Fix non-consecutive heading levels in ProblemSet pages

PhD-Course/book/ProblemSet/Corporate Finance.md

@@ -169,9 +169,9 @@ $$
 		- 利用机器学习构建基于“引用量”和“文本新颖度”的专利指标，测试其对企业未来销售增长和市值的预测能力。
 		- **核心发现：** 引用加权和文本新颖度指标均能显著预测未来业绩增长，证明**专利文本数据是度量企业无形资产和成长机会的有效实证工具**。
 
-### 1. Capital Structure
+## 1. Capital Structure
 
-#### 1-1 Literature Review
+## 1-1 Literature Review
 
 **Question** 对 capital structure 做 literature review。按 trade-off、pecking order、market timing、agency-based theory 分类，说明每类理论的机制、预测和代表文献。
 
@@ -224,7 +224,7 @@ $$
 
 Debt 一方面 discipline managers，减少 free cash flow agency problem（<span style="color:#1f6feb;font-weight:700">Jensen 1986</span>）；另一方面会造成 debt overhang（<span style="color:#1f6feb;font-weight:700">Myers 1977</span>）和 risk shifting。Agency theory 预测：high FCF + low growth firms 应使用更多 debt（discipline 价值高）；growth opportunities 高的 firms 应减少 debt（debt overhang cost 高）。<span style="color:#1f6feb;font-weight:700">Smith and Watts (1992)</span> 发现 growth firms 的 leverage 显著更低，支持 debt overhang 预测；mature firms with high FCF 更多使用 debt，支持 free cash flow hypothesis。
 
-#### 1-2 Research Proposal
+## 1-2 Research Proposal
 
 **Question** 设计一个 research proposal，识别 tax shield 是否影响 corporate leverage。需要写 research question、hypotheses、data、model、expected outcomes 和 threats。
 
@@ -298,7 +298,7 @@ $$
 - Alternative leverage measures: book leverage, market leverage, net debt.
 - Debt issuance and equity issuance as separate outcomes.
 
-#### 1-3 Mechanism Question
+## 1-3 Mechanism Question
 
 **Question** Briefly state the mechanism and testable predictions for three theories of capital structure: trade-off, pecking order, market timing, and agency-based theory. For each selected theory, summarize one empirical paper. Then design one ideal policy change and give two threats.
 
@@ -374,7 +374,7 @@ Prediction：$\beta<0$，treated firms reduce leverage and debt issuance after r
 1. High-leverage firms may have different pre-trends.
 2. Reform may also affect investment, credit supply, and payout.
 
-#### 1-4 Theory Comparison
+## 1-4 Theory Comparison
 
 **Question** 比较 capital structure 中 trade-off、pecking order、market timing 与 agency-based theory 的机制差异，并整理对应实证文章和支持结论。
 
@@ -415,9 +415,9 @@ $$
 \end{aligned}
 $$
 
-### 2. Payout Policy
+## 2. Payout Policy
 
-#### 2-1 Literature Review
+## 2-1 Literature Review
 
 **Question** 对 payout policy 做 literature review。按 tax clientele、signaling、agency、lifecycle、flexibility、market timing 分类，说明每类机制、预测和代表文献。
 
@@ -461,7 +461,7 @@ $$
 \end{aligned}
 $$
 
-#### 2-2 Research Proposal
+## 2-2 Research Proposal
 
 **Question** 设计一个 research proposal，检验公司 payout 决策是 market timing、signaling、agency discipline、tax clientele 还是 financial flexibility。
 
@@ -557,7 +557,7 @@ $$
 2. Concurrent earnings announcements or M&A may contaminate payout announcement CAR.
 3. Future fundamentals may drive payout decisions, creating reverse causality.
 
-#### 2-3 Mechanism Question
+## 2-3 Mechanism Question
 
 **Question** 比较 payout policy 的 tax clientele、signaling、agency、financial flexibility / repurchase timing 四类机制。每类配一篇 empirical paper，并设计一个检验 dividend tax clientele 的政策实验。
 
@@ -640,7 +640,7 @@ Prediction：$\beta>0$；dividends rise more for tax-sensitive firms, and ex-div
 1. Tax reform may coincide with macro shocks.
 2. Investor ownership composition may change endogenously.
 
-#### 2-4 Theory Comparison
+## 2-4 Theory Comparison
 
 **Question** 比较 payout policy 中 tax clientele、signaling、agency、life-cycle / flexibility 与 repurchase market timing 的机制差异，并整理相关实证文章和支持结论。
 
@@ -685,9 +685,9 @@ $$
 \end{aligned}
 $$
 
-### 3. Seasoned Equity Offerings
+## 3. Seasoned Equity Offerings
 
-#### 3-1 Literature Review
+## 3-1 Literature Review
 
 **Question** 对 Seasoned Equity Offerings 做 literature review。按 adverse selection、market timing、ownership-monitoring、price pressure、target leverage adjustment 分类，说明机制、预测和代表文献。
 
@@ -732,7 +732,7 @@ $$
 \end{aligned}
 $$
 
-#### 3-2 Research Proposal
+## 3-2 Research Proposal
 
 **Question** 设计一个 research proposal，检验 SEO announcement effects 是 adverse selection 还是 market timing。
 
@@ -823,7 +823,7 @@ If market timing matters, timing restrictions reduce the sensitivity of SEO issu
 1. Disclosure rule may also increase litigation risk and change issuer composition.
 2. Long-run SEO underperformance is sensitive to benchmark choice and sample selection.
 
-#### 3-3 Mechanism Question
+## 3-3 Mechanism Question
 
 **Question** Briefly state the economic mechanism and testable predictions for three SEO announcement-effect theories: information asymmetry / adverse selection, market timing, ownership-monitoring, and price pressure. For each selected theory, summarize one empirical paper and design one ideal policy change.
 
@@ -893,7 +893,7 @@ Mandatory pre-SEO disclosure. Expected outcome：SEO announcement CAR becomes le
 1. Policy may change issuer composition.
 2. Disclosure may affect litigation risk and underwriter screening, not just information asymmetry.
 
-#### 3-4 Theory Comparison
+## 3-4 Theory Comparison
 
 **Question** 比较 SEO announcement effects 的 adverse selection、market timing、ownership-monitoring 与 price pressure 机制差异，并整理相关实证文章和支持结论。
 
@@ -933,9 +933,9 @@ $$
 \end{aligned}
 $$
 
-### 4. Labor and Corporate Finance
+## 4. Labor and Corporate Finance
 
-#### 4-1 Literature Review
+## 4-1 Literature Review
 
 **Question** 对 Labor and Corporate Finance 做 literature review。按 labor supply shocks、labor adjustment costs、bargaining power、human capital、labor welfare 分类。
 
@@ -973,7 +973,7 @@ $$
 
 Key conclusion：labor frictions change optimal leverage, cash holdings, investment, safety investment, and technology adoption.
 
-#### 4-2 Research Proposal
+## 4-2 Research Proposal
 
 **Question** 设计一个 research proposal，检验 negative labor supply shock 是否导致 firms substitute IT capital for labor。
 
@@ -1051,7 +1051,7 @@ $$
 2. Firms may relocate or change plant composition, creating sample selection.
 3. Technology adoption may be driven by industry-level automation trends rather than local labor scarcity.
 
-#### 4-3 Mechanism Question
+## 4-3 Mechanism Question
 
 **Question** State three channels through which labor markets affect corporate finance: labor supply and automation, labor adjustment costs and leverage, bargaining power and strategic debt, labor welfare and financing constraints. For each channel, summarize one empirical paper and propose an ideal policy setting.
 
@@ -1122,7 +1122,7 @@ Randomized H-1B quota expansion or staggered labor protection reform. Use DiD /
 1. Labor policy may be adopted in states or industries with different trends.
 2. Spillovers across local labor markets may contaminate control groups.
 
-#### 4-4 Theory Comparison
+## 4-4 Theory Comparison
 
 **Question** 比较 labor and corporate finance 中 labor supply / automation、labor adjustment costs、labor bargaining / strategic debt 与 worker welfare mechanisms 的机制差异，并整理相关实证文章和支持结论。
 
@@ -1162,9 +1162,9 @@ $$
 \end{aligned}
 $$
 
-### 5. ESG and Climate
+## 5. ESG and Climate
 
-#### 5-1 Literature Review
+## 5-1 Literature Review
 
 **Question** 对 ESG and Climate 做 literature review。按 ESG measurement、green human capital、E-S trade-off、climate labor risk 分类。
 
@@ -1198,7 +1198,7 @@ $$
 
 ESG 不只是 disclosure 或 moral preference。分析中应将 ESG 表述为可观测 corporate policy：green hiring、safety investment、emissions, adaptation CAPEX, labor risk management, and future profitability。
 
-#### 5-2 Research Proposal
+## 5-2 Research Proposal
 
 **Question** 设计一个 research proposal，检验 firms 的 green hiring 是真实 capability building 还是 greenwashing。
 
@@ -1288,7 +1288,7 @@ Use a disclosure mandate, climate policy shock, or stakeholder-pressure shock th
 2. Job postings measure labor demand, not realized hiring.
 3. ESG policy shocks may also change regulation, financing constraints, or consumer demand.
 
-#### 5-3 Mechanism Question
+## 5-3 Mechanism Question
 
 **Question** Explain three mechanisms in ESG / Climate corporate finance: ESG measurement and inside view, green human capital, E-S trade-off, and climate-labor risk. For each, summarize one empirical paper and give testable predictions.
 
@@ -1360,7 +1360,7 @@ E-S trade-off theory 预测当 ESG resources 有限时，一个维度的强制
 2. Green hiring can be symbolic if postings do not turn into realized capabilities.
 3. Climate shocks may affect both labor productivity and local demand.
 
-#### 5-4 Theory Comparison
+## 5-4 Theory Comparison
 
 **Question** 比较 ESG / Climate 中 measurement / greenwashing、green human capital、E-S trade-off 与 climate-labor risk 的机制差异，并整理相关实证文章和支持结论。
 
@@ -1400,9 +1400,9 @@ $$
 \end{aligned}
 $$
 
-### 6. AI and Corporate Finance
+## 6. AI and Corporate Finance
 
-#### 6-1 Literature Review
+## 6-1 Literature Review
 
 **Question** 对 AI and Corporate Finance 做 literature review。按 AI measurement、AI as general-purpose technology、product innovation vs process innovation、GenAI exposure and valuation 分类。
 
@@ -1462,7 +1462,7 @@ X^f
 \end{aligned}
 $$
 
-#### 6-2 Research Proposal
+## 6-2 Research Proposal
 
 **Question** 设计一个 research proposal，检验 firm-level AI investment 是否提升 firm growth and valuation，并区分 product innovation 和 cost reduction 机制。
 
@@ -1566,7 +1566,7 @@ $$
 2. Job postings measure demand, not actual adoption; measurement error may bias OLS.
 3. IV exclusion may fail if historical university networks affect growth through other high-skill channels.
 
-#### 6-3 Mechanism Question
+## 6-3 Mechanism Question
 
 **Question** Explain three mechanisms in AI corporate finance: AI as general-purpose technology, product innovation vs process innovation, and GenAI exposure / repricing. For each, summarize one empirical paper and give predictions.
 
@@ -1624,7 +1624,7 @@ GenAI exposure theory 预测 GenAI 改变 task-level productivity expectations
 2. Market repricing may reflect hype or sentiment rather than realized productivity.
 3. Job postings capture intended hiring, not realized adoption or productive use.
 
-#### 6-4 Theory Comparison
+## 6-4 Theory Comparison
 
 **Question** 比较 AI and Corporate Finance 中 AI measurement、AI as GPT、product vs process innovation 与 GenAI exposure 的机制差异，并整理相关实证文章和支持结论。
 

PhD-Course/book/ProblemSet/Econometrics.md

@@ -1,6 +1,6 @@
 # Econometrics
 
-### 1. Residual Variance Consistency and CLT
+## 1. Residual Variance Consistency and CLT
 
 Consider
 
@@ -22,7 +22,7 @@ Show the consistency and limiting distribution of $s^2$.
 推导详见 [03_Asymptotics_OLS_Inference_Hypothesis_Testing](../Econometrics/EF8090/03_Asymptotics_OLS_Inference_Hypothesis_Testing.md)（残差方差的一致性及渐近正态性）。相关卡片：[OLS 渐近理论](../Econometrics/EF8090/cards/)。
 
 
-### 2. 2SLS Coefficient as One-Dimensional IV
+## 2. 2SLS Coefficient as One-Dimensional IV
 
 考虑一个含有一个内生变量 $D$、控制变量 $X$ 和 excluded instruments $Z$ 的 2SLS 模型：
 
@@ -57,7 +57,7 @@ $$
 推导详见 [05_IV_2SLS_Weak_Instruments](../Econometrics/EF8090/05_IV_2SLS_Weak_Instruments.md)（2SLS 的 FWL 推导及与 IV 的等价性）。关键卡片：[TwoSLS as projection](../Econometrics/EF8090/cards/TwoSLS_as_Projection.md)。
 
 
-### 3. Balanced Panel DID Mean Expressions
+## 3. Balanced Panel DID Mean Expressions
 
 考虑一个有前、后期划分的 balanced panel DiD 设计：
 
@@ -78,7 +78,7 @@ $$
 推导详见 [07_DiD_RD_Nonparametric_Kernel](../Econometrics/EF8090/07_DiD_RD_Nonparametric_Kernel.md)（面板 DiD 的 TWFE 分解）。关键卡片：[DID common trends](../Econometrics/EF8090/cards/DID_Common_Trends.md)。
 
 
-### 4. Fuzzy RDD Local Linear Wald Ratio
+## 4. Fuzzy RDD Local Linear Wald Ratio
 
 Consider fuzzy RDD with uniform kernel and common bandwidth $h$:
 
@@ -103,7 +103,7 @@ $$
 推导详见 [07_DiD_RD_Nonparametric_Kernel](../Econometrics/EF8090/07_DiD_RD_Nonparametric_Kernel.md)（Fuzzy RDD 的 local linear 2SLS 等价于 Wald ratio）。
 
 
-### 5. DID Estimator 与 ATE/ATT 推导
+## 5. DID Estimator 与 ATE/ATT 推导
 
 #DID #parallel_trends #ATE #ATT
 
@@ -305,7 +305,7 @@ $$
 
 
 
-### 6. DDD Estimator 推导
+## 6. DDD Estimator 推导
 
 #DDD #triple_differences #placebo_group
 
@@ -509,7 +509,7 @@ $$
 
 
 
-### 7. 2SLS 推导与性质证明
+## 7. 2SLS 推导与性质证明
 
 #2SLS #IV_estimation #consistency #asymptotic_normality
 
@@ -792,7 +792,7 @@ $$
 
 
 
-### 8. FWL 定理证明与应用
+## 8. FWL 定理证明与应用
 
 #FWL_theorem #partial_regression #orthogonalization
 
@@ -1036,7 +1036,7 @@ $$
 
 
 
-### 9. MLE 基础与性质
+## 9. MLE 基础与性质
 
 #MLE #Fisher_information #asymptotic_properties
 
@@ -1308,7 +1308,7 @@ $$
 
 
 
-### 10. Logit 模型推导与边际效应
+## 10. Logit 模型推导与边际效应
 
 #Logit_model #MLE #marginal_effects #odds_ratio
 
@@ -1560,7 +1560,7 @@ $$
 
 
 
-### 11. Panel Data: Fixed Effects vs Random Effects
+## 11. Panel Data: Fixed Effects vs Random Effects
 
 #panel-data #fixed-effects #random-effects #Hausman-test
 
@@ -1753,7 +1753,7 @@ where $k$ is the dimension of $\beta$.
 
 
 
-### 12. Probit Model and Marginal Effects
+## 12. Probit Model and Marginal Effects
 
 #probit #binary-choice #marginal-effects
 
@@ -1913,7 +1913,7 @@ AME preferred: averages over actual covariate distribution.
 ::::
 
 
-### 13. 考场默写版：DID/DDD、2SLS、FWL、MLE 和 Logit
+## 13. 考场默写版：DID/DDD、2SLS、FWL、MLE 和 Logit
 
 #DID #DDD #ATT #ATE #2SLS #FWL #MLE #Logit
 
@@ -2561,7 +2561,7 @@ $$
 
 ::::
 
-### 14. Roy Model, Self-Selection, LATE and MTE
+## 14. Roy Model, Self-Selection, LATE and MTE
 
 #RoyModel #Selection #LATE #MTE #ATT #ATE #PolicyEvaluation
 
@@ -3028,7 +3028,7 @@ $$
 
 
 
-### 15. Causal Inference: Medical Treatment, LATE, Probit, and IV
+## 15. Causal Inference: Medical Treatment, LATE, Probit, and IV
 
 #causal-inference #ATE #ATT #LATE #IV #2SLS #probit