The Response of Asset Prices to Monetary Policy Shocks: Stronger than Thought

Mainstream macroeconomic theory predicts a rapid response of asset prices to monetary policy shocks, which conventional empirical models are unable to reproduce. We argue that this is due to a deficient information set: Forward-looking economic agents observe vastly more information than the handful of variables included in standard VAR models. Thus, small-scale VARs are likely to suffer from nonfundamentalness and yield biased results. We tackle this problem by estimating a Structural Factor Model for a large euro area dataset. We find quicker and larger effects of monetary policy shocks, consistent with mainstream theory and the observed large swings in asset prices. Our results point to stronger financial stability consequences of an exogenous monetary policy tightening, also in the form of a quicker than expected unwinding of QE, than commonly thought.


Non-technical summary
Particularly in the aftermath of the global financial crisis and the current low interest rate environment, it is of utmost importance to properly asses the relationship between monetary policy and asset prices. In this paper we contribute to the empirical literature on this topic by estimating a Structural Factor Model (SFM). Compared to vector autoregressions (VARs), the most widely used model in the empirical literature, this factor model takes into account a significantly larger information set. Instead of a handful of macroeconomic variables that VARs are able to handle, our SFM incorporates more than a hundred monthly variables, covering real activity, prices, surveys, financial markets, as well as the US economy.
The advantages of using a large-scale model are twofold. First, in standard smallscale VARs only very few asset classes can be investigated at the same time. This is due to the "curse of dimensionality", i.e. the number of parameters one has to estimate increases substantially by adding further variables. Given that samples are typically relatively small in macroeconometric settings, a too large VAR may yield inaccurate estimates. Using a factor model, on the other hand, allows us to investigate a wide range of asset prices in a unified framework. In particular, we study stock and house prices, various exchange rates, as well as corporate bond yields of different rating classes. Secondly, in a data-rich environment we overcome the problem of nonfundamentalness, caused by a deficient information set: If the empirical model incorporates less information than that used by economic agents (e.g. central banks, households and firms), the model's results may be invalid. This issue is of particular relevance in small-scale VARs, since they can only handle a handful of macroeconomic variables, while economic agents arguably base their decisions on a much wider information set. In the

Introduction
There are at least two reasons behind the economic profession's renewed interest in the relationship between monetary policy and asset prices. First, until the global financial crisis, it was rather controversial whether central bankers should look at asset price dynamics over and above their impact on inflation. "Leaning against the wind" of rising asset prices by tightening the monetary policy stance was not an explicit objective of central banks. However, the 2008-2009 financial crisis and the economic crisis that followed, have shown that "mopping up the mess" after the burst of an asset price bubble may entail huge costs, also in terms of price stability (Brunnermeier et al., 2009).
The second reason is that an environment of prolonged low interest rates poses a concrete risk that some asset classes may more easily become overvalued and vulnerable to abrupt correction. Hence, it becomes even more important to understand the relationship between monetary policy and asset prices, in order to assess the financial stability consequences of a monetary policy shock (Allen and Gale, 2004;Disyatat, 2010).
Against this background, we provide evidence on the response of a set of asset prices to monetary policy shocks in the euro area. Several papers exist that attempt to estimate the impact of monetary policy shocks on asset prices, mostly on US data. However, in almost all of these papers, small-scale models are used. We build on this stream of literature by significantly enlarging the information set, well beyond the standard handful of macrofinancial variables. Moreover, we extend the set of examined asset prices and study stock and house prices, exchange rates, as well as corporate bond yields, distinguishing between high yield and investment grade.
In fact, we model more than a hundred time series by means of a Structural Factor Model (SFM, see Forni et al., 2009). By doing so, we are able to identify shocks ECB Working Paper 1967, September 2016 which cannot be correctly identified by conventional small-scale VAR models, as they are nonfundamental with respect to the limited information set those models are able to incorporate. Nonfundamentalness of the shocks in a macroeconometric setting can be linked to the role of expectations in the associated theoretical model. If agents behave according to their expectations, and these expectations are based on a larger information set than the one used in the empirical model, then this latter won't be able to recover the structural shocks. Asset prices are the prototypical example of an economic variable which is determined based on expectations. Moreover, the central bank monitors a very large set of indicators and sets the monetary policy stance based on this wide information set. For both of these reasons, as we show, the empirical results will differ depending on whether the empirical model includes all of the relevant variables or not.
Compared to the literature and our benchmark VAR model, the SFM points to stronger effects of monetary policy shocks on asset prices across the board. The impulse responses we estimate generally exhibit their peak effect shortly after the shock or even at impact. In other words, asset prices respond more and more quickly to monetary policy shocks than commonly thought, which implies stronger financial stability consequences of monetary policy decisions. Particularly in a low interest rate environment, our findings call for increased vigilance on the repercussions that a monetary policy tightening in whichever form -including a quicker than expected unwinding of unconventional measures -could have on financial markets.
The paper is structured as follows. In the following Section we provide a brief overview of the relevant literature. Section 3 presents three asset pricing models where the monetary policy shock turns out to be nonfundamental in a standard VAR setting.
This provides a theoretical motivation for the empirical investigations that follow. Section 4 describes the Structural Factor Model and outlines its estimation, Section 5 de-ECB Working Paper 1967, September 2016 scribes the dataset, and Section 6 discusses the model parametrization and the identification strategy. In Section 7 we present the estimation results while Section 8 concludes and discusses policy implications.

Literature overview
The effects of monetary policy on asset prices, especially stock prices, have been the subject of extensive empirical research. This section provides a brief overview of the relevant literature, grouping papers according to their focus (i.e. asset class) and/or the selected estimation approach (e.g. different identification strategies in a VAR setting).
Among the papers using a recursive identification scheme in a VAR framework, Li et al. (2010) find that US stocks drop by 1% on impact and by up to 8% a year and a half after an unanticipated 50bp rise in the policy rate. For Canada, the impact effect is virtually zero and the trough of 1.5% occurs after 4 months. Studying eight advanced economies in a similar recursive identification scheme, Neri (2004) finds considerable cross-country heterogeneity in stock price responses. The peak effects are reached after 2-12 months with drops of up to 3%. In a recent study, Galí and Gambetti (2015) find an even smaller and short-lived effect of monetary policy shocks on stock prices: the magnitude of the decline is less than 1% and fades away after just four months.
These findings stand in stark contrast with non-VAR studies, especially those exploiting higher frequency data. For example, Rigobon and Sack (2004)  to ours, Luciani (2015) finds that US house prices drop significantly on impact and by about 1% three years after a 50bp increase in the policy rate.
Regarding exchange rates, small-scale VAR models often exhibit the "delayed overshooting puzzle" (Eichenbaum and Evans, 1995;Grilli and Roubini, 1996). That is, exchange rates tend to react with a long delay to monetary policy shocks and are merely affected on impact. Faust et al. (2003) argue that this is due to the strict recursiveness assumption. By exploiting high-frequency data, they can attenuate but not fully solve the puzzle. The delayed exchange rate reaction is, of course, inconsistent with mainstream theory which predicts an instantaneous appreciation of the domestic currency.
This is precisely what Forni and Gambetti (2010), employing a factor model similar to ours, find for the US.
Finally, and somewhat surprisingly, the interaction between monetary policy and corporate bonds has received rather little consideration in the VAR literature. While most authors focus on government bond yields, Beckworth et al. (2012), employing long-run restrictions, find that corporate bond spreads react significantly to monetary policy shocks. However, the effect is negligible on impact and peaks only after 1-2 years, depending on the sample period. Even more puzzling, Gertler and Karadi (2015) report that with a recursive identification scheme, corporate bond spreads slightly decline after a contractionary monetary policy surprise. 1 The authors conclude that conventional recursive VARs are inept to study the effects of monetary policy on financial variables. Instead, they identify monetary policy surprises in a high-frequency approach and use them as external instruments in a VAR. This way, they find corporate bond yields to increase significantly after a contractionary monetary shock with the peak effect oc-curring on impact.
In this paper we stick to a recursive identification scheme and instead argue that most of the puzzling empirical results are due to nonfundamentalness of the structural shocks in small-scale VARs. That is, small-scale VARs are not able to incorporate all relevant information to correctly identify monetary policy shocks. In fact, by enlarging the information set in our Structural Factor Model, the above mentioned puzzles largely disappear.

Theoretical models
In this section we offer theoretical underpinnings to the empirical model that we estimate in the remainder of the paper. To do so, we present three theoretical models where the monetary policy shock turns out to be nonfundamental, i.e. not identifiable by means of a conventional small-scale VAR. The gist of the argument relies on the role of expectations. In a nutshell, when agents form their expectations based on information which is not captured by the empirical model, or when the expectation formation process is non-standard, the structural shocks are nonfundamental (in the context of that particular model), i.e. cannot be correctly identified. In other words, the empirical model suffers from an omitted variables problem. Hence, it yields invalid results.
Technically, nonfundamentalness is linked to the roots of the determinant of the matrix in the moving average (MA) representation. In particular, given a covariance stationary vector process x t and a white noise vector u t , the representation x t = A(L)u t is fundamental if the determinant of A(z) has no roots of modulus less than unity. 2 If at least one root is inside the unit disc, the MA representation is not invertible in the past. In other words, past information is not sufficient to recover the structural shocks, no matter how many lags are included in the VAR. The representation is only invertible in the future, i.e. the econometrician would need to know the future value of the observables in order to identify the shocks. 3 Fundamental and nonfundamental representations may be observationally equivalent and typically the nonfundamental case is ruled out by assumption. However, even simple theoretical models can be associated

Nonfundamentalness due to lagged shock effects
The first theoretical model we discuss is the textbook model for stock prices. In this model, the equilibrium value for stock prices p t is equal to the discounted sum of expected dividends, d t , as follows: The dynamics for the dividends can be assumed as follows: with u t and η t being disturbances. In particular, u t is a shock that has only an effect on dividends with a k-period lag, though being observed at time t by agents. This implies that agents will adapt their behavior already at time t, as they anticipate the future effects of u t on dividends already at time t. In other words, u t enters the information set on which agents form their expectations for d t+k . However, the econometrician will only be able to see the impact of u t at time t + k.
A type of shock having a lagged effect on the observables offers a wide range of interpretations. It could, for instance, be a technological innovation which takes time in order to translate into productivity gains. Alternatively, it could be a shock affecting government spending and taxation, which are both planned in advance with the budget law for the following year. Furthermore, it could be a shock related to the introduction that these operations would be carried out over a window of two years. Arguably, the bulk of the effects unwind at the time each of the TLTROs takes place, is contingent on its take-up, and is reflected into short-term rates. However, the announcement of the TL-TROs, together with information on their calendar, is a monetary policy shock in itself, which may not be fully captured by the short-term rate instantaneously but still affects the economy at large by influencing agents' expectations. Moreover, on the same occasion when it launched TLTROs, the ECB announced that it would "intensify preparatory work related to outright purchases of asset-backed securities (ABSs)". Again, this is a monetary policy shock linked to a nonstandard monetary policy measure, which already has an impact before being implemented, insofar agents already have an expectation on ECB Working Paper 1967, September 2016 it. As another example, since July 2013 the ECB has been providing forward guidance on the future path of policy rates (conditional on the inflation outlook). This induces expectations on the side of the markets, which will adjust accordingly. However, an econometrician will come to the wrong conclusions when trying to retrieve the underlying monetary policy shocks, if she only observes the actual level of policy rates and ignores the information coming from the ECB forward guidance.
In an attempt to address this problem, in the empirical analysis we replace the policy rate -which is constrained by the zero lower bound -with a shadow rate that exploits information on the whole term structure. This latter rate in principle incorporates the effects of unconventional policy measures. Though this rate is more appropriate than a constrained short-term rate, it is susceptible to debate if it fully captures the conditional character of the monetary policy measures. More generally, it may still be an imperfect measure of the monetary policy stance and it may fail to fully capture agents' expectations. Indeed, as we show, including the shadow rate in a small-scale SVAR is not enough to solve the issue of nonfundamentalness.
Going back to the model's equations, substituting the expression for E t d t+j into (2) yields: The structural moving average representation of this model is the following: The determinant of matrix A(z) is given by the following expression: Finding the zeros of this expression requires solving a k-th order equation. For the simple case where k = 2, the determinant vanishes for L = 1 and L = −β (see Forni et al., 2014). Hence, one of the roots is inside the unit circle, given that β is a discount factor, i.e. in modulus smaller than one.

Nonfundamentalness due to unobserved variables
Another case in which nonfundamentalness can arise is owing to the presence of unobserved factors driving asset price dynamics. The following simple model by Hansen and Sargent (1991) exemplifies the issue. More generally than in the previous case, let's assume that a set of economic variables including asset prices, z, depend on the future path of a broad set of unobserved factors ω t : Assume the following simple dynamics for ω t : where u t is the monetary policy shock. Substituting (7) into (6) yields: The only root of A(z) is (1 − βθ)/θ which can be inside the unit circle. If this is the case, the information contained in z t is not enough to recover the true structural shock The well-known "price puzzle" is an obvious example. Conventional VAR models typically find that an unexpected interest rate rise increases inflation, a finding directly at odds with macroeconomic theory. Many authors have argued that this puzzling observation is due to a deficient information set used in the VAR. That is, central banks may have information about future inflation, so the response represents in fact reverse causality (monetary policy is tightened today because inflation is likely to increase tomorrow). Since the econometric model typically does not include measures of expected inflation, it suffers from nonfundamentalness and yields invalid results. 4

Nonfundamentalness due to informational heterogeneity
Nonfundamentalness can also be linked to the existence of a heterogeneous beliefs equilibrium. Indeed, in order for a non-revealing equilibrium to exist, the model must be such that agents cannot infer private information in equilibrium, that is, they cannot identify structural shocks based on observations. In other words, agents can remain heterogeneously informed in equilibrium only if the model has a nonfundamental MA representation. An asset pricing model with persistent heterogeneous beliefs is developed by Kasa et al. (2014), of which what follows is a simplified version. Assume that fundamentals f t are the sum of two orthogonal serially uncorrelated components: and that the price p t is a function of fundamentals f t and is also influenced by noise, t . Heterogeneous symmetric information is modeled by assuming two types of agents.
Each agent type observes the price p t , the fundamentals f t and just one shock u it . The corresponding MA representation for type 1 traders is the following: where the polynomials π 1 (z), π 2 (z), π 3 (z) are pricing functions. The determinant of matrix A 1 (z) is equal to a 2 (z)π 3 (z). For the symmetric case of type 2 agents, the determinant of matrix A 2 (z) is equal to a 1 (z)π 3 (z). If we assume for simplicity that the prize puzzle can be attenuated but not fully resolved (see Christiano et al., 1999).
a 1 (z) = a 2 (z) = a(z), requiring this MA representation to be nonfundamental implies that either a(z) or π 3 (z) or both have at least one zero inside the unit circle. Given a nonfundamental representation, a non-revealing equilibrium exists because what agents do in equilibrium is to attempt to retrieve the structural shocks by estimating a VAR, hence assuming the corresponding fundamental representation. As a consequence, a problem of identification arises, as agents' information on one type of shock, on the price and on the fundamentals is not enough to retrieve both structural shocks u 1t and u 2t . As shown in Kasa et al. (2014),  Forni et al. (2009) show that by enlarging the space of observations one can solve the problem of nonfundamentalness (see also Giannone and Reichlin, 2006). Indeed, non-fundamentalness is not an issue for models which are able to handle very large panels of related time series. In particular, nonfundamentalness is nongeneric in the framework of dynamic factor models, i.e. it occurs with probability zero for N → ∞, with N being the number of series included in the model. 5 We estimate the Structural Factor Model (SFM) by Forni et al. (2009), which in turn is a special case of the model in Forni and Lippi (2001) and Forni et al. (2005). We refer to these papers for a detailed description of the assumptions of the model, and limit ourselves to outlining the main features.
Denote by x a panel of n stationary time series, where both the n and T dimensions are very large. In a factor model, each variable x it is assumed to be the sum of two unobservable components: the common component χ it and the idiosyncratic component ξ it . An important feature of this specific factor model and the closely related models by Stock and Watson (2002) and Bai (2003) is that the idiosyncratic components are allowed to be mildly cross-correlated (i.e. the factor model is approximate, as opposed to exact). The common component is assumed to be driven by q shocks u t = (u 1t . . . u qt ) which affect all variables in the panel, also referred to as dynamic common factors, with q << n. These are the structural shocks we aim at identifying. Formally: where χ t = (χ 1t . . . χ nt ) , ξ t = (ξ 1t . . . ξ nt ) , and B(L) is a one-sided n × q filter. Eq. 9 is called dynamic representation of the factor model. An alternative representation, which is called static representation, is the following: where the r > q entries of F t are the static common factors, and Λ is the n × r matrix of factor loadings.
The link between the two representations is given by defining the r × 1 vector of the static common factors in terms of the shocks, as follows: where N(L) is an r × r matrix polynomial and H is a maximum rank r × q matrix.
Finally, it is assumed that N(L) results from inversion of the VAR(m) where I r is the r-dimensional identity matrix, and A is an r × r matrix. Notice that t = Hu t , i.e. the residuals of the VAR on the static factors have reduced rank q.
More precisely, t ∈ span {u t }, i.e. the residuals belong to a q-dimensional linear space generated by the dynamic factors. Notice also that these latter, as well as the static common factors, are only identified up to a rotation.

The estimation procedure
The estimation of the SFM is based on Giannone et al. (2004) and Forni et al. (2009).
We make use of the static representation (10) together with the VAR(1) specification of the static factors: This state-space representation is equivalent to the dynamic representation (9), with filters defined as Before estimating (12)-(13), the number of dynamic factors q and the number of static factors r have to be determined (see Section 6).
The estimation procedure is in four steps.
STEP 1 Given a consistent estimator of the covariance matrix Γ x 0 , the static factors F t are consistently estimated as the r largest principal components. This yields also a consistent estimate of the loadings Λ. We extract the principal components from the panel in levels, following Bai (2004) who shows that given a large-dimension factor model with nonstationary dynamic factors, the common component of I(1) time-series can be consistently estimated via principal components if the idiosyncratic components are stationary. 6 We test this assumption by three different panel unit root tests, namely Maddala and Wu (1999), Choi (2001) and Levin et al. (2002), which all clearly reject the unit root hypothesis. is crucial to estimate the model in levels. As is well known from the VAR literature, a model in differences would be misspecified under these circumstances. Barigozzi et al. (2016) show that cointegration relationships are likely to be present in the context of 6 See also Peña and Poncela (2006). factor models, hence they argue in favor of estimating a VAR on the static factors in levels in this step. The ability of taking into account long-run relationships is a strong argument in favor of estimating a factor model in levels if the focus is on asset prices.
The reason being that the financial cycle has a much lower frequency than the business cycle, hence the focus needs to be on the medium-to-long term (see e.g. Drehmann and Tsatsaronis (2012)  To account for the fact that monetary policy has been subject to the zero lower bound in our sample period, we splice the EONIA rate (monthly average) with the shadow rate by Wu and Xia (2016). This series summarizes the stance of monetary policy based on information from the entire yield curve. More precisely, it is estimated as the policy rate that would generate the observed yield curve in the absence of a lower bound. The underlying model is an affine term structure model with three factors, where the shortterm interest rate is the maximum of the shadow rate and a lower bound, which is set at 0.25%. This series is available from September 2004 onwards and closely resembles the EONIA rate prior to the global financial crisis. The two series substantially diverge in late 2008 with the implementation of the ECB unconventional policy measures and the zero lower bound becoming an increasingly binding constraint for conventional interest rate policy (see Figure A1 in the Appendix for a comparison of both series). The use of shadow rates in macroeconometric models, including factor models, is not novel in ECB Working Paper 1967, September 2016 the literature. In particular, Wu and Xia (2016) themselves put forward an application where their shadow rate is included in a Factor-Augmented VAR and used to identify monetary policy shocks. They also suggest their shadow rate could replace the shortterm rate in any structural VAR. Other applications, also for the euro area, are in Chen and Zhu (2015) and Damjanović and Masten (2016).
Together with the short-term rate, other key variables in our study relate to asset prices. In particular, we focus on house prices and financial asset prices, namely stocks, corporate bonds -high-yield and investment grade -and currencies. Financial asset prices have frequently experienced large swings, often coinciding with the announcement of key monetary policy decisions. Figure A2 (2007) in different specifications points to numbers between 3 and 6, the test by Bai and Ng (2007) yields 4 as a result in most of its specifications and the criterion by Amengual and Watson (2007) is clearly out of range, pointing to q = 9. Indeed, it is difficult to imagine that the primitive shocks, source of business cycle fluctuations, are so many. Finally, on our dataset the test by Onatski (2009) always points to q = q max , where q max is a pre-defined parameter indicating the maximum value allowed for q. In line with the literature and with the evidence from statistical criteria, we set the number of dynamic factors as q = 4.
As for the number of static common factors, it should be noted that also most of the available tests for determining r are designed for a stationary setting. Thus, they may not ECB Working Paper 1967, September 2016 work as expected on a nonstationary panel. 7 We apply the criterion suggested by Alessi et al. (2010), which points, in all its specifications, to a number of static factors equal to 7. 8 However, we should take into account that our non-stationary dataset displays features which this criterion is not designed to handle, in particular linear time trends and unit roots. Hence, to be on the safe side and sure that enough variance is captured, we set r = 9 in our benchmark specification. 9 The first principal component, indeed, corresponds to a linear time trend. Naturally, many variables in the data set load heavily on it. 10 Real activity measures also load heavily on the second factor, while surveys, stock prices and corporate bond yields mainly load on the third factor. Factors 4-6 are important for some US and further financial series, e.g. sovereign bond yields. Lastly, price and real activity measures for the US load heavily on factors 7-9. However, it is useful to recall that principal components, or static common factors, do not have an economic interpretation. Principal components are just statistical constructs, while economic meaning is attached only to the dynamic common factors, or structural shocks, identified by suitably rotating the VAR residuals.
As a robustness test, we estimate the model for various specifications of r. The results are shown in Figure A5 in the Appendix. This exercise indicates that the model is robust for r ≥ 9. When r < 9, on the contrary, some unreasonable results emerge, e.g. the well-known "price puzzle". This is consistent with the findings in Forni and Gambetti (2010), who stress the importance of including a sufficient number of static factors.
To ensure comparability between our Structural Factor Model and the benchmark VAR, both models are estimated with a lag length of p = 1, as suggested by the BIC.
The shock size is set to a 50bp rise in the short-term rate.
Following Forni and Gambetti (2010), we apply the same Cholesky identification to both models. The monetary policy shock is identified by imposing a standard recursive scheme on industrial production, the consumer price index, the monetary policy rate, and various asset prices (cf. Eichenbaum and Evans, 1995). Our ordering implies that monetary policy reacts contemporaneously (i.e. within the same month) to shocks in real activity and consumer prices, while the opposite is not true. Asset prices, on the other hand, are allowed to react immediately to monetary policy shocks. In particular, the benchmark VAR includes five asset prices: house and stock prices, high-yield and investment-grade corporate bonds, and the USD/EUR exchange rate.
Confidence intervals are based on the following two-step bootstrap procedure. First, we generate artificial common components by reshuffling the shocks and applying filters to them, given by the impulse responses. In the second step, we adopt a standard non-overlapping block bootstrap technique for the idiosyncratic parts. In particular, we partition the idiosyncratic component into 5-year blocks. We then add the bootstrapped idiosyncratic component to the bootstrapped common components to obtain simulated data sets. We perform 1000 bootstrap repetitions, applying the bias correction proposed by Kilian (1998). For each artificial sample we repeat the estimation and obtain nonstructural impulse responses, which are then identified by imposing our identification assumptions.

ECB Working Paper 1967, September 2016 25
Let us now examine the responses of asset prices to a contractionary monetary policy shock. The difference in the responses between the benchmark VAR and the SFM is striking.
As shown in Figure 1, for stock prices the SFM suggests a rather rapid decline of roughly 3% on impact and a maximum decline of about 4% after four months. In the VAR, the stock price response peaks not until after one year, with the decline of only 2% being far from significant. House prices merely react at all to a contractionary shock in the VAR model. If anything, they slightly increase in the longer run. In the SFM, on the other hand, house prices drop on impact by about 1% and return to their previous level within 1-2 years. The last two rows of Figure 1 show the response of high-yield and investment-grade corporate bonds in the euro area. Again, we observe roughly the same pattern. The peak effect on both yield classes is 2-3 times bigger and reached much quicker in the SFM. In line with the financial accelerator and credit channel literature, the effect is multiple times higher for high-yield debt than for more credit-worthy borrowers in both frameworks. As for the exchange rate, the simple VAR model suggests a rather small and smooth response of the USD/EUR exchange rate, while in the SFM it spikes immediately with an appreciation of about 4%, four times stronger than in the VAR. 11 A major advantage of the SFM approach is the fact that impulse responses can be estimated for any of the 127 series in the underlying dataset. This yields more informa-tion and allows a more comprehensive check of the empirical plausibility of the model.  To wrap up, the SFM impulse responses are -in contrast to those of the benchmark 12 Notice that the response of this series refers to the expected annual growth rate of the HICP.
VAR -largely consistent with basic economic theory. They are also in line with recent empirical evidence employing innovative identification approaches, cf. Section 2: First, the rapid drop in stock prices is remarkably close to the estimates of Rigobon and Sack (2004) and Bohl et al. (2008). The large immediate exchange rate appreciation is in line with evidence for the US provided by Forni and Gambetti (2010): the factor model solves the delayed overshooting puzzle within a recursive identification approach. As for corporate bonds, we confirm the finding in Gertler and Karadi (2015) that the peak effect of a policy tightening on corporate bonds occurs on impact. 13 The significant drop in house prices, lastly, is in line with the results of Del Negro and Otrok (2007) and Luciani (2015).
Another method to compare the importance of monetary policy for asset prices between the two empirical models is via forecast error variance decomposition. As shown in The hump-shaped responses of asset prices we find in our benchmark small-scale VAR model are common in the literature, especially within a recursive identification framework. They are, however, at odds with both economic theory and the observed market volatility. Indeed, in standard macroeconomic models asset prices equal their expected discounted payoffs. That is, forward-looking agents discount the expected future cash flows associated with an asset to determine its price. The employed discount factor, in turn, is affected (at least in the short-run) by monetary policy due to its bearing on interest rates. Hence, we expect asset prices to respond quickly, and potentially  Solid lines refer to point estimates, shaded areas to 80% and 90% confidence bands, respectively. All responses are in percentage terms (yields in percentage points) and the x-axis corresponds to months after the shock. HY: high yield corporate bond yields; IG: investment-grade corporate bond yields. Solid lines refer to point estimates, shaded areas to 80% and 90% confidence bands, respectively. The first two rows of responses is in percentage points, the composite indicator of systemic stress (CISS) is normalized between 0 and 1 (Hollo et al., 2012) and the Eurostoxx volatility index roughly ranged between 10 and 60 in our sample. The x-axis corresponds to months after the shock. All results in percentages. Months after the monetary policy shock on the columns.  Results are obtained by re-estimating the model described in Section 6 (i.e. with q = 4 dynamic factors) for different values of r. Our benchmark specification for the number of static factors is r = 9. Note: numbers in square brackets correspond to the series in Table A1.

Structural VAR Structural Factor Model
Industrial production Solid lines refer to point estimates, shaded areas to 80% and 90% confidence bands, respectively. All responses are in percentage terms and the x-axis corresponds to months after the shock.