2.1 Data

Our baseline analysis departs from an n-dimensional vector $X_{t}$ of seasonally adjusted quarterly series: real GDP, core inflation, a policy interest rate, credit growth, the EBP, and stock prices. These are standard variables in empirical macro-financial studies.

We use the core CPI, excluding energy and food, to measure inflation. We choose core, instead of headline inflation, in order to disentangle financial shocks from commodity price shocks, such as oil shocks. We further investigate this issue in Section 4 by including the oil price in our baseline VAR model. ^{Footnote 7} The excess bond premium (EBP), which is taken from Simon Gilchrist’s website, is a risk premium that reflects systematic deviations in the pricing of US corporate bonds relative to the issuers’ expected default risk. It thus constitutes a proxy for the effective risk-bearing capacity of the financial sector, and is a direct price measure of credit supply. We measure credit growth using total credit to the private nonfinancial sector, taken from the Financial Accounts of the USA. In the robustness analysis, we also consider alternative credit measures. Nominal stock prices are taken from Robert Shiller’s website. We deflate the credit and stock price series by the CPI. Finally, we use the federal funds rate as the main policy interest rate. From 2008Q4 onwards, we replace the federal funds rate with the shadow short rate (SSR) from Krippner (Reference Krippner2015), which allows to account for unconventional monetary policy. The SSR reflects in fact changes in the term structure of interest rates, which is affected by quantitative easing and forward guidance policies (Gertler and Karadi (Reference Gertler and Karadi2015), Krippner (Reference Krippner2015)).

GDP and stock prices enter the model in logarithms, the policy rate and the EBP in levels, the CPI in year-on-year differences of logarithms. ^{Footnote 8} We filter outstanding credit using log year-on-year differences. Financial intermediaries’ balance sheet variables are subject to secular trends due to changes in the structure of the financial system and regulatory changes. Following Adrian et al. (Reference Adrian, Moench and Shin2016), we deal with this issue by using detrended credit. ^{Footnote 9} While the year-on-year change is a convenient way of detrending credit, we show below that our results are not affected when using a one-sided HP filter applied to outstanding credit. ^{Footnote 10} If not stated otherwise, we take the series from the FRED database of the Federal Reserve Bank of St. Louis.

The sample period ranges from 1988Q1 to 2019Q2. By choosing 1988Q1 as a starting point, we exclude any monetary regime prior to the Greenspan one. Moreover, the period since the mid-1980s until the beginning of the GFC is associated with the Great Moderation. Hence, our sample period excludes the Great Inflation period. We show below that, even though our key finding is not affected when we extent the sample period backwards to 1973, magnitudes are somewhat different, which indicates parameter instability over a longer sample. Moreover, we check to what extent parameters have changed with the GFC in Section 4.

2.2 Vector autoregression

We assume that the $n \times 1$ vector of endogenous variables $\mathbf{y}_t$ follows a VAR model of order p:

(1) \begin{equation}\mathbf{y}_t^{\prime} = \mathbf{x}_t^{\prime}\mathbf{B} + \mathbf{w}_t^{\prime},\quad\mathbb{E}(\mathbf{w}_t^{\prime})=0,\,\mathbb{E}(\mathbf{w}_t\mathbf{w}_t^{\prime})=\mathbf{\Sigma},\end{equation}

where the regressors’ matrix is defined as $\mathbf{x}_t^{\prime} = [\mathbf{y}_{t-1}^{\prime}, \dots, \mathbf{y}_{t-p}^{\prime}, 1]$ and $\mathbf{B}$ is a $(np+1) \times n$ matrix of reduced-form coefficients. The $n\times 1$ vector $\mathbf{w}_t$ denotes reduced-form innovations which are assumed to be Gaussian with mean zero and positive definite covariance matrix $\mathbf{\Sigma}$ . The lag length p is set to 2, as suggested by the Akaike and Hannan–Quinn information criteria. We estimate the VAR using Bayesian methods. We specify diffuse/uninformative priors so that the information in the likelihood is dominant. These priors lead to a normal-(inverted-) Wishart posterior with mean and variance parameters corresponding to OLS estimates.

2.3 Identifying financial shocks

Identifying financial shocks in the data is not trivial. Different structural macroeconomic models with a financial sector have different implications for key features of financial shocks, including their effect on important variables such as inflation (cf. Table 1). One reason is the different transmission channels embedded in the model. Consequently, there is no consensus in the literature on how to best identify financial shocks.

To identify financial shocks, we propose a strategy that combines short-run sign restrictions on impulse response functions, and narrative restrictions on the shock size and the historical decomposition. These identifying restrictions are summarized in Table 2. Our identifying assumptions are economically reasonable and consistent with a large body of theoretical and empirical work on the dynamic propagation of financial shocks. At the same time, we remain fully agnostic about the effects of financial shocks on inflation dynamics. We discuss sign and narrative restrictions in turn.

Table 2. Restrictions to identify financial, aggregate demand and aggregate supply shocks: This table shows the restrictions imposed on the impulse response functions of the endogenous variables in the baseline VAR to identify financial, aggregate demand and aggregate supply shocks. All restrictions are imposed on impact and are implemented as $\geq 0$ ( $\uparrow$ ) or $\leq 0$ ( $\downarrow$ ). See text for details

Sign restrictions

Throughout the paper, we focus on contractionary financial shocks which lead to a decrease in GDP. Furthermore, we restrict the EBP to increase and credit growth and stock prices to fall. ^{Footnote 11} These three restrictions are standard, and match key features of financial shocks in structural macroeconomic models.

We disentangle financial shocks from aggregate supply and aggregate demand shocks by assuming that contractionary financial shocks decrease credit growth by more than GDP. This relative restriction on credit growth and GDP is intuitively plausible. After contractionary aggregate supply and demand shocks, investors might increase risk premia and reduce credit in response to the economic downturn. However, it is reasonable to assume that investors adjust their lending and investment strategies only gradually in response to the shock. Hence, we should first observe a deterioration in economic activity, while credit growth should respond initially only mildly. Financial shocks, by contrast, originate in the financial sector (as seen in the GFC) and exogenously decrease credit supply. Lower credit supply, however, should transmit to the overall economy initially only weakly: entrepreneurs and households need some to time to fully adjust their production processes and demand decisions in response to the lower supply of credit. Hence, we should observe a fall in credit growth that exceeds the fall in output growth for some time. Note that this is similar to the intuition underlying the use of a zero contemporaneous restriction on output. However, our relative restriction is more agnostic than such a recursiveness assumption, which other empirical studies employ.

The relative restriction on credit growth and GDP is consistent with DSGE models featuring an active financial sector and shocks that directly affect banks’ balance sheets. Examples of these models include Covas and Driscoll (Reference Covas and Driscoll2013), Curdia and Woodford (Reference Curdia and Woodford2010), Gelain et al. (Reference Gelain, Lansing and Natvik2017), Gerali et al. (Reference Gerali, Neri, Sessa and Signoretti2010), Gertler and Karadi (Reference Gertler and Karadi2011), Hristov and Huelsewig (Reference Hristov and Huelsewig2017), Iacoviello (Reference Iacoviello2015), Meh and Moran (Reference Meh and Moran2010), and Villa (Reference Villa2016). ^{Footnote 12} Key to this credit-to-GDP response is a realistic banking sector that is subject to endogenous bank balance-sheet constraints due to financial frictions. By contrast, standard financial accelerator models along the lines of Bernanke et al. (Reference Bernanke, Gertler, Gilchrist, Taylor and Woodford1999) do not necessarily imply that credit relative to GDP decreases after a contractionary financial shock (see, e.g. Christiano et al. (Reference Christiano, Motto and Rostagno2010), De Fiore and Tristani (Reference De Fiore and Tristani2013)). ^{Footnote 13} The reason is that, in these models, firms effectively borrow directly from households while financial intermediaries are simply a veil. Given that we are interested in shocks and dynamics similar to those observed during the GFC—when the financial sector has been at the center stage—we choose to focus on restrictions consistent with models featuring a more complex financial sector.

Within the set of empirical studies, Eickmeier and Ng (Reference Eickmeier and Ng2015) impose the same restriction on the credit-to-GDP ratio as we do. Furthermore, our credit-to-GDP restriction is also consistent with empirical findings by Fornari and Stracca (Reference Fornari and Stracca2012) and De Santis and Darracq-Paries (Reference De Santis and Darracq-Paries2015), who have credit and GDP included in their model and identify financial shocks with sign restrictions, but leave the credit-to-GDP response unrestricted.

While we need the credit-to-GDP restriction to ex ante disentangle financial shocks from other shocks (especially when we re-estimate the model over the pre-GFC sample), this restriction is not crucial for our key findings. When the restriction is dropped, credit relative to GDP still declines after contractionary financial shocks, and our key results remains unchanged. ^{Footnote 14}

Finally, we disentangle financial shocks from monetary policy shocks by using a conditional sign restriction. ^{Footnote 15} Specifically, we impose the restrictions described above, and then check the inflation response for each model which yields financial shocks satisfying the restrictions. If inflation falls on impact, the response of a central bank following a Taylor rule is unambiguously negative. In this case, we restrict the policy rate to decrease on impact. If inflation increases, we do not restrict the policy rate. In this way, we disentangle financial from monetary policy shocks. In standard New Keynesian and structural VAR models, monetary policy shocks move the interest rate in one direction, and the price level and output in the other direction (e.g. Peersman (Reference Peersman2005)). Given that we use the SSR, which translates (at least parts of) unconventional monetary policy measures into short-term interest rate movements, we apply the identification scheme to the full sample estimate of the model without distinguishing between non-ZLB and ZLB periods. In Section 4, we check whether this is valid by re-estimating the model over the pre-GFC period, by more explicitly accounting for monetary policy shocks, and by discussing the relationship between financial and monetary policy shocks. ^{Footnote 16}

We note that similar restrictions have been used in previous empirical work, which focuses on the real effect of financial shocks. However, this literature either restricts inflation to be positive or not to react on impact, or it restricts the policy rate to increase after expansionary financial shocks, which might also bias the inflation response. ^{Footnote 17} The novelty of our identification scheme is that it disentangles financial shocks from other structural shocks, while being fully agnostic on the response of inflation and of the policy rate.

Paustian (Reference Paustian2007) shows that one can sharpen the shock identification by identifying additional shocks. Hence, in addition to financial shocks, we also explicitly identify two key standard macroeconomic shocks which are typically found to be important drivers of the economy: aggregate supply and demand shocks. Contractionary aggregate demand shocks lead to a decline in real GDP, credit, inflation and the policy rate, and raise the credit-to-GDP ratio. This last restriction disentangles financial and aggregate demand shocks, and is for instance consistent with the effects of a preference shock in Iacoviello (Reference Iacoviello2015), Hristov and Huelsewig (Reference Hristov and Huelsewig2017) and Gelain et al. (Reference Gelain, Lansing and Natvik2017), or with the effects of a fiscal shock in Hristov and Huelsewig (Reference Hristov and Huelsewig2017). Contractionary aggregate supply shocks lead to a decline in GDP and stock prices, raise the credit-to-GDP ratio, and lead to a higher inflation.

Finally, we restrict the remaining $n-3=3$ shocks not to have the same characteristics as the identified shocks. Hence, the identified financial, aggregate demand and aggregate supply shocks are the only shocks that satisfy the restrictions. We impose all sign restrictions only on impact, and hence remain relatively agnostic.

Narrative restrictions

Beside sign restrictions, we employ two narrative restrictions in our identification scheme. These are based on the assumption, now widely accepted, that financial shocks were extremely important during the GFC. ^{Footnote 18} The first narrative restriction is imposed on the financial shock series: we impose that the largest contractionary financial shock over our sample period occurs in 2008Q3. The second narrative restriction is imposed on the historical decomposition: the absolute value of the contribution of the financial shock to the dynamics of the EBP in 2008Q3 is larger than the sum of the absolute value of the contributions of all other structural shocks. These restrictions deserve some discussion.

Our approach closely follows Ludvigson et al. (Reference Ludvigson, Ma and Ng2020) and Reference Ludvigson, Ma and NgLudvigson et al. (forthcoming) who impose restrictions on shocks, as well as AntolÍn-DÍaz and Rubio-RamÍrez (Reference AntolÍn-DÍaz and Rubio-RamÍrez2018) who restrain the historical decomposition. We impose one restriction on the shock and one on the historical decomposition, and hence exploit knowledge about realizations of financial shocks over time, and in comparison with realizations of other shocks in 2008Q3.

We choose 2008Q3 because it includes the month (September) when Lehman Brothers filed for bankruptcy, which is commonly associated as the major trigger of the Great Recession (see also Reference Ludvigson, Ma and NgLudvigson et al. (forthcoming)). While there had been financial turmoil before that date, with the burst of the subprime mortgage bubble in 2007, it is widely agreed that the largest shock hit the US economy (and probably also the rest of the world) in 2008Q3, with the collapse of Lehman Brothers in September 2008. The government had previously bailed out other major financial institutions (Bear Sterns, Fannie Mae, and Freddie Mac), and it came as a surprise that it decided not to rescue Lehman Brothers as well. This triggered financial market panic: stock prices tanked, and investors fled money market mutual funds. The shock spread through 2008Q4 and subsequent quarters. By 2008Q4, policy had already reacted: the US Congress passed a bailout bill in October 2008 and central banks tried to restore liquidity, for example, by directly issuing short-term loans for businesses, lowering interest rates to basically zero, and coordinating actions of central banks throughout the globe. Our timing choice is in line with Reference Ludvigson, Ma and NgLudvigson et al. (forthcoming) who focus on uncertainty shocks and find evidence of a large positive financial uncertainty shock in September 2008. It is also not inconsistent with Ludvigson et al. (Reference Ludvigson, Ma and Ng2020) who, in one of their applications, restrict the EBP credit spread shock to be particularly large either in September 2008 or in October 2008 or in both. In our view 2008Q4 was mostly characterized by the reaction to the Lehman shock, rather than by another financial shock, which is why we focus on 2008Q3 here. We have also checked whether any other shock (demand or supply shocks as well as the three other rotated orthogonalized residuals) has its extremum in 2008Q3 and found this not to be the case. Hence, financial shocks are the only shocks that have their extremum in 2008Q3.

Beside imposing that a particularly large contractionary financial shock occurred in 2008Q3, we also impose that the contribution of this shock to the EBP is very large. Given that the EBP is constructed as systematic deviations in the pricing of US corporate bonds relative to the issuers’ expected default risk, it should be relatively exogenous with respect to the rest of the economy, and it is plausible to assume an “overwhelming” contribution of financial shocks (as AntolÍn-DÍaz and Rubio-RamÍrez (Reference AntolÍn-DÍaz and Rubio-RamÍrez2018) put it) to the EBP in 2008Q3. To what extent the EBP is really largely exogenous to the rest of the economy is somewhat controversial in the literature. On the one hand, Furlanetto et al. (Reference Furlanetto, Ravazzolo and Sarferaz2017) find that credit shocks identified with sign restrictions explain 44% of the EBP’s forecast error variance at the 1-quarter horizon, and only 16% at the 20-quarter horizon. Gertler and Karadi (Reference Gertler and Karadi2015) find, moreover, a significant reaction of the EBP to monetary policy shocks. On the other hand, Gilchrist and ZakrajŠek (Reference Gilchrist and ZakrajŠek2012) recursively identify financial shocks and find that they explain a very large share of the EBP (median estimate: over 80%). Moreover, Caldara et al. (Reference Caldara, Fuentes-Albero, Gilchrist and ZakrajŠek2016) impose that financial shocks maximize the response of the EBP over a predefined horizon. We are more agnostic than Caldara et al. (Reference Caldara, Fuentes-Albero, Gilchrist and ZakrajŠek2016) and impose that financial shocks explain a large fraction of the EBP only in 2008Q3. We will show that there is room left for other shocks to explain EBP dynamics during the Great Recession.

In Section 4, we explore the robustness of our key results against alternative identification schemes. Importantly, while our baseline model and identification scheme allow us to disentangle financial from standard (macro and conventional monetary policy) shocks, we modify the model to explicitly separate financial shocks from other shocks such as technology news shocks or oil shocks. We also illustrate the effects of imposing the narrative restrictions in addition to the sign restrictions.

To implement the restrictions, we follow the algorithm in AntolÍn-DÍaz and Rubio-RamÍrez (Reference AntolÍn-DÍaz and Rubio-RamÍrez2018), described in Appendix B. We obtain 1000 draws from the posterior of the reduced-form coefficients that satisfy the baseline restrictions. We approximate their weights in the importance step by using 1000 draws.

4.1 Responses of credit supply and banking variables to the financial shock

To better understand the characteristics of our financial shock, and to validate that we are indeed identifying a financial shock, we explore the behavior of credit supply measures and banking variables. The series are again added one by one to the VAR, treating the endogenous variables from our baseline model as block exogenous for the added variable. We present the results in Figure 4.

Figure 4. Response of credit supply and banking variables to a one-standard deviation contractionary financial shock: Plot shows median impulse responses (lines) and 68% credible sets (shaded areas). Responses of the willingness to lend to consumers, lending standards, the bank return on assets, the nonperforming loans ratio and the bank capital ratio in percentage points. See text for a description of the variables.

First, we add survey measures of credit supply in order to verify whether our identified shock is consistent with the answers of banking sector survey participants. We use data from the Senior Loan Officer Opinion Survey on Bank Lending Practices: the net percentage of domestic respondents tightening standards for C&I loans (“tightening standards”) and the net percentage of domestic respondents reporting increased willingness to make consumer installment loans (“willingness to lend to consumers”). ^{Footnote 25} The willingness to lend to consumers decreases on impact after the contractionary financial shock, and remains negative for 1 year. Similarly, banks tighten their credit standards markedly on impact, and keep them above baseline for more than 1 year. Hence, both survey measures move in the expected direction.

Second, we include data on the return on assets of commercial banks, the ratio of nonperforming loans to total loans, the ratio of bank capital to total assets and the volatility of bank stock prices. Bank return on assets, a measure of bank profitability, decreases significantly and remains negative for about 2 years. This decrease is reflected in the response of the bank capital ratio, which also drops significantly on impact and remains negative for almost a year. The lower profitability translates into lower net worth, for example, bank capital, thus generating a weaker capital position. The ratio of nonperforming loans to total loans also rises significantly. The response is hump shaped, reaching its maximum after more than a year. The behavior of the nonperforming loans ratio follows closely the movement of GDP. The fall in economic activity after the financial shock worsens the balance sheets of entrepreneurs and households, which in turn delays scheduled loan payments (higher nonperforming loans). In addition, the volatility of bank stock prices increases significantly after the financial shock.

Overall, the response of these credit supply and banking variables are consistent with a financial shock.

4.2 Is the Great Recession period different?

One potentially critical point is that the Great Recession period might be different from more “normal” times; for example, because financial frictions are larger in crisis times or because the policy rate was constrained at its zero lower bound. To address this point, we re-estimate the model over the pre-GFC period, that is over the period 1988Q1–2007Q2. Figure 5 (left panel) shows that the positive inflation response after a contractionary financial shock is slightly weaker in the pre-GFC subsample, but the credible sets overlap suggesting that differences are probably not significant. ^{Footnote 26}

Figure 5. Does the GFC make a difference? Left graph: Impulse response functions of inflation to contractionary financial shocks, median baseline estimate (red solid line), and 68% credible sets (shaded areas), and pre-GFC estimate (blue dotted lines). Right graph: Historical decomposition of inflation, baseline model (all shocks: black solid line, financial shocks: red bars), and counterfactual contributions of financial shocks (based on structural shocks estimated over the full sample and reduced-form parameters estimated over the pre-GFC sample: blue dotted line). See text for details.

We also conduct a counterfactual experiment as follows. ^{Footnote 27} We combine the structural shocks from the full model and the reduced-form parameters from the pre-GFC model in order to assess whether one could have predicted positive contributions of financial shocks (assuming the shocks had been observed) to inflation dynamics after the GFC. The answer is yes, even though the counterfactual contributions of financial shocks are slightly smaller compared to those resulting from the baseline model (blue dotted line in Figure 5, right panel). In particular, using the parameter estimates from the pre-GFC subsample, we find that the fall in inflation between 2008 and 2009 would have been 0.4 percentage points larger absent the negative financial shocks.

Overall, we can conclude that our main finding that contractionary financial shocks increase inflation also holds for less turbulent times. It is interesting to note that this key finding cannot be explained by the zero lower bound and monetary policy not being able to respond to negative financial shocks by lowering the interest rate. Also, based on pre-crisis parameters and assuming that financial shocks had been observed, one could have predicted that inflation would not fall as much as implied by a simple Phillips curve relationship. This corroborates the extended Phillips curve estimation results presented in the Appendix.

4.3 Understanding the role of the narrative restrictions

We assess next the importance of narrative restrictions by removing them from the set of identifying restrictions. Figure 6 compares the baseline impulse responses with those obtained from a specification without the two narrative restrictions (blue lines). When narrative restrictions are dropped, our key result remains the same: inflation increases temporarily after contractionary financial shocks. However, the responses of the EBP, GDP and credit growth to financial shocks are slightly weaker. Moreover, inference for EBP and inflation dynamics after the financial shock worsens. Figure 7 shows the corresponding historical decomposition. When the narrative restrictions are dropped, the contribution of financial shocks to the EBP, credit growth and GDP during the GFC is much smaller. In addition, the contribution to inflation is also smaller, both during and after the GFC.

Figure 6. Impulse responses to a one-standard deviation contractionary financial shock—role of the narrative restrictions: Plot shows median impulse responses and 68% credible sets in the baseline model (solid red lines and shaded areas), and in the model without narrative restrictions (solid and dotted blue lines). The response of GDP is in percent; those of the other variables are in percentage points.

Figure 7. Historical decomposition of key variables—effects of the narrative restrictions: Plot shows contribution of all shocks to explaining the deviation of key variables from their deterministic component in the baseline model (solid black lines), contribution of financial shocks in the baseline (red bars) and in the model without narrative restrictions (blue dotted lines). Contributions to GDP are in percent; those to the other variables are in percentage points.

Figures C2–C4 in the Appendix further show the effects of removing the narrative restrictions on either the shocks or the historical decomposition. The figures reveal that the restriction on the shock size improves inference for inflation, while the restriction on the historical decomposition leads to more plausible contributions of the financial shock during the GFC. ^{Footnote 28}

4.4 (Unconventional) monetary policy shocks

In Section 2.3, we have argued that our identification scheme disentangles financial shocks from monetary policy shocks typically identified in the literature. Recall that monetary policy shocks move interest rates in one direction, and prices and output in opposite directions. By contrast, our financial shocks either move output, inflation and the policy rate in the same direction or move output and inflation in opposite directions.

However, the aggregate supply channels that may influence the transmission of financial shocks could also play a role in the transmission of monetary policy shocks. The cost channel of monetary policy is one specific example of a transmission channel that could cause inflation to fall after expansionary monetary policy shocks. The cost channel of monetary policy has been in fact brought forward as one explanation of the “price puzzle”, for instance, by Castelnuovo (Reference Castelnuovo2012) and Gaiotti and Secchi (Reference Gaiotti and Secchi2006a). If the cost channel is a relevant transmission mechanism, our financial shocks may not be disentangled from monetary policy shocks. Put differently, a monetary policy shock that affects funding costs is a specific type of financial shocks.

This concern should be even more relevant for unconventional monetary policy, which is at least in part designed to explicitly stimulate credit supply and lower funding costs and, through that, to stimulate economic activity and inflation. ^{Footnote 29} Existing work already emphasizes the link between unconventional monetary policy and credit supply or financial shocks. De Santis and Darracq-Paries (Reference De Santis and Darracq-Paries2015) explicitly identify unconventional monetary policy shocks in the euro area in a VAR model as shocks that increase credit supply. Moreover, in a time-varying parameter VAR for the USA, Prieto et al. (Reference Prieto, Eickmeier and Marcellino2016a) find that credit spread shocks have contributed positively to GDP growth from 2010 onwards. They argue that those credit spread shocks probably capture unconventional monetary policy actions.

We investigate here to what extent monetary policy actions lie behind our financial shocks. Figure 7 plots our financial shock estimates (solid line) against the monetary “policy news shock” measure taken from Nakamura and Steinsson (Reference Nakamura and Steinsson2018) (dashed line) in the last two decades of the sample. ^{Footnote 30} This “policy news shock” is based on high-frequency responses of current and expected future interest rates in a 30-minute window surrounding scheduled Federal Reserve announcements, and captures the effects of forward guidance. ^{Footnote 31} We normalize the shock series in Figure 8 so that negative values represent a monetary policy easing (which can be expected to raise credit growth and lower funding costs) and expansionary financial conditions and that the standard deviation is one over the period over which we plot the shocks.

Figure 8. Financial and monetary policy shocks: Identified financial shocks (solid line) and Nakamura and Steinsson (Reference Nakamura and Steinsson2018) monetary policy shocks (dashed line). The shocks are standardized so that negative values represent expansionary monetary policy and financial shocks. Both series have standard deviation of 1 over the considered sample. See text for details.

Figure 8 reveals that the two shocks are basically uncorrelated over the sample (correlation coefficient: $-0.03$ ). Financial shocks seem, however, somewhat correlated with monetary policy shocks around the 2001 recession and the GFC. In both episodes, the Federal Reserve strongly lowered the federal funds rate and provided liquidity to financial institutions in order to stabilize the financial system. ^{Footnote 32} In addition, in the course of the GFC the Federal Reserve lent directly to borrowers and investors in credit markets, and purchased longer-term securities. ^{Footnote 33} This finding is consistent with Eickmeier et al. (Reference Eickmeier, Metiu and Prieto2016) who find a price puzzle after an expansionary monetary policy shock in high-volatility periods. Similarly, Fry-McKibbin and Zheng (Reference Fry-McKibbin and Zheng2016) find that prices decline after expansionary monetary policy shocks in financial stress periods, but not in low stress periods. They argue that this is consistent with cost channel effects during financial stress periods.

We conduct two further checks. First, we include the Nakamura and Steinsson (Reference Nakamura and Steinsson2018) monetary policy shock as an explanatory variable in the VAR, and rerun the estimation and shock identification. ^{Footnote 34} The idea is that the monetary policy shock should capture all remaining uncontrolled effects of monetary policy shocks. Second, we identify a monetary policy shock in addition to the baseline shocks, by imposing that the policy rate increases and inflation, output and credit growth decrease on impact after a contractionary monetary policy shock. Figure 13 in the Appendix shows that, even after explicitly accounting for monetary policy shocks, the contractionary financial shock continues to have inflationary effects.

To sum up, results suggest that our financial shock is barely contaminated by monetary policy shocks, and that contractionary financial shocks cleaned from monetary policy shocks still produce positive effects on inflation. We find, if anything, some correlation between financial and monetary policy shocks in financial stress periods. One implication is that a monetary policy measure targeting credit supply and borrowing costs may act as an expansionary financial shock and thus exert downward pressure on inflation through the mechanisms discussed above. This would not be desirable in an environment of already low inflation. However, our results do not imply that the overall effects of expansionary monetary policy on inflation are negative. Although expansionary monetary policy might put a downward pressure on inflation through credit supply effects, demand-side effects leading to an increase inflation could predominate. Analyzing those would go beyond the scope of this paper.

4.5 Further robustness checks: other shocks and alternative measures of interest rates, inflation, and credit

We carry out a large battery of further robustness checks. We test whether we disentangle financial from other shocks including housing shocks, technology news shocks, oil shocks, and uncertainty shocks. This is achieved by adding additional variables one by one to the baseline model, and imposing additional restrictions to identify one additional shock at a time, as discussed in Appendix C. We note that, for computational reasons, it is not feasible to identify all shocks simultaneously. Moreover, we replace our measures of interest rates, inflation and credit with alternative measures and add inflation expectations to the model. Finally, we re-estimate the model over a longer sample period starting in 1973 and a monthly version of our model. None of these alterations changes our results, and we refer to Appendix C for details.