22. Household Finance

Household finance is increasingly important: (1) mortgage lending has grown sharply since the 1980s in developed countries (Figure 22.1, Jordà et al. 2016); (2) household financing (demand side) is important in explaining recessions, while traditional theories (real business cycle, financial accelerator like Bernanke-Gertler 1989) only consider supply-side productivity shocks/actions and don't explain recessions well. The basic idea: shocks to household financing affect consumption decisions, with huge impacts on the real economy.

Eggertsson-Krugman (2012) provide a very simplified model of individual borrowing/consumption: a single friction (non-negativity of the real interest rate) makes a tightening individual borrowing constraint have a huge real impact. §22.2.1 Setup: a pure endowment economy, no aggregate saving/investment technology, individuals lend/borrow from each other. Two types: saver \(s\), borrower \(b\). Utility \(\mathbb E[\sum_{t=0}^\infty(\beta(i))^t\ln C_t(i)]\), \(0<\beta(b)<\beta(s)<1\) (the only heterogeneity is the discount rate). They borrow/lend at the risk-free rate \(r_t\), with debt \((1+r_t)D_t(i)\le D^{high}\); both types get the same endowment \(\frac12Y\) each period. §22.2.2 Household's problem: the budget

$$\underbrace{D_t(i)+\tfrac12 Y}_{\text{Total Inflow}}=\underbrace{(1+r_{t-1})D_{t-1}(i)+C_t(i)}_{\text{Total Outflow}} \tag{22.1}$$

f.o.c.s \(\mathbb E[(\beta(i))^t/C_t(i)]=\lambda_t\) (22.2), \(\lambda_t=\lambda_{t+1}(1+r_t)\) (22.3), combining into the Euler equation

$$\frac{1}{C_t(i)}=\beta(i)(1+r_t)\mathbb{E}_t\left[\frac{1}{C_{t+1}(i)}\right] \tag{22.4}$$

§22.2.3 Steady state: \(b\)'s constraint always binds, \((1+r)D_t(b)=D^{high}\), so by (22.1)

$$C(b)=\tfrac12 Y-\frac{r}{1+r}D^{high} \tag{22.5}$$

\(s\) clears the market \(C(s)=Y-C(b)\), and the Euler equation makes \(r\) endogenous: \(r=\frac{1-\beta(s)}{\beta(s)}\), \(\frac{r}{1+r}=1-\beta(s)\). So \(C(s)=\frac12Y+(1-\beta(s))D^{high}\), \(C(b)=\frac12Y-(1-\beta(s))D^{high}\).

§22.2.4 Tightening shock: \(D^{high}\to D^{low}long-run new steady state (subscript \(L\))

$$\begin{cases}C_L(s)=\tfrac12Y+\frac{r}{1+r}D^{low}\\ C_L(b)=\tfrac12Y-\frac{r}{1+r}D^{low}\\ r_L=\frac{1-\beta(s)}{\beta(s)}\end{cases} \tag{22.6}$$

(\(b\)'s long-run steady state improves — over-borrowing regulated by the stricter constraint). In the short run: \(b\)'s immediate consumption \(C_I(b)\) and immediate rate \(r_I\) satisfy (22.1):

$$C_I(b)=\tfrac12 Y+\left(\frac{D^{low}}{1+r_I}-D^{high}\right) \tag{22.7}$$

(\(b\) must cut consumption to deleverage); \(s\)'s immediate consumption must rise to clear the market

$$C_I(s)=\tfrac12 Y+\left(D^{high}-\frac{D^{low}}{1+r_I}\right) \tag{22.8}$$

this boost is induced by the endogenously lower rate \(r_I\) (pinned down by \(s\)'s Euler (22.4)):

$$r_I=r-\underbrace{\frac{D^{high}-D^{low}}{\beta(s)\left(\frac12Y+D^{high}\right)}}_{\text{increasing in }(D^{high}-D^{low})} \tag{22.9}$$

the more the tightening (larger \(D^{high}-D^{low}\)), the larger the drop from \(r\) to \(r_I\). Friction: with a freely moving rate, aggregate consumption is \(Y\) both short and long run, unchanged; but if the tightening is serious \(r_I\) might go negative (liquidity trap). With the non-negativity friction, \(s\) can only consume \(C_I^*(s)=\frac{C_L(s)}{\beta(s)}=\frac{\frac12Y+\frac{r}{1+r}D^{low}}{\beta(s)}\) (less than they should without the constraint), so

$$C_I^*(s)+C_I(b)

aggregate consumption falls — this is the recession caused by a household tightening borrowing constraint.

Guerrieri-Lorenzoni (2017) is idea-wise similar but technically different: (1) it assumes debt heterogeneity comes from accumulated past employment shocks (the unemployed borrow to smooth consumption), less simplified than Eggertsson-Krugman's "two types"; (2) it assumes agents know the tightening shock occurs with some probability, so they precautionary-save to hedge — in E-K agents don't know the possibility, so can do nothing. Solved computationally (not analytically), with and without the zero lower bound; with the zero lower bound output fluctuates more severely (Figure 22.2). Richer people (further from the constraint) raise consumption in response to the tightening, poorer people (closer) cut it, and the poorer they are the more they cut; the poor's cut exceeds the rich's increase (Figure 22.3).

Korinek-Simsek (2016) has the same intuition as E-K: at date 0 without the constraint, more impatient/indebted agents borrow more; those who borrow a lot cut consumption more massively when the constraint applies; due to the zero lower bound, less-indebted agents can't raise consumption enough to make up the shortfall → lower aggregate. Aggregate-demand externality: a pecuniary externality — an agent adjusting consumption → affects the interest rate → affects others' consumption/saving (no efficiency loss, as the aggregate is unchanged at the endogenous rate); a non-pecuniary externality — an agent adjusting consumption → affects others' income (efficiency loss, as cutting consumption → lowers others' income → further cuts consumption, a repeating feedback). K-S's innovation is the non-pecuniary externality in consumption adjustment, assuming date-1 aggregate income \(e_1\) decreases in aggregate demand \(D_1\), i.e. \(\frac{\partial e_1}{\partial D_1}<0\). Summary: higher household debt from previous periods → a more severe consumption cut when the constraint applies → due to the zero lower bound net lenders can't make up the shortfall → the non-pecuniary aggregate-demand externality aggravates the cut → recession. This boom-bust is caused by the household credit cycle, unrelated to fundamentals.

Exploit the natural experiment of the rise of the private-label securitization market (PLS market) to study credit-supply expansion and housing-market speculation. In the PLS market, shadow-banking lenders (non-core liability lenders, high-NCL lenders) provide mortgages through non-core deposit financing, then securitize and sell the loans. The sudden surge in the PLS market in late summer 2003 = the natural experiment (Figure 22.4). The PLS mortgage-origination share jumps while its interest rate falls simultaneously → consistent with a supply-side surge (a demand-side increase would raise the rate; Figure 22.5 across-type value of home purchased). Speculation and credit expansion: a "displacement" (financial innovation/deregulation) → credit expands to speculators → speculators use leverage to bid for the asset (house) → asset price up → attracts more speculators → a positive feedback, price and volume rising.

Data: HMDA (Home Mortgage Disclosure Act), lenders classified into banks (deposits under Fed regulation) and non-banks, aggregated to zip level. Design: define the lender-level non-core liability ratio \(\text{NCL Ratio}_{i,2002}=1-\frac{\text{Core Deposit}_{i,2002}}{\text{Total Liability}_{i,2002}}\) (sticky, representing all years); high-NCL lenders are mostly banks with low core-deposit ratio or non-banks not taking deposits; high- and low-NCL lenders have the same pre-surge trend but a large differential response (Figure 22.6). Lender-level first stage:

$$\ln(y_{i,t})=\alpha_i+\gamma_t+\sum_{t\ne2002}\beta_k\mathbf 1\{t=k\}\cdot\text{NCL Ratio}_{i,2002}+\varepsilon_{i,t} \tag{22.11}$$

(\(\beta_k\) = the growth of high- vs low-NCL lenders' origination; Figure 22.7). Zip level \(\text{NCL Share}_{z,2002}=\sum_i\omega_{z,i,2002}\text{NCL Ratio}_{i,2002}\) (\(\omega\) = lender \(i\)'s 2002 mortgage share in zip \(z\)), measuring the zip's PLS-surge exposure; the zip-level first stage

$$\ln(y_{z,t})=\alpha_z+\gamma_t+\sum_{t\ne2002}\beta_k\mathbf 1\{t=k\}\cdot\text{NCL Share}_{z,2002}+\varepsilon_{z,t} \tag{22.12}$$

(Figure 22.8). Exclusion: NCL Share is unrelated to credit-demand shocks (to identify the supply effect, dropping the demand side). Speculation analysis: speculators defined (buy two houses with mortgages within two years / buy one and close the mortgage within a year without refinancing, i.e. sold / buy a house when already having ≥2 first-lien mortgages), ~4% of individuals (2005/06). The zip first stage (\(y\) = first-lien purchase mortgage): going from bottom to top NCL-share quantile → a 19.1% increase in transaction volume. Regressing by speculation/ex-ante-risk/age groups gives each group's share \(\beta^i/\beta\) (Figure 22.9: multiple-house speculators, subprime-risk, age 30–40 contribute most). House prices and construction (Figure 22.10), mortgage default (Figures 22.11, 22.12: highest-credit-expansion areas have the highest default). Takeaway: cyclicality in the credit market (financial innovation/deregulation) can dramatically change the economy without fundamental forces, by giving purchasing power to riskier, more speculative marginal agents.

US household debt doubled to 14 trillion USD 2000–2007, growing faster than corporate debt (Figure 22.13). Such a huge increase can't all come from the extensive margin (marginal new buyers; 65% already owned a home in 1997). M-S (2011) focus on the intensive margin: existing homeowners borrow more as house prices rise (Figure 22.14). Data: Equifax credit reports, 74,149 US homeowners in 2307 zips across 68 MSAs. Target regression

$$\Delta\text{Debt}_{izm}=\boldsymbol\theta'\mathbf X_{izm}+\beta\Delta\text{House Price}_{izm}+\alpha_m+\varepsilon_{izm} \tag{22.13}$$

(\(\Delta\text{Debt}/\Delta\text{House Price}\) the debt and price change of household \(i\) (zip \(z\), MSA \(m\)) 2002–2006, \(\alpha_m\) MSA FE, \(\beta\) = the elasticity of debt w.r.t. house price = the marginal propensity to borrow as price rises). Endogeneity: an omitted variable in \(\varepsilon\) (e.g. permanent/expected stable income) affects both house price (housing demand) and debt. Instrument: MSA-level housing supply elasticity (orthogonal to demand-side omitted shocks; a footnote also uses MSA supply elasticity × zip subprime share as a second instrument). 2SLS with supply elasticity as the instrument for \(\Delta\text{House Price}\). Results: first stage (Figure 22.15) supply elasticity significantly affects price (strong); reduced form (Figure 22.16) affects debt change (strong); IV estimate (Figure 22.17) homeowners borrow 0.25 USD per 1 USD of price increase (MPB=0.25); heterogeneous by credit quality (Figure 22.18) worse-credit (poorer) homeowners borrow more when prices rise.

§22.4.1 Mian et al. (2013) differential consumption responses to a housing-net-worth shock: two questions — how does consumption respond to large negative wealth shocks? Do different wealth levels respond differently? Data: actual-expenditure consumption records (R.L. Polk zip-level auto sales 1998–2012; MasterCard county-level consumption 2005–2009). Wealth \(NW_t^i=S_t^i+B_t^i+H_t^i-D_t^i\) (stock + bond + house price − debt). Decompose the housing-net-worth shock

$$\text{HNW Shock}_z=\frac{p_{z,2009}-p_{z,2006}}{p_{z,2006}}\times\frac{H_z^i}{NW_z^i}$$

(= % price change × the share of housing wealth in net worth). RHS = HNW Shock, LHS = % consumption change → the parameter is the consumption elasticity; RHS = \(NW\times\)HNW Shock (dollar value), LHS = dollar consumption change → the parameter is the MPC. Elasticity/MPC need not be the same across zips; the negative shock may correlate with the preceding boom (not random), and an omitted variable (debt) correlates with both shock and consumption → endogeneity; heterogeneous effects only at the zip level (using auto data). Results: the consumption elasticity w.r.t. the HNW shock is significantly positive (negative shock → less consumption, Figure 22.19); MPC≈0.054 (1 USD price drop → 0.054 USD less consumption, mostly autos + non-durables, Figure 22.20); not interpretable as ATE; heterogeneous — low-income (AGI) and high-housing-leverage (Lev) agents respond most dramatically (highest MPC, Figures 22.21, 22.22).

§22.4.2 Mian-Sufi (2014) employment responses to the housing-net-worth shock (same idea): data CBP county-industry employment + ACS wages, wealth as in (2013). Two tradability measures (retail/restaurant = non-tradable; geographically dispersed = non-tradable). Non-tradable regression \(\Delta\ln E_c^{NT}=\alpha+\eta\cdot\Delta HNW_c+\varepsilon_c\) (22.14) (also regressing tradable employment, wage growth, population growth). Results: negative HNW → significant non-tradable unemployment (Figure 22.23); no significant tradable employment increase (the laid-off aren't relocated, Figure 22.24); wages don't change much (Figure 22.25); cross-county migration insignificant (Figure 22.26) — all through the demand-shock channel.

§22.4.3 Giroud-Mueller (2017) finer data (establishment level), a new channel — a non-tradable firm's financial constraint affects how many workers it lays off in a housing-net-worth shock. Data 2006–2009 (Census LBD establishment employment, COMPUSTAT balance sheets, Zillow house prices). Main regression

$$\Delta\text{Log(Emp)}_{07\text{-}09}=\alpha+\beta_1\Delta\text{Log(HP)}_{06\text{-}09}+\beta_2\text{Leverage}_{06}+\gamma(\Delta\text{Log(HP)}_{06\text{-}09}\times\text{Leverage}_{06})+\varepsilon \tag{22.15}$$

(\(\alpha\) industry/firm/zip/zip×industry FE; local FE needed since high-leverage firms may load more on the local economy, the leverage effect operating through omitted local-economy variables not the financial constraint). Results (Figure 22.27 scatter, Figure 22.28 regression): employment responds only for financially constrained firms (highest leverage quantile), more so the more constrained, robust; the tradable/non-tradable split (Figures 22.29, 22.30): responses only for non-tradable + financially constrained. Labor hoarding: in bad times demand falls and firms want to fire due to wage rigidity; but long-run optimization suggests hoarding labor; a short/long-run trade-off; weak-balance-sheet (constrained) firms can't hoard → more likely to lay off.

The recovery is slow; the key idea: frictions prevent a lower rate from transmitting to the real economy (monetary policy raises consumption/investment by lowering the borrowing cost). Agarwal et al. (2018) study the bank (to-household) lending channel of monetary policy, identifying via credit-limit discontinuities in the credit-card market. Data: the OCC's Credit Card Metrics (CCM) Jan 2008–Dec 2014 (account-level panel + portfolio-level info at the 8 largest banks). Design: with \(q\) aggregate borrowing (\(q_i\) consumer \(i\)'s), \(c\) the cost of capital, \(CL_i\) the credit limit faced by consumer \(i\),

$$-\frac{dq}{dc}=\int_i\underbrace{\frac{dCL_i}{dc}}_{=MPL_i}\times\underbrace{\frac{dq_i}{dCL_i}}_{=MPB_i}$$

(\(MPL_i\) the bank's marginal propensity to lend to \(i\), \(MPB_i\) consumer \(i\)'s marginal propensity to borrow). Identification: exploit credit-limit discontinuities in FICO scores (a quasi-experiment crossing the 660/700/720/740/760 thresholds); same type/bank/month/channel = the same origination group (>10,000 groups, the crucial assumption being the same credit-supply function within a group; Figure 22.31 two examples), with accounts within ±50 points used for a fuzzy RD (8.5 million accounts, ~11,400 per experiment). The Wald estimate

$$\tau=\frac{\lim_{x\downarrow\bar x}\mathbb{E}[y\mid x]-\lim_{x\uparrow\bar x}\mathbb{E}[y\mid x]}{\lim_{x\downarrow\bar x}\mathbb{E}[cl\mid x]-\lim_{x\uparrow\bar x}\mathbb{E}[cl\mid x]} \tag{22.16}$$

estimated by local linear regression with different slopes on the two sides, \(\min_{\alpha,\beta}\sum_i[\tilde y_i-\alpha_{\tilde y,d}-\beta_{\tilde y,d}(x_i-\bar x)]^2\mathbf 1\{|x_i-\bar x|Results: the reduced-form MPB (four metrics ADB/interest-bearing debt/balances across all cards/cumulative purchase volume, four FICO subgroups) Figure 22.34 — lower-FICO holders have higher MPB; MPL (Figure 22.35a) and 12-month MPB (Figure 22.35b): banks increase limits more for high-FICO and less for low-FICO, but high-FICO have very low MPB while low-FICO have high MPB → a friction in the credit-card market: banks want to lend to people who don't really want to borrow → the bank lending channel of monetary policy can't work well.