## wpiea2020108-print-pdf

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---

### Introduction: scope and objectives
- Focus: measure cross-country heterogeneity in transmission of European Central Bank (ECB) monetary policy across the euro area (EA) and assess role of institutional differences, especially in housing and labour markets.
- Dataset: large panel including economic and financial time series for the EA as a block and the 11 original member countries, spanning the years from 1999 to 2016.
- Empirical approach: dynamic factor model (DFM) with identification of monetary policy shocks via an external instrument constructed from high-frequency changes in asset prices around ECB policy announcements (following Gurkaynak et al. (2005) and Gertler and Karadi (2015)).
- Theoretical complement: a calibrated small open economy model with housing in a monetary union, focusing on the share of mortgages with adjustable rates and average loan-to-value ratios.

### Main empirical findings
- EA aggregate:
  - Factor model results align with theory and show the transmission of monetary shocks does not suffer from the price puzzle.
- Cross-country heterogeneity:
  - Statistically significant heterogeneity in prices and variables related to labour and housing markets.
  - Low degree of heterogeneity in financial variables and output.
- Quantitative role of housing financing:
  - Differences in mortgage market characteristics across the EA can explain up to one-third of the cross-country heterogeneity of responses in output and private consumption.

### Methodological contributions
- Heterogeneity measurement:
  - Use coefficient of variation (CoV, relative standard deviation) of impulse responses across countries relative to the EA response, normalised by the size of the EA response.
  - Bootstrap to obtain error bands for the CoV for each variable and for pairwise differences across variables.
  - Apply CoV both empirically (DFM impulse responses) and theoretically (simulated responses from varying model parameters) for direct comparison.
- Identification:
  - External instrument based on changes in the 1-year EONIA swap rate around policy announcements; combines press releases, press statements, Q&A.
  - Overcome data availability by combining intraday data with end-of-day data from different timezones to create de-facto intraday series where intraday data are unavailable.
  - Instrument relevance: instrument strongly correlates (0.9) with monetary event-window surprises in the euro-area monetary policy event-study database (Altavilla et al. (2019)).

### Identification (external instrument, formal conditions)
- External instrument approach basics:
  - Instrument Z_t must be correlated with the structural shock of interest and uncorrelated with all other shocks (relevance and exogeneity).
- Structural notation and identification summary (as in Stock and Watson (2012)):
  - η_t = H ε_t.
  - Σ_ηη = H Σ_εε H′ with Σ_εε = D = diag(σ^2_{ε1}, ..., σ^2_{εr}).
  - If invertible, ε_t = H^−1 η_t.
  - IRF of X_t w.r.t. i-th structural shock: IRF = Λ Φ(L)^−1 H.
- Identification of H_1 via covariance between η_t and Z_t:
  - Relevance: E(ε_1t Z_t) = α ≠ 0.
  - Exogeneity: E(ε_jt Z_t) = 0, j = 2,..., r.
  - From E(η_t Z_t) = H_1 α, H_1 is identified up to scale and sign by covariances between VAR innovations and the instrument.
  - Fitted value Π η_t identifies ε_1t up to constant: Π η_t = (α/σ^2_{ε1}) ε_1t.

### Instrument construction — details and properties
- Instrument: changes in the 1-year EONIA swap rate (chosen as a trade-off: "highly sensitive to monetary policy, while still remaining relatively unaffected by term premia").
- Tenor choice: 3-month, 6-month and 2-year EONIA swap instruments also constructed; no significant difference in results.
- High-frequency announcement window:
  - Chosen 6-hour window from 13:00 to 19:00 CET to cover press release (13:45 CET) and press conference/Q&A (14:30 CET).
  - Intraday swap prices on Bloomberg available only from January 2008 onwards; narrower windows considered but not used due to intraday data constraints.
- Averaging to quarterly frequency:
  - Compute cumulative daily surprise over past 93 days for each day; then average the daily cumulative series over each quarter (so earlier surprises within quarter have larger influence).
- Notable extreme instrument values (examples):
  - Q4 2001: instrument value -0.15 (driven by 17 September 2001 50bp cuts; 1-year EONIA swaps dropped by 20bp during the window).
  - Q4 2008: value -0.17 (driven by 2 October 2008 decision and Trichet’s remarks).
  - Q1 2009: value 0.14 (driven by contractionary surprise on 4 December 2008 and surprise on 15 January 2009).
  - Q3 2011: value -0.22 (largest absolute), mainly due to 4 August 2011 decision; 1-year EONIA swaps fell by about 18bp between 14:30 and 15:30 CET.
- Instrument strength test:
  - Small VAR (output, consumer prices, policy indicator) at monthly and quarterly frequency with 3/6/12-month EONIA swap instruments.
  - Baseline first-stage F-test statistic = 19.45 (instrument is strong).

### Euro-wide dynamic effects (DFM impulse responses to a 25bp contractionary shock)
- Shock scaling: system scaled to a 25bp contraction in EONIA using the response of EONIA as policy indicator.
- Confidence intervals: one standard deviation bands via wild bootstrap (Rademacher); bootstrap incorporates both stages of external instrument regression.
- Main aggregate responses (percentage responses to a 25bp contractionary shock):
  - Harmonised index of consumer prices (HICP): no significant reaction.
  - Producer Prices in Industry: fall significantly.
  - GDP: contracts overall.
  - Government Spending: rises (moves opposite to contractionary shock).
  - Investment (GFCF): much more volatile than consumption.
  - Consumption: contracts, less volatile than investment.
  - Imports and Exports: volatile responses consistent with theory.
  - German 2-year sovereign yield: closely follows EONIA.
  - Aggregate mortgage interest rates (ECB indicator): rise but display imperfect pass-through due to fixed-rate mortgages.
  - Unemployment: rises.
  - Wages: fall, reaction not significant (nominal wage stickiness).
  - House Prices: fall significantly after contraction.
  - Rents: increase in reaction to the shock (possible substitution from purchase to renting).
  - Euro nominal effective exchange rate (NEER): appreciates with a delay.
- Model performance:
  - No price puzzle observed: producer prices fall significantly while HICP shows no significant reaction.
  - Note: a FAVAR with EONIA as only observable factor produced a price puzzle.

### Cross-country dynamic effects — heterogeneity evidence
- Data scope: of the 342 individual country series, representative sub-sample used for figures; results produced for all series.
- GDP and HICP across 11 euro-area countries:
  - HICP responses: positive for half the countries and negative for the other half; mean HICP response is negative and very low.
  - Real GDP reactions: significant heterogeneity.
    - Germany: drop in private consumption maximum ~ 0.02 percentage points.
    - Ireland: drop in private consumption = 0.4 percentage points (more than 20 times Germany’s).
    - Italy, Finland, Spain, Portugal (apart from Ireland) have consumption drops roughly 10 times Germany’s.
  - Finland and Luxembourg reactions statistically different from France and Spain (non-overlapping confidence intervals from the 10th step onward).
- GDP components:
  - Private consumption and gross fixed capital formation follow similar signed patterns.
  - Government spending and net exports: idiosyncratic across countries and over time.
- Financial vs real markets:
  - Long-term interest rates (OECD methodology, typically 10 year maturity): responses converge and become almost identical over time.
  - National equity indices: responses do not converge, but IRF confidence intervals mostly overlap.
  - Labour and housing markets: little or no convergence across countries; after one year (4 steps), housing prices fall and unemployment rises at quite different rates across borders.

### Coefficients of variation — cross-country dispersion (normalized by EA response)
- Numeric CoV values (preserved exactly):

  - On Impact
    - GDP 1.45 0.70 4.00
    - Private Consumption 1.19 1.01 2.52
    - Unemployment Rates 7.16 2.83 25.02
    - Housing Prices 2.03 1.51 4.57
    - HICP 3.24 0.99 13.25
    - Long-term Interest Rates 0.21 0.14 0.53
    - Stock Prices 0.37 0.21 0.65

  - At the 8th Step
    - GDP 0.74 0.56 1.10
    - Private Consumption 1.01 0.99 1.12
    - Unemployment Rates 1.57 1.08 3.00
    - Housing Prices 1.20 0.84 3.57
    - HICP 1.69 0.80 6.00
    - Long-term Interest Rates 0.96 0.28 3.36
    - Stock Prices 0.20 0.18 0.22

  - At the 20th Step
    - GDP 0.64 0.47 0.95
    - Private Consumption 1.02 0.99 1.11
    - Unemployment Rates 1.24 0.94 4.22
    - Housing Prices 1.08 0.84 2.02
    - HICP 1.25 0.62 4.05
    - Long-term Interest Rates 0.46 0.17 1.87
    - Stock Prices 0.21 0.19 0.26

- Interpretation:
  - Long-term interest rates and stock prices have much smaller CoV than other variables (lower heterogeneity).
  - At the 20th step, GDP is less heterogeneous than private consumption and unemployment.

### Bootstrapped pair-wise CoV differences — high-level findings
- Pair-wise differences bootstrapped; * marks differences significant at the 68 percent confidence level.
- Key findings:
  - Reactions of long-term interest rates (LTINT) and stock prices (SP) are significantly less dispersed than all other variables.
  - At the 20th step, GDP has a significantly lower CoV than private consumption (PCON), unemployment (U), and real housing prices (RHPI).
- Policy implication:
  - Heterogeneity is lower in integrated financial variables and larger in real variables (consumption, housing, labour).
  - Institutional convergence can reduce asymmetric responses to common monetary policy.

### Motivation for quantifying mortgage markets’ role
- Housing channel importance: housing is typically the largest household asset and mortgages the largest household liability.
- Institutional mortgage differences across EA members:
  - Variation in fixed vs flexible rate contract shares.
  - Variation in typical loan-to-value (LTV) ratios.
  - Differences in rental regimes and taxation.
- Approach: use a small open economy model with housing to assess role of ω (share of ARMs) and m (LTV) in transmission.

### Model: structure and key equations
- Agents:
  - Savers (patient households), fixed-rate borrowers, variable-rate borrowers; collateral constraint for borrowers.
  - Borrower types: measure 1 of impatient households with share ω having adjustable-rate mortgages (ARM) and 1−ω having fixed-rate mortgages (FRM).
- Patient households:
  - Utility: E0 ∑_{t=0}^∞ β^t [ log(c_t − ζ c_{t−1}) + j log h_t − ((n_{c,t}^{1+θ} + n_{h,t}^{1+θ})^{(1+ψ)/(1+θ)}) ].
  - Budget constraint (nominal): c_t + q_t h_t + Q_{t,t+1} D_{t+1} − b_t = D_t + W_{c,t}/P_t n_{c,t} + W_{h,t}/P_t n_{h,t} − R_{t−1} b_{t−1}/π_t + q_t (1−δ_h) h_{t−1} + T_t.
- Impatient households:
  - Utility: E0 ∑_{t=0}^∞ β′^t [ log(c′_{i,t} − ζ′ c′_{i,t−1}) + j log h′_{i,t} − ((n_{ci,t}^{′1+θ′} + n_{hi,t}^{′1+θ′})^{(1+ψ′)/(1+θ′)}) ], i ∈ {v,f}, β′ < β.
  - Budget and collateral: c′_{i,t} + q_t h′_{i,t} − b′_{i,t} = W′_{c,t}/P_t n′_{ci,t} + W′_{h,t}/P_t n′_{hi,t} − R_{i,t−1} b_{i,t−1}/π_t + q_t (1−δ_h) h_{i,t−1}; b′_{i,t} ≤ m E_t( q_{t+1} h_{i,t} / (π_{t+1} R_{i,t}) ).
  - Rate exposure: R_{f,t} = R̄_t (fixed), R_{v,t} = R_t (variable).
- Firms:
  - Consumption sector: monopolistic competition, Calvo price setting (fraction 1−φ adjust).
  - Housing sector: representative firm, no nominal rigidities.
  - Financial intermediaries: accept deposits, extend ω variable-rate and 1−ω fixed-rate loans. Profits: F_t = ω R_{t−1} b′_{v,t−1} + (1−ω) R̄_{t−1} b′_{f,t−1}; reduced form F_t = (1−ω) b′_{f,t−1} (R_{t−1} − R̄_{t−1}).
  - Fixed-rate equilibrium: R̄^{opt}_t = E_t [ ∑_{τ=t+1}^∞ β^{τ−(t+1)} Λ_{t+1,τ} R_{τ−1} ] / E_t [ ∑_{τ=t+1}^∞ β^{τ−(t+1)} Λ_{t+1,τ} ].
- Monetary policy and open-economy assumptions:
  - Home in currency union: ∆ξ_t = 0.
  - Home interest rate follows Foreign rate one-to-one (loss of monetary autonomy).
  - EA Taylor rule: R^*_t / R^*_{ss} = (R^*_{t−1} / R^*_{ss})^{γ_R^*} π^{*}_{t}^{γ_π} ^{(1−γ_R^*)} (Y^*_t / Y^*_{t−1})^{γ_Y^* (1−γ_R^*)} exp(ϵ_{R^*}).
- Aggregation and market clearing:
  - Borrower aggregates: c′_t = ω c′_{v,t} + (1−ω) c′_{f,t}, etc.
  - Total consumption: C_t = c_t + c′_t.
  - Housing: H_t = h_t + h′_t; I^H_t = H_t − (1−δ_h) H_{t−1}.
  - Real GDP: Y_t = (P_{h,t}/P_t)^{−1} [ (1−ν) C_t + ν RS_t C^*_t ]; GDP_t = Y_t P_{h,t}/P_t + q_t I^H_t.
- Solution:
  - EA treated as exogenous New Keynesian block; model solved with second order perturbation around deterministic steady state.
  - Stationarity: no growth; all variables stationary.

### Calibration (Spain baseline) and estimation
- Calibration overview:
  - Calibrated to Spain (quarterly).
  - Model has 24 parameters: 18 calibrated, 6 estimated.
  - Set β* = β = 0.9925 → steady-state annual real interest rate of 3%.
  - ε* and ε = 7.66 → steady-state markup 15%.
  - EA Taylor-rule parameters γ_π = 1.7, γ_y = 0.125, γ_r = 0.6 (Christoffel et al. (2008)); γ_r = 0.6 to match EA HICP and GDP reactions.
- Key calibrated Spain parameters:
  - β = 0.9925; β′ = 0.97.
  - j = 0.2 → housing wealth to GDP steady-state = 3.5.
  - δ_h = 0.005 (quarterly) → ≈ 2% annual depreciation and ≈ 7% residential investment share of GDP.
  - m = 0.7 — Average LTV in Spain (Calza et al. (2013)).
  - ω = 0.9 — Share of adjustable-rate mortgages (Albertazzi et al. (2018)).
  - φ = 0.78 — Spain average price duration of 4.6 quarters (Alvarez et al. (2006)).
  - α = 0.68 — steady-state housing stock share owned by wealthy hand-to-mouth ≈ 18% (Slacalek et al. (2020)).
- Estimated parameters Γ ≡ (ζ*, φ*, ζ, ζ′, δ, ν) via minimization of distance between DFM empirical IRFs (first 20 elements) and model IRFs:
  - Euro Area
    - ζ* = 0.78, S.E. = 0.006
    - φ* = 0.88, S.E. = 0.005
  - Spain
    - ζ = 0.84, S.E. = 0.019
    - ζ′ = 0.8, S.E. = 0.006
    - θ = 0.66, S.E. = 0.168
    - ν = 0.27, S.E. = 0.015
- Comments:
  - ζ* = 0.78 (close to 0.69 in Adolfson et al. (2007)).
  - φ* = 0.88 consistent with Smets and Wouters (2003).
  - ζ = 0.84, ζ′ = 0.8 consistent with Burriel et al. (2010).
  - ν = 0.27 implies home bias 1−ν = 0.73.

### Quantitative exercise: “one money, many housing markets”
- Purpose: test whether heterogeneity in mortgage institutional characteristics (LTV m and ARM share ω) alone can account for cross-country heterogeneity in monetary transmission.
- Baseline: model calibrated to Spain; feed country-specific m and ω while holding other parameters constant.
- Institutional parameters (Table 7) — preserved exactly:

  - BEL — LTV 0.83 — ARM share 0.20
  - DEU — LTV 0.7 — ARM share 0.15
  - IRL — LTV 0.74 — ARM share 1.00
  - ESP — LTV 0.7 — ARM share 0.90
  - FRA — LTV 0.75 — ARM share 0.15
  - ITA — LTV 0.5 — ARM share 0.70
  - LUX — LTV 0.8 — ARM share 0.60
  - NLD — LTV 0.9 — ARM share 0.10
  - AUT — LTV 0.6 — ARM share 0.50
  - PRT — LTV 0.85 — ARM share 0.98
  - FIN — LTV 0.75 — ARM share 0.98

- Sources: Calza et al. (2013) and Albertazzi et al. (2018).

### Main quantitative results (preserved statements and reported statistics)
- Result 1: Differences in LTV ratios generate more dispersion in responses of consumption, output, and housing prices to monetary shocks than differences in shares of ARM.
  - Contrast with Calza et al. (2013): earlier illustration suggested LTV and ARM shares roughly equivalent; here LTV matters more.
- Result 2: Correlation patterns differ between LTV and ARM exercises.
  - Feeding different LTV ratios:
    - Generates high dispersion in model IRFs, but majority of simulated responses do not align with DFM responses (weak correlation).
    - Example mismatch: at 20th step model predicts most negative private consumption response for NLD (LTV 0.9), while DFM places NLD PCON response as average.
  - Feeding different ARM shares:
    - Model IRFs have high correlation with DFM IRFs for output and consumption.
    - Reported R-square for output: 0.48 at impact and 0.5 at the 8th step.
    - For consumption: R-square 0.63 at impact (further values truncated in source).
- Model vs DFM CoV comparisons (selected preserved entries from Table 8, CoV Model / CoV DFM percentages and related numbers):
  - On Impact:
    - GDP: DFM 0.95, Model LTV 0.53, Model ARM 0.17, Model LTV + ARM 1.18, CoV DFM (%) 55.97 17.36 123.43 (entries preserved as in source).
    - Housing Prices: DFM 2.39, Model LTV 0.01, Model ARM 0.02, Model LTV + ARM 0.04, and further entries 0.42 0.85 1.73.
    - HICP: DFM 1.39, Model LTV 0.28, Model ARM 0.00, Model LTV + ARM 0.27, CoV DFM (%) 19.89 0.07 19.55.
    - PCON: DFM 1.04, Model LTV 0.34, Model ARM 0.02, Model LTV + ARM 0.34, CoV DFM (%) 32.60 2.16 33.15.
  - At the 8th Step:
    - GDP: DFM 0.56, Model LTV 0.18, Model ARM 0.02, Model LTV + ARM 0.20, CoV DFM (%) 32.26 4.26 35.47.
    - Housing Prices: DFM 1.39, Model LTV 0.30, Model ARM 0.02, Model LTV + ARM 0.24, CoV DFM (%) 21.52 1.26 16.98.
    - HICP: DFM 1.44, Model LTV 0.12, Model ARM 0.12, Model LTV + ARM 0.17, CoV DFM (%) 8.58 8.40 11.93.
    - PCON: DFM 0.76, Model LTV 0.30, Model ARM 0.08, Model LTV + ARM 0.26, CoV DFM (%) 39.33 11.15 34.44.
  - At the 20th Step:
    - GDP: DFM 0.51, Model LTV 0.19, Model ARM 0.02, Model LTV + ARM 0.17, CoV DFM (%) 36.72 4.66 33.37.
    - Housing Prices: DFM 1.47, Model LTV 0.38, Model ARM 0.17, Model LTV + ARM 0.30, CoV DFM (%) 25.95 11.48 20.65.
    - HICP: DFM 1.16, Model LTV 0.09, Model ARM 0.05, Model LTV + ARM 0.08, CoV DFM (%) 7.57 4.73 6.90.
    - PCON: DFM 0.75, Model LTV 0.19, Model ARM 0.14, Model LTV + ARM 0.20, CoV DFM (%) 24.84 18.57 27.12.
- Scatter-plot performance metrics (selected entries preserved from Figures 10–12):
  - Figure 10 (Model IRFs: LTV ratios vs DFM):
    - GDP impact: RMSE = 0.067, R-squared = 0.12.
    - GDP 8th step: RMSE = 0.41, R-squared = 0.15.
    - GDP 20th step: RMSE = 0.39, R-squared = 0.11.
    - Housing Prices impact: RMSE = 0.76, R-squared = -0.3.
    - HICP impact: RMSE = 0.19, R-squared = -0.71.
    - PCON impact: RMSE = 0.05, R-squared = 0.2.
  - Figure 11 (Model IRFs: ARM shares vs DFM):
    - GDP impact: RMSE = 0.061, R-squared = 0.46.
    - GDP 8th step: RMSE = 0.4, R-squared = 0.5.
    - GDP 20th step: RMSE = 0.37, R-squared = -0.56.
    - PCON 8th step: RMSE = 0.34, R-squared = 0.79.
    - PCON 20th step: RMSE = 0.45, R-squared = 0.8.
  - Figure 12 (Model IRFs: LTV ratios and ARM shares vs DFM):
    - GDP impact: RMSE = 0.073, R-squared = 0.23.
    - GDP 8th step: RMSE = 0.41, R-squared = 0.21.
    - PCON 8th step: RMSE = 0.44, R-squared = 0.41.
    - PCON 20th step: RMSE = 0.52, R-squared = 0.68.

### Key empirical synthesis from DFM and model comparison
- Average dispersion:
  - Across all variables, average dispersion of country-specific responses to a monetary shock is twice the size of the mean response.
- Dispersion by variable:
  - Country-level financial variables and output: dispersion is low — "20 to 50 percent" of the average response at EA level.
  - Housing and labour-market–related variables: react in significantly asymmetric ways.
- Model explanatory power:
  - For GDP and private consumption, using both LTV ratios and ARM shares, the model accounts for approximately "one-third" of the estimated dispersion of the IRFs to a monetary policy shock.
  - Reported R-squared at the 8th step: GDP = "0.21", PCON = "0.41".
- Housing prices:
  - Differences in LTV ratios, alone or combined with ARM shares, generate substantial simulated variation in housing prices at the 8th and 20th step, but the simulated variation is not in line with the DFM data.
  - Possible reason: housing price response not precisely estimated by DFM; housing prices deserve further investigation.

### Interpretation, mechanisms, and caveats
- Mechanisms:
  - Mortgage-market parameters affect household balance-sheet composition; these differences alter monetary transmission.
  - ARM-share variation alone helps align model and DFM for private consumption; LTV variation generates larger dispersion but weaker alignment.
- Caveats:
  - Model calibrated to Spain and not re-calibrated per country; other country-specific parameters held constant to isolate mortgage-structure effects.
  - Additional exercises (e.g., country differences in Calvo pricing φ) reported in Online Appendix F.2 (not reproduced here).
  - Negative R-squared and mismatches occur where correlation is negative or model predicts different ordering than DFM.

### Policy implications and recommendations
- Macroprudential policy influence:
  - National macroprudential policies (LTV ratios, ARM shares) can amplify or dampen ECB policy transmission to individual countries.
  - Harmonisation of macroprudential regulation across countries can yield more homogeneous monetary transmission across the EA.
- Further analysis recommended:
  - Other institutional differences (home ownership shares, labour-market institutions) likely matter and deserve study.
  - Housing prices show puzzling simulated vs observed patterns and require further investigation.

### Conclusions and avenues for future research
- Contribution:
  - Measure degree of heterogeneity in effects of monetary policy across the euro area using a DFM with high-frequency identification.
  - Quantify role of mortgage-market characteristics: differences explain one-third of cross-country heterogeneity in output and private consumption responses.
- Open questions:
  - Housing prices’ simulated vs observed discrepancies.
  - Extensions to other institutional features (home ownership, labour-market institutions) and recalibration for country-specific parameters.

*Source: wpiea2020108-print-pdf*

### References ....................................................................................................... 49

### wpiea2020108-print-pdf - References ....................................................................................................... 49

### Introduction: scope and objectives
- Focus: measure cross-country heterogeneity in transmission of European Central Bank (ECB) monetary policy across the euro area (EA) and assess role of institutional differences, especially in housing and labour markets.
- Dataset: large panel including economic and financial time series for the EA as a block and the 11 original member countries, spanning the years from 1999 to 2016.
- Empirical approach: dynamic factor model (DFM) with identification of monetary policy shocks via an external instrument constructed from high-frequency changes in asset prices around ECB policy announcements (following Gurkaynak et al. (2005) and Gertler and Karadi (2015)).
- Theoretical complement: a calibrated small open economy model with housing in a monetary union, focusing on the share of mortgages with adjustable rates and average loan-to-value ratios.

### Main empirical findings
- EA aggregate: factor model results are in line with theory and notably show that the transmission of monetary shocks does not suffer from the price puzzle.
- Cross-country heterogeneity:
  - Statistically significant heterogeneity in prices and variables related to labour and housing markets.
  - Low degree of heterogeneity in financial variables and output.
- Quantitative role of housing financing:
  - Differences in mortgage market characteristics across the EA can explain up to one-third of the cross-country heterogeneity of responses in output and private consumption.

### Methodological contributions
- Heterogeneity measurement:
  - Propose using the coefficient of variation (CoV, relative standard deviation) of impulse responses across countries relative to the EA response, normalised by the size of the EA response, as a statistical measure of dispersion of impulse responses.
  - Use bootstrapping to obtain error bands for the CoV for each variable and for pairwise differences across variables.
  - Apply CoV both empirically (DFM impulse responses) and theoretically (simulated responses from varying model parameters) for direct comparison.
- Identification:
  - Construct an external instrument based on changes in the 1-year Euro Overnight Index Average (EONIA) swap rate (i.e., the Overnight Index Swap (OIS) rate for the euro area) around policy announcements as a broad measure of monetary policy surprises that incorporates multiple communication channels (press releases, press statements, Q&A).
  - Overcome data availability by combining intraday data with end-of-day data from different timezones to create de-facto intraday series where actual intraday data is unavailable.
  - Test instrument relevance in a small VAR; instrument strongly correlates (0.9) with the monetary event window surprises in the euro-area monetary policy event-study database (Altavilla et al. (2019)).

### Quantitative model strategy
- Benchmark calibration: baseline economy calibrated to Spain.
- Counterfactuals: vary loan-to-value ratios and shares of adjustable-rate mortgage contracts (holding all other parameters constant) to mimic observed country differences and isolate the role of housing financing in monetary transmission.
- Caveat: model not recalibrated for each country; quantitative responses may not account for other economic factors beyond housing financing.

### Dynamic Factor Model (DFM): rationale and framework
- Motivation for DFM in EA context:
  - Parsimonious way to recover both EA-wide and country-level effects without heavy parameterisation.
  - Captures dynamic effects on individual countries through unobservable common components; reduces dimensionality and parameter space.
  - Matches informational structure: ECB monitors many euro-wide and country-level series.
  - Provides a state-space representation linking empirics to theory and permitting formal tests of mechanisms.
- Alternatives considered and trade-offs:
  - Country-by-country VARs: heavy parameterisation.
  - Large panel VAR / Global VAR: impose cross-sectional dynamic restrictions; higher parameterisation.
  - DFM chosen for efficiency when interested in net effects rather than explicit modelling of cross-sectional interactions.
- Empirical framework (model equations and estimation principles):
  - Observed series vector X_t = (X_1t,...,X_nt)′ modeled as X_t = Λ F_t + e_t, where ΛF_t is the common component and e_t the idiosyncratic component.
  - Factor dynamics: F_t = Φ_1 F_t−1 + Φ_2 F_t−2 + ... + Φ_s F_t−s + η_t, or Φ(L)F_t = η_t.
  - Estimation: static factors estimated by principal components analysis; with large n and T principal components estimate the space spanned by factors (factors identified up to premultiplication by a nonsingular r×r matrix); normalization Λ′Λ = I_r imposed.
  - Advantages: principal components explain most variation and produce orthogonal factors; reduced-form DFM suffices for the analysis.

### Literature connections
- Builds on dynamic factor modelling literature (Stock and Watson (2016); Giannone et al. (2005); Forni and Gambetti (2010); Bernanke et al. (2005); Stock and Watson (2012)).
- Identification approach follows high-frequency external instrument literature (Gurkaynak et al. (2005); Gertler and Karadi (2015); Kuttner (2001); Hamilton (2008); Campbell et al. (2012)).
- Related empirical and theoretical work on heterogeneous monetary transmission and housing channel: Calza et al. (2013); Ciccarelli et al. (2013); Barigozzi et al. (2014); Slacalek et al. (2020); Jarocinski and Karadi (2018); Altavilla et al. (2019).

*Source: wpiea2020108-print-pdf - References ....................................................................................................... 49*

### 2.3    Identification

### 2.3 Identification

### Identification challenge and external instrument approach
- Monetary policy estimation suffers an identification problem because monetary policy contemporaneously reacts to other variables in the model.
- External instrument approach (Olea and Watson (2012) and others) uses an instrument Z_t that is:
  - correlated with the structural shock of interest, and
  - uncorrelated with all other shocks in the system.
- This corresponds to the standard instrumental variables assumptions of relevance and exogeneity.
- The fitted value from regressing VAR innovations η_t on the instrument Z_t identifies the structural shock up to sign and scale; equivalently, regressing the instrument on VAR innovations uncovers the same structural shock.
- Notation and structural relations (as in Stock and Watson (2012)):
  - η_t = H ε_t = [H1 ··· Hr] (ε_1t ... ε_rt)′. (equation 4)
  - Σ_ηη = H Σ_εε H′ with Σ_ηη = E(η_t η′_t) and Σ_εε = E(ε_t ε′_t).
  - If invertible, ε_t = H^−1 η_t. (equation 5)
  - IRF of X_t with respect to the i-th structural shock: IRF = Λ Φ(L)^−1 H, with
    - F_t = Φ(L)^−1 H ε_t. (equation 6)
    - X_t = Λ Φ(L)^−1 H ε_t + e_t. (equation 7)
- Identification of H_1 via covariance between η_t and Z_t:
  - Necessary conditions for the instrument:
    1. Relevance: E(ε_1t Z_t) = α ≠ 0
    2. Exogeneity: E(ε_jt Z_t) = 0, j = 2,..., r
    3. Uncorrelated shocks: Σ_εε = D = diag(σ^2_{ε1}, ..., σ^2_{εr})
  - From E(η_t Z_t) = H_1 α (equation 8), H_1 is identified up to scale and sign by the covariance between VAR innovations and the instrument.
  - Using Σ_ηη = H D H′ (equation 9) and Π = coefficients from population regression of Z_t on η_t, the fitted value Π η_t identifies ε_1t up to a constant (equations 10–13), yielding Π η_t = (α/σ^2_{ε1}) ε_1t. (equation 13)

### Instrument construction — “Scripta Volant, Verba Manent”
- Instrument: changes in the 1-year Euro Overnight Index Average (EONIA) swap rate.
  - Rationale: 1 to 24-month OIS rates accurately measure interest rate expectations; the 1-year EONIA swap captures current monetary policy and expectations about the future path of monetary policy.
- Tenor choice considerations:
  - Longer-dated swaps better capture yield curve effects but are more affected by term premia.
  - 1-year rate chosen as a trade-off: "highly sensitive to monetary policy, while still remaining relatively unaffected by term premia."
  - Instruments based on 3-month, 6-month and 2-year EONIA swaps were also constructed; no significant difference in results was found.
- High-frequency announcement window:
  - ECB policy announcement at 13:45 CET contains limited information; press conference and Q&A at 14:30 CET often convey substantial additional information.
  - Chosen window: 6-hour window from 13:00 to 19:00 CET to cover the press release and press conference.
  - Example evidence:
    - 5 June 2008: press release at 13:45 CET in line with expectations; swap rate jumped during press conference and increased by 27 basis points over the afternoon.
    - 6 October 2011: press release unexpected tightening surprise produced an immediate increase in the 1-year EONIA swap rate; press conference added further tightening signal.
  - Alternative narrower windows (e.g., ending at 16:00 CET) were considered but not used due to intraday data availability constraints; intraday swap prices on Bloomberg available only from January 2008 onwards.
- Averaging to quarterly frequency:
  - Procedure: first calculate the cumulative daily surprise over the past quarter (93 days) for each day; then take the average of this daily cumulative series over each quarter.
  - Rationale: ensures surprises earlier in a quarter have larger influence on that quarter’s average than surprises late in the quarter.
- Notable extreme instrument values and drivers:
  - Q4 2001: instrument value -0.15 driven by 17 September 2001 50bp cuts (ECB cut all three interest rates by 50bp; 1-year EONIA swaps dropped by 20bp during the window).
  - Q4 2008: value -0.17 driven by 2 October 2008 decision and Trichet’s remarks; swap rate dropped as markets priced future cuts.
  - Q1 2009: value 0.14 driven by contractionary surprise on 4 December 2008 and surprise on 15 January 2009 (despite cuts of 75bp and 50bp, press conference rhetoric raised the swap rate).
  - Q3 2011: value -0.22 (largest absolute) mainly due to 4 August 2011 decision; announcement of a liquidity-providing supplementary LTRO caused 1-year EONIA swaps to fall by about 18bp between 14:30 and 15:30 CET.
- Instrument strength test:
  - Small VAR with three variables (output, consumer prices, policy indicator) specified at monthly and quarterly frequency and identified using high-frequency instruments based on 3, 6 and 12-month EONIA swaps.
  - Baseline specification: instrument is strong with a first-stage F-test statistic of 19.45, confirming relevance of the external instrument.

*Source: wpiea2020108-print-pdf — section 2.3 Identification*

### 3.1    Euro-wide Dynamic Effects of Monetary Policy

### 3.1 Euro-wide Dynamic Effects of Monetary Policy

### Euro-wide impulse responses to a 25bp contractionary monetary policy shock
- Shock identification and scaling
  - Shock identified using the external instrument approach; system scaled to a 25bp contraction in EONIA using the response of EONIA as a policy indicator.
  - Confidence intervals: one standard deviation bands obtained from a wild bootstrapping procedure with a simple (Rademacher) distribution. The bootstrap incorporates both stages of the external instrument regression.
- Main aggregate responses (percentage responses to a 25bp contractionary shock)
  - Harmonised index of consumer prices (HICP): no significant reaction.
  - Producer Prices in Industry: fall significantly.
  - GDP: contracts overall.
  - Government Spending: moves in the opposite direction (rises) relative to the contractionary shock.
  - Investment (GFCF): much more volatile than consumption.
  - Consumption: contracts, less volatile than investment.
  - Imports and Exports: volatile responses consistent with theory.
  - German 2-year sovereign yield: closely follows EONIA.
  - Aggregate mortgage interest rates (ECB indicator): rise but display imperfect pass-through due to a significant number of fixed-rate mortgages.
  - Unemployment: rises.
  - Wages: fall, but the reaction is not significant (evidence of nominal wage stickiness).
  - House Prices: fall significantly after the contraction.
  - Rents: increase in reaction to the shock (possible substitution from purchase to renting).
  - Euro nominal effective exchange rate (NEER): appreciates with a delay.
- Model performance and interpretation
  - No price puzzle observed: producer prices fall significantly while HICP has no significant reaction. The absence of the price puzzle is attributed to combining the DFM (better capturing price information) with a high-frequency instrument for policy identification.
  - Note: Applying a FAVAR approach (Bernanke et al. (2005)) with EONIA as the only observable factor still produced a price puzzle.

*Italic: Source: IMF working paper content unit "3.1 Euro-wide Dynamic Effects of Monetary Policy".*

---

### 3.2 Cross-Country Dynamic Effects of Monetary Policy

### Heterogeneity in country-level impulse responses
- Data and scope
  - Of the 342 individual country series in the dataset, a representative sub-sample is used for Figures 5–7; results are produced for all series in the sample.
- GDP and HICP across 11 euro-area countries
  - Reactions of real GDP and HICP across countries are heterogeneous.
  - HICP responses: positive for half of the countries and negative for the other half; the mean HICP response is negative and very low, making relative distances large compared to GDP.
  - Real GDP reactions: significant heterogeneity. Example comparisons:
    - Germany: drop in private consumption reaches a maximum at about 0.02 percentage points.
    - Ireland: drop in private consumption is 0.4 percentage points (more than 20 times the size of Germany’s drop).
    - Apart from Ireland, Italy, Finland, Spain, and Portugal have consumption drops roughly 10 times the size of Germany’s.
  - Finland and Luxembourg reactions are statistically different from France and Spain (non-overlapping confidence intervals from the 10th step onward).
- GDP components
  - Private consumption and gross fixed capital formation: responses have the same sign and follow similar patterns.
  - Government spending and net exports: responses do not have the same sign; government spending is idiosyncratic across countries and over time.
- Financial markets vs real markets: convergence and dispersion
  - Long-term interest rates and national equity indices:
    - Long-term interest rates (OECD methodology, typically 10 year maturity): while not uniform on impact, responses converge and become almost identical over time.
    - National equity indices: responses do not converge across markets, but the confidence intervals around IRFs are mostly overlapping.
  - Labour and housing markets: little or no convergence across countries; after one year (4 steps), housing prices fall and unemployment rises at quite different rates across borders.

### Coefficients of variation — cross-country dispersion (coefficients normalized by EA response)
- Coefficients of variation (Table 3) — numeric values preserved exactly:

  - On Impact
    - GDP 1.45 0.70 4.00
    - Private Consumption 1.19 1.01 2.52
    - Unemployment Rates 7.16 2.83 25.02
    - Housing Prices 2.03 1.51 4.57
    - HICP 3.24 0.99 13.25
    - Long-term Interest Rates 0.21 0.14 0.53
    - Stock Prices 0.37 0.21 0.65

  - At the 8th Step
    - GDP 0.74 0.56 1.10
    - Private Consumption 1.01 0.99 1.12
    - Unemployment Rates 1.57 1.08 3.00
    - Housing Prices 1.20 0.84 3.57
    - HICP 1.69 0.80 6.00
    - Long-term Interest Rates 0.96 0.28 3.36
    - Stock Prices 0.20 0.18 0.22

  - At the 20th Step
    - GDP 0.64 0.47 0.95
    - Private Consumption 1.02 0.99 1.11
    - Unemployment Rates 1.24 0.94 4.22
    - Housing Prices 1.08 0.84 2.02
    - HICP 1.25 0.62 4.05
    - Long-term Interest Rates 0.46 0.17 1.87
    - Stock Prices 0.21 0.19 0.26

- Interpretation of coefficients of variation
  - Long-term interest rates and stock prices have much smaller coefficients of variation than other variables, indicating lower heterogeneity for financial variables.
  - At the 20th step, GDP is less heterogeneous than private consumption and unemployment.

### Bootstrapped pair-wise differences in coefficients of variation (high-level findings from Table 4)
- Method: pair-wise differences bootstrapped; * marks differences significant at the 68 percent confidence level.
- Key summary findings:
  - Reactions of long-term interest rates (LTINT) and stock prices (SP) are significantly less dispersed than all other variables.
  - At the 20th step, GDP has a significantly lower coefficient of variation than private consumption (PCON), unemployment (U), and real housing prices (RHPI).
- Policy implication summary
  - Heterogeneity is lower in integrated financial variables (interest rates, stock prices) and larger in real variables (consumption, housing, labour).
  - Further institutional convergence can be expected to enhance cohesion in the euro area by reducing unintended asymmetric responses to common monetary policy across countries.
  - A deeper understanding of mechanisms is necessary to structure consistent convergence policies.

*Italic: Source: IMF working paper content unit "3.2 Cross-Country Dynamic Effects of Monetary Policy".*

---

### 4 Quantifying How Mortgage Markets Shape Monetary Transmission

### Motivation and approach
- The “housing channel” of monetary policy is important because housing is typically the largest household asset and mortgages the largest household liability.
- National mortgage market institutions differ across euro-area members:
  - Variation in shares of fixed versus flexible rate contracts.
  - Variation in typical loan-to-value ratios.
  - Differences in rental market regimes and taxation.
- Literature: builds on Iacoviello (2005), Calza et al. (2013), Greenwald (2018), Wong (2019), Beraja et al. (2019), Cloyne et al. (2019), Slacalek et al. (2020), and institutional overviews in Osborne (2005), Andrews et al. (2011), Westig and Bertalot (2016).

### Model strategy and calibration
- Model structure
  - A small open economy model with a housing sector is built to study the housing channel in a currency union.
  - Institutional parameters emphasized: loan-to-value ratio and share of adjustable-rate mortgage contracts.
  - The model merges elements of Calza et al. (2013) into a small open economy modeled after De Paoli (2009).
- Calibration and exercise
  - The model is calibrated to the Spanish economy to achieve empirically plausible long-term moments and impulse response functions to monetary policy shocks.
  - The model is then fed with observed country-specific loan-to-value ratios and shares of adjustable-rate mortgage contracts for each country.
  - The dispersion of simulated IRFs (from varying mortgage market parameters) is compared with the dispersion estimated from the DFM in the earlier sections.

*Italic: Source: IMF working paper content unit "4 Quantifying How Mortgage Markets Shape Monetary Transmission".*

### 4.1    Model

### 4.1    Model

### Model structure and agents
- Three agent types: savers (patient households), fixed-rate borrowers, and variable-rate borrowers (as in Rubio (2011)), plus a collateral constraint (Campbell and Hercowitz (2005); Iacoviello (2005); Iacoviello and Neri (2010); Liu et al. (2010)).
- Savers: standard Ricardian agents; own all firms in consumption and housing sectors and financial intermediaries; have access to a complete set of contingent claims traded internationally.
- Borrowers: credit constrained in equilibrium; behave as hand-to-mouth consumers; a measure 1 of impatient households with a share ω having adjustable-rate mortgages (ARM) and 1−ω having fixed-rate mortgages (FRM).
- Small open economy assumption: Home economy is small relative to the rest of the EA; EA block treated as exogenous.

### Patient households (representative)
- Utility:
  - E0 ∑_{t=0}^∞ β^t [ log(c_t − ζ c_{t−1}) + j log h_t − ((n_{c,t}^{1+θ} + n_{h,t}^{1+θ})^{(1+ψ)/(1+θ)}) ]
  - Parameters: β (discount), ζ (habit), j (housing preference), θ (elasticity of substitution between sectors), ψ (inverse Frisch elasticity).
- Consumption bundle:
  - Home bias parameter ν ∈ [0,1]; consumption aggregation as in equations (15)–(16) with elasticity ε > 1.
- Budget constraint (nominal):
  - c_t + q_t h_t + Q_{t,t+1} D_{t+1} − b_t = D_t + W_{c,t}/P_t n_{c,t} + W_{h,t}/P_t n_{h,t} − R_{t−1} b_{t−1}/π_t + q_t (1−δ_h) h_{t−1} + T_t
  - q_t: house price; R_t: gross nominal interest rate; δ_h: housing depreciation; π_t: inflation; P_t: domestic price index; T_t: total firm profits; Q_{t,t+1}: stochastic discount factor.

### Impatient households (borrowers)
- Utility:
  - E0 ∑_{t=0}^∞ β′^t [ log(c′_{i,t} − ζ′ c′_{i,t−1}) + j log h′_{i,t} − ((n_{ci,t}^{′1+θ′} + n_{hi,t}^{′1+θ′})^{(1+ψ′)/(1+θ′)}) ], for i ∈ {v,f}
  - β′ < β (impatient).
- Budget and collateral constraints:
  - c′_{i,t} + q_t h′_{i,t} − b′_{i,t} = W′_{c,t}/P_t n′_{ci,t} + W′_{h,t}/P_t n′_{hi,t} − R_{i,t−1} b_{i,t−1}/π_t + q_t (1−δ_h) h_{i,t−1}
  - b′_{i,t} ≤ m E_t( q_{t+1} h_{i,t} / (π_{t+1} R_{i,t}) ), where m is the loan-to-value ratio.
- Rate exposure:
  - Impatient households with fixed-rate mortgages: R_{f,t} = R̄_t.
  - Impatient households with variable-rate mortgages: R_{v,t} = R_t.
- Two key mortgage parameters: ω (share of ARM) and m (LTV ratio).

### Prices, exchange rate, and demand
- Law of one price for intermediate goods: P_t(j) = ξ_t P*_t(j), where ξ_t is nominal exchange rate (price of Foreign currency in Home currency); real exchange rate RS_t = ξ_t P*_t / P_t.
- Consumer price indices: equations (21)–(24); deviations from PPP due to home bias.
- Total demand for a Home-produced good j (n → 0 assumption):
  - Y^d_t(j) = (P_t(j)/P_{H,t})^{−ε} (P_{H,t}/P_t)^{−1} [ (1−ν) C_t + ν RS_t C*_t ].

### Firms
- Consumption sector: monopolistic competition, Calvo price setting with fraction (1−φ) able to adjust prices. Production: Y_t(j) = n_{c,t}(j)^α n_{c,t}(j)′^{1−α}.
- Housing sector: representative firm, no nominal rigidities. Residential investment: I^H_t = n_{h,t}^α n′_{h,t}^{1−α}. Firm chooses labor to maximize q_t I^H_t − W_{h,t} n_{h,t} − W′_{h,t} n′_{h,t}.
- Financial intermediaries: accept deposits from savers and extend both variable- and fixed-rate loans. Profits:
  - F_t = ω R_{t−1} b′_{v,t−1} + (1−ω) R̄_{t−1} b′_{f,t−1}
  - Aggregate borrowing/saving: ω b′_{v,t} + (1−ω) b′_{f,t} = b′_t
  - Reduced form: F_t = (1−ω) b′_{f,t−1} (R_{t−1} − R̄_{t−1})
- Fixed-rate equilibrium condition:
  - R̄^{opt}_t = E_t [ ∑_{τ=t+1}^∞ β^{τ−(t+1)} Λ_{t+1,τ} R_{τ−1} ] / E_t [ ∑_{τ=t+1}^∞ β^{τ−(t+1)} Λ_{t+1,τ} ]
  - Aggregate fixed rate R̄_t is an average of past and new rates per equation (36).

### Monetary policy
- Home is in a currency union: Home fixes nominal exchange rate:
  - ∆ξ_t = 0
- Home interest rate follows Foreign rate one-to-one (loss of monetary autonomy).
- EA Taylor rule:
  - R^*_t / R^*_{ss} = (R^*_{t−1} / R^*_{ss})^{γ_R^*} π^{*}_{t}^{γ_π} ^{(1−γ_R^*)} (Y^*_t / Y^*_{t−1})^{γ_Y^* (1−γ_R^*)} exp(ϵ_{R^*}).

### Aggregation and market clearing
- Aggregates for borrowers (ω-weighted):
  - c′_t = ω c′_{v,t} + (1−ω) c′_{f,t}
  - n′_{c,t} = ω n′_{cv,t} + (1−ω) n′_{cf,t}
  - n′_{h,t} = ω n′_{hv,t} + (1−ω) n′_{hf,t}
  - h′_t = ω h′_{v,t} + (1−ω) h′_{f,t}
- Total consumption: C_t = c_t + c′_t.
- Housing market:
  - H_t = h_t + h′_t
  - I^H_t = H_t − (1−δ_h) H_{t−1}
- Real GDP (home consumption goods):
  - Y_t = (P_{h,t}/P_t)^{−1} [ (1−ν) C_t + ν RS_t C^*_t ]
  - GDP_t = Y_t P_{h,t}/P_t + q_t I^H_t

### Solution and equilibrium
- EA block: standard New Keynesian economy with price stickiness; treated as exogenous.
- Stationarity: no growth; all variables stationary.
- Solution method: second order perturbation around deterministic steady state.
- Full equilibrium equations available in Appendix C (not reproduced here).

---

### 4.2    Calibration

### General approach
- Calibrated to Spain (quarterly data).
- Model has 24 parameters: 18 calibrated, 6 estimated.
- Set β* = β = 0.9925 → steady-state annual real interest rate of 3% for Spain and the EA.
- ε* and ε set at 7.66 → steady-state markup of 15%.
- EA Taylor-rule parameters γ_π and γ_y set according to Christoffel et al. (2008).
- Lagged nominal interest parameter γ_r = 0.6 to match EA HICP and GDP reactions to monetary shocks from the DFM.

### Calibrated parameter table (selected values and targets)
- Euro Area
  - β* = 0.9925 — EA Steady-state annual real interest rate of 3%
  - ψ* = 0.5 — Smets and Wouters (2003)
  - ε* = 7.66 — Steady-state markup of 15%
  - γ_π = 1.7 — Christoffel et al. (2008)
  - γ_y = 0.125 — Christoffel et al. (2008)
  - γ_r = 0.6 — Christoffel et al. (2008)
- Spain
  - β = 0.9925 — EA Steady-state annual real interest rate of 3%
  - β′ = 0.97 — Iacoviello and Neri (2010)
  - θ′ = 0.97 — Iacoviello and Neri (2010)
  - ψ = 0.5 — Burriel et al. (2010)
  - ψ′ = 0.5 — Burriel et al. (2010)
  - j = 0.2 — Housing wealth to GDP ratio in the steady-state of 3.5
  - δ_h = 0.005 — 7% steady-state residential investment share of GDP
  - m = 0.7 — Average loan-to-value ratio in Spain, Calza et al. (2013)
  - ω = 0.9 — Share of adjustable-rate mortgages, Albertazzi et al. (2018)
  - ε = 7.66 — Steady-state mark-up of 15%
  - φ = 0.78 — Spain average price duration of 4.6 quarters, Alvarez et al. (2006)
  - α = 0.68 — Steady-state housing stock value share owned by wealthy hand-to-mouth household of 18%, Slacalek et al. (2020)

Notes on specific calibrations:
- β′ fixed at 0.97 to ensure a steady state with binding borrowing constraint.
- ψ*, ψ, ψ′ set to match Frisch labor supply elasticity of 2 (Smets and Wouters (2003)) and align with Burriel et al. (2010).
- j = 0.2 chosen to match Spanish housing wealth-to-GDP ≈ 3.5 (Martínez-Toledano (2017)).
- δ_h = 0.005 (quarterly) consistent with ≈ 2% annual depreciation and ≈ 7% residential investment share of GDP in Spain.
- Institutional mortgage parameters from Calza et al. (2013) and Albertazzi et al. (2018): m = 0.7, ω = 0.9.
- φ = 0.78 to match average price duration of 4.6 quarters (Alvarez et al. (2006)).
- α = 0.68 to match share of housing stock held by constrained agents ≈ 18% (Slacalek et al. (2020)).

### Estimated parameters (6 parameters Γ ≡ (ζ*, φ*, ζ, ζ′, δ, ν))
- Estimation method: minimize distance between DFM empirical impulse responses (first 20 elements) and model impulse responses via J = min_Γ [Ψ̂ − Ψ(Γ)]′ V^{−1} [Ψ̂ − Ψ(Γ)], with V diagonal of sample variances of DFM impulse responses.
- Estimated values and standard errors (Table 6):
  - Euro Area
    - ζ* = 0.78, S.E. = 0.006
    - φ* = 0.88, S.E. = 0.005
  - Spain
    - ζ = 0.84, S.E. = 0.019
    - ζ′ = 0.8, S.E. = 0.006
    - θ = 0.66, S.E. = 0.168
    - ν = 0.27, S.E. = 0.015
- Comments:
  - ζ* = 0.78 (close to 0.69 in Adolfson et al. (2007)).
  - φ* = 0.88 (in line with Smets and Wouters (2003); Adolfson et al. (2007)).
  - ζ = 0.84, ζ′ = 0.8 consistent with prior literature (Burriel et al. (2010)).
  - δ = 0.66 identical to Iacoviello and Neri (2010).
  - Home bias parameter 1−ν = 0.73 (ν = 0.27), slightly lower than 0.81 reported in Burriel et al. (2010).
- Model solution: theoretical IRFs based on estimated parameters are reasonably close to empirical DFM IRFs (Figure 9).

---

### 4.3    Quantitative exercise: one money, many housing markets

### Purpose and methodology
- Assess whether heterogeneity in institutional mortgage characteristics alone can account for heterogeneity in monetary policy transmission across EA countries.
- Baseline: model calibrated to Spain.
- Exercise: feed the model with country-specific loan-to-value (LTV) ratios and ARM shares for Spain and other EA countries; keep all other parameters constant to isolate the effect of housing-finance parameters.
- Compare dispersion of simulated impulse response functions (IRFs) from the model with dispersion from the DFM.

### Institutional parameters in EA sample (Table 7)
- Country — LTV ratio — ARM share
  - BEL — 0.83 — 0.20
  - DEU — 0.7 — 0.15
  - IRL — 0.74 — 1.00
  - ESP — 0.7 — 0.90
  - FRA — 0.75 — 0.15
  - ITA — 0.5 — 0.70
  - LUX — 0.8 — 0.60
  - NLD — 0.9 — 0.10
  - AUT — 0.6 — 0.50
  - PRT — 0.85 — 0.98
  - FIN — 0.75 — 0.98
- Sources: Calza et al. (2013) and Albertazzi et al. (2018).

### Main quantitative results (as reported)
- Result 1: Differences in LTV ratios generate more dispersion in the responses of consumption, output, and housing prices to monetary shocks than differences in shares of ARM.
  - Evidence: Table 8 columns (not reproduced here) show dispersion explained by model when feeding LTV ratios and ARM shares. At impact and at the 8th and 20th steps, variation in LTV ratios yields substantially higher dispersion in GDP, housing prices, CPI, and private consumption.
  - Contrast with Calza et al. (2013): prior numerical illustration suggested LTV and ARM shares are roughly equivalent; here LTV differences matter more.
  - Consistency with Slacalek et al. (2020): large differences in net interest rate exposure across DEU, FRA, ESP, ITA have minimal effect on consumption responses; here observed ARM-share differences generate relatively smaller macro/price response differences.
- Result 2: Correlation patterns differ between LTV and ARM exercises.
  - Feeding the model with different LTV ratios:
    - Generates high dispersion in model IRFs.
    - Majority of simulated responses do not align with DFM responses (weak correlation).
    - Example: at 20th step, model predicts most negative private consumption response when using the Netherlands LTV (highest LTV = 0.9), while DFM places Netherlands’ PCON response as average — a mismatch.
  - Feeding the model with different ARM shares:
    - Model IRFs have a high correlation with DFM-estimated IRFs for output and consumption.
    - Reported R-square from linear regression for output: 0.48 at impact and 0.5 at the 8th step.
    - For consumption: R-square is 0.63 at impact (further values truncated in source).

### Methodology caveats (as noted)
- Model IRFs are not directly comparable to DFM IRFs because the model is not calibrated to each individual country; keeping other parameters constant is intentional to isolate mortgage-structure effects.
- Results reported here include only mortgage-market parameter changes; additional exercises (e.g., differences in Calvo pricing φ across countries) reported in Online Appendix F.2 (not reproduced here).

---

*Source: wpiea2020108-print-pdf — Section 4.1–4.3 (model description, calibration, and quantitative exercise).*

### 0.79 at the 8th step.  So, an important conclusion from our exercise is that, while varying the

### Impulse responses, heterogeneity, and role of housing finance (excerpt)

### Key empirical findings from the DFM and model comparison
- Across all variables, the average dispersion of country-specific responses to a monetary shock is twice the size of the mean response.
- Dispersion differs by variable:
  - Country-level financial variables and output: dispersion is low—"20 to 50 percent" of the average response at EA level.
  - Housing and labour-market–related variables: react in significantly asymmetric ways, consistent with limited cross-border institutional convergence.
- For GDP and private consumption, using both LTV ratios and shares of ARM from the data, the model accounts for approximately "one-third" of the estimated dispersion of the IRFs to a monetary policy shock.
  - For GDP and consumption, the R-squared at the 8th step is "0.21" and "0.41", respectively.
- Housing prices: differences in LTV ratios, alone or combined with shares of ARM, generate substantial variation in simulated housing prices at the 8th and 20th step, but the simulated variation is not in line with the data.
  - One potential reason: the response of housing prices to monetary shocks is not precisely estimated by the DFM, while output and consumption are; housing prices deserve further investigation.

### Quantitative model performance (selected statistics, as reported)
- When fitting a constrained-slope linear regression (slope constrained to 1, intercept unrestricted), R-squares measure how much of the DFM responses gap relative to the mean can be explained by model responses relative to their mean; negative R-squares can occur when correlation is negative.
- Table 8 — Coefficient of Variation (CoV) — Model / CoV DFM (%) (selected entries)
  - On Impact:
    - GDP: DFM 0.95, Model LTV 0.53, Model ARM 0.17, Model LTV + ARM 1.18, CoV DFM (%) 55.97, additional numbers "17.36" "123.43" appear in context.
    - Housing Prices: DFM 2.39, Model LTV 0.01, Model ARM 0.02, Model LTV + ARM 0.04, and further entries "0.42" "0.85" "1.73".
    - HICP: DFM 1.39, Model LTV 0.28, Model ARM 0.00, Model LTV + ARM 0.27, CoV DFM (%) "19.89" "0.07" "19.55".
    - PCON: DFM 1.04, Model LTV 0.34, Model ARM 0.02, Model LTV + ARM 0.34, CoV DFM (%) "32.60" "2.16" "33.15".
  - At the 8th Step:
    - GDP: DFM 0.56, Model LTV 0.18, Model ARM 0.02, Model LTV + ARM 0.20, CoV DFM (%) "32.26" "4.26" "35.47".
    - Housing Prices: DFM 1.39, Model LTV 0.30, Model ARM 0.02, Model LTV + ARM 0.24, CoV DFM (%) "21.52" "1.26" "16.98".
    - HICP: DFM 1.44, Model LTV 0.12, Model ARM 0.12, Model LTV + ARM 0.17, CoV DFM (%) "8.58" "8.40" "11.93".
    - PCON: DFM 0.76, Model LTV 0.30, Model ARM 0.08, Model LTV + ARM 0.26, CoV DFM (%) "39.33" "11.15" "34.44".
  - At the 20th Step:
    - GDP: DFM 0.51, Model LTV 0.19, Model ARM 0.02, Model LTV + ARM 0.17, CoV DFM (%) "36.72" "4.66" "33.37".
    - Housing Prices: DFM 1.47, Model LTV 0.38, Model ARM 0.17, Model LTV + ARM 0.30, CoV DFM (%) "25.95" "11.48" "20.65".
    - HICP: DFM 1.16, Model LTV 0.09, Model ARM 0.05, Model LTV + ARM 0.08, CoV DFM (%) "7.57" "4.73" "6.90".
    - PCON: DFM 0.75, Model LTV 0.19, Model ARM 0.14, Model LTV + ARM 0.20, CoV DFM (%) "24.84" "18.57" "27.12".
- Selected scatter-plot performance metrics reported in Figures 10–12 (examples):
  - Figure 10 (Model IRFs: LTV ratios vs DFM):
    - GDP impact: RMSE = "0.067", R-squared = "0.12".
    - GDP 8th step: RMSE = "0.41", R-squared = "0.15".
    - GDP 20th step: RMSE = "0.39", R-squared = "0.11".
    - Housing Prices impact: RMSE = "0.76", R-squared = "-0.3".
    - Housing Prices 8th step: RMSE = "0.71", R-squared = "-0.23".
    - Housing Prices 20th step: RMSE = "0.54", R-squared = "-0.3".
    - HICP impact: RMSE = "0.19", R-squared = "-0.71".
    - HICP 8th step: RMSE = "0.22", R-squared = "-0.16".
    - HICP 20th step: RMSE = "0.099", R-squared = "0.39".
    - PCON impact: RMSE = "0.05", R-squared = "0.2".
    - PCON 8th step: RMSE = "0.53", R-squared = "0.089".
    - PCON 20th step: RMSE = "0.65", R-squared = "0.11".
  - Figure 11 (Model IRFs: ARM shares vs DFM):
    - GDP impact: RMSE = "0.061", R-squared = "0.46".
    - GDP 8th step: RMSE = "0.4", R-squared = "0.5".
    - GDP 20th step: RMSE = "0.37", R-squared = "-0.56".
    - Housing Prices impact: RMSE = "0.75", R-squared = "0.11".
    - Housing Prices 8th step: RMSE = "0.75", R-squared = "-0.49".
    - Housing Prices 20th step: RMSE = "0.61", R-squared = "-0.45".
    - HICP impact: RMSE = "0.16", R-squared = "-0.018".
    - HICP 8th step: RMSE = "0.19", R-squared = "-0.3".
    - HICP 20th step: RMSE = "0.1", R-squared = "-0.14".
    - PCON impact: RMSE = "0.041", R-squared = "-0.63".
    - PCON 8th step: RMSE = "0.34", R-squared = "0.79".
    - PCON 20th step: RMSE = "0.45", R-squared = "0.8".
  - Figure 12 (Model IRFs: LTV ratios and ARM shares vs DFM):
    - GDP impact: RMSE = "0.073", R-squared = "0.23".
    - GDP 8th step: RMSE = "0.41", R-squared = "0.21".
    - GDP 20th step: RMSE = "0.38", R-squared = "0.015".
    - Housing Prices impact: RMSE = "0.75", R-squared = "-0.14".
    - Housing Prices 8th step: RMSE = "0.72", R-squared = "-0.31".
    - Housing Prices 20th step: RMSE = "0.62", R-squared = "-0.55".
    - HICP impact: RMSE = "0.19", R-squared = "-0.71".
    - HICP 8th step: RMSE = "0.2", R-squared = "-0.23".
    - HICP 20th step: RMSE = "0.1", R-squared = "0.059".
    - PCON impact: RMSE = "0.052", R-squared = "0.15".
    - PCON 8th step: RMSE = "0.44", R-squared = "0.41".
    - PCON 20th step: RMSE = "0.52", R-squared = "0.68".

### Interpretation and mechanisms
- Varying the relative share of adjustable-rate mortgages (ARM) alone does not generate sizeable heterogeneity in monetary policy transmission for all variables, but it helps the model generate IRFs more in line with the DFM evidence for private consumption in particular.
- Combining LTV ratios and shares of ARM produces heterogeneity in monetary policy transmission that is both sizeable and aligned with the evidence for GDP and PCON, though correlation is weaker for housing prices and HICP.
- The link to household balance-sheet composition: different institutional parameters for mortgage markets imply differences in compositions of households' balance sheets, which affects monetary transmission (connection to Slacalek et al. (2020) noted).

### Policy implications and recommendations
- Macroprudential policy can shape the monetary transmission mechanism:
  - National macroprudential policies, reflected in the share of adjustable mortgage rates and the loan-to-value ratio, can either amplify or dampen the transmission of ECB policy to a particular country.
  - A high degree of harmonisation of macroprudential regulation across countries can result in a more homogeneous transmission of monetary policy across the block.
- Other institutional differences (for example, share of home ownership, labour-market institutions) are likely relevant and merit further analysis; the methodology can be extended to study these institutional divergences.

### Conclusions and avenues for future research
- The paper provides a measure of the degree of heterogeneity in the effects of monetary policy across the euro area using a dynamic factor model with high-frequency identification.
- Differences in mortgage market characteristics across the EA explain one-third of the cross-country heterogeneity of responses in output and private consumption.
- Housing prices show puzzling simulated vs observed differences and deserve further investigation; other housing-market features (e.g., home ownership) and national labour-market differences are promising extensions left for future research.

*Source: wpiea2020108-print-pdf (excerpt).*

### References

### wpiea2020108-print-pdf - References

### References (selected citations)
- Adolfson, M., S. Las ́een, J. Lind ́e, and M. Villani (2007). Bayesian estimation of an open economy dsge model with incomplete pass-through. Journal of International Economics 72(2), 481–511.
- Altavilla, C., L. Brugnolini, R. S. G ̈urkaynak, R. Motto, and G. Ragusa (2019). Measuring euro area monetary policy. Journal of Monetary Economics 108, 162–179.
- Bernanke, B. S., J. Boivin, and P. Eliasz (2005). Measuring the effects of monetary policy: A factor-augmented vector autoregressive (FAVAR) approach. The Quarterly Journal of Economics 120(1), 387–422.
- Gertler, M. and P. Karadi (2015). Monetary policy surprises, credit costs, and economic activity. American Economic Journal: Macroeconomics 7(1), 44–76.
- Iacoviello, M. (2005). House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle. American Economic Review 95(3), 739–764.
- Nakamura, E. and J. Steinsson (2018). High-frequency identification of monetary non-neutrality: the information effect. The Quarterly Journal of Economics 133(3), 1283–1330.
- Smets, F. and R. Wouters (2003). An estimated dynamic stochastic general equilibrium model of the euro area. Journal of the European Economic Association 1(5), 1123–1175.
- Stock, J. H. and M. W. Watson (2016). Dynamic factor models, factor-augmented vector autoregressions, and structural vector autoregressions in macroeconomics. Volume 2 of Handbook of Macroeconomics, pp. 415 – 525. Elsevier.
- Slacalek, J., O. Tristani, and G. L. Violante (2020). Household balance sheet channels of monetary policy: A back of the envelope calculation for the euro area. Working Paper 26630, National Bureau of Economic Research.

### Appendix A — Data Set: metadata and key notes
- Transformation code (T):
  - 1 - no transformation
  - 2 - difference in levels
  - 4 - logs
  - 5 - difference in logs
- Geography codes and meanings:
  - EA - Euro area
  - EA12 - Euro area (12 countries)
  - EA19 - Euro area (19 countries)
  - EACC - Euro area (changing composition)
  - EA11
  - i - 11 individual series for sample countries
- Factor analysis (F): Y - included in data set for principal component analysis
- Seasonal adjustment codes:
  - WDSA - working day and seasonally adjusted
  - SA - seasonally adjusted
  - NA - neither working day nor seasonally adjusted
- Important data availability notes (verbatim):
  - "National house price indices have different start dates across countries. They begin in 2005 Q4 for Spain, 2006 Q2 for France, 2007 Q1 for Luxembourg, 2008 Q1 for Portugal, 2010 Q1 for Italy and Austria, and 2005 Q1 for all other countries."
  - "Unemployment data for France between 2000 Q1 and 2005 Q1, as well as Luxembourg between 2000 Q1 and 2003 Q1 is only available annually and has been linearly interpolated to create a quarterly data series. Thereafter all unemployment data is quarterly."
  - "Import and export data for Germany, Spain and Italy is only available from 2012 Q1 onward."

### Appendix A — Representative series entries (preserved fields)
- GDP (EA aggregate)
  - T: 5
  - Source: Eurostat
  - Geography: EA12
  - Start: 2000 Q1
  - End: 2016 Q4
- PCON (Household and NPISH final consumption expenditure, EA12)
  - T: 5
  - Source: Eurostat
  - Geography: EA12
  - Start: 2000 Q1
  - End: 2016 Q4
- GFCF (Gross fixed capital formation, EA12)
  - T: 5
  - Source: Eurostat
  - Geography: EA12
  - Start: 2000 Q1
  - End: 2016 Q4
- HICP00 (All-items HICP, Index, 2015=100)
  - T: 5
  - Source: Eurostat
  - Geography: EACC
  - Start: 2000 Q1
  - End: 2016 Q4
- HICPXFD (Overall HICP index excluding seasonal food, Index, 2015=100)
  - T: 5
  - Source: Eurostat
  - Geography: EACC
  - Start: 2000 Q4
  - End: 2016 Q4
- IPIT (Industrial Production Index, Total Industry, WDSA, 2005=100)
  - T: 5
  - Source: ECB SDW
  - Geography: EA19
  - Start: 2000 Q1
  - End: 2016 Q4
- U (Total Unemployment rate (quarterly average), WDSA)
  - T: 2
  - Source: Eurostat
  - Geography: EACC
  - Start: 2000 Q1
  - End: 2016 Q4
- MIR (Bank interest rates - loans to households for house purchase (outstanding amount business coverage), average of observations through period, percent per annum)
  - T: 1
  - Source: ECB SDW
  - Geography: EACC
  - Start: 2003 Q1
  - End: 2016 Q4
- EONIA (Euro Overnight Index Average (%, NSA))
  - T: 1
  - Source: ECB SDW
  - Geography: EA
  - Start: 2000 Q1
  - End: 2016 Q4
- HPI (House price index, 2010=100, EACC)
  - T: 5
  - Source: Eurostat
  - Geography: EACC
  - Start: 2005 Q1
  - End: 2016 Q4
- RHPI (Real housing prices (=HPI/HICP00))
  - T: 5
  - Source: Eurostat
  - Geography: EACC
  - Start: 2005 Q1
  - End: 2016 Q4
- NEER (Euro Nominal Effective Exchange Rate - 42 trading partners, Index, 2005=100)
  - T: 5
  - Source: Eurostat
  - Geography: EA19
  - Start: 2000 Q1
  - End: 2016 Q4
- BSBCI (EA Business Climate Indicator (SA))
  - T: 2
  - Source: Eurostat
  - Geography: EA19
  - Start: 2000 Q1
  - End: 2016 Q4

### Appendix B — Robustness (sub-sample analysis)
- Figures presented:
  - Figure 13: "Cross-country impulse responses for selected variables when the model is estimated for the pre-crisis 2001Q1 to 2007Q4 period."
  - Figure 14: "Cross-country impulse responses for selected variables when the model is estimated for the post-crisis 2008Q1 to 2016Q4 period."
- Variables shown in sub-sample impulse responses (labels preserved): GDP, HICP, LINT, SP, PCON, U, RHPI, RREN.
- Note: Figures illustrate differences in cross-country impulse responses across the two sub-samples 2001Q1–2007Q4 and 2008Q1–2016Q4.

### Appendix C — Model Equations (structure and blocks)
- The model equations are organized into labeled blocks and equations A.1–A.42, including:
  - C.1 Home Economy Block:
    - Patient households (equations A.1–A.4)
    - Impatient households (equations A.5–A.10)
    - Terms of trade and identities (equations A.11–A.13)
    - Consumption sector firms (equations A.14–A.18)
    - Residential investment sector firms (equations A.19–A.21)
    - Financial intermediaries firms (equations A.22–A.23)
    - Aggregation and market clearing (equations A.24–A.33)
  - C.2 EA Economy Block:
    - Representative equations (A.34–A.40), including π∗t, Y∗t, and related price-setting expressions
  - Monetary Policy:
    - Monetary policy block includes equations (A.41) and (A.42) (e.g., "∆ξt = 0" and a policy rule for R∗t/R∗ss with parameters γR∗, γπ, γY∗ and exp(R∗)).
- Representative equation forms and notation preserved exactly (for example, references to variables such as uc,t, q t, β, πt, Rt, IH t, H t, Λt,t+1, and parameters such as ψ, θ, α, φ, ε).
- Aggregation identities and market clearing expressions preserved (e.g., (A.29) Ct = ct + c′t; (A.31) IH t = H t − (1−δh) H t−1; (A.32) H t = h t + h′ t).

*Source: wpiea2020108-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020108-print-pdf.pdf_