23. Credit Cycles and Credit Supply

Jun He May 31, 2026
公司金融Corporate Finance 信贷周期Credit Cycles 信贷供给Credit Supply 信用利差Credit Spread 市场分割Market Segmentation 安全资产Safe Asset 政府挤出Government Crowd-Out 学习笔记Study Note
Note

本章主题：信贷周期与信贷供给。 §23.1 信贷周期的可预测性：Greenwood-Hanson (2013) 简约模型——信用利差 \(s_{\theta t}=\pi_{\theta t}+\beta_\theta\delta_t\)（违约概率 + 整体超额回报因子），繁荣期债务发行向高风险倾斜 (23.1)–(23.3)；以发行人质量代理（\(ISS^{EDF}\) (23.5)、高收益份额 \(HYS\) (23.6)）预测风险公司债的低超额回报 (23.7)。Baron-Xiong (2017) 用 20 国 1920–2012 数据：银行信贷/GDP 扩张预测更低（甚至负）的银行股回报（3 年后 −37.3%）——行为性过度乐观。§23.2 Chernenko-Sunderam (2012) 信贷市场分割：很多机构只能买投资级债 → 用 BBB−/BB+ 配对差分 (23.8)–(23.10) 识别——高收益基金流入越多、高收益类公司投资越多（分割效应仅在评级分割点 BBB−/BB+ 显著）。§23.3 私人 vs 政府信贷供给：对安全资产的需求无弹性，政府不供给时私人发「伪安全」产品（系统性风险源）。Greenwood et al. (2010) 理论：偏好习性投资者 + 风险厌恶套利者 + 企业，政府长期债 \(g\) 越多→企业长期债发行 \(f^*(P)\) 越少 (23.15)（挤出）。Krishnamurthy-Vissing-Jorgensen (2015) 实证：政府国库券供给高→经济净短期债低（挤出）。Greenwood et al. (2015)：短期政府债权衡（滚动风险 vs 满足流动性需求+挤出私人危险的伪安全债）；价格渠道 (23.16)(23.17) + 挤出 (23.18)(23.19)，以税历季节性作 IV (23.20)。

Note

Chapter theme: credit cycles and credit supply. §23.1 Predictability of credit cycles: Greenwood-Hanson (2013) reduced-form model — credit spread \(s_{\theta t}=\pi_{\theta t}+\beta_\theta\delta_t\) (default probability + an overall-excess-return factor), with booms tilting debt issuance toward higher risk (23.1)–(23.3); using issuer-quality proxies (\(ISS^{EDF}\) (23.5), high-yield share \(HYS\) (23.6)) to predict the low excess returns of risky corporate bonds (23.7). Baron-Xiong (2017) use 20-country 1920–2012 data: bank-credit/GDP expansion predicts lower (even negative) bank-equity returns (−37.3% three years out) — behavioral overoptimism. §23.2 Chernenko-Sunderam (2012) credit-market segmentation: many institutions can only buy investment-grade bonds → identified by BBB−/BB+ matched differencing (23.8)–(23.10) — more high-yield fund inflow → more investment by high-yield-category firms (the segmentation effect is significant only at the BBB−/BB+ cutoff). §23.3 Private vs government credit supply: inelastic demand for safe assets, with the private sector issuing "pseudo-safe" products (a source of systematic risk) when the government doesn't supply. Greenwood et al. (2010) theory: preferred-habitat investors + risk-averse arbitrageurs + firms, more government long-term debt \(g\) → less firm long-term debt issuance \(f^*(P)\) (23.15) (crowd-out). Krishnamurthy-Vissing-Jorgensen (2015) empirics: high government Treasury supply → low net short-term debt in the economy (crowd-out). Greenwood et al. (2015): the trade-off of short-term government debt (roll-over risk vs satisfying liquidity demand + crowding out dangerous private pseudo-safe debt); a price channel (23.16)(23.17) + crowd-out (23.18)(23.19), with tax-calendar seasonality as an IV (23.20).

23.1 Predictability of Credit Cycles

23.1.1 繁荣期信用质量恶化预示低回报：Greenwood-Hanson (2013). 公司债信用质量在信贷繁荣期恶化、预测债券持有人的低超额回报。简约模型——信用利差（公司债收益与同期限无风险利率之差）

$$s_{\theta t}=\pi_{\theta t}+\beta_\theta\delta_t$$

\(\theta\) 公司类型、\(\pi_{\theta t}\) 时变违约概率、\(\delta_t\) 整体信贷资产的时变期望回报（\(\beta_\theta\) 因子载荷）；\(\beta_\theta\delta_t\)=公司 \(\theta\) 债券的期望超额回报。利差低有两因：违约概率 \(\pi_{\theta t}\) 低、期望超额回报 \(\beta_\theta\delta_t\) 低。两类 \(\theta\in\{L,H\}\)，\(\pi_{Lt}<\pi_{Ht}\)、\(\beta_L<\beta_H\)。各公司选最优债务发行 \(d_{\theta t}^*\)（权衡低信贷成本与偏离最优债务的惩罚）：

$$\max_{d_{\theta t}}\underbrace{-\beta_\theta\delta_t\cdot d_{\theta t}}_{\text{expected cost}}\underbrace{-\frac{\gamma}{2}[d_{\theta t}-(\xi_t+\varepsilon_{\theta t})]^2}_{\text{cost of deviation}} \tag{23.1}$$

f.o.c. \(\Rightarrow d_{\theta t}^*=\xi_t+\varepsilon_{\theta t}-\frac{\beta_\theta}{\gamma}\delta_t\) (23.2)（期望超额回报 \(\delta_t\) 越低、发债越多）。去掉共同因子 \(\xi_t\) 得质量代理

$$d_{Ht}^*-d_{Lt}^*=\varepsilon_{Ht}-\varepsilon_{Lt}-\frac{\beta_H-\beta_L}{\gamma}\delta_t \tag{23.3}$$

另一质量指标 \(ISS_t=\mathbb E_t[\pi_i\mid\text{High }d^*]-\mathbb E_t[\pi_i\mid\text{Low }d^*]\) (23.4)。数据：第一度量 \(ISS_t^{EDF}=\frac{\sum_{i\in\text{High }d}EDF_{it}}{N^{High}}-\frac{\sum_{i\in\text{Low }d}EDF_{it}}{N^{Low}}\) (23.5)（\(EDF\)=违约概率估计、NYSE 债务净发行上/下分位）；第二度量高收益份额 \(HYS_t=\frac{\sum_{i\text{ High Yield}}B_{it}}{\sum_{i\text{ High Yield}}B_{it}+\sum_{i\text{ Inv Grade}}B_{it}}\) (23.6)（Moody's Ba1 或更低=高收益；二度量一致，图 23.1）。整体信用利差 \(\delta_t\)=Moody's BBB 指数减长期政府债收益。主回归

$$rx_{t+k}=a+bX_t+u_{t+k} \tag{23.7}$$

\(rx_{t+k}\) 第 \(t+k\) 年超额回报（\(rx^{HY}=r^{HY}-r^G\) 等），\(X_t\)=发行人质量（\(ISS^{EDF}\)、\(\log(HYS)\)）。结果（图 23.2）：发行人质量越差（\(ISS^{EDF}\) 或 \(\log(HYS)\) 越高）显著预测风险公司债（高收益）更低超额回报；对安全（AAA）债无此预测性；不同 \(k\)、子样本稳健。

23.1.1 Deteriorating credit quality in booms forecasts low returns: Greenwood-Hanson (2013). Corporate-debt credit quality deteriorates in credit booms, predicting bondholders' low excess returns. Reduced-form model — the credit spread (corporate yield minus same-maturity risk-free rate)

$$s_{\theta t}=\pi_{\theta t}+\beta_\theta\delta_t$$

\(\theta\) firm type, \(\pi_{\theta t}\) time-varying default probability, \(\delta_t\) the time-varying expected return on the overall credit asset (\(\beta_\theta\) a loading); \(\beta_\theta\delta_t\) = firm \(\theta\)'s bond expected excess return. The spread is low for two reasons: low default probability \(\pi_{\theta t}\), or low expected excess return \(\beta_\theta\delta_t\). Two types \(\theta\in\{L,H\}\), \(\pi_{Lt}<\pi_{Ht}\), \(\beta_L<\beta_H\). Each firm chooses optimal issuance \(d_{\theta t}^*\) (trading off low credit cost vs the penalty of deviating):

$$\max_{d_{\theta t}}\underbrace{-\beta_\theta\delta_t\cdot d_{\theta t}}_{\text{expected cost}}\underbrace{-\frac{\gamma}{2}[d_{\theta t}-(\xi_t+\varepsilon_{\theta t})]^2}_{\text{cost of deviation}} \tag{23.1}$$

f.o.c. \(\Rightarrow d_{\theta t}^*=\xi_t+\varepsilon_{\theta t}-\frac{\beta_\theta}{\gamma}\delta_t\) (23.2) (lower expected excess return \(\delta_t\) → more issuance). Removing the common factor \(\xi_t\) gives the quality proxy

$$d_{Ht}^*-d_{Lt}^*=\varepsilon_{Ht}-\varepsilon_{Lt}-\frac{\beta_H-\beta_L}{\gamma}\delta_t \tag{23.3}$$

another quality indicator \(ISS_t=\mathbb E_t[\pi_i\mid\text{High }d^*]-\mathbb E_t[\pi_i\mid\text{Low }d^*]\) (23.4). Data: the first measure \(ISS_t^{EDF}=\frac{\sum_{i\in\text{High }d}EDF_{it}}{N^{High}}-\frac{\sum_{i\in\text{Low }d}EDF_{it}}{N^{Low}}\) (23.5) (\(EDF\) = default probability estimate, top/bottom quantiles of NYSE net issuance); the second, high-yield share \(HYS_t=\frac{\sum_{i\text{ High Yield}}B_{it}}{\sum_{i\text{ High Yield}}B_{it}+\sum_{i\text{ Inv Grade}}B_{it}}\) (23.6) (Moody's Ba1 or lower = high yield; the two are consistent, Figure 23.1). The overall credit spread \(\delta_t\) = Moody's BBB index minus long-term government yield. Main regression

$$rx_{t+k}=a+bX_t+u_{t+k} \tag{23.7}$$

\(rx_{t+k}\) the year-\(t+k\) excess return (\(rx^{HY}=r^{HY}-r^G\), etc.), \(X_t\) = issuer quality (\(ISS^{EDF}\), \(\log(HYS)\)). Results (Figure 23.2): worse issuer quality (higher \(ISS^{EDF}\) or \(\log(HYS)\)) significantly predicts lower excess returns of risky (high-yield) corporate bonds; no such predictability for safe (AAA) bonds; robust across \(k\) and sub-samples.

23.1.2 Bank Credit/GDP Predicts Bank Equity Returns: Baron and Xiong (2017)

Baron-Xiong (2017) 用 20 个发达国家 1920–2012 数据，表明存在过度乐观——银行股投资者在信贷扩张繁荣期忽视银行股的未来崩盘风险。数据：发达经济体（IMF）至少 40 年信贷扩张 + 银行股指回报。银行信贷/GDP 比的变化

$$\Delta\left(\frac{\text{bank credit}}{\text{GDP}}\right)_t=\frac{\left(\frac{\text{bank credit}}{\text{GDP}}\right)_t-\left(\frac{\text{bank credit}}{\text{GDP}}\right)_{t-3}}{3}$$

称信贷扩张（银行信贷=银行部门对国内家庭+非金融企业的信贷）；用对数超额银行股指回报。结果：信贷扩张（更高 \(\Delta(\text{bank credit}/\text{GDP})\)）显著预测银行股指 1、2、3 年后更低的平均回报（图 23.3，跨规范稳健）；超过高分位阈值预测负超额回报（图 23.4–23.6；大信贷扩张即 >95% 分位时，3 年后超额回报 −37.3%）。这支持行为性过度乐观（理性投资者本应套掉这种可预测的系统性负回报、但没有）。

Tip

Remark 23.1 信贷周期对实体经济影响巨大。§22 讨论了信贷周期繁荣与萧条向实体的传导，那些论文都聚焦家庭需求渠道而非传统公司投资渠道——这有道理，因 Mian-Sufi (2018b) 论证如今家庭需求渠道在传导中占主导。

Baron-Xiong (2017) use 20-developed-country 1920–2012 data to show overoptimism — bank-equity investors neglect future crash risks during credit-expansion booms. Data: advanced economies (IMF) with at least 40 years of credit expansion + bank-equity index returns. The change in the bank-credit/GDP ratio

$$\Delta\left(\frac{\text{bank credit}}{\text{GDP}}\right)_t=\frac{\left(\frac{\text{bank credit}}{\text{GDP}}\right)_t-\left(\frac{\text{bank credit}}{\text{GDP}}\right)_{t-3}}{3}$$

is called credit expansion (bank credit = banking-sector credit to domestic households + non-financial corporations); log excess bank-equity index returns are used. Results: credit expansion (higher \(\Delta(\text{bank credit}/\text{GDP})\)) significantly predicts lower mean bank-equity index returns 1, 2, 3 years ahead (Figure 23.3, robust across specifications); over a high percentile threshold it predicts negative excess returns (Figures 23.4–23.6; with a large expansion, >95th percentile, the 3-year-ahead excess return is −37.3%). This supports behavioral overoptimism (rational investors should arbitrage away this predictable systematic negative return, but don't).

Tip

Remark 23.1 Credit cycles have a tremendous impact on the real economy. §22 discussed the transmission of both booms and busts in credit cycles to the real economy, with those papers all focusing on the household demand channel rather than the traditional firm-investment channel — which makes sense, as Mian-Sufi (2018b) argue the household demand channel is dominant in the transmission nowadays.

23.2 Credit Market Segmentation and Real Activities: Chernenko and Sunderam (2012)

Chernenko-Sunderam (2012) 表明信贷市场的分割（很多机构投资者只能买投资级债）对公司实际投资有影响。数据：CRSP/COMPUSTAT 合并、美国国内公司（剔金融/公用）1986Q1–2010Q4。变量：\(\frac{CAPX_{i,t}}{PPE_{i,t-1}}\)（资本支出/上期 PP&E）、\(\frac{CF_{i,t}}{PPE_{i,t-1}}\)（现金流，标准化）、\(Q_{i,t}\)（Tobin's Q，越高投资机会越好）。主回归

$$y_{i,t}=\alpha_i+\beta_Q Q_{i,t-1}+\beta_{CF}\frac{CF_{i,t}}{PPE_{i,t-1}}+\beta_{Flow}(R_i)\cdot\text{High yield fund flows}_{t-1}+\text{Investment opportunities}_i(S_i)+\varepsilon_{i,t} \tag{23.8}$$

\(y=\frac{CAPX}{PPE}\)、High yield fund flows=流入高收益债共同基金的总现金、\(\beta_{Flow}(R_i)\) 为信用评级 \(R_i\) 的函数、Investment opportunities\(_i(S_i)\) 为信用质量（不可观测）的函数。匹配：将特征相似但一家恰为 BBB−（最低投资级）、另一家恰为 BB+ 的公司配成基本面相似对（同行业/规模/杠杆/Z 分数/现金/销售增长，差异在一个标准差内），使 Investment opportunities\(_i(S_i)=\)Investment opportunities\(_j(S_j)\)。对匹配对取差分 (23.9) 消去不可观测投资机会，得

$$\Delta\frac{CAPX_{i,t}}{PPE_{i,t-1}}=\alpha_i+\beta_{Flow}\cdot\text{High yield fund flows}_{t-1}+\beta_Q\Delta Q_{i,t-1}+\beta_{CF}\Delta\frac{CF_{i,t}}{PPE_{i,t-1}}+\varepsilon_{i,t} \tag{23.10}$$

\(\beta_{Flow}\) 为兴趣参数（高收益公司减投资级公司）。稳健性：其他评级分割点（A & A−、A− & BBB+、B+ & B）重复。结果（图 23.7 主、图 23.8 安慰剂）：流入高收益基金的钱越多、高收益类公司投资越多（非因高收益公司财务受限，而是分割使高收益公司有更多可用资金）；图 23.8 仅在债券评级分割点（BBB−/BB+）系数显著 → 债券评级仅在市场分割点影响公司实际活动，与「实际高收益公司活动受资金被限于不投高收益债所影响」一致。

Chernenko-Sunderam (2012) show that segmentation (many institutional investors can only buy investment-grade bonds) in the credit market affects firms' real investment. Data: CRSP/COMPUSTAT merged, US domestic firms (excl. financial/utility) 1986Q1–2010Q4. Variables: \(\frac{CAPX_{i,t}}{PPE_{i,t-1}}\) (capex/lagged PP&E), \(\frac{CF_{i,t}}{PPE_{i,t-1}}\) (normalized cash flow), \(Q_{i,t}\) (Tobin's Q, higher = better opportunities). Main regression

$$y_{i,t}=\alpha_i+\beta_Q Q_{i,t-1}+\beta_{CF}\frac{CF_{i,t}}{PPE_{i,t-1}}+\beta_{Flow}(R_i)\cdot\text{High yield fund flows}_{t-1}+\text{Investment opportunities}_i(S_i)+\varepsilon_{i,t} \tag{23.8}$$

\(y=\frac{CAPX}{PPE}\), High yield fund flows = aggregate cash into high-yield-bond mutual funds, \(\beta_{Flow}(R_i)\) a function of credit rating \(R_i\), Investment opportunities\(_i(S_i)\) a function of (unobserved) credit quality. Matching: pair firms similar in characteristics but one just BBB− (lowest investment grade) and the other just BB+ as fundamentally similar credit-quality pairs (same industry/size/leverage/Z-score/cash/sales growth, within one std), so Investment opportunities\(_i(S_i)=\)Investment opportunities\(_j(S_j)\). Differencing (23.9) over matched pairs removes the unobserved opportunities, giving

$$\Delta\frac{CAPX_{i,t}}{PPE_{i,t-1}}=\alpha_i+\beta_{Flow}\cdot\text{High yield fund flows}_{t-1}+\beta_Q\Delta Q_{i,t-1}+\beta_{CF}\Delta\frac{CF_{i,t}}{PPE_{i,t-1}}+\varepsilon_{i,t} \tag{23.10}$$

\(\beta_{Flow}\) the parameter of interest (high-yield minus investment-grade). Robustness: repeat at other rating cutoffs (A & A−, A− & BBB+, B+ & B). Results (Figure 23.7 main, Figure 23.8 placebo): more high-yield fund inflow → more investment by high-yield-category firms (not because they're financially constrained, but because segmentation gives them more available funds); Figure 23.8 shows coefficients significant only at the bond-rating cutoff (BBB−/BB+) → ratings affect real activities only at the segmentation point, consistent with real high-yield-firm activity being affected because funds are restricted from high-yield bonds.

23.3.1 Government Crowds Out Private Long-Term Debt: Greenwood et al. (2010)

这些论文共享一个思想：对安全资产的需求无弹性，政府不供给时企业供「安全信贷产品」（实非安全）→ 成系统性信贷危机来源之一。

Greenwood et al. (2010) 理论：三期 \(t=0,1,2\)，四类主体——偏好习性投资者（养老/寿险/捐赠基金，\(t=0\) 无弹性需求 \(L\) 单位长期债）；政府（\(t=0\) 发 \(G\) 单位长期债，超额长期债 \(g=G-L\) 外生）；风险厌恶套利者（零初始财富、买 \(h\) 单位长期债并以短期借款融资，终值 \(w=\underbrace{h\frac1P}_{\text{long term payoff}}-\underbrace{h(1+r_1)(1+r_2)}_{\text{short term cost}}\)，均值-方差偏好 \(U(w)=\mathbb E[w]-\frac1{2\gamma}\text{Var}(w)\)）；企业（筹 \(C\)、长期债比例 \(f\)、目标比例 \(z\)，偏离成本 \(\frac12\theta C(f-z)^2\)）。套利者一阶条件

$$h^*=\gamma\frac{\frac1P-(1+r_1)(1+\mathbb E[r_2])}{(1+r_1)^2\text{Var}(r_2)} \tag{23.11}$$

市场出清

$$\underbrace{h^*(P)+L}_{\text{demand}}=\underbrace{G+f^*(P)C}_{\text{supply}}\Rightarrow h^*(P)=g+f^*(P)C \tag{23.12}$$

企业最小化利息+约束成本，f.o.c.

$$f^*(P)=z-\frac{\frac1P-(1+r_1)(1+\mathbb E[r_2])}{\theta} \tag{23.13}$$

联立 (23.12)、(23.13) 解出均衡价 \(P^*\)（23.14），代回 (23.13) 得主结果

$$f^*(P)=z-\frac{(1+r_1)^2\text{Var}(r_2)}{\gamma\theta+C(1+r_1)^2\text{Var}(r_2)}(g+zC) \tag{23.15}$$

解读：政府长期债 \(g\) 越多 → 企业长期债发行比例 \(f^*(P)\) 越少 = 政府挤出效应。实证（图 23.9，1963–2005 COMPUSTAT）：长期公司债份额与短期政府债份额同向，即短期政府债越多（长期政府债越少）→ 长期公司债越多，与 (23.15) 一致。

These papers share an idea: demand for safe assets is inelastic, and when the government doesn't supply, firms supply "safe credit products" (not really safe) → a source of systematic credit crisis.

Greenwood et al. (2010) theory: three periods \(t=0,1,2\), four agent groups — preferred-habitat investors (pension/life-insurance/endowment, inelastically demanding \(L\) units of long-term bonds at \(t=0\)); the government (issues \(G\) units of long-term bonds at \(t=0\), excess long-term debt \(g=G-L\) exogenous); risk-averse arbitrageurs (zero initial wealth, buy \(h\) units financed by short-term borrowing, terminal wealth \(w=\underbrace{h\frac1P}_{\text{long term payoff}}-\underbrace{h(1+r_1)(1+r_2)}_{\text{short term cost}}\), mean-variance preference \(U(w)=\mathbb E[w]-\frac1{2\gamma}\text{Var}(w)\)); firms (raise \(C\), long-term fraction \(f\), target \(z\), deviation cost \(\frac12\theta C(f-z)^2\)). The arbitrageur f.o.c.

$$h^*=\gamma\frac{\frac1P-(1+r_1)(1+\mathbb E[r_2])}{(1+r_1)^2\text{Var}(r_2)} \tag{23.11}$$

market clearing

$$\underbrace{h^*(P)+L}_{\text{demand}}=\underbrace{G+f^*(P)C}_{\text{supply}}\Rightarrow h^*(P)=g+f^*(P)C \tag{23.12}$$

firms minimize interest + constraint cost, f.o.c.

$$f^*(P)=z-\frac{\frac1P-(1+r_1)(1+\mathbb E[r_2])}{\theta} \tag{23.13}$$

combining (23.12), (23.13) solves the equilibrium price \(P^*\) (23.14), and substituting back into (23.13) gives the main result

$$f^*(P)=z-\frac{(1+r_1)^2\text{Var}(r_2)}{\gamma\theta+C(1+r_1)^2\text{Var}(r_2)}(g+zC) \tag{23.15}$$

Interpretation: more government long-term debt \(g\) → a lower firm long-term-debt fraction \(f^*(P)\) = the government crowd-out effect. Empirically (Figure 23.9, 1963–2005 COMPUSTAT): the long-term corporate-debt share comoves with the short-term government-debt share, i.e. more short-term government debt (less long-term government debt) → more long-term corporate debt, consistent with (23.15).

23.3.2 Krishnamurthy-Vissing-Jorgensen (2015) & 23.3.3 Greenwood et al. (2015)

Krishnamurthy-Vissing-Jorgensen (2015) 也聚焦对安全/流动资产的无弹性需求，但不像 Greenwood et al. (2010) 区分政府债期限结构——把所有政府债视为安全流动。私人部门可发短期债（商业票据，视为安全）以满足安全需求（当政府供给低时），但当政府供给高时私人短期「安全」资产被挤出。数据：美国 1875–2014。变量：净长期投资=（长期资产）−（长期债）；净短期债=（短期债）−（短期资产）−（政府/Fed 供给的资产）。结果：图 23.10——政府国库券（安全资产）供给高时、经济净短期债低 → 政府挤出；图 23.11 控制内生性（剔问题年份、控贷款需求）后，政府国库券供给对净短期债的负挤出效应显著、稳健。

Greenwood et al. (2015) 对政府该如何处理短期债给出规范建议。短期政府债权衡——弊：暴露政府于滚动风险→困难时期（人们边际效用高时）高税（更糟）；利：满足对流动性的无弹性需求；更多政府短期债挤出金融部门创造的真正危险的短期「安全」债。数据：美国 1983–2009 国库、GDP、商业票据。变量：\(z\)-spread \(z_t^{(n)}=y_t^{(n)}-\hat y_t^{(n)}\)（实际减拟合 \(n\) 周国库券收益，度量因供给意外致的回报意外增）、\((BILLS/GDP)_t\)、\((NONBILLS/GDP)_t\)、\((FINCP/GDP)_t\)（无担保金融商业票据/GDP）、\(\Delta_k\) 为 \(k\) 周变化。回归 1（价格渠道）：水平 (23.16)、变化

$$\Delta_k z_t^{(n)}=b^{(n)}\Delta_k(BILLS/GDP)_t+c^{(n)}\Delta_k(NONBILLS/GDP)_t+\Delta_k\varepsilon_t^{(n)} \tag{23.17}$$

回归 2（挤出）：水平 (23.18)、变化

$$\Delta_k(FINCP/GDP)_t=b\,\Delta_k(BILLS/GDP)_t+c\,\Delta_k(NONBILLS/GDP)_t+\Delta_k u_t \tag{23.19}$$

IV：取差分去时间趋势；并用国库供给的季节性变异（受联邦税历驱动，图 23.12）作工具：\(\Delta_4(BILLS/GDP)_t=c+\sum_{w=2}^{53}d^{(w)}\mathbf 1\{week(t)=w\}+\Delta_4\nu_t\) (23.20)，周虚拟变量外生，第一阶段拟合后代入 (23.17)(23.19)。结果：图 23.13（回归 1）更高 \((BILLS/GDP)_t\)→更高 \(z\)-spread（国库券收益意外）→政府短期国库供给经价格渠道影响金融部门（更高供给→更高回报/更低价→金融部门发短期债更贵→减其发债激励）；图 23.14（回归 2）更高政府短期国库供给直接挤出金融部门发的商业票据。

Krishnamurthy-Vissing-Jorgensen (2015) also focus on inelastic demand for safe/liquid assets, but unlike Greenwood et al. (2010) don't differentiate the term structure of government debt — treating all government debt as safe and liquid. The private sector can issue short-term debt (commercial paper, deemed safe) to satisfy the safe-asset demand (when government supply is low), but the private short-term "safe" asset is crowded out when government supply is high. Data: US 1875–2014. Variables: net long-term investment = (long-term assets) − (long-term debt); net short-term debt = (short-term debt) − (short-term assets) − (assets supplied by the government/Fed). Results: Figure 23.10 — when government Treasury (safe asset) supply is high, net short-term debt is low → crowd-out; Figure 23.11, after controlling endogeneity (dropping problematic years, controlling loan demand), the negative crowd-out effect of Treasury supply on net short-term debt is significant and robust.

Greenwood et al. (2015) give normative suggestions on how the government should handle short-term debt. The trade-off of short-term government debt — con: it exposes the government to roll-over risk → high taxes in hard times (when people's marginal utility is high, worse); pro: it satisfies inelastic liquidity demand; more government short-term debt crowds out the financial sector's creation of dangerous short-term "safe" debt. Data: US 1983–2009 Treasury, GDP, commercial paper. Variables: the \(z\)-spread \(z_t^{(n)}=y_t^{(n)}-\hat y_t^{(n)}\) (actual minus fitted \(n\)-week Treasury yield, measuring the return surprise from a supply surprise), \((BILLS/GDP)_t\), \((NONBILLS/GDP)_t\), \((FINCP/GDP)_t\) (unsecured financial commercial paper/GDP), \(\Delta_k\) a \(k\)-week change. Regression 1 (price channel): level (23.16), change

$$\Delta_k z_t^{(n)}=b^{(n)}\Delta_k(BILLS/GDP)_t+c^{(n)}\Delta_k(NONBILLS/GDP)_t+\Delta_k\varepsilon_t^{(n)} \tag{23.17}$$

Regression 2 (crowd-out): level (23.18), change

$$\Delta_k(FINCP/GDP)_t=b\,\Delta_k(BILLS/GDP)_t+c\,\Delta_k(NONBILLS/GDP)_t+\Delta_k u_t \tag{23.19}$$

IV: differencing removes the time trend; and use the seasonal variation in Treasury supply (driven by the federal tax calendar, Figure 23.12) as an instrument: \(\Delta_4(BILLS/GDP)_t=c+\sum_{w=2}^{53}d^{(w)}\mathbf 1\{week(t)=w\}+\Delta_4\nu_t\) (23.20), the week dummies exogenous, fitted in the first stage and plugged into (23.17)(23.19). Results: Figure 23.13 (Regression 1) higher \((BILLS/GDP)_t\) → higher \(z\)-spread (Treasury-yield surprise) → government short-term Treasury supply affects the financial sector through a price channel (higher supply → higher return/lower price → more expensive for the financial sector to issue short-term debt → reduces its issuance incentive); Figure 23.14 (Regression 2) higher government short-term Treasury supply directly crowds out the financial sector's commercial paper.

References