A Semi-Structural Model with Household Debt for Israel

This paper proposes a semi-structural DSGE model for the Israeli economy incorporating household credit frictions to demonstrate that effective monetary policy should respond to credit spreads, while macroprudential policy can mitigate debt crises and stimulate demand by reducing leverage-induced borrowing costs.

The Gist

Here is an explanation of the Bank of Israel paper, translated into simple language with everyday analogies.

The Big Picture: A House with a Leaky Roof

Imagine the Israeli economy as a giant house. The Bank of Israel is the landlord (the Central Bank) whose job is to keep the house comfortable (stable prices) and the lights on (steady economic activity).

Usually, landlords just watch the thermostat (inflation) and the electricity bill (economic growth). But this paper argues that the landlord is ignoring a leaky roof in the "borrowing room" (the household credit market).

The authors, Alex Ilek and Nimrod Cohen, built a computer model of the Israeli economy to see what happens when they fix that leak. They found two main things:

1. The Landlord needs to listen to the roof: If the landlord ignores the leak, the house gets damaged faster.
2. The "Safety Valve" (Macroprudential Policy): There is a special tool that can tighten the roof before it leaks, preventing the house from getting soaked in the first place.

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1. The Problem: The "Debt Hangover"

In Israel, about 40% of families have mortgages. The paper noticed a simple fact: The more debt a family has, the higher the interest rate they pay.

• The Analogy: Think of a credit card. If you owe $100, the bank charges you 5%. If you owe $100,000, the bank gets nervous. They think, "If something goes wrong, this person might not pay us back." So, they charge 8% to cover that risk.
• The Model: The authors put this into their computer model. They call this a "Financial Friction." It's like a speed bump. As families pile up more debt, the "speed bump" (interest rate) gets higher, making it harder to drive (spend).

2. The Two Tools in the Toolbox

The paper looks at two ways the Bank of Israel can manage this:

Tool A: The Thermostat (Monetary Policy)

This is the standard interest rate the Bank sets for the whole country.

• Old Way: The Bank only looks at inflation and GDP. If prices are rising, they turn up the heat (raise rates). If the economy is cold, they turn it down. They ignore the debt levels.
• New Way (The Paper's Suggestion): The Bank should also look at the "Debt Hangover." If families are taking on too much debt and interest rates are spiking, the Bank should react sooner.

Tool B: The Safety Valve (Macroprudential Policy)

This is a set of rules that makes borrowing harder or more expensive specifically for risky borrowers.

• Examples: Limiting how much you can borrow relative to your income, or forcing banks to hold more cash reserves for risky loans.
• The Effect: This makes the "speed bump" steeper. If you try to borrow too much, the cost shoots up immediately. This stops people from over-borrowing in the first place.

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3. What Happens When Things Go Wrong? (The Scenarios)

The authors ran simulations with three different "versions" of the economy:

1. The Ideal World: No friction (borrowing is free and easy, regardless of debt).
2. The Real World: Friction exists (rates go up as debt goes up), but no special safety rules.
3. The Regulated World: Friction exists, AND the "Safety Valve" is turned on (rates go up sharply if debt gets too high).

Scenario 1: The Bank Raises Rates (Monetary Shock)

• What happens: The Bank raises rates to cool down inflation.
• Result: In all three worlds, the economy slows down. However, in the "Regulated World," the drop in borrowing is actually smoother. Because the safety valve was already there, the shock doesn't cause a panic.
• Key Takeaway: The "Financial Friction" actually acts like a shock absorber here. When rates go up, people pay down debt, which lowers their risk, which lowers their interest rate slightly. This helps cushion the blow.

Scenario 2: The Bank Accidentally Loosens the Rules (Credit Supply Shock)

• What happens: Suddenly, banks decide to lend money too easily (like a flood of cheap credit).
• Result: Without the Safety Valve, families go crazy borrowing. This leads to a bubble. When the bubble bursts, everyone tries to pay back debt at once, crashing the economy.
• With the Safety Valve: As soon as people start borrowing too much, the "Safety Valve" kicks in, making borrowing expensive. It stops the bubble from forming in the first place.

Scenario 3: People Get Greedy (Credit Demand Shock)

• What happens: Families suddenly want to borrow more (maybe they are optimistic about the future).
• Result:
  • Without Safety Valve: They borrow a ton. The economy booms, but it's a "fake boom" built on debt.
  • With Safety Valve: As they try to borrow, the interest rates spike immediately. This acts as a speed limit. It stops the borrowing from getting out of control.
  • The Trade-off: The "boom" is smaller, but the economy is safer. The authors argue this is a good trade-off to prevent a future crash.

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4. The Big Lesson: Don't Ignore the Leaky Roof

The paper concludes with two major findings for the Bank of Israel:

1. The Landlord Must Listen to the Roof (Monetary Policy)
If the Bank of Israel ignores the credit market and only looks at inflation, it makes mistakes.

• The Analogy: Imagine the house is getting wet (debt crisis), but the thermostat says the room is the perfect temperature (stable inflation). If the landlord only listens to the thermostat, they won't turn on the dehumidifier until the floor is soaked.
• The Fix: The Bank should react to "credit spreads" (the extra interest charged for risky debt). If spreads are widening, the Bank should adjust rates before the economy crashes. This makes the Bank much more effective at keeping prices and jobs stable.

2. The Safety Valve is Crucial (Macroprudential Policy)
Rules that make borrowing more sensitive to debt levels are powerful.

• The Analogy: It's like putting a speed camera on a dangerous road. Even if drivers want to speed (borrow too much), the camera (regulation) makes them slow down because the fine (interest rate) is too high.
• The Benefit: This prevents the "Debt Hangover" from becoming a "Debt Coma." It stops families from over-borrowing, which prevents a future crisis where everyone tries to pay back debt at the same time.

Summary in One Sentence

The Bank of Israel should stop ignoring how much debt families have; by watching the credit market closely and using rules that make risky borrowing expensive, they can prevent financial crashes and keep the economy running smoothly.

Technical Summary

Here is a detailed technical summary of the paper "A Semi-Structural Model with Household Debt for Israel" by Alex Ilek and Nimrod Cohen (Bank of Israel, 2023).

1. Problem Statement

The paper addresses the debate regarding the role of monetary policy and macroprudential policy in managing financial stability, specifically within the context of the Israeli economy. The core problem is whether central banks should incorporate financial variables (such as credit spreads and household leverage) into their monetary policy rules ("Leaning Against the Wind" or LAW) or rely solely on traditional targets like inflation and output gaps.

The authors focus on the household sector credit market, noting that:

• Approximately 40% of Israeli households are borrowers.
• Household debt is almost entirely domestic (mortgages constitute ~2/3 of debt).
• Empirical evidence suggests a positive relationship between household leverage and credit spreads (interest rates), indicating the presence of financial frictions.
• There is a lack of a structural framework specifically calibrated for Israel to evaluate how these frictions interact with monetary and macroprudential policies.

2. Methodology

The authors propose a semi-structural Dynamic Stochastic General Equilibrium (DSGE) model tailored for Israel as a Small Open Economy (SOE).

Model Structure

The model consists of two main blocks:

1. Standard SOE Block: Based on Laxton et al. (2006), featuring New-Keynesian dynamics (Phillips curve, IS curve, Uncovered Interest Rate Parity) but without a financial sector.
2. Household Credit Block: Incorporates financial frictions inspired by Benigno et al. (2020) and Cúrdia and Woodford (2016).
   • Agents: The economy is split into borrowers (households with debt) and lenders (savers). Lenders are not explicitly modeled as their activity is redundant given the aggregate focus.
   • Financial Friction: Modeled as a positive relationship between the household leverage ratio (Debt/Income) and the credit spread (the difference between the borrower's interest rate and the risk-free rate).
   • Leverage Definition: Unlike standard models using Debt/Output, the authors define leverage as Household Debt / Household Income. This allows the model to generate either a "financial accelerator" or "financial decelerator" depending on calibration.
   • Natural Rate of Interest (NRI): The NRI is endogenous and negatively affected by the credit spread and borrower preference shocks.

Key Equations & Mechanisms

• Credit Spread Equation: $\hat{\Delta}_t = \beta_{lev} \cdot \widehat{lev}_t + \varepsilon^\Delta_t$. The parameter $\beta_{lev}$ captures the sensitivity of the spread to leverage.
• Macroprudential Intervention: Modeled as an exogenous increase in $\beta_{lev}$. This represents regulations (e.g., higher capital requirements, LTV caps) that make banks more sensitive to borrower risk, thereby increasing the cost of borrowing for highly leveraged households.
• Monetary Policy Rule: A Taylor-type rule where the Central Bank (CB) reacts to the NRI, inflation, and output gap. The authors compare two regimes:
  • Fully Informative (FI): The CB reacts to the correct NRI, which includes the credit spread.
  • Partially Informative (PI): The CB reacts to a misspecified NRI that ignores financial variables (standard LAW vs. non-LAW comparison).

Calibration

• Data: Calibrated using Israeli data (2004–2022), including mortgage leverage, credit spreads, and macroeconomic aggregates.
• Key Parameters:
  • $\beta_{lev} = 0.031$: Estimated elasticity of spread to debt-to-GDP ratio (validated via regression).
  • $\alpha_{\Delta}^{NRI} = -0.5$: Elasticity of NRI to the spread (lower magnitude than US models due to SOE characteristics).
  • Debt Aversion ($v$): The model tests two cases: low aversion ($v=0.0225$, households are less sensitive to debt levels) and high aversion ($v=1.25$, households are very conservative).

3. Key Contributions

1. Empirical Validation for Israel: The paper provides empirical evidence (via regression and stylized facts) confirming a positive correlation between mortgage leverage and credit spreads in Israel, justifying the inclusion of financial frictions in the model.
2. Financial Decelerator Mechanism: The authors demonstrate that under their specific calibration (where the denominator of leverage is time-variant income), a positive monetary shock reduces leverage and spreads, acting as a financial decelerator (mitigating shocks) rather than an accelerator. This contrasts with some closed-economy models.
3. Policy Interaction Analysis: The paper uniquely analyzes the interplay between monetary policy (reacting to NRI) and macroprudential policy (modifying the spread-leverage elasticity) in a semi-structural framework specific to Israel.
4. Loss Function Evaluation: It quantifies the welfare costs of ignoring financial variables in monetary policy using stochastic simulations and various loss function specifications.

4. Key Results

A. Implications of Financial Friction

• Monetary Shocks: A contractionary monetary shock reduces leverage, which lowers the credit spread. This "financial decelerator" effect partially offsets the contractionary impact on consumption and output.
• Credit Supply Shocks: When credit supply tightens (spread shock), financial friction leads to a reduction in leverage, which subsequently lowers the spread, softening the blow to the economy compared to a frictionless model.
• Credit Demand Shocks: A positive preference shock (increased borrowing demand) increases leverage and spreads. Here, financial friction acts as a stabilizer by raising borrowing costs, dampening the demand surge.

B. Role of Macroprudential Policy

• Prevention of Over-borrowing: Increasing the sensitivity of the spread to leverage ($\beta_{lev}$) via macroprudential policy effectively curbs excessive borrowing during booms.
• Stabilization during Downturns: In a demand weakness scenario, a higher $\beta_{lev}$ allows for a larger reduction in spreads as households deleverage, providing an automatic stabilizer that stimulates demand.
• Dependence on Aversion: The policy is most effective when households have low debt aversion (they are prone to over-borrowing). If households are already highly risk-averse (high $v$), macroprudential tightening has a marginal effect because they do not borrow excessively in the first place.

C. Monetary Policy Analysis (FI vs. PI)

• Efficiency Loss: When the Central Bank ignores credit spreads (PI rule), it fails to stabilize the economy efficiently during financial shocks.
  • Spread Shocks: The PI rule leads to a delayed and stronger reaction, causing larger fluctuations in output and inflation compared to the FI rule.
  • Demand Shocks: Ignoring the spread leads to suboptimal stabilization of real activity.
• Loss Function Results: Stochastic simulations (10,000 periods) show that the loss function is significantly higher (2 to 3 times larger) under the PI rule compared to the FI rule across various specifications (inflation/output variance, interest rate volatility).
• Trade-off: While the FI rule stabilizes the real economy better, it results in higher volatility of the policy interest rate because the NRI itself is more volatile when it includes financial variables.

5. Significance and Policy Implications

• Leaning Against the Wind (LAW): The paper provides strong theoretical and quantitative support for the view that monetary policy in Israel should react to financial variables (specifically credit spreads) to achieve its primary goals of price and output stability. Ignoring the financial sector leads to suboptimal outcomes.
• Macroprudential Synergy: Macroprudential policy is not just a tool for financial stability but also enhances the effectiveness of monetary policy. By increasing the elasticity of spreads to leverage, it prevents debt bubbles and creates a mechanism that automatically reduces borrowing costs during deleveraging phases, aiding economic recovery.
• Israel-Specific Context: The findings are crucial for the Bank of Israel, given the high household debt-to-GDP ratio and the dominance of domestic mortgage debt. The model suggests that the current "weak" relationship between leverage and spreads (low elasticity) may be insufficient to prevent over-borrowing, necessitating stronger macroprudential interventions.

In conclusion, the paper argues that a semi-structural model incorporating household debt frictions reveals that ignoring financial conditions in monetary policy is costly, and macroprudential policy serves as a vital complement to mitigate debt cycles and improve overall economic stability in Israel.