One Money, Many Markets: Monetary Transmission and Housing Financing in the Euro Area1

Giancarlo Corsetti; Joao B. Duarte; Samuel Mann

doi:10.5089/9781513548746.001.A001

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One Money, Many Markets: Monetary Transmission and Housing Financing in the Euro Area¹

Author: Giancarlo Corsetti¹, Joao B. Duarte², and Samuel Mann³

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
| ² 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
| ³ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Author’s E-Mail Address: gc422@cam.ac.uk, joao.duarte@novasbe.pt, smann2@imf.org

Publication Date:: 26 Jun 2020

eISBN:: 9781513548746

Language:: English

Keywords:: WP; coefficient of variation; nominal exchange rate; Monetary Policy; High-Frequency Identification; Monetary Union; Housing Market; Loan-to-value Ratio; Adjustable Mortgage Rates; monetary policy shock; housing price; nominal interest rate; contractionary monetary policy; depreciation rate; fixed interest rate; exchange rate; Housing prices; Housing; Consumption; Mortgages; Private consumption; Europe; Global; wealth effect; monetary policy decision; asset price movement; term premia

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We study the transmission of monetary shocks across euro-area countries using a dynamic factor model and high-frequency identification. We develop a methodology to assess the degree of heterogeneity, which we find to be low in financial variables and output, but significant in consumption, consumer prices, and variables related to local housing and labor markets. Building a small open economy model featuring a housing sector and calibrating it to Spain, we show that varying the share of adjustable-rate mortgages and loan-to-value ratios explains up to one-third of the cross-country heterogeneity in the responses of output and private consumption.

Abstract

1 Introduction

Monetary policy in the euro area (EA) has long been challenged by financial, economic, and institutional heterogeneity among member countries. Although there has been some convergence over time in financial markets, the convergence process has slowed down markedly since the financial crisis (see ECB, 2017). Other markets have remained remarkably different across member countries. Most notably, the institutional backgrounds in labour and housing are highly dissimilar across the currency block. Because of these slow developments, policy and academic researchers have long been faced with two questions. First, to which extent is the transmission of the European Central Bank’s (ECB) monetary policy heterogeneous across borders? Second, how do differences in institutional characteristics of specific markets weigh on the observed heterogeneity?¹

In this paper, we provide novel empirical and quantitative answers to these questions, developing a methodology suitable to analyze and test the degree of cross-country heterogeneity in the transmission of monetary policy. On empirical grounds, we set up a dynamic factor model (DFM) and assemble a large dataset 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. The high dimensionality of the data allows us to carry out a formal comparison of the degree of heterogeneity among responses to monetary policy shocks across different dimensions of the economy, such as output and asset prices, as well as housing and labour markets. We identify monetary policy shocks by constructing an external instrument using high-frequency changes in asset prices around ECB policy announcements, following Gurkaynak et al. (2005) and Gertler and Karadi (2015). To bring theory to bear on our findings, we build a small open economy with housing operating in a monetary union and assess quantitatively how much of the variation in individual EA countries’ responses to a monetary policy shock can be explained by differences in housing financing. Our focus is on the share of mortgages with adjustable rates and average loan-to-value ratios.

Our main results are as follows. First, at the aggregate EA level, we find that results from the factor model are in line with theory and, notably, that the transmission of monetary shocks does not suffer from the price puzzle. Second, we show that the estimated country-level effects are significantly heterogeneous in prices and variables related to labour and housing markets—some of the least integrated markets in the euro area. The degree of heterogeneity among responses to policy is instead low in financial variables and output. Third, we find that 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.

On methodological grounds, our main contributions are, first, how to measure and statistically test heterogeneity in the responses of economic variables to a common shock in both theoretical and empirical applications. While confidence intervals around impulse response functions and Wald tests on the differences of these functions test whether responses are statistically different, they do not provide a measure of the degree of heterogeneity. To bridge this gap, we propose the following: for each set of impulse responses (e.g., GDP across member countries), we calculate the coefficient of variation statistic, also known as relative standard deviation. The coefficient of variation (CoV) for a variable is defined as the standard deviation of responses across countries with respect to the EA response, normalised by the size of the EA response. This statistical measure of the dispersion of impulse responses allows for an intuitive and meaningful comparison of variables. As a first application using the CoV, we measure the degree of heterogeneity in the DFMs estimated monetary transmission to key macro variables across EA member countries, and carry out hypothesis testing based on a bootstrapping procedure, which yields error bands for the coefficient of variation of each variable as well as pairwise differences across variables. As a second application, we use the CoV to measure the heterogeneity in the simulated theoretical responses from varying model parameters, which can then be directly compared to its empirical counterpart.

Our second contribution consists of a quantitative assessment of the effects of crosscountry differences in mortgage markets on monetary policy transmission in a monetary union. We calibrate our baseline economy to Spain, and, using this benchmark calibration, vary the loan-to-value ratios and shares of adjustable-rate mortgage contracts to mimic observed data for different countries. This procedure allows us to compare the dispersion of the simulated impulse response functions with the dispersion we estimated in the empirical section of the paper. As we do not recalibrate the model for each country in our sample, our quantitative responses may not account for several economic factors other than housing financing that may potentially help to match the evidence. However, holding all parameters other than the share of adjustment-rate mortgages and loan-to-value ratio constant allows us to isolate more clearly the specific role played by housing financing in monetary transmission.

Literature In specifying our empirical model, we build on the factor modeling literature developed in the 1970s² and recently popularised in the context of monetary policy analysis. In their seminal contribution, Bernanke et al. (2005) model macroeconomic interaction with a factor-augmented VAR (FAVAR) that combines factors and perfectly observable series, typically interest rates, in one dynamic system. The dynamic factor model that we employ in our analysis is a special case of FAVARs, in that it only contains unobservable factors. From an applied perspective, the prime advantage of a factor approach is its ability to keep track of individual country-level responses to a common monetary policy shock without heavy parameterisation. Looking at the alternatives, country-by-country VARs incur the cost of heavy parameterisation, while a large panel VAR with all countries imposes restrictions on the individual dynamics. The dynamic factor model solves both problems and provides dynamic effects on the individual countries—including net spillovers—while keeping the parameter space small. In addition, the assumptions on the information structure in the dynamic factor model naturally fit the EA setting. The ECB follows not only a large number of euro-wide series but also series in individual member countries. Hence, an empirical model with a small number of variables that does not include country-level data is unlikely to span the information set used by the ECB.³

While closely following the methodology of Stock and Watson (2012) in constructing our DFM, we identify monetary policy shocks with an external high-frequency instrument. As is well known, estimations of monetary policy transmission suffer from an identification problem. One common way to overcome this problem and identify monetary policy shocks is to impose additional internal structure on the VAR, such as timing or sign restrictions. Alternatively, one can add information from outside of the VAR, termed an external instrument approach. We make use of the latter. As in Gurkaynak et al. (2005) and Gertler and Karadi (2015), we pursue a high-frequency approach, stipulating that asset price movements occurring within a narrow time window around policy announcements are most likely associated with monetary policy shocks.⁴

We construct our external instrument series 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. This instrument has been proven to be economically meaningful, in that it highlights the implications of using various means of policy communication—press releases, press statements, and Q&A sessions—for the transmission of current and expected future policy (see e.g. Altavilla et al., 2019). Our instrument series is a broad measure of monetary policy surprises that incorporates all of the communication channels above.

Relative to the literature, our contribution is to show how to overcome data availability issues by combining intraday data with end-of-day data from different timezones, creating de-facto intraday series where actual intraday data is unavailable.⁵ We test for the relevance of the series in a small VAR, confirming its validity as an external instrument. Based on historical tick data, Jarocinski and Karadi (2018) use the high-frequency co-movement of interest rates and stock prices around a narrow window of the policy announcement to disentangle policy from information shocks. The effects of the monetary shocks we identify in this paper are close to the effects of the policy shocks (as opposed to information shocks) these authors document in their work.

The analysis of the housing channel conducted in our paper is closely related to Calza et al. (2013), who also study how heterogeneity in the structure of housing financing across the euro area can affect the transmission of monetary policy to housing prices, consumption and output. Relative to this work, our paper differs in the empirical methodology and identification, and, most importantly, in that it provides a quantitative assessment using a fully calibrated model. More generally, our work is related to the vast body of policy and academic research that, given the importance of the topic, has been devoted to the heterogeneous transmission of monetary policy across EA member states. Among the leading examples are Ciccarelli et al. (2013), who look at heterogeneity from the perspective of financial fragility, as well as Barigozzi et al. (2014) who, similar to the methodology followed in this paper, rely on a factor model, although identifying shocks with sign restrictions and pursuing a less comprehensive study, both in the number of variable included and the methodological and empirical questions addressed. Recently, Slacalek et al. (2020) develop a back-of-the-envelope calculation, applying a HANK model to the EA to study the effects of monetary policy on household consumption. They conclude that the housing wealth effect is a relevant determinant of the aggregate consumption response to monetary policy and helps explain the cross-country heterogeneity in these responses in the EA.

The rest of the paper is organized as follows. In the next section, we describe the methodology used in the empirical analysis and provide details on the external instrument used for the identification of monetary policy shocks. In Section 3, we present our results, tracing out the effects of monetary policy on the EA as a whole, as well as on individual member countries. Section 4 introduces our analytical model to uncover how institutional differences in housing markets affect monetary transmission across the euro area. Section 5 concludes.

2 A Dynamic Factor Model for the EA

We begin by motivating the use of a dynamic factor model for the EA and laying out the empirical framework. Later in this section, we provide details about the external instrument we construct to identify monetary policy shocks. At the end of the section, we discuss the large data set and estimation.

2.1 Motivation

Given the EA setting, we are fundamentally interested in studying the effects of a common monetary policy shock on the EA as a block and on its member countries.⁶ Recovering both the effects on the block and member countries imposes some empirical challenges and tradeoffs. On the one hand, fully recovering the effects of monetary policy on each individual country comes with heavy parameterisation. On the other hand, reducing the parameter space by imposing restrictions prevents us from studying the full width of heterogeneous effects. In addition, a small data sample in the time dimension, as encountered in the context of the EA, further increases the acuteness and relevance of this trade-off.

We propose a dynamic factor model for the EA as a parsimonious way to avoid heavy parameterisation while keeping track of individual country responses to the common monetary policy shock. The dynamic factor model allows us to capture dynamic effects on individual countries through unobservable common components. The dimensionality reduction achieved through the factor model allows us to get statistically robust dynamic effects on the individual countries while keeping the parameter space small.

The dynamic factor model has another set of appealing features for the EA. Firstly, we can relax the informational assumption that both the ECB and the econometrician perfectly observe all relevant economic variables. Secondly, as the ECB monitors a large number of indicators in the process of policy formulation, including on the country level, it is necessary for the econometrician to take account of the same information set. The DFM achieves this. Finally, the dynamic factor model provides a format that is consistent with economic theory. We next address each of these points.

In using a dynamic factor model, we do not have to take a stand on specific observable measures corresponding to theoretical concepts. This point was convincingly put forward by Bernanke et al. (2005). In the EA context, this relaxation becomes more relevant as it is harder to find observable euro wide variables—often weighted averages of individual member countries—that correspond to concepts of economic theory. For example, the concept of economic activity in the EA may not be perfectly measured by taking a weighted average of real GDP across countries, given compositional changes that cannot be captured by treating the EA as a single economy in a theoretical model.

The European Central Bank follows not only a large number of euro wide series but also a large number of individual member countries’ series. Hence, an empirical model, with a small number of variables, that does not include country data is unlikely to span the information set used by the ECB. This issue naturally motivates the inclusion of country-level series in our analysis.

The state-space representation of the dynamic factor model also provides a clear link with economic theory, which creates the opportunity to formally test different mechanisms aimed at explaining the dynamic effects found in this paper. Moreover, given the large size of the dynamic effects found in observables, it is possible to test interactions of different mechanisms using the same model and dataset.

There are alternatives to the DFM approach chosen by us—notably Panel VAR and Global VAR models. Both of these approaches involve restricting or explicitly modelling the dynamics through which variables in different units affect each other. These restrictions come at the cost of higher parameterisation relative to the dynamic factor model. Given that we are not explicitly interested in these interactions at the cross-sectional level, but rather in the final net effect, we choose the dynamic factor model for efficiency gains. Ciccarelli et al. (2013) provide a further insightful discussion of the differences between these three approaches.

2.2 Empirical Framework

We consequently use the DFM to model macroeconomic interaction. In doing so, we largely follow the methodology proposed by Stock and Watson (2012).

Given a vector of n macroeconomic series X_t = (X_1t,..., X_nt)’ we first model each series as a combination of factors and idiosyncratic disturbances:

\begin{matrix} X_{t} = Λ F_{t} + e_{t}, & (1) \end{matrix}

where F_t is a vector of unobserved factors, Λ is an n x r matrix of factor loadings and e_t = (e_1t,..., e_nt)’ denotes a vector of n disturbances. We can interpret ΛF_t as the ‘common component’ of X_t, whilst e_t is the ‘idiosyncratic component’. The evolution of factors is characterised by the following VAR:

\begin{matrix} F_{t} = Φ_{1} F_{t - 1} + Φ_{2} F_{t - 2} + \dots + Φ_{s} F_{t - s} + η_{t}, & (2) \end{matrix}

which can be rewritten with lag-operator notation as

\begin{matrix} Φ (L) F_{t} = η_{t}, & (3) \end{matrix}

where Φ(L) is a p x r matrix of lag polynomials and η_t a vector of r innovations. This equation characterises all dynamics in the model. As it stems solely from the interaction of factors, there is no need to model the co-movement of observed variables, hence avoiding the curse of dimensionality.

The static factors can be estimated by suitable cross-sectional averaging. Whilst a setup with multiple factors and general factor loadings does not allow for simple cross-sectional averaging to produce a consistent estimate of the factors, the idea can be generalised using principal components analysis. Given large n and T, the principal components approach estimates the space spanned by the factors, even though the factors themselves are not estimated consistently. Put differently, F_t is estimated consistently up to premultiplication by an arbitrary nonsingular r x r matrix. The resulting normalisation problem can be resolved by imposing the restriction that Λ’Λ = I_r. Given that this restriction is chosen arbitrarily, the factors cannot be directly interpreted in an economic sense. For most parts, we will work with the reduced-form DFM, making the normalisation inconsequential.

More generally, principal component analysis provides the factors that explain the most variation in the data, while at the same time avoiding an information overlap between the factors as they are orthogonal to each other⁷.

2.3 Identification

This section turns to the identification of the monetary policy shocks in the DFM. As is well known, estimations of monetary policy suffer from an identification problem, as monetary policy contemporaneously reacts to other variables in the model. To find the part of the variation in monetary policy that is orthogonal to other variables, various approaches have been proposed in the literature. In traditional VAR-type models, researchers have typically imposed some internal structure on the coefficients in the VAR, such as timing restrictions or sign restrictions. More recently, Olea and Watson (2012) as well as others have proposed an additional method, where information from outside the VAR is used to identify monetary policy. In the so-called external instrument approach, an instrument is employed that is correlated with the structural shock that the researcher tries to uncover, while being uncor-related with all other shocks in the system. This corresponds to the standard assumptions of relevance and exogeneity in the instrumental variables literature.

The main concept behind using an external instrument is that when regressing the VAR innovations η_t on the instrument Z_t, the fitted value of the regression identifies the structural shock—up to sign and scale. In fact, as this approach uncovers the covariance between η_t and Z_t, a regression of the instrument on the VAR innovations would equally uncover the structural shock.

Following the VAR literature and the notation in Stock and Watson (2012), we model a linear relationship between the VAR innovations η_t and the structural shocks ε_t:

\begin{matrix} η_{t} = H ε_{t} = [H_{1} \dots H_{r}] (\begin{matrix} ε_{1 t} \\ ⋮ \\ ε_{r t} \end{matrix}), & (4) \end{matrix}

where H is a matrix of coefficients and H₁ is the first column of H. It follows that $Σ_{η η} = H Σ_{ε ε} H^{'}, w i t h Σ_{η η} = E (η_{t} η_{t}^{'}) a n d Σ_{ε ε} = E (ε_{t} ε_{t}^{'})$ . If the system is invertible—a standard assumption in the VAR literature—structural shocks can be expressed as linear combinations of innovations:

\begin{matrix} ε_{t} = H^{- 1} η_{t} . & (5) \end{matrix}

The main interest in the DFM, as in other VAR-type models, lies in uncovering impulse response functions (IRFs) to a specific shock. To find the impulse response function of X_t with respect to the i^th structural shock, we can use equations 3 and 5 to get

\begin{matrix} F_{t} = Φ {(L)}^{- 1} H ε_{t} . & (6) \end{matrix}

Substituting 6 into 1, we find that

\begin{matrix} X_{t} = Λ Φ {(L)}^{- 1} H ε_{t} + e_{t} . & (7) \end{matrix}

where the IRF is ΛΦ(L)^-1H. Λ and Φ(L) are already identified from the reduced form, equation 2, which we can estimate via ordinary least squares. However, this leaves the identification of H_t, which is dealt with in the next section.

As mentioned above, we identify the shock of interest, say ε_1t, using the instrumental variable Z_t. The necessary conditions are:

1. Relevance: E(ε_1tZ_t) = α ≠ 0
2. Exogeneity: E(ε_1tZ_t) = 0, j = 2,..., r
3. Uncorrelated shocks: $Σ_{ε ε} = D = d i a g (σ_{ε_{1}}^{2}, \dots, σ_{ε_{r}}^{2}),$ ,

where D is an r x r matrix. The last condition is the standard structural VAR assumption that structural shocks are uncorrelated. This assumption does not fix the variance of shocks. From equation 4 we get

\begin{matrix} E (η_{t} Z_{t}) = E (H ε_{t} Z_{t}) = (H_{1} \dots H_{r}) (\begin{matrix} E (ε_{1 t} Z_{t}) \\ ⋮ \\ E (ε_{r t} Z_{t}) \end{matrix}) = H_{1} α, & (8) \end{matrix}

where the last identity follows from the relevance and exogeneity conditions. It follows that H₁ is identified up to scale and sign by the covariance between the VAR innovations and the instrument. To identify the shocks themselves, we need the third condition on uncorrelated shocks. It implies that we can rewrite the varianance-covariance matrix of η_t as

\begin{matrix} Σ_{η η} = H Σ_{ε ε} H^{'} = H D H^{'} . & (9) \end{matrix}

Moreover, defining by II the matrix of coefficients from the population regression of Z_t on η_t, the fitted value of this regression is

\begin{matrix} Π_{η_{t}} = E (Z_{t} η_{t}^{'}) Σ_{η η}^{- 1} η_{t}, & (10) \end{matrix}

which, using equation 8 and 9, can be written as

\begin{matrix} E (Z_{t} η_{t}^{'}) Σ_{η η}^{- 1} η_{t} = α H_{1}^{'} {(H D H^{'})}^{- 1} η_{t} . & (11) \end{matrix}

By simplifying and using equation 5, we obtain

\begin{matrix} α H_{1}^{'} {(H D H^{'})}^{- 1} η_{t} = α (H_{1}^{'} {(H^{'})}^{- 1}) D^{- 1} ε_{t} . & (12) \end{matrix}

Finally, we note that H^-1H₁ = e₁, where e₁ = (1,0,...,0)’, which implies that

\begin{matrix} α (H_{1}^{'} {(H^{'})}^{- 1}) D^{- 1} ε_{t} = (α / σ_{\in_{1}}^{2}) ε_{1 t} = Π_{η_{t}} . & (13) \end{matrix}

This conforms with the original statement that the fitted value of a regression of the instrument on the innovations, i.e. Πη_t, identifies the structural shock ε_1t up to a constant. For additional intuition, Stock and Watson (2012) point out that if the structural shocks ε_t were observable and we could hence regress the instrument on the structural shocks, the predicted value would again uncover the shock ε_1t, up to scale, as the coefficients on all other elements of ε_t would be zero. This follows from the relevance and exogeneity conditions of the instrument. Equation 13 shows that the projection of Z_t on η_t provides the exact same result, uncovering ε_t. Note that to estimate the structural shock, we use the sample analogue of the above equation.

2.3.1 Instrument – “Scripta Volant, Verba Manent”⁸

To obtain an instrument that fulfills the necessary requirement of only being correlated with the monetary policy shock, we build a new series of high frequency surprises around ECB policy announcements. The key idea is that by choosing a narrow time window around policy announcements, any surprises occurring within the window are most likely only associated with monetary policy shocks. Put differently, the assumption is that no other major structural shocks occur during the chosen window around the policy announcement. Correspondingly, all endogenous monetary policy, i.e. all expected monetary policy, is assumed to already have been priced in before the window starts. Consequently, endogenous monetary policy would not cause a change in the instrument at the time of the announcement.

For the instrument we choose changes in the 1-year Euro Overnight Index Average (EO-NIA) swap rate. The logic goes that while expectations about future policy rate changes are already priced in, unexpected policy shocks will cause the swap to appreciate or depreciate instantly. If market participants, for example, expect a hike in the policy rate by a certain amount, the announcement of such a hike will not cause the 1-year EONIA swap rate to move. However, should a hike or cut be out of line with expectations, the swap rate will adjust as soon as the announcement is made. Similarly, any policy action that changes expectations about future rate movements—often termed ‘forward guidance’—will have an impact on the swap. Lloyd (2017a) and Lloyd (2017b) demonstrates that 1 to 24-month Overnight Indexed Swap (OIS) rates accurately measure interest rate expectations. As our chosen EONIA swap rate is the corresponding OIS rate for the euro area, this finding is directly applicable to our instrument, allowing us to capture not only current monetary policy, but also expectations about the future path of monetary policy.

When deciding on the tenor of the EONIA swap, two considerations have to be taken into account. Firstly, to capture how a monetary policy shock affects interest rates across the whole yield curve, a longer dated swap is better suited compared to one with a shorter tenor. On the other hand, however, term premia play a larger role at longer horizons, potentially contaminating the information about future short rates. In dealing with this trade-off, we choose the 1-year rate, based on the observation that 1-year rates are highly sensitive to monetary policy, while still remaining relatively unaffected by term premia. That said, we also construct instruments based on 3-month, 6-month and 2-year EONIA swaps and do not find a significant difference in our results.

For their high frequency analysis of US monetary policy, Gertler and Karadi (2015) choose a window of 30 minutes around the policy announcement (starting 10 minutes before the Federal Open Market Committee (FOMC) announcement and ending 20 minutes after). The main policy announcement of the FOMC contains a large amount of information about the decision as well as the view of the committee about the state of the economy and expectations of future policy action. This means that within the 30 minute window, the market can fully integrate recent policy changes and adjust the price of the instrument. The procedure of policy releases is somewhat different at the ECB, as also recently pointed out by contemporaneous work by Jarocinski and Karadi (2018) and Altavilla et al. (2019). The release of the monetary policy decision at 13:45 CET only contains a limited amount of information on the latest policy actions. A significant amount of information is disseminated to the market at a later stage, through the press conference and Q&A with the President, starting at 14:30 CET. For this reason, we decided to extend the window for our analysis to cover not only the prime release, but also the press conference. Specifically, we choose a 6-hour window from 13:00 to 19:00 CET.⁹

Figures 1 and 2 show examples of characteristic movements in the 1-year EONIA swap on ECB meeting days, highlighting the importance of including the Q&A in the high-frequency window if one wants to study the effect of all monetary actions. On 5 June 2008, the Governing Council of the ECB decided that policy rates will remain unchanged. As this was in line with market expectations, the 1-year EONIA swap rate did not move much in reaction to the press release at 13:45 CET. During the press conference however, the president expressed concern about increased risks to price stability, setting expectations of rate hikes in the near future. In reaction to this information, the swap rate immediately jumped higher and over the afternoon increased by 27 basis points. This example clearly demonstrates that information about ECB policy information can to a large degree be contained in the press conference, compared to the policy announcement. An example where both the original announcement, as well as the press conference convey substantial information to market participants is the meeting on 6 October 2011. The press release once again stated that rates would remain unchanged. However, this was not in line with market expectations for a cut and hence created a tightening surprise that led to an immediate increase in the 1-year EONIA swap rate. During the press conference, the then ECB President Jean-Claude Trichet re-emphasised that inflation rates had remained at elevated levels. This in turn pushed market expectations towards tighter monetary policy and caused a further jump in the swap rate. Naturally, there are also examples where the press conference does not convey a significant amount of information to the market, but the above cases highlight the need to include the press release in the high-frequency window.

The above discussion raises the question to which degree the various forms of information dissemination could be used to develop a more differentiated understanding of the nature of policy shocks. On one hand, Jarocinski and Karadi (2018) have suggested a separation of monetary policy instrument shocks from monetary policy communication shocks, sometimes also termed target and path shocks. On the other hand, Altavilla et al. (2019) have separately constructed monetary surprises for the press release and Q&A event window. For the purpose of our paper, we want to use a broad measure of monetary policy shocks that encompasses all forms of surprises related to monetary actions.

As we estimate a quarterly VAR, we have to turn the surprises on ECB meeting days into quarterly average surprises. In practice, we first calculate the cumulative daily surprise over the past quarter (93 days) for each day in our sample. In the next step we take the average of this daily cumulative series over each quarter. In doing so, we incorporate the information that some meetings happen early within a quarter while others happen later. Our averaging procedure makes sure that a surprise happening late in the quarter has less influence on the quarterly average than a surprise at the beginning of the quarter.¹⁰

To get a better understanding of our instrument, we plot its time series in Figure 3. In particular, we want to point out events that led to particularly large positive or negative values in the instrument to develop an intuition regarding the behaviour of the series. Proceeding chronologically, the earliest of the four largest surprises happened in the fourth quarter of 2001, with a value of -0.15. This data point is driven by the aggressive interest rate cut on 17 September 2001, in response to the 9/11 terrorist attacks.¹¹ The ECB cut all three interest rates by 50bp leading to a drop in 1-year EONIA swaps of 20bp during our window. Another particularly large negative shock appears in the fourth quarter of 2008. The value of -0.17 is mostly driven by the monetary policy decision on 2 October 2008. Interest rates were kept unchanged on the day, in line with expectations. However, President Trichet highlighted financial market turmoil and weakness in the EA economy during his statement, leading to a large drop in the swap rate between 14:30 and 15:30 CET as markets priced in future cuts to the policy rate. In the following quarter, Q1 2009, our instrument records a particularly high reading of 0.14. This goes back in large part to a contractionary monetary policy surprise during the meeting of 4 December 2008, but also to a surprise during the meeting of 15 January 2009. Interestingly, during both meetings, which happened at the height of the financial crisis, interest rates were cut—by 75bp and 50bp, respectively. While this led to momentarily lower swap rates on both occasions, rhetoric during the press conference led to further increases in the rate. In fact, on both occasions, the President’s various dovish and hawkish comments led to the rate moving up and down, but the contractionary sentiment dominated overall. Finally, we investigate the events driving our instrument during Q3 2011. The negative value of -0.22—the largest value in absolute terms during our sample period—mainly goes back to the policy decision on 4 August 2011. After an interest rate hike at the previous meeting, policymakers left interest rates unchanged on the day. As this was in line with expectations, the swap rate did not move at 13:45 CET. During the press conference, however, the ECB announced the decision to conduct a liquidity-providing supplementary longer-term refinancing operation (LTRO), based on observed tensions in financial markets within the euro area. This policy action amounted to a large dovish surprise and 1-year EONIA swaps fell by about 18bp between 14:30 and 15:30 CET.

Finally, we test the strength of our instrument. We do so in a small VAR containing only three variables: output, consumer prices and a policy indicator. The model is specified both at monthly and quarterly frequency and is identified using high-frequency instruments based on 3, 6 and 12-month EONIA swaps. We report further details and all results in Online Appendix B, but note here that in our baseline specification the instrument is strong, with a first-stage F-test statistic of 19.45. This confirms the relevance of our external instrument.

2.4 Data and Estimation

Our data set consists of quarterly observations from 1999 Q4 to 2016 Q4 on 90 area-wide measures such as prices, output, investment, employment and housing, as well as 342 individual country time series for the 11 early adopters of the Euro: Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, Portugal and Spain. The vintage of the data is June 2017. Appendix A lists all data series with detailed descriptions and notes on the completeness and length of the individual series.

All data series are transformed to induce stationarity. Depending on the nature of the data, this was done either by taking the first difference in logs or levels. Details on transformations can also be found in Appendix A. As we lose one observation by differencing, our working dataset starts in 2000 Q1.

Principal component analysis is sensitive to double-counting¹² and we consequently only use a subset of our data for factor extraction. In practice, we avoid double-counting along two dimensions. Firstly, we do not include euro-area aggregates for indicators where we have included all individual country series. Secondly, we do not include category aggregates, such as GDP, when we have included its components, such as the components of GDP. Where possible, we avoid using high-level aggregate series altogether and instead include disaggregate series. In total, we use 179 series for factor extraction.

We rely on a number of specific tests and information criteria to determine the number of common factors r. Specifically, we estimate them by means of the test proposed by Onatski (2009), which suggests r ∈ 2,3 (Table 1), the eigenvalue difference method proposed by

^{Table 1:}

Determining the number of common factors: Onatski (2009) test. The Table shows p-values of the null of q₀ common shocks against r₀ < r ≤ r₁ common shocks.

^{Table 1:}

Determining the number of common factors: Onatski (2009) test. The Table shows p-values of the null of q₀ common shocks against r₀ < r ≤ r₁ common shocks.

r₀ VS To < r ≤ r₁	1	2	3	4	5	6	7
0	0.727	0.089	0.122	0.153	0.18	0.209	0.232
1	0	0.05	0.089	0.122	0.153	0.18	0.209
2	0	0	0.521	0.414	0.539	0.632	0.705
3	0	0	0	0.229	0.414	0.539	0.632
4	0	0	0	0	0.794	0.595	0.746
5	0	0	0	0	0	0.336	0.595
6	0	0	0	0	0	0	0.561

^{Table 1:}

Determining the number of common factors: Onatski (2009) test. The Table shows p-values of the null of q₀ common shocks against r₀ < r ≤ r₁ common shocks.

r₀ VS To < r ≤ r₁	1	2	3	4	5	6	7
0	0.727	0.089	0.122	0.153	0.18	0.209	0.232
1	0	0.05	0.089	0.122	0.153	0.18	0.209
2	0	0	0.521	0.414	0.539	0.632	0.705
3	0	0	0	0.229	0.414	0.539	0.632
4	0	0	0	0	0.794	0.595	0.746
5	0	0	0	0	0	0.336	0.595
6	0	0	0	0	0	0	0.561

Onatski (2010) suggesting r = 2, the criterion by Bai and Ng (2002) suggesting r = 5, and the bi-cross-validation method proposed by Owen et al. (2016)¹³ suggesting r = 8. We choose as our baseline specification r = 5, that is, the average of these results. Figure ?? in Online Appendix A shows the variance of the data explained by each additional factor. Five factors account for 80 percent of the total data variance.¹⁴

On the basis of Akaike and Bayes Information Criteria we include one lag for the baseline of the DFM.

To get a better understanding of how well the extracted factors characterise the data, Table 2 shows the variation in the data explained by the five factors. The second column shows the fraction of explained variation for a selection of aggregate area-wide series. The third column shows the corresponding average across series from individual member countries. In particular, two observations stand out. Firstly, the variation in most aggregate series is remarkably well explained by the five factors. With a few exceptions, notably the exchange rate, the R-squared ranges between 70 percent and 99 percent. Secondly, despite the granularity of the individual country series, the factors on average still explain more than half of all variation. In some cases, such as HICP inflation, government spending and, most notably, long-term interest rates, they explain considerably more. Columns 4 and 5 show the same information as column 3, but differentiate between the size of the countries. In particular, we separate the 5 countries in our sample with the largest economies (by nominal GDP) from the 6 countries with the smallest economies. As expected, the factors pick up information from the large economies to a much greater extent than for smaller economies. With the exception of exports, imports and rents, data from larger economies is consistently explained better by the factors. This difference is particularly strong for GDP (70 percent vs. 45 percent) and unemployment (68 percent vs. 36 percent). As concrete examples of the above, Figure ?? in Online Appendix D plots fitted series on the basis of the 5 extracted factors against actual (transformed) series for GDP and HICP in the euro area, Germany and Luxembourg.

^{Table 2:}

R-squared for regression of data series on five principal components. *Germany, France, Italy, Spain, Netherlands. **Belgium, Austria, Ireland, Finland, Portugal, Luxembourg.

^{Table 2:}

R-squared for regression of data series on five principal components. *Germany, France, Italy, Spain, Netherlands. **Belgium, Austria, Ireland, Finland, Portugal, Luxembourg.

	EA aggregate	Average across individual country series	Average across large* countries	Average across small** countries
Gross Domestic Product	0.85	0.56	0.70	0.45
Harmonised Index of Consumer Prices	0.81	0.64	0.71	0.59
Housing Prices	0.71	0.46	0.52	0.40
Exports	0.76	0.54	0.49	0.58
Imports	0.75	0.58	0.45	0.69
Government Spending	0.18	0.68	0.77	0.59
Gross Fixed Capital Formation	0.76	0.33	0.51	0.19
Consumption	0.61	0.30	0.34	0.27
Unemployment	0.72	0.51	0.68	0.36
Long-term Rates	0.99	0.98	0.98	0.98
Rents	0.41	0.35	0.32	0.38
Share Prices	0.65	0.58	0.59	0.57
Producer Prices in Industry	0.87	-	-	-
Wages	0.75	-	-	-
Employment	0.74	-	-	-
GER 2Y yield	0.98	-	-	-
Cost of Borrowing indicator	0.91	-	-	-
EONIA	0.99	-	-	-
Nominal Effective Exchange Rate	0.12	-	-	-

^{Table 2:}

R-squared for regression of data series on five principal components. *Germany, France, Italy, Spain, Netherlands. **Belgium, Austria, Ireland, Finland, Portugal, Luxembourg.

	EA aggregate	Average across individual country series	Average across large* countries	Average across small** countries
Gross Domestic Product	0.85	0.56	0.70	0.45
Harmonised Index of Consumer Prices	0.81	0.64	0.71	0.59
Housing Prices	0.71	0.46	0.52	0.40
Exports	0.76	0.54	0.49	0.58
Imports	0.75	0.58	0.45	0.69
Government Spending	0.18	0.68	0.77	0.59
Gross Fixed Capital Formation	0.76	0.33	0.51	0.19
Consumption	0.61	0.30	0.34	0.27
Unemployment	0.72	0.51	0.68	0.36
Long-term Rates	0.99	0.98	0.98	0.98
Rents	0.41	0.35	0.32	0.38
Share Prices	0.65	0.58	0.59	0.57
Producer Prices in Industry	0.87	-	-	-
Wages	0.75	-	-	-
Employment	0.74	-	-	-
GER 2Y yield	0.98	-	-	-
Cost of Borrowing indicator	0.91	-	-	-
EONIA	0.99	-	-	-
Nominal Effective Exchange Rate	0.12	-	-	-

3 Empirical Results

This section gives an overview of our empirical findings, starting at the aggregate level for the euro area and subsequently exploring results on the country level.

3.1 Euro-wide Dynamic Effects of Monetary Policy

We start our description of the results with an overview of a selection of aggregate series across the euro area. Figure 4 shows percentage responses to a contractionary monetary policy shock of 25 basis points (bp). As discussed in Section 2.3, the external instrument approach identifies the shock only up to sign and scale. Using the response of EONIA as a policy indicator, we scale the system to a 25bp contraction in EONIA. The shaded area around the point estimates signify confidence intervals of one standard deviation, obtained from a wild bootstrapping procedure with a simple (Rademacher) distribution. Given a strong instrument, the confidence intervals obtained under this approach are valid despite the presence of heterogeneity. Because both stages of the regression are incorporated in the bootstrapping procedure, the error from the external instrument regression is accounted for. A similar approach has been followed by Mertens and Ravn (2013) and Gertler and Karadi (2015).

Notably, our results do not suffer from the prize puzzle—the occurrence of rising prices in reaction to a contractionary monetary policy shock. In fact, while the harmonised index of consumer prices (HICP) does not have any significant reaction, our producer prices fall significantly, in line with economic theory. Given the longstanding struggle of VAR-type models to get rid of the price puzzle, we interpret these findings as an indication of the ability of the model to accurately characterise economic dynamics. In particular, we attribute the non-existence of the price puzzle to the combination of correctly capturing information about prices in the economy (via the DFM) and precisely identifying monetary policy shocks (via the high frequency instrument).¹⁵ The remainder of the series in Figure 4 also behave as suggested by theory. GDP contracts overall, as do all components with the exception of Government Spending, which moves in the opposite direction of the monetary shock. In line with theory, investment (GFCF) is a lot more volatile than consumption, as are imports and exports. The reaction of the German 2-year sovereign yield closely follows EONIA. The aggregate indicator for mortgage interest rates in the euro area as compiled by the ECB also rises in reaction to a shock, but displays imperfect pass-through as a significant number of mortgages are characterised by fixed rates that do not adapt to changes in policy. In the labour market, unemployment rises, while wages fall. Interestingly, the reaction in wages is not significant, hinting at a large degree of nominal wage stickiness. In the housing market, housing prices fall significantly after a contraction, following economic theory that higher policy rates make mortgages more expensive and consequently suppress demand for houses. Rents, on the other hand, increase in reaction to a shock. Recent research (see e.g. Dias and Duarte (2019)) suggests that a worsening of conditions in the mortgage market leads agents to substitute house purchase with renting, thus exerting pressure on rental prices. The euro exchange rate appreciate, although only with a delay.

3.2 Cross-Country Dynamic Effects of Monetary Policy

Moving on to results at the country level, we start to uncover the full potential of the DFM when it comes to providing results for a large number of series. Of the 342 individual country series in our data set, we have selected a representative sub-sample for Figures 5–7. In particular, this section takes a closer look at the responses of GDP, the components of GDP, interest rates, equities, housing prices and unemployment. We point out, however, that the model produces impulse response functions for all series in our sample.¹⁶

Figure 5 shows the responses of real GDP and HICP across the 11 euro-area countries in our sample. While we omitted error bands for ease of presentation, it is noteworthy that reactions of real GDP and HICP across countries appear to be quite heterogeneous.¹⁷ In terms of HICP, the responses are positive for half of the countries while they are negative for the other half. In addition, the mean HICP response is negative and very low, which makes the relative distance of responses quite large when compared to that of real GDP. Turning to real GDP, at one end of the spectrum, the reaction of Irish GDP clearly differs from the five countries with the weakest reaction. That said, even the reactions of Finland and Luxembourg are statistically different from France and Spain, having non-overlapping confidence intervals from the 10th step onward. This heterogeneity is in itself noteworthy, but also raises the question which parts of the economy are particularly prone to asymmetric reactions.

For a first pass at this question, Figure 6 contains the reactions of the components of GDP. The IRFs highlights two main observations. Firstly, the responses of national private consumption and gross fixed capital formation, have the same sign and follow similar patterns. In contrast, the responses of national government spending and net exports do not have the same sign. In part, these differences in the general nature of responses can be explained by the determinants of the individual series. Government spending, for example, is notoriously idiosyncratic, depending on the degrees of pro- and counter-cyclicality of fiscal policy that tend to vary both across countries and over time.

Secondly, whether or not the responses move in the same direction, there is a visible degree of heterogeneity. In particular, consider the disparity in the reaction of private consumption. While the drop in private consumption reaches a maximum at about 0.02 percentage points in Germany, the drop in Ireland is more than 20 times as large, at 0.4 percentage points. Aside from Ireland, which could be considered an outlier, the drop in consumption in Italy, Finland, Spain and Portugal is roughly 10 times the size of the drop in Germany.

In some notable cases, we find that the degree of heterogeneity in the impulse responses may reflect (inversely) the state of convergence in particular markets across the euro area. In particular, financial markets have experience a relatively stronger convergence than other markets.¹⁸ This can be seen in the reaction of interest rates and stock prices across countries. Figure 7 shows that, while the response of long-term interest rates to a policy shock is not uniform across countries on impact, it converges and become almost identical over time. By the same token, while the responses of national equity indices, displayed in the same figure, does not converge across equity markets, the confidence intervals around the IRF are mostly overlapping.

Among the markets with records of little or no convergence in institutional characteristics are the labour and housing markets. In Figure 8, we show that, after one year (4 steps) the shocks, housing prices fall and unemployment rises at quite different rates across border. ¹⁹ To gain a firmer insight on the degree of heterogeneity in the impulse responses across countries, in what follows we propose and implement a more rigorous approach to testing. For each set of responses, we calculate the coefficient of variation, i.e. the standard deviation of responses (among countries) with respect to the EA response of the same variable. To make this measure comparable across different series, we normalise it by the size of the EA response. By doing so, we create a numerical measure for the dispersion of impulse responses that allows for intuitive and meaningful comparison between series. Table 3 reports the coefficients of variation for a selection of variables, evaluated on impact, as well as at the 8th and the 20th step. The table also reports a lower and a upper bound for the coefficients of variation, which we obtain from our bootstrapping procedure. The table shows that long-term interest rates and stock prices have a much smaller coefficient of variation than the other variables, in line with our discussion above suggesting a lower degree of heterogeneity for financial than for real variables. Remarkably, however, the table also shows that at the 20th step, GDP is also less heterogeneous than other real variables, namely private consumption and unemployment.

^{Table 3:}

Coefficient of variation of the cross-country responses to a 25bp monetary policy shock.

^{Table 3:}

Coefficient of variation of the cross-country responses to a 25bp monetary policy shock.

Variable		Coefficient of Variation	Lower Bound	Upper Bound
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

^{Table 3:}

Coefficient of variation of the cross-country responses to a 25bp monetary policy shock.

Variable		Coefficient of Variation	Lower Bound	Upper Bound
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

As some of the intervals around coefficients of variation are overlapping, we also bootstrap pair-wise differences in the coefficient of variation. The results, presented in Table 4, mostly confirm earlier observations. Reactions of long-term interest rates (LTINT) and stock prices (SP) are significantly less dispersed than all other variables. Moreover, at the 20th step, GDP has a significantly lower coefficient of variation than private consumption (PCON), unemployment (U), and real housing prices (RHPI).

^{Table 4:}

Bootstrapped pair-wise differences in the coefficient of variation of the cross-country responses to a 25bp monetary policy shock. * marks differences in variation that are significant at the 68 percent confidence level. The inference is drawn from a bootstrap procedure.

^{Table 4:}

	GDP	HICP	LTINT	SP	PCON	U	RHPI
On Impact
GDP	0	-0.99	1.20*	1.06*	0.16	-5.42*	-0.84
HICP	1.10	0	3.02*	2.85*	1.69	-3.81	0.66
LTINT	-1.19*	-3.02*	0	-0.13	-0.90*	-6.66*	-1.79*
SP	-1.04*	-2.85*	0.13	0	-0.84*	-6.84*	-1.60*
PCON	-0.16	-1.69	0.90*	0.84*	0	-5.20*	-0.75
U	5.32*	3.81	6.66*	6.84*	5.20*	0	5.02
RHPI	0.87	-0.66	1.79*	1.60*	0.75	-5.02	0
At the 8th Step
GDP	0	-0.86	-0.23	0.54*	-0.30	-0.73*	-0.44
HICP	0.86	0	3.02*	2.85*	1.69	-3.81	0.66
LTINT	0.23	-0.60	0	-0.13	-0.90*	-6.66*	-1.79*
SP	-0.54*	-1.45*	-0.74*	0	-0.84*	-6.84*	-1.60*
PCON	0.30	-0.59	0.10	0.80*	0	-5.20*	-0.75
U	0.73*	-0.08	0.65	1.38*	0.51*	0	5.02
RHPI	0.44	-0.16	0.49	1.03*	0.18	-0.19	0
At the 20th Step
GDP	0	-0.55	0.21	0.45*	-0.39*	-0.59*	-0.43*
HICP	0.55	0	0.64	1.02*	0.19	-0.18	-0.16
LTINT	-0.21	-0.64	0	0.24	-0.60	-0.99*	-0.62
SP	-0.45*	-1.02*	-0.24	0	-0.80*	-1.04*	-0.85*
PCON	0.39*	-0.19	0.60	0.80*	0	-0.20	0.00
U	0.59*	0.18	0.99	1.04*	0.20	0	0.20
RHPI	0.43*	0.16	0.62	0.85*	0.00	-0.20	0

^{Table 4:}

	GDP	HICP	LTINT	SP	PCON	U	RHPI
On Impact
GDP	0	-0.99	1.20*	1.06*	0.16	-5.42*	-0.84
HICP	1.10	0	3.02*	2.85*	1.69	-3.81	0.66
LTINT	-1.19*	-3.02*	0	-0.13	-0.90*	-6.66*	-1.79*
SP	-1.04*	-2.85*	0.13	0	-0.84*	-6.84*	-1.60*
PCON	-0.16	-1.69	0.90*	0.84*	0	-5.20*	-0.75
U	5.32*	3.81	6.66*	6.84*	5.20*	0	5.02
RHPI	0.87	-0.66	1.79*	1.60*	0.75	-5.02	0
At the 8th Step
GDP	0	-0.86	-0.23	0.54*	-0.30	-0.73*	-0.44
HICP	0.86	0	3.02*	2.85*	1.69	-3.81	0.66
LTINT	0.23	-0.60	0	-0.13	-0.90*	-6.66*	-1.79*
SP	-0.54*	-1.45*	-0.74*	0	-0.84*	-6.84*	-1.60*
PCON	0.30	-0.59	0.10	0.80*	0	-5.20*	-0.75
U	0.73*	-0.08	0.65	1.38*	0.51*	0	5.02
RHPI	0.44	-0.16	0.49	1.03*	0.18	-0.19	0
At the 20th Step
GDP	0	-0.55	0.21	0.45*	-0.39*	-0.59*	-0.43*
HICP	0.55	0	0.64	1.02*	0.19	-0.18	-0.16
LTINT	-0.21	-0.64	0	0.24	-0.60	-0.99*	-0.62
SP	-0.45*	-1.02*	-0.24	0	-0.80*	-1.04*	-0.85*
PCON	0.39*	-0.19	0.60	0.80*	0	-0.20	0.00
U	0.59*	0.18	0.99	1.04*	0.20	0	0.20
RHPI	0.43*	0.16	0.62	0.85*	0.00	-0.20	0

Summing up. Our empirical evidence suggests that, in line with our conjecture, heterogeneity in the responses to monetary shocks is lower in financial variables, such as interest rates and stock prices, reflecting a relatively high degree of integration, relative to variables related to much less integrated markets, such as the labour and housing markets. We also show that the heterogeneity in the response larger in consumption and consumer prices, than is in the response of output output. Our evidence, showing that in some cases the response can even have a different sign, has straightforward implications for policy. Further institutional convergence can be expected to enhanced cohesion in the euro area, by reducing unintended responses to common monetary stimulus or contraction across countries. That said, a much deeper understanding of the mechanisms at play is necessary to motivate and structure consistent convergence policies.

4 Quantifying How Mortgage Markets Shape Monetary Transmission

A growing body of literature has recently reconsidered a “housing channel” in the transmission of monetary policy (Iacoviello (2005), Calza et al. (2013), Greenwald (2018), Wong (2019), Beraja et al. (2019), Cloyne et al. (2019) and Slacalek et al. (2020)). The importance of this channel is commonly motivated by noting that, for most households, their home is the single most important item on the asset side of their balance sheet, and their mortgage is the household’s largest liability. In this section, we build an small open economy model featuring a housing sector, and use it to investigate the housing channel of monetary policy in a currency union in some detail. Specifically, we will make use of the European institutional setting to explore variation in the housing channel across EA countries, reflecting different characteristics of housing financing across member countries.

Many institutional characteristics of national housing markets differ substantially across EA members. Mortgage markets display marked variation in the relative share of fixed versus flexible rate contracts and typical loan-to-value ratios; rental markets are subject to different regimes and controls; taxation is very heterogeneous, to name but a few aspects—see Osborne (2005), Andrews et al. (2011) and Westig and Bertalot (2016) for a comprehensive overview. The importance of these differences for monetary policy transmission in Europe has not gone unnoticed, and previous literature, most notably Calza et al. (2013), has produced empirical and qualitative assessments. However, to our knowledge, there is no quantitative assessment using a fully calibrated model.

In what follows, we study quantitatively how much of the variation in individual EA country responses to a monetary policy shock can be explained by differences in mortgage market characteristics. First, we describe the model, focusing on a set of institutional parameters that affect housing financing, namely the loan-to-value ratio and the share of adjustable-rate mortgage contracts. Our analysis merges the main elements of Calza et al. (2013) into a small open economy modeled after De Paoli (2009). Doing so allows us to quantitatively assess the importance of differences in institutional characteristics of mortgage markets in the transmission of monetary policy. Second, we calibrate the model to the Spanish economy in order to get empirically plausible long-term moments and impulse response functions to monetary policy shocks. Finally, we feed the model with the loan-to-value ratios and shares of adjustable-rate mortgage contracts observed in the data for each country, and compare the dispersion from these simulated IRFs with the dispersion we estimated using the DFM in the previous section.

4.1 Model

The economy features three types of agents — savers, fixed-rate borrowers, and variable-rate borrowers, as proposed by Rubio (2011) — and a collateral constraint in line with Campbell and Hercowitz (2005), Iacoviello (2005), Iacoviello and Neri (2010), and Liu et al. (2010). Savers are standard Ricardian agents who own all firms in the consumption and housing sectors as well as financial intermediaries, while borrowers are credit constrained in equilibrium and behave as hand-to-mouth consumers. As customary in the literature, we assume that the domestic economy is so small relative to the rest of the EA that domestic economic dynamics are irrelevant for equilibrium outcomes in the rest of the EA (see e.g. De Paoli (2009)).

4.1.1 Patient Households

There is a continuum of measure 1 of patient agents. Their economic size is measured by their wage share, which is assumed to be constant reflecting a Cobb-Douglas production function with unit elasticity of substitution. A representative patient household maximizes:

\begin{matrix} E_{0} \sum_{t = 0}^{\infty} β^{t} (1 o g (c_{t} - ζ c_{t - 1}) + j \log h_{t} - \frac{{(n_{c, t}^{1 + θ} + n_{h, t}^{1 + θ})}^{\frac{1 + ψ}{1 + θ}}}{1 + ψ}), & (14) \end{matrix}

where β is the discount factor, c_t is consumption of goods other than housing, j is a housing preference over consumption parameter, ζ captures consumption habit formation, θ indicates the elasticity of substitution between working in the consumption or housing sectors, and ψ is the inverse Frisch elasticity of labor supply. n_c,t and n_h,t denote hours worked in the consumption and housing sectors, respectively, and h_t denotes the consumption of housing services. The consumption of goods c_t is a bundle of home and foreign goods with the following form:

\begin{matrix} c_{t} = \frac{c_{H, t}^{1 - {(1 - n)}_{ν}} c_{F, t}^{(1 - n) ν}}{{(1 - {(1 - n)}_{ν})}^{(1 - {(1 - n)}_{ν})} {((1 - n) ν)}^{(1 - n) ν}} & (15) \end{matrix}

Here v ∈ [0,1] measures the home bias in consumption²⁰. Here, the bundles of Home- and Foreign-produced goods are defined as follows:

\begin{matrix} c_{H, t} = {[{(\frac{1}{n})}^{\frac{1}{ε}} \int_{0}^{n} c_{H, t} (j) \frac{ε - 1}{ε} d_{j}]}^{^{\frac{ε}{ε - 1}}}, c_{F, t} = {[{(\frac{1}{1 - n})}^{\frac{1}{ε}} \int_{n}^{1} c_{F, t} {(j)}^{\frac{ε - 1}{ε}} d j]}^{\frac{ε}{ε - 1}}, & (16) \end{matrix}

where c_H,t(j) and C_F,t(j) denote differentiated intermediate goods produced in Home and Foreign, respectively, and ε > 1 measures the elasticity of substitution between intermediate goods produced within the same country.

Patient households own all firms in this economy, accumulate houses and make loans to impatient households. Patient households maximize their utility subject to:

\begin{matrix} c_{t} + q_{t} h_{t} + Q_{t, t + 1} D_{t + 1} - b_{t} = D_{t} + \frac{W_{c, t}}{P_{t}} n_{c, t} + \frac{W_{h, t}}{P_{t}} n_{h, t} - \frac{R_{t - 1} b_{t - 1}}{π_{t}} + q_{t} (1 - δ_{h}) h_{t - 1} + T_{t} & (17) \end{matrix}

where q_t is the house price, W_c>t is the nominal wage in the consumption sector, W_h,t is the nominal wage in the housing sector, R_t is the gross nominal interest rate, δ_h is the housing depreciation rate, π_t is the inflation rate, P_t is the domestic price level index, T_t is total firm profits and Q_t,t+1 is the stochastic discount factor for one-period ahead nominal pay-offs relevant to the domestic household. We assume that patient households have access to a complete set of contingent claims, traded internationally.

4.1.2 Impatient Households

There is a measure 1 of impatient households, a share ω of which have mortgage contracts with variable interest rates, denoted by subscript v, while the remaining 1 — ω possess a fixed-rate mortgage contract, denoted by subscript f. Similarly to patient households, they maximize

\begin{matrix} E_{0} \sum_{t = 0}^{\infty} β^{' t} (1 o g (c_{i, t}^{'} - ζ^{'} c_{i, t - 1}^{'}) + j \log h_{i, t}^{'} - \frac{{(n_{c i, t}^{1 + θ^{'}} + n_{h i, t}^{1 + θ^{'}})}^{\frac{1 + ψ^{'}}{1 + θ^{f}}}}{1 + ψ'}), f o r i = {υ, f}, & (18) \end{matrix}

where β’ < β, which makes these households impatient. Differently from patient households, they do not own firms nor can they trade contingent claims internationally, and are subject to the following budget and collateral constraints:

\begin{matrix} c_{i, t}^{'} + q_{t} h_{i, t}^{'} - b_{i, t}^{'} = \frac{W_{c, t}^{'}}{P_{t}} n_{c i, t}^{'} + \frac{W_{h i, t}^{'}}{P_{t}} n_{h i, t}^{'} - \frac{R_{i, t - 1} b_{i, t - 1}}{π_{t}} + q_{t} (1 - δ_{h}) h_{i, t - 1}, f o r i = {υ, f}, & (19) \end{matrix}

\begin{matrix} b_{i, t}^{'} \leq m E_{t} (q_{t + 1} h_{i, t} \frac{π_{t + 1}}{R_{i, t}}) & (20) \end{matrix}

where m is the loan-to-value ratio. In the steady state without uncertainty this last constraint will bind since β’ < β. Impatient households with fixed-rate mortgages face $R_{f, t} = {\bar{R}}_{t}$ , while those with variable-rate mortgages face R_v,t = R_t.

The two key institutional characteristics relevant to housing financing are thus encapsulated in the two parameters ω and m. The first is the share of households that finance their housing purchase with adjustable-rate mortgages, the second is the loan-to-value ratio.

4.1.3 Relationship among inflation, terms of trade and exchange rate

When maximizing utility, households take prices as given. Let P_t(j) denote the price that the producer of good j charges in the Home country, denoted in Home currency. Let P_t(j) denote the price that the producer charges for the same good in the Foreign country, expressed in Foreign currency. The consumer price indices in Home and Foreign are given by

\begin{matrix} P_{t} = P_{H, t}^{(1 - (1 - n) ν)} P_{F, t}^{(1 - n) ν} & (21) \end{matrix}

\begin{matrix} P_{t}^{*} = P_{F, t}^{* (1 - (1 - n) ν)} P_{H, t}^{* (1 - n) ν} & (22) \end{matrix}

where $P_{H, 1} (P_{H, t}^{*})$ is the price sub-index for Home-produced goods expressed in domestic (foreign) currency and $P_{F, t} (P_{F, t}^{*})$ the price sub-index for Foreign-produced goods expressed in the domestic (foreign) currency.

\begin{matrix} P_{H, t} = [(\frac{1}{n}) \int_{0}^{n} P_{t} {(j)}^{1 - ε} d j]^{\frac{1}{1 - ε}}, P_{F, t} = [(\frac{1}{1 - n}) \int_{0}^{n} P_{t} {(j)}^{1 - ε} d j]^{\frac{1}{1 - ε}} & (23) \end{matrix}

\begin{matrix} P_{H, t}^{*} = [(\frac{1}{n}) \int_{0}^{n} P_{t}^{*} {(j)}^{1 - ε} d j]^{\frac{1}{1 - ε}}, P_{F, t}^{*} = [(\frac{1}{1 - n}) \int_{0}^{n} P_{t}^{*} {(j)}^{1 - ε} d j]^{\frac{1}{1 - ε}} & (24) \end{matrix}

Moreover, we assume that the law of one price holds for intermediate goods, so that

\begin{matrix} P_{t} (j) = ξ_{t} P_{t}^{*} (j) & (25) \end{matrix}

ξ_t is the nominal exchange rate measured as the price of Foreign currency in terms of Home currency. A rise in ξ_t, thus, marks a nominal depreciation from Home’s perspective.

Therefore, equations (21), (22) together with condition (25), imply that $P_{H, t} = ξ_{t} P_{H, t}^{*} a n d P_{F, t} = ξ_{t} P_{F, t}^{*}$ . However, as equations (23) and (24) illustrate, the home bias specification leads to deviations from purchasing power parity, that is, $P_{t} \neq ξ_{t} P_{t}^{*}$ . For this reason, we denote the real exchange rate by $R S_{t} = \frac{ξ_{t} P_{t}^{*}}{P_{t}}$ .

Assuming that n → 0, and using the preferences of consumers, we can derive total demand for a generic good j, produced in country H:

\begin{matrix} Y_{t}^{d} (j) = {(\frac{P_{t} (j)}{P_{H, t}})}^{- ε} {(\frac{P_{H, t}}{P_{t}})}^{- 1} [(1 - ν) C_{t} + ν R S_{t} C_{t}^{*}] & (26) \end{matrix}

4.1.4 Firms

Consumption Sector. Producers of intermediate consumption goods operate under monopolistic competition and face the demand function (26). The production function is given by:

\begin{matrix} Y_{t} (j) = n_{c, t} {(j)}^{α} n_{c, t} {(j)}^{' 1 - α}, & (27) \end{matrix}

where n_c,y(j) and n_c,y(j)’ denote labor services from patient and impatient households, respectively, employed by firm j ∈ [0,n] in period t. We assume that prices are set in the currency of the producer and that price setting is constrained exogenously a la Calvo, such that in each period only a fraction of intermediate good producers (1 — (φ) may adjust their price. When firm j has the opportunity, it sets ${\bar{P}}_{t} (j)$ to maximize the expected discounted value of net profits:

\begin{matrix} \max_{{\bar{P}}_{H, t} (j)} E_{t} {Σ_{s = 0}^{\infty} {(ϕ β)}^{s} Λ_{t, t + s} (Y_{t + s} (j) ({\bar{P}}_{H, t} (j) - M C_{t + s}^{n}))} & (28) \end{matrix}

subject to the sequence of demand constraints

\begin{matrix} Y_{t + s} (j) \leq Y_{t + s}^{d}, & (29) \end{matrix}

where Λ_t,t+s is the stochastic discount factor and ${M C}_{t + s}^{n}$ denotes the nominal marginal cost.

Housing Sector. We rule out nominal rigidities in the housing market. On the one hand, housing is relatively expensive on a per-unit basis, implying large incentives to negotiate on the price. On the other hand, most homes are priced for the first time only when they are sold.

In the housing sector there is a representative firm that produces residential investment according to the following technology:

\begin{matrix} I H_{t} = n_{h, t} α {n_{h, t}^{'}}^{1 - α} & (30) \end{matrix}

Hence, assuming perfect competition, this firm takes the price of housing as fixed and optimally chooses labor input in order to maximize profits.

\begin{matrix} \max_{n_{h, t}, n_{h, t}^{'}} q_{t} I H_{t} - W_{h, t} n_{h, t} - W_{h, t}^{'} / n_{h, t}^{'} . & (31) \end{matrix}

Financial Intermediaries. There is a financial intermediary that accepts deposits from savers and extends both fixed- and variable-rate loans to borrowers. We assume a competitive framework under which the intermediary takes variable interest rates as given. The profits of the financial intermediary are defined as

\begin{matrix} F_{t} = ω R_{t - 1} b_{υ, t - 1}^{1} + (1 - ω) {\bar{R}}_{t - 1} b_{f, t - 1}^{'}, & (32) \end{matrix}

In equilibrium, aggregate borrowing and saving must be equal, that is:

\begin{matrix} ω b_{υ, t}^{'} + (1 - ω) b_{f, t}^{'} = b_{t}^{'} . & (33) \end{matrix}

Substituting (33) into (32), one obtains,

\begin{matrix} F_{t} = (1 - ω) b_{f, 1 - 1}^{'} (R_{t - 1} - {\bar{R}}_{t - 1}) . & (34) \end{matrix}

In order for the two types of mortgages to be offered in equilibrium, the fixed interest rate has to be such that the intermediary is indifferent between lending at a variable or fixed rate. Hence, the expected discounted profits from issuing new debt in a given period at a fixed interest rate must be equal to those from issuing at a variable rate. Also, since the financial intermediaries are owned by the savers, their stochastic discount factor is applied in computing the optimal equilibrium value of the fixed rate in period t, given by:

\begin{matrix} {\bar{R}}_{t}^{o p t} = \frac{E_{t} \sum_{τ = t + 1}^{\infty} β^{τ - (t + 1)} Λ_{t + 1, τ} R_{τ - 1}}{E_{t} \sum_{τ = t + 1}^{\infty} β^{τ - (t + 1)} Λ_{t + 1, τ}} & (35) \end{matrix}

Hence, new debt issued at date t is associated with a different fixed interest rate set by equation (35). However, this implies that the aggregate return on the whole stock of debt is a function of new debt as well as rates set on past debt. Therefore the aggregate fixed interest rate that a financial intermediary charges at date t is an average of what was charged last period for the previous stock of mortgages and what is charged for new debt:

\begin{matrix} {\bar{R}}_{t} = {\begin{cases} \frac{{\bar{R}}_{t - 1} + b_{f, t - 1}^{'} + {\bar{R}}_{t}^{o p t} (b_{f, t}^{'} - b_{f, t - 1}^{'})}{b_{f, t}^{'}}, i f b_{f, t}^{'} > b_{f, t - 1}^{'} \\ {\bar{R}}_{t - 1}, i f b_{f, t}^{'} \leq b_{f, t - 1}^{'}, \end{cases} & (36) \end{matrix}

4.1.5 Monetary Policy

Since the Home economy belongs to a currency union, its monetary policy adjusts interest rates so as to make sure that the nominal exchange rate is unchaged for all periods:

\begin{matrix} Δ ξ_{t} = 0. & (37) \end{matrix}

In doing so, the Home country gives up monetary autonomy. Given a fixed nominal exchange rate and uncovered interest parity, Homes interest rate in equilibrium follows the Foreign rate one-to-one. Finally, the monetary authority for the currency union adjusts interest rates according to the following Taylor rule:

\begin{matrix} R_{t}^{*} / R_{s s}^{*} = {(R_{t - 1}^{*} / R_{s s}^{*})}^{γ R^{*}} π_{t}^{* γ π (1 - γ_{R} *)} {(Y_{t}^{*} / Y_{t - 1}^{*})}^{χ Y * (1 - γ R *)} \exp (ε R^{*}) . & (38) \end{matrix}

4.1.6 Aggregation and Market Clearing

Total borrowers’ consumption, labor supply in the consumption and housing sectors, and housing are given by:

\begin{matrix} c_{t}^{'} = ω c_{υ, t}^{'} + (1 - ω) c_{f, t}^{'} & (39) \end{matrix}

\begin{matrix} n_{c, t}^{'} = ω n_{c v, t}^{'} + (1 - ω) n_{c f, t}^{'} & (40) \end{matrix}

\begin{matrix} n_{h, t}^{'} = ω n_{h v, t}^{'} + (1 - ω) n_{h f, t}^{'} & (41) \end{matrix}

\begin{matrix} n_{t}^{'} = ω h_{v, t}^{'} + (1 - ω) h_{f, t}^{'} & (42) \end{matrix}

The aggregate consumption is given by:

\begin{matrix} C_{t} = c_{t} + c_{t}^{'}; & (43) \end{matrix}

and housing and goods market clear:

\begin{matrix} H_{t} = h_{t} + h_{t}^{'}, & (44) \end{matrix}

\begin{matrix} I H_{t} = H_{t} - (1 - δ_{h}) H_{t - 1} . & (45) \end{matrix}

Finally, we define the real GDP measure defined in terms of home consumption goods for our economy:

\begin{matrix} Y_{t} = {(\frac{P_{h, t}}{P_{t}})}^{- 1} [(1 - ν) C_{t} + ν R S_{t} C_{t}^{*}] & (46) \end{matrix}

\begin{matrix} G D P_{t} = Y_{t} \frac{P_{h, t}}{P_{t}} + q_{t} I H_{t} & (47) \end{matrix}

4.1.7 Equilibrium

In our model, the EA block can be treated as exogenous to the Home economy. The EA block is a standard New Keynesian economy with price stickiness. We dispense with a full description as the definition of equilibrium in this economy is standard.²¹ Since there is no growth in this model, all variables are stationary. The model is solved with a second order perturbation method around the deterministic steady state.

4.2 Calibration

We calibrate the model to the Spanish economy. We pick parameters to reflect quarterly data and to match well both the relevant long-term moments of the Spanish economy as well as short-term dynamics of the transmission of monetary policy shocks to the Spanish and EA economies. We have 24 parameters in our model, out of which 18 are calibrated and the remaining 6 are estimated. Table 5 summarises our calibration. We set β* = β = 0.9925, implying a steady-state annual real interest rate of 3 percent both for Spain and the EA. The elasticity of substitution in intermediate goods consumption in both regions, ε* and ε, is set at 7.66 in order to get a steady-state markup of 15 percent, as in Iacoviello and Neri (2010). The EA Taylor rule parameters regarding inflation and the output gap, γπ and γ_y, are set according to Christoffel et al. (2008). For the lagged nominal interest rate parameter γ_r we choose a slightly lower value — 0.6 instead of 0.8 — because we want to match the EA HICP and GDP reactions to monetary policy shocks with the ones estimated in the DFM.

^{Table 5:}

Calibrated parameters.

^{Table 5:}

Calibrated parameters.

Parameter	Value	Target
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)

^{Table 5:}

Calibrated parameters.

Parameter	Value	Target
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)

Following Iacoviello (2005) we fix the discount of the impatient households β’ at 0.97 to ensure that a steady-state with binding borrowing constraint is accurate. We fix ψ* = ψ = ψ’ to match a Frisch labor supply elasticity of 2 for the EA as in Smets and Wouters (2003), as well as for both savers and borrowers in Spain, in line with Burriel et al. (2010). Next, we pick the housing preference parameter j, which essentially governs the steady-state housing wealth-to-GDP ratio, to be at 0.2. This value twice the size of the parameter used in Iacoviello (2005) and Iacoviello and Neri (2010), as the ratio of housing wealth to GDP is much higher in Spain than in the US. According to Martínez-Toledano (2017), the housing wealth-to-GDP ratio for the time period we study was at approximately 3.5 in Spain. The quarterly housing depreciation rate δh is set at 0.005 which is consistent with an empirically reasonable 2 percent annual depreciation rate and with a steady-state residential investment share of GDP in Spain of approximately 7 percent. The institutional parameters on housing financing are taken from previous studies. The typical loan-to-value ratio in Spain reported in Calza et al. (2013) is 70 percent, while the average share of adjustable-rate mortgages is around 90 percent according to bank-level data reported in Albertazzi et al. (2018). The share of firms that do not reset prices each period φ is set at 0.78 in order to match the average price duration of 4.6 quarters in Spain as reported in Alvarez et al. (2006). Finally, the share of borrowing constrained agents α is set at 0.68 in order to match the share of housing stock in the hands of agents that face liquidity constraints to a level of 18 percent as reported in Slacalek et al. (2020).

Since we only include one shock in the economy, the remaining 6 parameters are estimated using a limited information approach. First, we pick the model variables that are of interest in relation with the observed heterogeneity found in the empirical section. Second, we select the following variables for the small open economy: GDP, aggregate consumption, inflation and housing prices. For the EA we pick GDP, nominal interest rates and inflation. Third, we estimate these parameters by minimizing a measure of the distance between the DFM’s empirical impulse responses and the model responses. Let Γ = (ξ*, φ*,ξ,ξ’,δ,ν) be a vector with the remaining 6 parameters, and let Ψ(Γ) denote the mapping from the deep parameters Γ to the model impulse response functions. Further, let $\hat{Ψ}$ denote the corresponding empirical DFM estimates. We include the first 20 elements of each response function. Our estimator of Γ is the solution to

\begin{matrix} J = \min_{Γ} [\hat{Ψ} - Ψ (Γ)]' V^{- 1} [\hat{Ψ} - Ψ (Γ)], & (48) \end{matrix}

where V is a weighting matrix. We choose V to be the inverse of the matrix with the sample variances of the DFM’s impulse responses on the main diagonal. Table 6 summarizes our point estimates and standard errors of the parameters in vector Γ. The point estimates we get are in line with the previous literature and are precisely estimated.²² The point estimate for the habit formation parameter in the EA ξ* is 0.78 which is reasonably close to the 0.69 estimated in Adolfson et al. (2007). The point estimate for the Calvo price parameter in the EA φ* is 0.88, in line with both Smets and Wouters (2003) and Adolfson et al. (2007). The point estimates for the parameter on habit formation in consumption for savers and borrowers, ξ and ξ’, are 0.84 and 0.8, respectively. These are consistent with the value of 0.847 reported in Burriel et al. (2010). The point estimate for the parameter on labor mobility between sectors of savers δ is 0.66, which surprisingly is identical to the estimate reported in Iacoviello and Neri (2010). Finally, we get a slightly lower home bias estimate 1 – ν of 0.73 than the 0.81 reported in Burriel et al. (2010). In Figure 9 we show that the theoretical impulse response functions based on estimated parameters are reasonably close to their empirical counterparts.

^{Table 6:}

Estimated parameters and their standard errors.

4.3 Quantitative Exercise: one money, many housing markets

In this section, we delve into an assessment of the extent to which differences in institutional characteristics of mortgage markets alone can account for the heterogeneity in monetary policy transmission in the EA. To this end, we take the model calibrated to the Spanish economy, and feed it with the loan-to-value (LTV) ratios and shares of adjustable-rate mortgages (ARM) for Spain as well as the other EA countries. We then compare the dispersion of the simulated impulse response functions using the model, with the dispersion estimated using our DFM. In other words, we look at how different the transmission of monetary policy in Spain would be if this country had the LTV ratios and ARM shares of other EA member countries. A comment is in order concerning our methodology. One the one hand, the model’s impulse response functions are not directly comparable to those obtained from the DFM because, by construction, we do not calibrate the model to each individual country. On the other hand, keeping all other parameters constant allows us to isolate the effect of changing the housing financing parameters on monetary policy transmission, consistent with the goal of our exercise.

In Table (7) we report loan-to-value ratios and the shares of Adjustable-rate mortgage in our EA sample countries. The discrepancy in these institutional characteristics is apparent. Notably, there are countries, such as Belgium and France, that combine a high LTV ratio with a low shares of ARM. For these reasons, we find it important to use both in the model, so to assess the impact of potentially counteracting forces.

^{Table 7:}

Institutional parameters of EA countries’ mortgage systems.

Source: Calza et al. (2013) and Alber-tazzi et al. (2018).

^{Table 7:}

Institutional parameters of EA countries’ mortgage systems.

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

Source: Calza et al. (2013) and Alber-tazzi et al. (2018).

^{Table 7:}

Institutional parameters of EA countries’ mortgage systems.

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

Source: Calza et al. (2013) and Alber-tazzi et al. (2018).

In Table 8 and Figures 10 – 12 we present the main results of the quantitative exercise.²³ Our main results are fourfold. First, differences in LTV ratios generate more dispersion in the responses of consumption, output, and housing prices to monetary shocks than differences in the shares of ARM. This result follows from comparing the different columns of Table 8, which show how much of the dispersion in the DFM responses at different horizons (steps) is explained by the model, when we feed the LTV ratios and shares of ARM of the countries in our sample. Both on impact and at the 8th and 20th step, the variation in LTV ratios generates a substantially higher level of dispersion in GDP, housing prices, CPI, and private consumption. This result stands in contrast to the numerical illustration by Calza et al. (2013), suggesting that LTV ratios and the share of ARM are roughly equivalent in explaining the impulse responses. In our calibrated model, differences in the observed shares of ARM generate relatively smaller differences in the macro and price responses to monetary shocks. Furthermore, under the reasonable assumption that the share of ARM correlates with the households’ net interest rate exposure, our results are also in line with the result shown in Figure 7 of Slacalek et al. (2020). These authors show that large differences in net interest rate exposure across Germany, France, Spain, and Italy, have a minimal effect on the response of consumption to monetary policy shocks in these countries.

^{Table 8:}

Coefficient of variation of the cross-country responses to a 25bp monetary policy shock — estimated DFM vs. model.

^{Table 8:}

Coefficient of variation of the cross-country responses to a 25bp monetary policy shock — estimated DFM vs. model.

Variable		Coefficient of Variation (CoV)				CoVfviodel/CoVDFM (%)
		DFM	LTV	ARM	LTV + ARM	LTV	ARM	LTV + ARM
On Impact
	GDP	0.95	0.53	0.17	1.18	55.97	17.36	123.43
	Housing Prices	2.39	0.01	0.02	0.04	0.42	0.85	1.73
	HICP	1.39	0.28	0.00	0.27	19.89	0.07	19.55
	PCON	1.04	0.34	0.02	0.34	32.60	2.16	33.15
At the 8th Step
	GDP	0.56	0.18	0.02	0.20	32.26	4.26	35.47
	Housing Prices	1.39	0.30	0.02	0.24	21.52	1.26	16.98
	HICP	1.44	0.12	0.12	0.17	8.58	8.40	11.93
	PCON	0.76	0.30	0.08	0.26	39.33	11.15	34.44
At the 20th Step
	GDP	0.51	0.19	0.02	0.17	36.72	4.66	33.37
	Housing Prices	1.47	0.38	0.17	0.30	25.95	11.48	20.65
	HICP	1.16	0.09	0.05	0.08	7.57	4.73	6.90
	PCON	0.75	0.19	0.14	0.20	24.84	18.57	27.12

^{Table 8:}

Coefficient of variation of the cross-country responses to a 25bp monetary policy shock — estimated DFM vs. model.

Variable		Coefficient of Variation (CoV)				CoVfviodel/CoVDFM (%)
		DFM	LTV	ARM	LTV + ARM	LTV	ARM	LTV + ARM
On Impact
	GDP	0.95	0.53	0.17	1.18	55.97	17.36	123.43
	Housing Prices	2.39	0.01	0.02	0.04	0.42	0.85	1.73
	HICP	1.39	0.28	0.00	0.27	19.89	0.07	19.55
	PCON	1.04	0.34	0.02	0.34	32.60	2.16	33.15
At the 8th Step
	GDP	0.56	0.18	0.02	0.20	32.26	4.26	35.47
	Housing Prices	1.39	0.30	0.02	0.24	21.52	1.26	16.98
	HICP	1.44	0.12	0.12	0.17	8.58	8.40	11.93
	PCON	0.76	0.30	0.08	0.26	39.33	11.15	34.44
At the 20th Step
	GDP	0.51	0.19	0.02	0.17	36.72	4.66	33.37
	Housing Prices	1.47	0.38	0.17	0.30	25.95	11.48	20.65
	HICP	1.16	0.09	0.05	0.08	7.57	4.73	6.90
	PCON	0.75	0.19	0.14	0.20	24.84	18.57	27.12

Second, in Figure 10 through 12, we plot the responses from the DFM against the responses from the model obtained from changing either LTV ratios, or the share of ARM, or both. A key result from comparing the figures is that the correlation is weak for LTV ratios, strong for the share of ARM. In other words, while feeding the model with different LTV ratios generates a high level of dispersion in the IRFs, the majority of the simulated responses do not align with the DFM responses. By way of example, in Figure 10 bottom right corner, the model predicts that, at the 20th step, the most negative response of private consumption (PCON) is obtained by using the Netherlands LTV ratio, which is the highest in our countries sample. At the same time, however, in the estimated DFM, the PCON response in the Netherlands is average relative to other countries. This is in contrast with the results from feeding different shares of ARM: the model’s IRFs have a high correlation with those estimated in the DFM. In Figure 11, this high correlation is apparent for output and consumption. The R-square from a linear regression for output is 0.48 for the impact response and 0.5 at the 8th step.²⁴ For consumption, the R-square is 0.63 at impact and 0.79 at the 8th step. So, an important conclusion from our exercise is that, while varying the relative share of ARM does not generate sizeable heterogeneity in monetary policy transmission, it does help the model to generate IRFs that are more in line with the evidence from DFM’s.

Third, when we use both LTV ratios and the shares of ARM from the data, the model can account for approximately one-third of the estimated dispersion of the IRFs to a monetary policy shock for GDP and private consumption. The simulated responses are remarkably in line with the DFM’s. In Figure 12, for GDP and consumption, the R-squared at the 8th step is 0.21 and 0.41, respectively. Using our institutional parameters jointly produces heterogeneity in monetary policy transmission that is both sizeable and in line with the evidence. Nonetheless, the correlation is much weaker for the other two variables²⁵, which brings us to our final result.

Fourth, we find that differences in LTV ratios, alone or when combined with differences in the shares of ARM, generate substantial variation in housing prices at the 8th and 20th step. Yet, the simulated variation is not in line with what we observe in the data. One possible reason for this puzzling²⁶ result is that the response of housing prices to monetary shocks are not precisely estimated by our DFM, while output and consumption are. Housing prices clearly deserve further investigation.

Overall, in addition to providing novel and disaggregated empirical and quantitative evidence on the role of different institutional features of housing financing, our analysis lends support to the empirical findings of Calza et al. (2013), obtained using a different methodology. Also, they are in line with the back-of-the-envelope calculation using a HANK model in Slacalek et al. (2020), which shows how the monetary policy transmission in the EA is affected by differences in households’ balance sheets across countries. The link between our results and those in Slacalek et al. (2020) is best understood in light of the fact that, in equilibrium, different institutional parameters for mortgage markets imply differences in the compositions of households’ balance sheets.

Our analysis has notable implications for macroprudential policy. While previous studies, such as Arena et al. (2020), have focused on uncovering the effect of macroprudential policies on housing prices, our work highlights the potential for such measures to shape the monetary transmission mechanism. Our results suggest that 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. They provide quantitative insight on how a high degree of harmonisation of macroprudential regulation across countries can result in a more homogeneous transmission of monetary policy across the block.

5 Conclusion

Using a dynamic factor model with high-frequency identification, this paper investigates the heterogeneous effects of monetary policy across the euro area. We contribute to the literature a measure of the degree of heterogeneity in the effects of monetary policy. Focusing on housing financing as a case study, we provide quantitative evidence and insight into institutional determinants of country-specific transmission mechanisms.

In our findings, across all variables of interest, the average dispersion of country-specific responses to a monetary shock is twice the size of the mean response. There are, however, significant differences across variables. Country-level financial variables and output react fairly similarly across borders: the dispersion in their responses is low—20 to 50 percent of the average response at EA level. On the contrary, variables naturally related to markets that have experienced little convergence, such as housing and labour markets, react in significantly asymmetric ways. This is novel evidence lending empirical support to the idea that the degree of heterogeneity is inversely related to the degree of cross-border institutional convergence.

We elaborate on this point with a case study of European housing markets. We build a model of a small open economy featuring housing, operating in a monetary union. We use this model to quantitatively assess how much of the variation in individual country-level responses to a EA monetary policy shock can be explained by differences in housing financing. We find that differences in mortgage market characteristics across the EA explain one-third of the cross-country heterogeneity of responses in output and private consumption.

Other features of the housing market can be expected to weigh on the transmission of monetary policy. By way of example, prima facie evidence points to a specific role of the share of home ownership.²⁷ In addition, our methodology could be extended to the analysis of institutional divergences in other markets, such as national labor markets. These are promising and intriguing areas that we leave to future research.

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Appendix

A Data Set

Table 9 contains a complete list of the series in our data set as well as detailed descriptions and information regarding transformations, geographical coverage and sources. Abbreviations and codes are laid out in the following:

Transformation code (T)

1 – no transformation

2 – difference in levels

4 – logs

5 – difference in logs

Geography

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

WDSA – working day and seasonally adjusted

SA – seasonally adjusted

NA – neither working day nor seasonally adjusted

Note: 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. Furthermore, 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. Finally, import and export data for Germany, Spain and Italy is only available from 2012 Q1 onward.

		Description	T	Source	Geography	Start	End	F
	GDP & Personal Income
GDP		Gross Domestic Product at market prices, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
PCON		Household and NPISH final consumption expenditure, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
G		Final consumption expenditure of general government, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
GFCF		Gross fixed capital formation, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
EX		Exports of goods and services, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
IM		Imports of goods and services, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
GDP_i		Gross Domestic Product at market prices, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EAll_i	2000 Q1	2016 Q4
CON_i		Final consumption expenditure, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EAllj	2000 Q1	2016 Q4
PCONj		Household and NPISH final consumption expenditure, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EAllj	2000 Q1	2016 Q4	Y
G_i		Final consumption expenditure of general government, Chain linked volumes, 2010=100, WDSA	5	Eurostat	EAllj	2000 Q1	2016 Q4	Y
GFCF_i		Gross fixed capital formation, Chain linked volumes (2010), million euro, WDSA	5	Eurostat	EAllj	2000 Q1	2016 Q4	Y
EX_i		Exports of goods and services, Chain linked volumes, 2010=100, unadjusted data	5	Eurostat	EAllj	2000 Q1	2016 Q4	Y
IM_i		Imports of goods and services, Chain linked volumes, 2010=100, unadjusted data	5	Eurostat	EAllj	2000 Q1	2016 Q4	Y
	Prices/Deflators
GDPDEF		Gross domestic product at market prices, Price index (implicit deflator), 2010=100, euro, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
PCONDEF		Household and NPISH final consumption expenditure, Price index (implicit deflator), 2010=100, euro, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
GDEF		Final consumption expenditure of general government, Price index (implicit deflator), 2010=100, euro, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
GFCFDEF		Gross fixed capital formation, Price index (implicit deflator), 2010=100, euro, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4
EXDEF		Exports of goods and services, Price index (implicit deflator), 2010=100, euro, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4	Y
IMDEF		Imports of goods and services, Price index (implicit deflator), 2010=100, euro, WDSA	5	Eurostat	EA12	2000 Q1	2016 Q4	Y
PPI		Producer prices in industry, domestic market, index 2010=100, unadjusted data	5	Eurostat	EA19	2000 Q1	2016 Q4
HICPOO		All-items HICP, Index, 2015=100	5	Eurostat	EACC	2000 Q1	2016 Q4
HICP01		HICP Food and non-alcoholic beverages, Index, 2015=100

Topics

Countries

Series

About

Resources

Contributor Notes

Abstract

1 Introduction

2 A Dynamic Factor Model for the EA

2.1 Motivation

2.2 Empirical Framework

2.3 Identification

2.3.1 Instrument – “Scripta Volant, Verba Manent”8

2.4 Data and Estimation

3 Empirical Results

3.1 Euro-wide Dynamic Effects of Monetary Policy

3.2 Cross-Country Dynamic Effects of Monetary Policy

4 Quantifying How Mortgage Markets Shape Monetary Transmission

4.1 Model

4.1.1 Patient Households

4.1.2 Impatient Households

4.1.3 Relationship among inflation, terms of trade and exchange rate

4.1.4 Firms

4.1.5 Monetary Policy

4.1.6 Aggregation and Market Clearing

4.1.7 Equilibrium

4.2 Calibration

4.3 Quantitative Exercise: one money, many housing markets

5 Conclusion

References

Appendix

A Data Set

2.3.1 Instrument – “Scripta Volant, Verba Manent”⁸