# Paper C: The Commitment Trap ## Table of Contents with Abstract, Figures, Tables **Source of Truth:** `[[📢BULLETIN]]` **Registry:** `[[🗄️REGISTRY]]` --- ## 📜 ABSTRACT When does the very commitment that secures funding become a trap? Analyzing a panel of **123,906 ventures**, we document the **Capital-Flexibility Paradox**: early capital ($E$) systematically reduces strategic flexibility (|ΔV|), yet flexibility significantly predicts growth ($\rho = +0.159$, $p < 0.001$). Flexible ventures achieve **2.7× higher growth** compared to rigid ones. We verify three hypotheses: **H1** confirms that among ventures with similar early funding, more flexible ones grow faster ($\rho = +0.158$). **H2** shows that controlling for initial vagueness, more capital leads to less flexibility ($\rho = -0.052$). Most strikingly, **H3** reveals that capital's effect on growth varies by positioning: it *hurts* Analyst-channel ventures (Low V: $\rho = -0.05$) but *helps* Believer-channel ventures (High V: $\rho = +0.08$). This pattern aligns with Paper U's U-shape: the "Murky Middle" gets trapped in their commitments, while the extremes either escape through flexibility (Believer) or thrive through focus (Analyst). We introduce the concept of **Abandonment Option Cost (AOC)** to explain why capital crystallizes into a "Golden Cage." **Keywords:** Commitment Trap, Capital-Flexibility Paradox, Abandonment Option Cost, Golden Cage, Strategic Flexibility --- ## 📑 TABLE OF CONTENTS ### Section 1: Introduction (¶43-49) → File: `[[section1(c)]]` | ¶ | Role | First Sentence | |:-:|:-----|:---------------| | 43 | 📿 복음 | RBV: 더 많은 자본 → 더 많은 실험 → 더 나은 성과 (Barney 1991). | | 44 | 🧩 퍼즐 | 그러나 유연한 벤처가 경직된 벤처보다 **2.7×** 더 성장. | | 45 | 😮 RQ | 초기 성공이 **함정**이 되는 조건은? | | 46 | 🔎 렌즈 | 반사실적 비용 프레임워크: E[Y\|유연] - E[Y\|고정]. | | 47 | 😆 해법 | 자본 → 헌신 → 동질화 → 학습 차단. | | 48 | 🗺️ 인접 | Nanda (2020), Kerr et al. (2014)와의 차별점. | | 49 | 🗄️ 로드맵 | 2절 이론, 3절 실증, 4절 논의. | ### Section 2: Theory (¶50-58) → File: `[[section2(c)]]` | ¶ | Role | First Sentence | Asset | |:-:|:-----|:---------------|:------| | 50 | 문헌: 자원 | RBV — H₀: 자원이 실험을 돕는다. | | | 51 | 문헌: 경직성 | Leonard-Barton (1992) 핵심 경직성. | | | 52 | 문헌: 피벗 | Ries (2011), McDonald & Gao (2019). | | | 53 | 갭 | 자원 풍요 → 피벗 비용 증가의 정량화 부재. | | | 54 | 메커니즘: AOC | 포기 옵션 비용(AOC) 도입. | | | 55 | 메커니즘: Golden Cage | 높은 E → 높은 AOC → 현상 유지 강제. | `[[🖼️C_S2_mechanism]]` | | 56 | 계보: Real Options | Put Option 행사 가격 ↔ AOC. | | | 57 | 모델 | 세 가지 가설: H1, H2, H3. | | | 58 | 가설 | **H2: 같은 V → 더 많은 E → 덜 유연**. | | ### Section 3: Empirics (¶59-69) → File: `[[section3(c)]]` | ¶ | Role | First Sentence | Asset | |:-:|:-----|:---------------|:------| | 59 | 맥락 | Paper U의 부분집합: **N = 133,945** 패널. | | | 60 | 표본 | 2010-2018 코호트, 5년 추적. | | | 61 | DV | Y = total_raised / first_financing_size. | | | 62 | IV | \|ΔV\| = 전략적 유연성. | | | 63 | 조절 | E = 초기 자본. | | | 64 | 기술통계 | **ρ(E, \|ΔV\|)_within_V = -0.052***. | `[[🗄️C_S3_correlations]]` | | 65 | 식별 | V decile 내 분석으로 내생성 통제. | | | 66 | 명세 | 세 가설 검정. | | | 67 | H1,H2,H3 | **Three Hypotheses Verified**. | `[[🖼️C_S3_hypotheses]]` `[[🗄️C_S3_hypotheses]]` | | 68 | Decile | 자본 십분위별 유연성 감소. | `[[🖼️C_S3_decile]]` | | 69 | Gap | **Flexibility Gap = 2.7×**. | `[[🖼️C_S3_cohort]]` `[[🗄️C_S3_gap]]` | ### Section 4: Discussion (¶70-74) → File: `[[section4(c)]]` | ¶ | Role | First Sentence | |:-:|:-----|:---------------| | 70 | 공헌 1 | "Golden Cage" 실증: 돈은 기회가 아니라 족쇄. | | 71 | 공헌 2 | 피벗 연구에 비용 관점 통합: AOC ∝ E. | | 72 | 공헌 3 | 투자자 경고: 과도한 초기 자본이 옵션 가치 파괴. | | 73 | 한계 | AOC 측정의 간접성; 직접 측정 필요. | | 74 | 결론 | 성공은 자원 축적이 아닌 **유연성 유지**에 달려 있음. | --- ## 🖼️ LIST OF FIGURES | # | Module | Caption | Page | |:-:|:-------|:--------|:----:| | C.1 | `[[🖼️C_S2_mechanism]]` | The Capital-Flexibility-Growth Mechanism | TBD | | C.2 | `[[🖼️C_S3_hypotheses]]` | Three Hypotheses Verification | TBD | | C.3 | `[[🖼️C_S3_decile]]` | Commitment Cost by Early Funding Decile | TBD | | C.4 | `[[🖼️C_S3_cohort]]` | The 2.7× Flexibility Gap | TBD | --- ## 🗄️ LIST OF TABLES | # | Module | Caption | Page | |:-:|:-------|:--------|:----:| | C.1 | `[[🗄️C_S3_correlations]]` | Key Correlations | TBD | | C.2 | `[[🗄️C_S3_hypotheses]]` | Three Hypotheses Test Results | TBD | | C.3 | `[[🗄️C_S3_gap]]` | The 2.7× Flexibility Gap | TBD | --- ## 📊 KEY NUMBERS (from [[📢BULLETIN]]) | Metric | Value | |:-------|:------| | Panel Sample | **123,906** | | ρ(Y, \|ΔV\|) | **+0.159***| | ρ(E, \|ΔV\|)_within_V | **-0.052*** | | Flexibility Gap | **2.7×** | | H1 (Flexibility→Growth) | ρ = +0.158*** | | H2 (Capital→Less Flex) | ρ = -0.052*** | | H3 Low-V | ρ = -0.05 | | H3 High-V | ρ = +0.08 | --- ## 🔗 CROSS-PAPER LINKS | To Paper | Connection | |:---------|:-----------| | → U | H3 pattern mirrors U-shape: extremes thrive, middle suffers | | → N | AOC feeds into CR calculation for optimal k* | --- *Paper C managed by 🟠G + 🟢J* *Verified by 🔴K*