{m}^{*}$ occupy the shadow region.

To examine a market or action attribute $z$, write the components as $E_{m}(a, z)$ and $C_{m}(P, a, z)$. If both are continuously differentiable near the threshold and $C_{p}(P_{m}^{*}, a, z) > 0$, the implicit-function theorem gives

All derivatives are evaluated at $(P_{m}^{*}, a, z)$. Attributes that strengthen category expansion more than localized pressure enlarge the spotlight region; attributes that strengthen localized pressure more strongly enlarge the shadow region. The proposition therefore identifies all-shadow, all-spotlight, and mixed regimes and specifies how focal-action and market conditions move their boundary.

2.3 Competitive proximity, temporal classification, and the administrative marker

The theoretical $P_{im}$ is not a numerical difference or percentile in reimbursement price. It describes a relation between actors; within-arena reimbursement rank is a separately observed administrative position score. It may contain useful information because products at different regulated price positions can face different institutional and commercial conditions, but its correspondence with relational proximity must be established rather than assumed.

Maximum reimbursable amounts are not transaction prices, equal amounts create ties, changes in arena membership alter percentiles mechanically, and clinical substitution may depend on prescribing routines, formulation, reputation, or distribution arrangements that are not observed. Marker validity therefore requires evidence beyond computational precision. Cutoff stability can diagnose dependence on a partition, but it cannot establish convergence with demand overlap or resource similarity.

The 10/30/70 partition is a descriptive score rather than a theoretical law. Among non-TOP products, it assigns T1 through the 10th percentile, T2 above the 10th through the 30th percentile, T3 above the 30th through the 70th percentile, and T4 above the 70th percentile. Alternative 5/25/65 and 15/35/75 partitions and the rank/N formula are marker-coding sensitivities; ties and focal-event definitions are event sensitivities. Decile and continuous-percentile summaries are raw distribution checks rather than model-based robustness estimates.

Temporal classification is part of marker construction whenever position is path-dependent. An estimand is the target quantity that connects statistical evidence to theory (Lundberg et al., 2021); changing when a marker is assigned can therefore change what the analysis describes. Let $M_{it}$ denote the administrative position of item i when it appears in year t, and let $M_{iT}$ denote its position at the endpoint T. If later price changes, survival, or arena membership affect $M_{iT}$, classifying an earlier appearance by $M_{iT}$ combines the contemporaneous event with subsequent history. Endpoint- and arrival-coded estimates are comparable as historical position estimates only if classification is invariant or later reclassification and matchability are ignorable for the intended contrast.

Temporal-classification corollary. When $M_{iT}$ incorporates post-appearance changes or selective persistence, an endpoint-coded historical position association generally combines the contemporaneous marker with later selection and reclassification. A difference between endpoint- and arrival-coded estimates diagnoses measurement dependence; it does not by itself identify the cause of the change or validate either marker as competitive proximity.

2.4 From latent theory to admissible claims

The threshold account can be evaluated only when empirical variables correspond to its focal actor, relational proximity, timing, response, and comparison. The five-link chain specifies the evidence needed to connect the theory to the administrative application. Following the principle that validity depends on correspondence between a systematized concept and its observations (Adcock and Collier, 2001), each link can have absent, partial, or sufficient warrant for the stated claim. Partial warrant may support a contracted claim; absent warrant removes claims that require that premise.

Actor validity concerns the correspondence between the observed focal listing and the theoretically relevant actor. A top-price product may be a reference product, generic, relisted product, or another product type. Without an independently verified actor field, the event cannot be labeled an originator or dominant-firm event.

Marker validity concerns the correspondence between reimbursement-price position and relational proximity. Edwards and Bagozzi (2000) emphasize that construct–measure relations require explicit conceptual specification. Price rank has face relevance as an administrative ordering but lacks independent validation against substitution, market commonality, resource similarity, prescribing, or channel overlap.

Temporal validity concerns when the marker and risk set are measured. A current price schedule applied to earlier years can incorporate later price changes, later listings, and selective persistence. Historical snapshots are therefore required to compute arena membership and rank at each observed time.

Outcome validity concerns what an appearance or disappearance means. A product newly appearing relative to a preceding HIRA snapshot is an administrative reimbursement-list appearance; it is not necessarily a first-ever approval, commercial launch, or voluntary strategic decision. HIRA disappearance and MFDS cancellation are distinct endpoints, neither of which directly measures sales exit.

Identification validity concerns the event-time comparison. The first observed TOP-position arrival is selected by an evolving administrative market, and event timing is not shown to be exogenous. Credible interpretation therefore requires transparent comparison support, physically absent simultaneous event observations, pre-event diagnostics, and claims no stronger than the observed design.

The links are noncompensatory across logically distinct premises. Better temporal alignment cannot establish actor identity; a more credible counterfactual cannot validate the relational marker; and marker stability cannot transform an administrative listing into strategic behavior. For a target claim $K$, let $J(K)$ contain the five universal translations and any additional premise logically required by the specific mechanism invoked. The claim is admissible only if every required premise has the warrant demanded by its exact actor label, relational meaning, behavioral verb, population, timing, and causal force.

When a premise is absent or only partial, the claim contracts to the observed administrative referent or a qualified association; strength on another dimension cannot compensate.

Validation subsamples, independent indicators, or explicitly modelled uncertainty can strengthen warrant within a link. The rule requires correspondence, not error-free data.

Proposition 3 ― Claim ceiling. A construct-, mechanism-, or causal-level spillover claim cannot exceed its weakest essential universal link or claim-specific premise. Temporal alignment can upgrade an endpoint-coded marker to a contemporaneous administrative association, but it cannot establish competitive distance, strategic response, causality, or a named mechanism when the corresponding warrant remains absent.

The result is level-asymmetric inference. Administrative records can support analyses of their own coding stability and associations. They support construct- or theory-level conclusions only when the required bridges are warranted. Until then, neither a favorable nor an adverse marker association determines the theory.

2.5 Mapping the pharmaceutical application

The original marker coding, developed before the present reconstruction, assigned a negative direction to T2 as its shadow-coded marker and a positive direction to T3 as its spotlight-coded marker. The present audit retains these directions only as retrospective administrative benchmarks. They are not formal tests of Propositions 1–2 because the data do not establish that T2 and T3 are ordered values of relational proximity $P_{im}$ or that the relevant category-expanding action is present.

The application evaluates which claims this administrative implementation can support. It strengthens temporal alignment but lacks sufficient actor, relational-marker, strategic-outcome, and causal-identification warrant. T2 and T3 are evaluated as neutral administrative position categories; “shadow” and “spotlight” are reserved for the latent regions defined by $P_{m}^{*}$.

No identity or mediation hypothesis is formulated: the data contain no direct identity, marketing, reputation, formulary, or category-expansion measure, and a post-event T3 stock cannot identify a sequential mechanism.

3.1 Korean reimbursement setting

South Korea introduced the positive-list reimbursement system in December 2006, and HIRA convened its first Drug Reimbursement Evaluation Committee meeting in 2007 (Health Insurance Review and Assessment Service [HIRA], 2007; Park et al., 2012). HIRA price lists record reimbursement status and each product’s maximum reimbursable amount. These fields provide detailed administrative histories, but they are not product-level sales, prescriptions, transaction prices, or market shares.

The 2012 drug-pricing reform abolished parts of the earlier stepwise pricing structure and generally moved products more than one year after listing toward a 53.55% rule, while retaining separate first-year calculations and exceptions (Cho et al., 2015; Ministry of Health and Welfare [MOHW], 2011). The reform provides institutional context for the administrative price environment. It did not make all products identical, eliminate all price differences, or supply evidence of an identity mechanism; it is not a mechanism test.

Three administrative endpoints must remain distinct. Appearance between adjacent annual HIRA snapshots is a reimbursement-list appearance. Disappearance is HIRA reimbursement delisting. An MFDS cancellation date records regulatory cancellation. None is automatically interpreted as commercial launch or sales exit.

3.2 Data sources and historical reconstruction

The source archive contains 16 HIRA snapshots covering 2009, 2010, and 2012–2025. The parser scanned 441,335 rows and retained 317,119 positive-price rows; product-code, ingredient, and dosage-form fields were complete in those records. Because 2011 is unavailable and the analysis requires adjacent annual snapshots and lagged arena membership, the analytic position panel covers 2012–2025.

Restricting the 317,119 positive-price rows to 2012–2025 leaves 287,914 rows. Removing 43 invalid historical-arena rows and 321 rows attached to ambiguous or unmatched HIRA codes leaves 287,550; collapsing multiple codes that identify the same item-by-arena-by-snapshot record produces a net reduction of 1,758 rows, and excluding 295 within-key price-conflict rows yields the 285,497-record canonical panel. These steps close the row-count reconciliation; they do not constitute an additional sample-selection model.

HIRA product codes are linked to the MFDS standard-code master through cleaned product-code and standard-barcode mappings. Among 44,345 distinct valid HIRA codes in the primary window, 44,253 link uniquely, yielding 99.79% code coverage and 99.89% row-weighted coverage. Two ambiguous codes account for 17 rows, and 90 unmatched codes account for 304 rows. The bridge stabilizes item identity and attaches regulatory dates; it does not replace the arena recorded in a historical HIRA snapshot.

The primary unit is an MFDS item observed in a contemporaneous HIRA ingredient–form arena and snapshot. The canonical item-snapshot panel contains 285,497 observations, 32,909 items, 40,957 item-by-arena units, and 8,202 arenas. A product-code-by-arena panel provides a unit sensitivity. Items observed in more than one arena remain in the canonical panel. At a transition boundary, an item appearing in a new arena while present elsewhere in the preceding snapshot is censored from the appearance count; an item disappearing from one arena while remaining elsewhere is censored from the delisting count.

3.3 Arena, TOP position, and tier outcomes

An arena is the ingredient-and-dosage-form code recorded in each historical HIRA snapshot. This is a regulatory grouping, not a direct measure of clinical substitutability. An arena-year’s TOP position is the maximum listed reimbursement amount among products observed in that arena and year. It is an arena-relative maximum, not a single common legal price assigned to the arena.

All products tied at the arena-year maximum are classified as TOP. For arenas with more than one product, price is ranked from high to low, ties receive the average rank, and the main percentile is (midrank − 1)/(N − 1), bounded to the unit interval, where N is the total number of products in the arena-year. Singleton arenas are classified as TOP and do not enter non-top tier cutoffs. For non-top products, T1 through T4 use the descriptive 10/30/70 boundaries stated above.

The observed percentile is kept distinct from $P_{im}$. In Section II, $P_{im}$ represents latent relational proximity; the tier score used here is an administrative classification whose correspondence with $P_{im}$ remains unverified.

A product is newly appearing when its item-by-arena unit is absent in the immediately preceding observed annual snapshot and present in the current snapshot, after identifiable arena migration is censored. This is not necessarily the product’s first appearance over its lifetime: a product returning after an observed absence can be counted again. The outcome is therefore a transition-specific administrative appearance. Its tier is measured in the snapshot in which it appears and is an outcome category rather than a predetermined strategic position.

For HIRA delisting and MFDS cancellation, an incumbent is classified by its tier in the immediately preceding snapshot. This avoids assigning a disappeared item a later price rank. A separate landmark description classifies incumbents by their event-time −1 tier.

3.4 Event, left censoring, transitions, and risk set

An established arena is an arena observed in the immediately preceding annual snapshot with at least one listed product. The event is the first observed transition in the clean analytic window in which a newly appearing product occupies the contemporaneous TOP position of such an arena. Because the window begins in 2012 and 2011 is absent, “first observed” does not establish the arena’s first such event over its full history. The event definition is left-censored and may also include a returning listing after an observed absence.

An arena must be observed at event times −2, −1, +1, and +2 to enter the eligible event registry. Here, “observed” means that the historical snapshot contains at least one eligible positive-price listing in that arena. An absent arena-year is not imputed as zero: it may represent administrative risk-set exit, no eligible reimbursed product, or a break introduced by bridge and eligibility rules. An arena with an observed marker arrival that fails this support rule is excluded, not recoded as a never-event arena. Here, “never-event” denotes an arena with no qualifying marker arrival observed during 2012–2025; it does not imply that no such event occurred before 2012.

Marker-event arenas must remain administratively observable through +2, whereas comparison arenas with no observed marker event receive no hypothetical event-specific ±2 requirement. The primary estimand is therefore conditional on that future-observability contract for event arenas.

Event time 0 is physically absent from every estimation panel. The focal product and other same-snapshot appearances are interval-censored within the same annual transition, so their within-interval order cannot be established.

Because the primary risk set treats future observability asymmetrically, a retrospective common-support diagnostic applies one calendar rule to both groups. It fixes event cohorts at 2020–2022, restricts comparisons to arenas with no marker event observed during 2012–2025, and requires every event and comparison arena to be observed in all calendar years 2017–2025. Eligibility is determined before each event-year row is removed. This yields 235 event arenas, 2,240 never-observed-marker-event comparison arenas, and 22,040 estimation rows. The diagnostic changes both the population and comparison group: it describes a balanced late-cohort administrative risk set and is not a substitute estimate for all observed events.

The common-support restriction is itself selective. Among initially eligible 2020–2022 event arenas, included arenas are larger at event time −1 than excluded arenas (standardized difference = 0.490), and the 2022 cohort is less likely to satisfy the rule in a predetermined-covariate linear-probability diagnostic (−0.281, heteroskedasticity-robust p < .001).

Symmetric observability removes the original group asymmetry, but the complete-window sample is neither representative nor exogenous: among never-event candidates, complete- versus incomplete-window standardized differences are 1.227 for log arena size and 0.727 for size momentum.

The historical bridge identifies a structural transition at the 2015–2016 boundary. The sequential-transition reconstruction contains 2,434 arena transitions, 2,252 of which arrive in 2016. A separate code-linkage audit examines 2,365 arena switches across that boundary and links 2,315 through an unchanged current code or an explicit pre-cleanup code. Calendar year 2016 is therefore absent as a transition endpoint in the primary analysis, and support is rechecked after its removal.

The event registry contains 626 initially eligible event arenas and 6,638 never-observed-marker-event comparison candidates. Fifty-three events occurring in 2016 are removed, and 206 otherwise eligible event arenas lose the required support after calendar year 2016 is removed. Thirty-four comparison candidates have no observation outside 2016 and therefore leave the model panel. The primary event-study panel contains 367 event arenas in five cohorts―70 in 2019, 104 in 2020, 127 in 2021, 45 in 2022, and 21 in 2023―and 6,604 comparison arenas, for 6,971 arenas and 43,798 arena-year observations.

Before estimator balancing, raw eligible-panel support equals 367 event-arena observations at +1 and +2, 344 at +3, 292 at +4, and 168 at +5. The balanced +1 to +3 estimator uses the 2019–2022 cohorts, with 346, 346, and 344 observed event arenas across those three event times; the 2023 cohort is excluded.

The long-window estimators use the 2019 and 2020 cohorts only and have 168 observed event arenas at +5. Raw support at −5 is 95, but the balanced dynamic estimate at −5 uses cohorts 2019, 2020, and 2022 and 79 observed event arenas because the 2021 cell falls in calendar 2016 and the 2023 cohort is excluded. Appendix A3 reports the contributing cohort lists and total observed event-arena counts.

3.5 Outcomes

The primary outcomes are arena-year counts of products newly appearing on the reimbursement list, classified as T2 or T3 by their contemporaneous arrival-snapshot administrative position. They count new listing flows; they do not count incumbent products that merely move between ranks as arena composition changes. Secondary listing outcomes are TOP, T1, T4, total appearance counts, binary indicators, decile counts, and continuous percentile mass. Because tier-specific counts combine the number of new appearances and their assigned positions, they are described as tier-specific listing patterns rather than as shares of a fixed total.

Three administrative departure measures remain separate. One-snapshot HIRA delisting records absence at the next snapshot after identifiable arena migration is censored. Persistent HIRA delisting requires continued absence in the following snapshot when that horizon is observable. MFDS cancellation records an authorization cancellation date between adjacent snapshot dates for an incumbent item. These endpoints do not observe sales discontinuation.

The event-time −1 tier landmark reports post-event status for incumbents present at that reference time. It has no valid lead structure and is descriptive. It is not treated as a survival model or a mechanism test.

3.6 Estimation, temporal-classification design, and diagnostic hierarchy

The primary estimator follows the group-time difference-in-differences framework of Callaway and Sant’Anna (2021), implemented through outcome regression with not-yet-event comparisons; arenas with no marker event observed during 2012–2025 remain eligible comparisons throughout. The model uses an unbalanced panel, event time −1 as the universal base period, arena as the panel and clustering unit, 999 multiplier-bootstrap repetitions, and 95% simultaneous bands for the displayed dynamic path.

For each cohort and event time, the estimator first calculates a contrast relative to that cohort’s event-time −1 observation. At each supported event time, the aggregation procedure averages the estimable cohort-specific contrasts using cohort shares renormalized over the cohorts available at that event time. The reported +1 to +3 association is the simple average of those three event-time aggregates. Its standard error is calculated from the corresponding influence functions and therefore retains their covariance rather than treating the three estimates as independent.

The +1 to +3 aggregate and displayed dynamics require support through event time +3 and therefore use the 2019–2022 cohorts. The 2023 cohort contributes to the eligible panel and raw support at +1 and +2 but is excluded from this aggregate because +3 is not observed. Cohort shares use the registered cohort sizes 70, 104, 127, and 45; within those cohorts, observed event-arena counts are 346 at +1, 346 at +2, and 344 at +3. Available event-time −1 and post-event observations enter each group-time contrast without imputing missing arena-years; at +3, 103 of 104 cohort-2020 arenas and 126 of 127 cohort-2021 arenas are observed.

The +1 to +5 and +4 to +5 aggregates use only the 2019 and 2020 cohorts and have 168 observed event arenas at +5. Event timing is endogenous and some pre-event diagnostics reject, so the estimates are described as cohort-weighted event-time associations rather than causal average treatment effects.

The displayed dynamic window is −5 through −2 and +1 through +3; −1 is the reference and 0 is absent. Average post-event associations are calculated for +1 to +3, +1 to +5, and +4 to +5. Local pre-event diagnostics jointly test −3 and −2. Wider diagnostics jointly test −5 through −2.

Because the removed 2016 calendar cell interrupts different cohorts at different leads, the balanced dynamic estimate still changes composition across the lead vector: −5 uses cohorts 2019, 2020, and 2022 (79 observed event arenas); −4 uses 2019, 2021, and 2022 (170); −3 uses 2020, 2021, and 2022 (259); and −2 uses all four 2019–2022 cohorts (346). The joint tests are therefore diagnostics, not proof of parallel trends; p > .05 is not interpreted as equivalence because an insignificant pre-trend test does not establish parallel trends (Roth et al., 2023).

Across 120 outcome-specific group-time cells, 20 have weak or unavailable support. Of 45 raw-support cells, 33 are adequate, nine are unavailable, and three are weak; Appendix A3 reports the contributing cohort lists and total observed event-arena counts.

Horizon and diagnostic roles. The +1 to +3 average is the longest balanced near-term summary supported by the 2019–2022 cohorts after the 2016 transition is removed; it is a support-defined administrative horizon, not a theory-derived mechanism lag. The +1 to +5 and +4 to +5 summaries are secondary descriptions carried only by the 2019 and 2020 cohorts.

The coding audit and its stress grid were assembled retrospectively, so the paper does not designate a confirmatory hypothesis family. Exact p-values and intervals characterize sampling uncertainty but do not determine a theory verdict.

Simultaneous bands summarize uncertainty within each displayed dynamic path; joint lead tests flag design concerns; the ten-row grid compares nonexchangeable definitions qualitatively; and common-support, endpoint-pairing, estimator, and departure analyses are auxiliary diagnostics. The Holm values for the common-support T2/T3 pair are a local two-outcome sensitivity, not familywise confirmation of the larger retrospective analysis. No conclusion is upgraded because a nominal threshold is crossed.

The paired historical-versus-endpoint classification comparison is the primary temporal diagnostic. The paired-classification transition sample links historical listing appearances by the same item identifier and arena to the 2025 snapshot. Model A uses all 2,316 transitions with their arrival-snapshot tiers. Models B and C use the 1,446 transitions that remain in the same arena in 2025: B retains the historical tier, whereas C substitutes the 2025 tier.

A direct arena-year difference outcome, C minus B, isolates the consequence of changing the classification of those common rows from arrival-snapshot to 2025 price tiers.

The B−A point-estimate difference reflects endpoint matchability and persistence selection; no sampling uncertainty for that derived cross-model difference is claimed. Comparing B with C describes endpoint reclassification among matchable listing appearances. The paired difference does not identify why later classifications differ, recover unmatched transitions, or estimate a causal effect of price adjustment.

The following point-estimate accounting identity organizes the two sources of difference:

The first term records the B−A point-estimate change associated with endpoint matchability and persistence selection; it is not itself a directly estimated contrast with a reported standard error. The second term is the directly estimated paired reclassification contrast among the same rows. Neither term is causal without additional assumptions. Separating them prevents reclassification from being mistaken for a stable historical position effect.

The common-support diagnostic uses the same outcome-regression implementation but fixes cohorts at 2020–2022, uses comparison arenas with no marker event observed in 2012–2025, and reports event times −3, −2, +1, +2, and +3. All three cohorts and all 235 event arenas contribute at every displayed event time, so the local joint test no longer changes cohort composition. T2/T3 post-window p-values are also Holm-adjusted as a two-outcome family. These safeguards diagnose composition and risk-set sensitivity; they do not make non-rejection an equivalence test or remove endogenous event timing.

Section III.7 defines the scope of the retrospective ten-specification sensitivity grid, which Table 4 reports in Section IV. Auxiliary diagnostics vary transition exclusions, comparison groups, never-concurrent multi-arena handling, predetermined size and momentum, common support, and endpoint-price classification without entering that grid.

Sun–Abraham cohort-interacted estimates, linear two-way fixed-effects estimates, and binary linear-probability models retain 43,199 observations and 6,372 arenas after within-model exclusions (Sun and Abraham, 2021). Poisson fixed-effects models retain only 363 observations in 44 arenas for T2 and 1,497 observations in 175 arenas for T3 because of extreme separation attrition; they are treated as attrition diagnostics rather than substantive stability evidence.

3.7 Retrospective evaluation of the original marker coding

The original marker coding predates the present reconstruction. We retain its negative T2 and positive T3 directions as retrospective marker-level benchmarks. “Shadow” and “spotlight” are not used as empirical labels for these categories because T2 has not been validated as relational proximity and T3 has not been validated as relational distance.

The evaluation is explicitly retrospective. The original endpoint-coded results were known before the historical reconstruction, five-link framework, ten-row stress grid, and current classifications were integrated.

The rules for the supplementary common-support, stable-cohort, endpoint-pairing, sparsity, and event-semantic diagnostics were documented before those diagnostics were run, and the reporting rule required favorable, null, and adverse results to be retained. This sequence records the limited timing of the supplementary diagnostics; it does not make the application preregistered, ex ante, or independently confirmatory. Appendix A12 summarizes the stages and their evidentiary roles.

Before the historical reconstruction, the original endpoint-price specification had rejected its joint pre-event test (p < .001) and reversed the T2 sign after momentum adjustment (+0.042). Because that specification used the superseded endpoint-price and current-master construction, those findings motivated reconstruction and are not confirmatory evidence. The historical panel reports the corresponding predetermined-covariate diagnostic separately below and in Appendix A11.

The ten-row stress grid covers four distinct implementation uncertainties: marker partition, focal-event semantics, counting unit and arena multiplicity, and bridge or arena concordance. Transition exclusions, comparison-group changes, predetermined covariates, common support, endpoint pairing, and alternative estimators remain separately labelled diagnostics because they change the transition set, target population, or estimator rather than the marker implementation alone. This organization clarifies the role of each diagnostic; it is not claimed to be outcome-independent.

4.1 Historical reconstruction and sample support

Table 1 reports the historical sample and event support. The item panel contains 18,496 raw newly appearing item-by-arena transitions. Censoring 749 identifiable migration-in transitions leaves 17,747 appearance transitions. Of 19,769 raw disappearances, 6,366 are identifiable migrations to another arena, leaving 13,403 HIRA delisting transitions. At the 2016 endpoint alone, 3,877 of 4,344 raw disappearances are classified as migration.

Comparison candidates and model comparisons have different denominators. The registry includes 6,638 arenas with no marker event observed during 2012–2025, but 34 are observed only at the removed 2016 endpoint. The primary event-study panel therefore contains 6,604 comparison arenas and 367 event arenas. Appendix A8 reports estimator-specific retention: fixed-effects reconciliations lose 599 arenas, and Poisson separation leaves only 44 T2 arenas and 175 T3 arenas.

Event semantics further bound the construct. The first marker event is observed in 1,439 arenas, but only 129 (9.0%) have a single TOP-position product in the full arrival snapshot; 1,310 therefore have more than one product tied at the TOP position. In 452 events, more than one newly appearing product itself occupies TOP. Across all eligible appearance rows, 570 (3.2%) are returns after an observed gap, and 43 first marker events (3.0%) involve such a returning TOP listing. After the first marker event, 683 arenas have at least one later TOP arrival, totaling 2,094 recurrent arena-years. These counts support the administrative event label and preclude treating it as a single, uniform originator action.

The tier-specific listing flows are extremely sparse and overdispersed. In the 43,798-row primary event-study panel, the mean T2 count is 0.0030, 99.893% of rows are zero, and the variance-to-mean ratio is 6.21. For T3 the mean is 0.0191, 99.498% are zero, and the variance-to-mean ratio is 21.45.

At event time −1, event arenas already average 0.030 T2 and 0.550 T3 listings, compared with pooled calendar-aligned comparison means of 0.003 and 0.015. Because event time −1 is the universal reference, negative post-event contrasts are compatible with normalization after an unusually elevated listing episode or selection on the reference-period base rather than deterrence. The sparsity does not explain away direction reversals or pre-event differences; it clarifies why count magnitude, extensive margin, and pre-event diagnostics must be reported together.

4.2 Temporal coding changes the apparent position pattern

The temporal-classification diagnostic precedes the tier-specific results. Of the 2,316 listing-appearance transitions in the paired-classification sample, 1,446 (62.4%) remain in the same arena and can be classified under both the historical and 2025 endpoint schemes. Among these matched transitions, 778 (53.80%) retain the same category. Table 2 separates the full historical result (A), the endpoint-matchable transitions classified at arrival (B), and those same transitions classified in 2025 (C).

For T2, the same matched transitions produce −0.0071 (p = .241) under historical classification and −0.0082 (p = .549) under endpoint classification. The directly estimated endpoint-minus-historical difference is −0.0011 (SE = 0.0139, 95% CI [−0.0283, 0.0261], p = .9363). Its local and wider pre-event joint-test p-values are .9712 and .5668. This small and imprecise point difference is not an equivalence result.

For T3, the matched historical association is −0.3581 (p = .080), whereas endpoint classification of the same transitions yields −0.0853 (p = .570). The directly estimated endpoint-minus-historical difference is +0.2728 (SE = 0.0879, 95% CI [0.1005, 0.4451], p = .0019). The difference outcome’s local and wider pre-event joint-test p-values are .1170 and .2108, although the classification-specific models retain problematic local diagnostics (p = .0167 and .0204). The paired result shows a numerically material temporal-coding difference among the matched transitions. It does not establish the direction of reverse causality or a corrected causal effect. The remaining listing results use arrival-snapshot classification unless endpoint classification is explicitly indicated.

4.3 Position-resolved administrative decomposition

Table 3 reports the position-resolved estimates, and Figure 1 displays the corresponding T2 and T3 dynamic paths. The baseline decomposition describes how the position-specific coefficients relate to the aggregate. Over event times +1 to +3, TOP-position listings rise by 0.5107 per arena-year (SE = 0.0986, p < .001). T1, T2, T3, and T4 estimates are −0.0562, −0.0172, −0.5340, and −0.0782, respectively. The sum of these position-specific coefficients equals the total-listing estimate of −0.1749 (SE = 0.2723, p = .521).

Note. Points are cohort-share-weighted event-time associations. Bars are pointwise 95% intervals, and shaded regions are simultaneous 95% bands. The upper panel reports the limited, definition-sensitive T2 administrative pattern; the lower panel reports the T3 path that does not support the originally predicted positive direction and has failed pre-event diagnostics. Neither panel directly measures relational competitive distance. The displayed analysis requires support through event time +3, so the 2023 cohort is excluded. Marker fill carries no significance coding. Daggers flag at least one weak or unavailable raw cohort cell. Event time −1 is the reference and 0 is absent. Appendix A3 reports the actual cohort composition and treated-arena contributions at each displayed event time.

The position-specific coefficients place the aggregate estimate in context. A positive TOP-position coefficient and negative non-TOP coefficients sum to a total-listing estimate that is not detectably different from zero, showing how an aggregate headcount can mask position-specific components. This arithmetic does not establish reallocation or constitute a formal test of equality across tiers. The TOP outcome lacks a usable joint lead test, while T3, T4, and total listings fail at least one pre-event diagnostic. The decomposition is therefore descriptive rather than a test of Propositions 1–2.

4.4 Definition-sensitive T2 administrative association

In the selected evaluable historical risk set, the T2 association over event times +1 to +3 is −0.0172 (SE = 0.0083, p = .0369). Unless a simultaneous or Holm procedure is named explicitly, p-values and intervals in this section are unadjusted descriptive diagnostics and do not determine the interpretive classification.

The local and wider pre-event joint tests yield p = .114 and .073. The nonrejections do not establish that the pre-event path is equivalent to zero: lead estimates use changing cohort composition, no equivalence margin was specified, and the wide vector has thin support.

The +1 to +5 and +4 to +5 averages are −0.0372 (p = .0166) and −0.0364 (p = .0148), but both use only the 2019 and 2020 cohorts, with 168 observed event arenas at +5.

Adjustment for predetermined size and momentum leaves the T2 coefficient negative (−0.0169, p = .0546), with local and wider pre-event p-values of .139 and .088. The adjustment does not, however, resolve the event-definition problem.

The common-support diagnostic preserves the negative direction but attenuates it to −0.0076 (SE = 0.0094, p = .420; Holm-adjusted p = .420; 95% CI [−0.0261, 0.0109]). Its joint test over event times −3 and −2 yields p = .734. Unlike the primary lead vector, every displayed event time contains all three 2020–2022 cohorts and all 235 event arenas. That design removes the original group-specific observability rule, but it does not validate a zero pretrend or create a representative comparison: the balanced late-cohort sample is observably selected on prior arena size and cohort.

Distinct focal-event definitions in the retrospective ten-row grid do not preserve the main T2 direction. Requiring the first-event arrival snapshot to contain a single TOP-position product produces a positive but imprecise +1 to +3 estimate (+0.0138, p = .521). Requiring the focal product to meet the preceding arena maximum yields a result descriptively close to zero (+0.00006, p = .992), without establishing equivalence. The 5/25/65 partition produces a larger negative association, while the 15/35/75 partition produces a smaller, imprecise negative estimate. As an auxiliary transition diagnostic, excluding calendar years 2016 and 2019 yields +0.0008 (p = .834) with only two cohorts.

The historical T2 association is limited and definition-contingent: its magnitude and sign vary with focal-event semantics and risk-set construction, and T2 is not a validated proximity measure. The prior-maximum result adds descriptive instability but does not establish equivalence.

4.5 T3 administrative association and failed pre-event diagnostics

The primary T3 association runs opposite to the originally predicted positive direction. The +1 to +3 average is −0.5340 (SE = 0.2358, p = .0236), the +1 to +5 average is −0.9650 (SE = 0.4572, p = .0348), and the +4 to +5 average is −0.9521 (SE = 0.4663, p = .0412). The local pre-event joint test rejects (p = .0185), and the wider test rejects (p = .0255). Estimates at event times −5 through −2 are already negative relative to −1, so the post-event contrast cannot be isolated from a different pre-event path.

The single-TOP-position-product and prior-maximum event restrictions yield positive but statistically imprecise +1 to +3 estimates (+0.0855, p = .255; +0.0108, p = .564). Excluding calendar years 2016 and 2019 yields +0.1058 (p = .464) with two cohorts. Alternative cutoffs retain the main negative direction and failed pre-event tests; code-level and stable-unit estimates are negative, smaller, and less precise.

In the common-support diagnostic, the T3 association remains negative but attenuates to −0.1848 (SE = 0.1107, p = .095; Holm-adjusted p = .190; 95% CI [−0.4019, 0.0323]). The joint test over event times −3 and −2 yields p = .061.

The event-time −3 estimate is −0.2238 (pointwise p = .042; 95% simultaneous interval [−0.4458, −0.0018]), although its Holm-adjusted p across the two administrative outcomes at that event time is .084. A simultaneous pre-event interval therefore excludes zero even though the two-lead joint p-value is just above .05. The selected balanced risk set neither establishes parallel pre-event paths nor provides a causal repair.

The current implementation does not support the originally predicted positive T3 direction. Positive estimates from restricted samples are imprecise and cohort-limited, while the negative primary association has failed lead diagnostics and uses a category not validated as relational distance. Neither pattern identifies a shadow or another adverse mechanism.

4.6 Definition and common-support sensitivity

Table 4 and Figure 2 present the retrospective ten-specification grid for marker, event, unit, and bridge definitions. The T2 definition sensitivities complement the focal-event comparisons above. The 5/25/65 partition produces −0.073, the 15/35/75 partition produces −0.015, code-level counting yields −0.013, requiring a revised-product-code bridge in every observed snapshot yields approximately zero, and a single-arena restriction produces −0.042. The predetermined size-and-momentum adjustment remains an auxiliary diagnostic outside the grid, reported in Appendix A11. Transition-year, comparison-group, common-support, and matched endpoint-classification diagnostics are likewise separated from the ten rows.

Note. Points show +1 to +3 cohort-share-weighted associations with pointwise 95% intervals. The display is a retrospective definition-sensitivity map: the negative T2 association is limited and definition-contingent, and the originally predicted positive T3 direction is not supported. Intervals characterize uncertainty and do not select a preferred model or produce a confirmatory verdict. Marker fill carries no significance coding. T2 and T3 are reimbursement-rank bins, not measures of shadow or spotlight.

For T3, alternative cutoffs remain near −0.54 to −0.55 with rejected pre-event tests. Code-level, revised-product-code-bridge-available, and HIRA–MFDS arena-agreement restrictions attenuate the negative estimates. Requiring a single TOP-position product in the first-event arrival snapshot produces a positive but imprecise value, while prior-maximum produces an estimate close to zero. These nonexchangeable specifications are interpreted qualitatively, not as a sign vote. They leave the T2 classification definition-contingent and the originally predicted positive T3 direction unsupported.

Linear fixed-effects and Sun–Abraham estimates are generally negative for both outcomes, but their lead coefficients do not show a clean pre-event pattern. Poisson estimates offer little stability evidence because they retain only 44 T2 arenas and 175 T3 arenas. Appendix A8 reports estimator retention, and Appendix A12 distinguishes the retrospective and supplementary diagnostics.

4.7 HIRA delisting and MFDS cancellation

The three administrative departure outcomes―HIRA delisting, persistent delisting, and MFDS cancellation—provide no coherent tier-specific corroboration. For prior-T2 incumbents, the +1 to +3 associations are −0.0014 (p = .762), +0.0015 (p = .722), and +0.0012 (p = .387), respectively. For prior-T3 incumbents, they are −0.0075 (p = .692), −0.0120 (p = .489), and +0.0040 (p = .548).

The endpoints differ institutionally, estimates are imprecise, and wider pre-event tests reject for all three T3 endpoints. Detailed results and the descriptive event-time −1 landmark are reported in Appendix A9–A10. The evidence does not identify commercial survival, sequential crowding, or market exit.

5.1 What the temporal-classification diagnostic establishes

The clearest empirical result concerns when administrative position is measured. Among the same 1,446 endpoint-matchable listing-appearance transitions, replacing arrival-snapshot T3 with 2025 T3 changes the post-window association by +0.2728 (p = .0019), while the paired T2 change is small and imprecisely estimated. Only 53.80% of matched transitions retain the same category, and only 62.4% of the 2,316 transitions in the paired-classification sample are endpoint-matchable. The finding is therefore a T3 reclassification result among matchable transitions, not a general estimate for all historical appearances. It sits within the broader accounting of reclassification and selective persistence.

The paired result leaves the cause of later rank changes and the direction of reverse causality unresolved, and it does not validate historical rank as relational proximity. Its narrower implication is clear: endpoint rank is not a predetermined historical position. Arena membership and reimbursement rank must be calculated within each dated snapshot before the marker receives strategic meaning.

5.2 Claim ceilings in archival strategy research

The five-link rule specifies how far the administrative evidence can travel. Historical reconstruction strengthens temporal warrant, but focal-actor identity, relational-marker validity, strategic-outcome meaning, and exogenous event timing remain unverified. The present claim therefore stops at a historically aligned marker-level association. Table 5 shows how each link sets that boundary.

An example shows how the rule changes the admissible claim. A coefficient-first reading might say, “originator entry suppresses T2 rivals.” That sentence is not admissible because actor identity, relational proximity, strategic behavior, and causality are unverified. The supported statement is narrower: “Within the selected evaluable historical HIRA risk set, T2 reimbursement-list appearances are negatively associated with a first observed TOP-position arrival, but the magnitude and direction are sensitive to event definition and support.” The five-link rule prevents the marker from carrying meanings the data do not establish.

The rule connects established approaches through a common claim-admissibility decision. Construct–measure scholarship supplies correspondence logic (Adcock and Collier, 2001; Edwards and Bagozzi, 2000; Godfrey and Hill, 1995); archival-proxy work exposes field-to-construct mismatch (Boyd et al., 2005); relational strategy theory makes competitive distance pair-specific (Chen, 1996); and event-study methods discipline the comparison once event, outcome, and risk set have been coded. The five-link procedure specifies the evidentiary bridge required before those inputs can carry the higher-level strategy claim.

5.3 The shadow–spotlight threshold as a motivating benchmark

The threshold model organizes the shadow–spotlight account around the relative strength of expansion and localized pressure. Localized pressure and market expansion may coexist, and their relative magnitude determines all-shadow, all-spotlight, or mixed regimes. Propositions 1–2 further show how an action or market attribute moves the boundary depending on whether it strengthens expansion or localized pressure more strongly. This formulation preserves the original intuition that a focal market action can have heterogeneous competitive consequences while making its comparative statics explicit.

The present application does not measure relational proximity $P_{im}$, expansion $E_{m}(a)$, or competitive pressure $C_{m}(P_{im}, a)$. It therefore does not evaluate Propositions 1–2, and no theory verdict follows from the T2/T3 associations. What the application evaluates is whether the original administrative implementation can reach that inferential level. It cannot: T2 shows a limited, definition-contingent negative marker association, while T3 does not display a diagnostically credible positive association. These conclusions concern administrative position bins. They are neither verdicts on the theoretical propositions nor evidence that all competitors experience suppression.

5.4 What would be required to name the mechanism

Current data do not support an identity interpretation. Rejecting one price explanation would not establish identity as the alternative, and the analysis has no direct measures of detailing, reputation, formulary access, physician attention, or actor recognition. The 2012 pricing reform is a broad institutional change with exceptions and contemporaneous industry developments, not a substitute for the missing identity measure.

Sequential crowding likewise remains unidentified. Conditioning on a T3 stock measured after the focal event could block an event-related path, induce post-event selection, or describe arenas in which T2 appearances were already less likely. A causal sequential account would require pre-event pipeline measures, independently timed supply variation, or another design that separates the proposed stages.

The departure outcomes reinforce this boundary: HIRA delisting and MFDS cancellation are institutionally distinct and display no coherent tier-specific pairing. Without sales or distribution data, neither can be translated into commercial survival or competitive displacement.

5.5 Administrative and managerial use of the claim ceiling

For competitive intelligence and policy analysis, the claim ceiling identifies the evidence required for each step toward a strategic interpretation. Without actor identity, the description stops at a TOP-position arrival; without relational overlap, at reimbursement-rank bins; without outcome or identification warrant, at selected administrative associations. Naming shadow or spotlight regions requires all of those links. Analysts must therefore preserve dated product risk sets, distinguish applications, reimbursement listings, regulatory cancellations, and commercial activity, and report cutoff and support dependence.

Managers can use reimbursement rank to summarize an administrative position, but not as a sufficient statistic for rivalry. A competitor map based only on rank can overlook asymmetric market commonality, resource similarity, formulary access, physician adoption, patent position, and firm pipelines. The validity chain identifies which additional evidence is needed before an administrative score can support a strategic inference.

5.6 Limitations and additional data

The temporal reconstruction has three limitations. First, no 2011 HIRA snapshot is available, so the analysis cannot reconstruct every transition surrounding the 2012 reform. The 2009 code system is also outside the primary bridge. Second, annual snapshots interval-censor appearances and disappearances; event time 0 is absent because ordering within the annual interval is unknown. Third, the 2016 recoding wave creates a tradeoff between transition contamination and cohort support.

The event definition and support rules impose further limits. The event is first observed only within the clean analytic window and may be left-censored. Among 17,747 eligible appearance transitions, 570 are returns after a gap. Of 1,439 first observed marker events, only 129 arrival snapshots contain a single TOP-position product; 452 contain more than one newly appearing TOP product, and 43 involve a returning TOP listing. A further 683 arenas have 2,094 later recurrent TOP-arrival arena-years. These counts make first observed TOP-position arrival a bounded administrative event, not a verified first-ever originator action.

Eligibility also conditions on arena observability through +2. Of observed TOP-position arrivals, 813 fail the initial support rule and 206 more lose support after 2016 is removed. Because absent arena-years are not imputed as zero, the reported associations apply only to the selected evaluable administrative risk set.

Current public reference-drug or patent-linkage fields could improve actor classification for a subset, but they would not establish perceived identity or market dominance for every historical event.

The analysis also lacks reimbursement applications, development pipelines, prescriptions, sales, detailing, formulary placement, and physician-level adoption. Application data could separate firm submission from administrative acceptance. Claims or prescription data could evaluate demand changes and validate overlap. Patent and reference-drug histories could improve actor classification. Private detailing, formulary, or reputation measures would be needed to evaluate an identity channel. Pre-event pipeline information or credible external timing variation would be required for a sequential-crowding design.

A direct test of the threshold model would require independently verified focal-actor histories, dyadic demand or strategic-overlap measures for $P_{im}$, dated category-expanding activity for $E_{m}(a)$, outcomes corresponding to $R_{im}(a)$, and event timing or comparison variation capable of supporting the intended counterfactual.

Population and time boundaries further limit generalization. Eligible event cohorts are concentrated in 2019–2023 after the 2016 transition is removed, but the primary balanced +1 to +3 estimand uses only 2019–2022. The 2016 gap changes cohort composition across the primary lead vector, and long post windows use only the 2019 and 2020 cohorts. A stricter diagnostic fixes cohorts at 2020–2022 and complete observation at 2017–2025, but retains only 235 event arenas and 2,240 comparison arenas with no marker event observed during 2012–2025 and is observably selective. Endpoint-price matching covers only 62.4% of listing-appearance transitions in the paired-classification transition sample. Neither diagnostic restores population representativeness. The results should not be generalized automatically to earlier Korean institutional periods or to pharmaceutical systems with different reimbursement and prescribing arrangements.