Loan Supply Shocks and the Business Cycle

This paper provides empirical evidence on the role played by loan supply shocks over the business cycle in the Euro Area, the United Kingdom and the United States from 1980 to 2010 by applying a time-varying parameters VAR model with stochastic volatility and identifying these shocks with sign restrictions. The evidence suggests that loan supply shocks appear to have a significant effect on economic activity and credit market variables, but to some extent also inflation, in all three economic areas. Moreover, we report evidence that the short-term impact of these shocks on real GDP and loan volumes appears to have increased in all three economic areas over the past few years. The results of the analysis also suggest that the impact of loan supply shocks seems to be particularly important during slowdowns in economic activity. As regards to the most recent recession, we find that the contribution of these shocks can explain about one half of the decline in annual real GDP growth during 2008 and 2009 in the Euro Area and the United States and possibly about three fourths of that observed in the United Kingdom. Finally, the contribution of loan supply shocks to the decline in the annual growth rate of loans observed from the peaks of 2007 to the troughs of 2009/2010 was slightly less than half of the total decline in the Euro Area and the United States and somewhat more than half of that in the United Kingdom.


Non-technical summary
It is widely agreed that financial intermediaries and credit markets more in general appear to have played a significant role in the context of the events which led to the severe recession experienced during 2008 and 2009 by advanced economies such as the Euro Area, the United Kingdom and the United States. Together with a number of other historical episodes in recent decades, such as the well documented "capital crunch" during the early 1990s recession in the US, these represent clear indications that credit markets may play a non-negligible role over the business cycle on a recurrent basis. In the context of understanding the role of credit markets over the business cycle, from a policy perspective it is important to assess the relative role of supply and demand forces in driving credit, output and inflation developments, as these factors may call for a very different response of monetary and fiscal policy. For example, an insufficient provision of loans to the private sector by banks caused by balance sheet constraints affecting financial intermediaries may require a different policy response compared to the case of declining loan growth due to declining demand from households and enterprises. In the former case measures to directly support the banking system may be needed, while in the latter case measures to directly support the real economy are likely to have priority. Another key challenge which policy-makers face is to disentangle the role of credit markets as propagators of shocks originating in other sectors of the economy (such as technological innovations, unexpected changes in oil prices or investors' changes in confidence, to make few examples relating to both aggregate supply and aggregate demand shocks) and as impulse mechanisms, that is sources of disturbances or shocks. Indeed, the provision of loans to the private sector by banks depends on the state of banks' capital and financing capability, which in turn change both (endogenously) due to the economy's changing conditions as well as (exogenously) due to factors directly affecting banks balance sheets. Clearly, the source of the potential problem is different in these two cases.
Against this background, it is important to quantify the contribution of supply shocks to loan growth. In this paper we propose a methodology which allows for such contributions to be estimated in the context of an empirical model which takes into account potentially important changes in the macroeconomy. To account for possibly significant changes in the macroeconomic environment is a potentially very important step in deriving reliable estimates of the impact of loan supply shocks, as major changes have been taking place in recent years, including the so-called Great Moderation starting in the mid-1980s to the early 1990s until the recent crisis started. Thus, we apply a time-varying parameter VAR with stochastic volatility and identify loan supply shocks with sign restrictions on impulse response functions. Moreover, we provide a systematic comparison of the role of loan supply shocks over the business cycle across the Euro Area, the United Kingdom and the United States from 1980 to 2010.
The main results of the empirical analysis are the following. First, loan supply shocks appear to have a significant effect on economic activity and credit markets, but to some extent also inflation, in all three economic areas. However, some differences across geographic areas can also be uncovered. For example, the short-term impact on real GDP and loan volumes appears to be stronger in the United States and, especially for loan growth, in the United Kingdom, than in the Euro Area. Second, the impact of these shocks may have changed over time, as for example the short-term impact of these shocks on real GDP and loans seems to have increased in all three economic areas over the past few years. Third, it appears that the contribution of loan supply shocks is particularly important during slowdowns.

Introduction
Financial intermediaries and credit markets more in general appear to have played a signi…cant role in the context of the events which led to the severe recession experienced during 2008 and 2009 by advanced economies such as the Euro Area, the United Kingdom and the United States. Indeed, the economic crisis was preceded and accompanied by …nancial turbulence in various segments of …nancial markets, such as the US subprime mortgage market and the international interbank short-term liquidity market. Moreover, Lehman Brothers'default in September 2008 clearly exacerbated the …nancial and economic crisis, also bringing at the centre of the attention questions regarding the actual state of banks'balance sheets and their ability to provide loans to households and non-…nancial corporations to …nance consumption and investment expenditure, among other e¤ects. In addition, it is widely agreed that speci…c developments in the banking industry, such as the process of securitisation and the increasing recourse to short-term debt, contributed markedly to the lending boom and housing bubble of the mid-2000s and subsequent credit slowdown and house price fall (Brunnermeier, 2009;Diamond and Rajan, 2009;Gorton, 2009).
From a policy perspective it is important to assess the relative role of supply and demand forces in driving credit, output and in ‡ation developments, especially during periods around crises such as the recent one. Indeed, these factors may call for a very di¤erent response of monetary and …scal policy. Clearly, an insu¢ cient provision of loans to the private sector by banks caused by balance sheet constraints a¤ecting …nancial intermediaries may require a di¤erent policy response compared to the case of declining loan growth due to declining demand from households and enterprises. Thus, for a central bank it is essential to know whether loan ‡ows to the private sector decline mainly because of problems a¤ecting balance sheets of banks or largely because the demand for credit is diminishing. In the former case measures to support the banking system may be needed, while in the latter case measures to support the real economy may have priority. Another key challenge which policy-makers face is to disentangle the role of credit markets as propagators of shocks originating in other sectors of the economy (such as technological innovations, unexpected changes in oil prices or investors'changes in con…dence, to make few examples relating to both aggregate supply and aggregate demand shocks) and as impulse mechanisms, that is sources of disturbances or shocks. Indeed, the provision of loans to the private sector by banks depends on the state of banks'capital and …nancing capability, which in turn change both (endogenously) due to the economy's changing conditions as well as (exogenously) due to factors directly a¤ecting banks balance sheets. Clearly, the source of the potential problem is di¤erent in these two cases.
Against this background, a key challenge for policy-makers is to quantify the contribution of supply shocks to loan growth. The purpose of this paper is to propose a methodology which allows for such contributions to be estimated in the context of an empirical model which takes into account potentially important changes in the macroeconomy and to provide some empirical evidence for the Euro Area, the United Kingdom and the United States. To account for possibly signi…cant changes in the macroeconomic environment is a potentially very important step in deriving reliable estimates of the impact of loan supply shocks, as major changes have been taking place in recent years. For example, there is evidence that the volatility of shocks my have changed over time (Cogley andSargent, 2005, Fernández-Villaverde andRubio-Ramírez, 2010). Moreover, in addition to the evidence for a Great Moderation starting in the mid-1980s to the early 1990s, depending on the countries considered, the recent economic and …nancial crisis may have induced a further gradual structural change in the economy, for example a¤ecting persistently economic agents' risk aversion, and although it may be too early to conclude to which extent fundamental underlying changes may have taken place it is important to allow for them. Thus, it is critical to estimate the impact of loan supply shocks in a framework which allows for possible changes in stochastic volatility and timevarying parameters. The model we use, a time-varying parameter VAR with stochastic volatility, seems particularly suited for the purpose of this paper. This is one of the main advantages of the approach adopted in this study compared to the macroeconomic literature which has attempted to estimate the e¤ects of loan supply shocks, which typically is based on …xed parameters and constant volatility models (Lown and Morgan, 2006;Bassett et al., 2010;Busch et al., 2010;Ciccarelli et al., 2010;De Nicolò and Lucchetta, 2011;Gilchrist and Zakrajšek, 2011;Hristov et al., 2011). The identi…cation of loan supply shocks we adopt is based on sign restrictions. The latter have been applied before to identify these shocks (see for example Musso, 2009;Busch et al., 2010;De Nicoló and Lucchetta, 2011;Hristov et al., 2011), but the way they have been speci…ed has in most cases limitations which we try to overcome, as we will argue below. A parallel literature, based on microeconomic data for banks and/or …rms, provides some insight into the relevance of credit supply shocks for recent loan developments in a number of economies (see for example, Albertazzi and Marchetti, 2010;Berrospiedo and Edge, 2010;Jiménez et al, 2012). These contributions, which can be seen as providing complementary evidence to the question addressed in this paper, are however conditioned by the more limited time span of the available data and econometric di¢ culties in applying time-varying parameters, thus forcing their authors to assume constant parameters, as opposed to the present contribution. Moreover, our paper is the …rst to provide a systematic comparison across the Euro Area, the United Kingdom and the United States.
The main results of the empirical analysis are the following. First, loan supply shocks appear to have a signi…cant e¤ect on economic activity and credit markets, but to some extent also in ‡ation, in all three economic areas. However, some di¤erences across geographic areas can also be uncovered. For example, the short-term impact on real GDP and loan volumes appears to be stronger in the United States and, especially for loan growth, in the United Kingdom, than in the Euro Area. Second, the impact of these shocks may have changed over time, as for example the short-term impact of these shocks on real GDP and loans seems to have increased in all three economic areas over the past few years. Third, it appears that the contribution of loan supply shocks is particulary important during slowdowns. For example, the contribution of these shocks can explain about one half of the decline in annual real GDP growth during 2008 and 2009 in the Euro Area and the United States and possibly about three fourths of that observed in the United Kingdom. Finally, the contribution of loan supply shocks to the decline in the annual growth rate of loans observed from the peaks of 2007 to the troughs of 2009/2010 was slightly less than half of the total decline in all three economic areas. The remainder of the paper is structured as follows. Section 2 illustrates the empirical approach and describes the data. Section 3 reports and discusses the results. Section 4 provides conclusions.

The empirical approach
In this section we describe the econometric model used as well as the data for the three economic areas considered.

The model
We carry out the analysis using a time-varying VAR model with stochastic volatility. Over the last few years, this model has become a quite popular tool in macroeconomics to address questions related to the evolution of the structure of the economy and the volatility of the shocks (see Cogley and Sargent, 2005, Primiceri, 2005, Benati, 2008, Canova and Gambetti, 2009, Gali and Gambetti, 2009. Moreover, D'Agostino, Gambetti and Giannone (2011) shows that the model has a good forecasting performance.
Let y t be a vector containing the variables of interest (real GDP, consumer prices, loan volumes, a composite lending rate and a reference short-term interest rate) and assume it satis…es y t = A 0;t + A 1;t y t 1 + ::: where A 0;t is a vector of time-varying intercepts, A i;t are matrices of time-varying coef-…cients, i = 1; :::; p and " t is a Gaussian white noise with zero mean and time-varying covariance matrix t . Let A t = [A 0;t ; A 1;t :::; A p;t ], and t = vec(A 0 t ); where vec( ) is the column stacking operator. Conditional on such an assumption, we postulate the following law of motion for t : where ! t is a Gaussian white noise with zero mean and covariance . We let t = F t D t F 0 t , where F t is lower triangular, with ones on the main diagonal, and D t a diagonal matrix. Let t be the vector of the diagonal elements of D 1=2 t and i;t , i = 1; :::; n 1 the column vector formed by the non-zero and non-one elements of the (i + 1)-th row of F 1 t . We assume that where t and i;t are Gaussian white noises with zero mean and covariance matrix and i , respectively. Let t = [ 0 1;t ; : : : ; 0 n 1;t ], t = [ 0 1;t ; : : : ; 0 n 1;t ], and be the covariance matrix of t . We assume that i;t is independent of j;t , for j 6 = i, and that t , t , ! t , " t are mutually uncorrelated at all leads and lags. Details about the estimation can be found in Appendix A.
The impulse response functions in this model are derived from the approximated MA representation where C t (L) = P 1 k=1 C k;t L k , C 0;t = I, t = P 1 k=0 C k;t A 0t , C k;t = S n;n (A k t ), A t = At I n(p 1) 0 n(p 1);n and S n;n (X) is a function which selects the …rst n rows and n columns of the matrix X.
Structural impulse response functions are derived using the (lower triangular) Cholesky factor S t of t (S t S 0 t = t ) and any orthogonal matrix H t (H t H 0 t = I). The class of structural representation is therefore de…ned as where e t = H 0 t S 1 t " t and D t (L) = C t (L)S t H t are the impulse response functions to structural shocks.

Data
For each economy we estimate one model including …ve variables: real GDP, a consumer price index, non-…nancial private sector loan volumes, a composite lending rate and a reference short-term interest rate. Chart 1 shows all time series used in the analysis, while details on the de…nition, treatment and sources of the data are reported in Appendix B.
The evolution of real GDP growth shows how all three economic areas experienced recessions in similar periods (the early 1980s, the early 1990s and between 2008 and 2009), although with some variation in terms of turning points. Moreover, the data are consistent with the evidence for a Great Moderation from the mid-1980s until the most recent crisis. It is striking how synchronised and of similar magnitude the slowdown in real GDP growth was between 2008 and 2009 across these economic areas.
The consumer price index selected for each economic area is that representing the main reference for the corresponding central bank: the harmonised index of consumer prices (HICP) for the Euro Area, the retail prices index (RPI) for the United Kingdom and the consumer price index (CPI) for the United States. In all three economic areas it is apparent how in ‡ation gradually declined during the 1980s and has been at relatively low and stable levels since the early 1990s, with signs of increased volatility only reappearing over the last few years.
The reference short-term interest rates are represented by the 3-month Treasury bill rates for the United Kingdom and the United States, while for the Euro Area we use the 3-month Euribor up to the beginning of the recent crisis. The crisis which started in August 2007 a¤ected interbank money markets signi…cantly with a loss of con…dence and associated disruption of unsecured interbank lending market, implying that the corresponding interest rates (Euribor or Eonia) may be of questionable representativeness as reference interest rates. Thus, we use the 3-month Euro Repo rate, for secured interbank lending, from 2007 onwards as a reference short-term interest rate for the Euro Area.
As regards to loan volumes, we consider series which correspond to indices for the outstanding amounts of loans granted by …nancial intermediaries to households and non-…nancial corporations, corrected for the impact of loan sales and securitisation. The latter correction is important to gauge the amount of loans originated by banks, as in recent years the fraction of loans granted and subsequently securitised and taken o¤ banks' balance sheets has been signi…cant. For the US we use data from the ‡ow of funds statistics, which include not only loans obtained by US households and non-…nancial corporations by commercial banks, which in contrast to the Euro Area and to some extent also the United Kingdom represent only a small fraction to total loans obtained by these sectors, but also loans from other sources (see for example ECB, 2009). The data show how the credit cycles in the three economic areas appear to be relatively synchronised.
For the composite lending rates a weighted average of lending rates for loans to households and for loans to non-…nancial corporations are used, with weights corresponding to the respective loan outstanding amounts. Since no o¢ cial series exists for any of these economic areas, we have constructed such series using available interest rates and (for the weights) loan data for the various loan categories. These series have some limitations, especially for the 1980s, as they do not cover all types of loans and are based on data not fully harmonised (for example across Euro Area countries, especially for the 1980s and to some extent also 1990s). The constructed series do not display unexplainable movements or excessive volatility and they seem to behave similarly across the three economic areas, but the limited quality of these data represents a source of uncertainty for the results of any analysis like the present one.

Identi…cation
We identify three shocks: a loan supply shock, an aggregate supply shock and an aggregate demand shock. Intuitively, a loan supply shock can be associated with various events, such as unexpected changes in bank capital available for loans (for example due to a change in regulatory capital ratio requirements), changes in bank funding (for instance following bank runs or the introduction of credible deposit insurance schemes or changes in the ceiling of the latter), changes in the risk perception of potential borrowers by bank management (for example following changes in key bank managerial positions or innovations in bank monitoring technology) or changes in the degree of competition in the banking sector. Examples of aggregate supply shocks include technology or productivity shocks, oil price shocks and labour supply shocks. Aggregate demand shocks include consumption or preference shocks, investment demand shocks, monetary policy shocks and …scal policy shocks.
Although the main focus of the paper is on loan supply shocks, identi…cation of aggregate supply and demand disturbances helps the identi…cation of the loan supply shock. Identi…cation is achieved by means of sign restrictions. As conventionally done, it is assumed that aggregate supply shocks move output and prices in the opposite direction, while aggregate demand shocks a¤ect the two variables with a response of the same sign. The three shocks, if expansionary (i.e., if causing an expansion in real GDP growth), increase loan supply (while contractionary shocks will have symmetric e¤ects). However, while expansionary aggregate demand and supply shocks increase the lending rate, loan supply shocks reduce it. The restrictions are summarized in Table 1 and are imposed on the variables only on impact (the sensitivity analysis section provides a discussion of how results change if restrictions are imposed also up to three periods after the shock). No restriction is imposed on the sign of the responses of short-term interest rates to any shock.
The idea underlying these restrictions is that, in the case of an expansionary loan supply shock, if a bank decides exogenously to expand the supply of loans to the private sector it would do so by increasing the quantity made available and/or by decreasing the lending rate (or, more likely, both), such that at aggregate level both e¤ects are observed. This would have an expansionary e¤ect on output as households would borrow more and use some of these funds to expand their consumption and enterprises would borrow more and use some of these funds to expand their investments. However, in contrast to other studies (for example, Busch et al. 2010) we leave the e¤ect on in ‡ation unspeci…ed as it is to some extent uncertain. Indeed, while the increased consumption and investment expenditure would imply in ‡ationary pressures, the lower lending rate implies a lower cost to …rms which could potentially respond by decreasing prices of their products. Since it is not obvious which e¤ect might prevail, we leave this impact unspeci…ed. Hristov et al. (2011) provide a discussion on how some benchmark DSGE models with a banking sector lead to e¤ects consistent with those imposed here for loan volumes and spreads (or lending rates) and real GDP, while the e¤ect on aggregate prices is ambiguous. The results suggest that the loan supply shock identi…ed has di¤erent features than a standard monetary policy shock, as for example the former leads to a decrease in short-term interest rates but a decrease in in ‡ation in the short run. Nevertheless, the robustness section also identi…es a fourth shock, a standard monetary policy shock, and shows that results for the loan supply shock are very similar. As regards aggregate supply and aggregate demand shocks, it is assumed that expansionary shocks of either category would induce an increase in the demand for loans, leading to an increase in loan quantities as well as an increase in the lending rate. Note that the aggregate demand shock includes also loan demand shocks, but we do not di¤erentiate the latter from other aggregate demand shocks as the variables included in the model do not allow for such distinction. The restrictions are imposed on the lending rate and not on the spread between the lending rate and the short-term interest rate as changes in the latter as well as loan volumes may also be induced by shocks other than loan supply, including for example wealth shocks (i.e. an expansionary wealth shock may induce an increase in the demand for loans, leading to a possible increase in the lending rate but also in ‡ationary pressures with a possible increase in the policy rate, with an uncertain sign of the spread in the short run). The robustness analysis section shows, however, that results are very similar if instead the restriction is imposed on the spread.
Technically speaking, at each point in time and for each draw of the reduced form coe¢ cients we draw H t in such a way that the elements of each row represent the coordinates of a point uniformly distributed over the unit hypersphere and that is orthogonal to the other points de…ned by the remaining columns, see Rubio-Ramirez, Waggoner and Zha (2009).

Evidence of time-variation
The evolution of the residual time-varying variances is shown in Chart 2. In most cases there is evidence of signi…cant time-variation in the residual variances, with spikes appearing most often in the most recent years in correspondence to the latest economic and …nancial crisis. Moreover, for interest rate there are clear signs of a decrease in their volatility during the …rst half of the sample. Overall, the evidence supports the use of stochastic volatility speci…cations for all three models. Table 2 shows the posterior mean of the trace of as well as 68% con…dence bands and the trace of 0 (i.e. the prior variance-covariance matrix). This is a way to establish whether time-variation in the parameters is a feature of the data, see Cogley and Sargent (2005). In all three cases, it appears to be the case that the trace of 0 is lower than the 16% percentile, pointing to the presence to time-variation in the data, as the sample points towards greater time-variation in the parameters than that of the prior selected.

The average e¤ect of loan supply shocks
The average impulse response functions to loan supply shocks over the whole sample period show remarkable similarities across the three economic areas. The posterior mean of the impulse responses and the 68% con…dence bands appear in most cases very similar (see Chart 3). For example, an expansionary loan supply shock seems to have a large but short-lasting (less than a year) impact on real GDP in all three cases. However, it appears to be stronger in the short run for the United Kingdom and United States, than for the Euro Area, although only moderately so. Moreover, for all three economic areas the impact on in ‡ation tends to be negative in the short run but positive in the medium run, suggesting that beyond the very short run the channel operating through the expansion of demand seems to prevail. However, in most cases the response of in ‡ation is very close to zero. On average, expansionary loan supply shocks seem to correspond to a larger increase in loan volumes in the United States and especially the United Kingdom compared to the Euro Area, and to a bigger decline in the lending rate in the United Kingdom than in the Euro Area and United States. However, the persistence of the e¤ect of the initial shocks tends to di¤er across areas, with a longer-lasting e¤ect appearing for both loan volumes and the lending rate in the United Kingdom.
It can be noticed that for the Euro Area and the United States the average short-term response of real GDP growth to a loan supply shock appears to be stronger than that of loan growth, which may appear puzzling at …rst sight. However, a possible explanation of such result can be associated with the possible reaction of …rms to such shock: for example, in the presence of an adverse loan supply shock, …rms may decide to cut immediately investments, with negative consequences for real GDP growth, while at the same time compensate for the lower availability of new loans by drawing on previously agreed upon credit lines, for example in order to maintain their stocks of products and for other short-term expenses. It can also be noticed that, as already mentioned, loan supply shocks tend to be associated with a decline in short-term interest rates in the short term but also with a decline in in ‡ation in the short term, thus suggesting that these shocks have di¤erent e¤ects than standard monetary policy shocks.
The average importance of loan supply shocks can be assessed on the basis of variance decompositions, shown in Chart 4 for various horizons. Overall, these shocks seem to explain a sizeable fraction of the variance of all variables in all three economic areas, especially beyond the very short horizon of one quarter. In all three areas, these shocks appear to explain about one …fth of the variance of both real GDP growth and in ‡ation. Loan supply shocks seem to explain a larger fraction of the variance of loan volumes in all three cases, ranging between 20% and 30% beyond very short horizons. Loan supply shocks appear to be less important to explain the variance of interest rates (both the lending rate and the short-term interest rate), explaining between 10% and 20% on average.

The evolution of the e¤ect of loan supply shocks over time
The evolution of the impulse responses over time for di¤erent horizons suggests that some time-variation can be detected in several cases (see Charts 5 to 9, as well as Appendix C). In general, it appears that the short-term impact of these shocks on real GDP and loans may have increased in all three economic areas over the past few years (see Charts 5 and 7). For loan growth, also the medium-run (i.e. one-to three-year) impact of loan supply shocks seems to have increased in the most recent years (see Chart 7). For in ‡ation, the response to loan supply shocks appears to be most often close to zero (Chart 6). Finally, the responses of the lending rate and the short-term interest rate appear to have remaind close to zero beyond the short term in all three areas over the whole period, with at most signs of a slightly stronger response of the lending rate in the initial part of the sample in all three economic areas (see Chart 8).
Observing variance decompositions over time also provides some impression of timevariation in some cases (see Chart 10 and Appendix D). More speci…cally, the fraction of real GDP growth variance explained by loan supply shocks appears to have increased in the Euro Area since the mid-1990s and in the United States since the early 2000s. Similar evidence can be detected for the lending rate. By contrast, for in ‡ation, loan growth and short-term interest rates no major signs of time-variation can be detected in all three economic areas.
The evolution of the e¤ect of loan supply shocks can also be assessed on the basis of historical decompositions, or counterfactuals (which indicate how each variable would have evolved in the absence of these shocks). Overall, it appears that the contribution of loan supply shocks is particulary important during slowdowns (see Chart 11). For example, the contribution of these shocks can explain about one half of the decline in annual real GDP growth during 2008 and 2009 in the Euro Area and the United States and possibly about three fourths of that observed in the United Kingdom. Similarly, in all three economic areas loan supply shocks appear to have contributed to a large extent to the recessions of the early 1990s. Loan supply shocks accounted also for signi…cant fractions in the evolution of loan volumes in all three economies over the whole sample period. In particular, in the absence of loan supply shocks the decline in the annual growth rate of loans observed from the peaks of 2007 to the troughs of 2009/2010 would have been about 30% smaller in the United States and 40% smaller in both the Euro Area and the United Kingdom. The sensitivity exercises suggest that these estimates may be slightly higher for the Euro Area and United States, but the di¤erence is minor and does not change the picture substantially. Loan supply shocks also contributed to drive the evolution of in ‡ation and interest rates in all three economies in speci…c periods. This appears to be the case, for example, for the decline in in ‡ation in 2009 as well as the declines in the lending rate and short-term interest rates from 2008 to 2010.

The role of loan supply shocks during speci…c recessions and recoveries
As discussed in the previous section, counterfactuals indicate that loan supply shocks appear to have played signi…cant roles in driving both the early 1990s and the 2008/2009 recessions in all three economic areas. This is con…rmed by the impulse responses of real GDP especially during the most recent recession in all three economies, as the impact responses are clearly stronger than the average ones (see Charts 12 to 14). 1 By contrast, the di¤erence between the responses during the early 1990s recession do not seem very much di¤erent from the average ones. Similar evidence emerges for the responses of loans to loan supply shocks, with stronger impacts observed for the most recent recession, especially for the Euro Area and the United Kingdom, while not much di¤erence can be observed for the early 1990s recession.
A comparison of the responses across recent recessions and the subsequent recoveries -de…ned here as developments in the four quarters following the trough -suggests that no major asymmetries emerge. In particular, in most cases the response of real GDP to loan supply shocks during the recessions discussed and subsequent recoveries appears very similar. Similarly, the responses of loan growth to the loan supply shock are very similar across these recessions and recoveries. Thus, there does not seem to emerge evidence of systematic asymmetries across business cycle phases in the response of loan supply shocks.
Beyond counterfactuals and impulse responses during speci…c business cycle phases, the series of structural shocks can also provide useful information on the role of loan supply shocks around recession periods. Moreover, a visual inspection of these series can provide an indirect way to assess the plausibility of the method adopted to identify loan supply shocks. Indeed, although there is no perfect way to assess whether the shocks identi…ed correspond in fact to exogenous or unexpected changes in loan supply, an informal assessment of their plausibility can be undertaken by observing the series of structural shocks and discussing particular spikes with reference to anecdotal information on real world events. Chart 15 shows the series for the loan supply shocks for all three economic areas. It can be observed that large negative spikes can be found in all three cases in the periods around the default of Lehman Brothers (September 2008), which presumably had an immediate unexpected adverse e¤ect on the balance sheet of most banks, among other e¤ects. For the Euro Area three negative spikes can be seen from 2008Q2 to 2008Q4 and a bigger one in 2009Q1, while for the United Kingdom and the United States two consecutive negative spikes can be found for 2008Q2 and 2008Q3. Moreover, for the United States large negative spikes can also be observed in the early 1990s, in coincidence with the so-called "capital crunch " associated to the early 1990s recession (Bernanke and Lown, 1991;Peek and Rosengren, 1995) and in 1999, in the aftermath of the Long-Term Capital Management crisis. 2 Overall, it can be observed that in all three economies considered a number of consecutive negative spikes can be found during the most of the main recessions. Moreover, these series are in line with a signi…cant role played by adverse loan supply shocks during the early 1990s and 2008/2009 recessions in all three economies.

Sensitivity analysis
In order to assess the robustness of results, we undertake various exercises. First, we examine how the main results change if the identi…cation restrictions are imposed on more than one period, up to four periods. Second, we carry out the analysis estimating the model with only four variables, that is without the short-term interest rate which was not used in the identi…cation scheme but was included as a core variable typically included in VARs. Third, we estimate the model with only four variables but with the spread between the lending rate and the short-term interest rate instead of the lending 2 A comparison of the loans supply shocks with available banking survey data would be tempting but would have severe limitations. Indeed, indicators from surveys such as the ECB Bank Lending Survey, the Federal Reserve's Senior Loan O¢ cer Opinion Survey or the Bank of England's Credit Conditions Survey are all endogenous, that is they re ‡ect changes in response to both the economic situation and exogenous changes independent of the latter. Trying to estimate both components is di¢ cult and inevitably a¤ected by high uncertainty, not least due to the short span of the survey indicators.
rate. Fourth, we use the baseline model with the …ve variables used in the main analysis but also identify a fourth shock, more precisely a standard monetary policy shock. Rather than showing how all results change with these modi…cations we focus on two main sets of results, the average impulse responses and the counterfactuals.
As regards the …rst sensitivity exercise, Chart 16 shows the average impulse responses (with 68% percentiles) for four cases. In the …rst, restrictions are imposed only on impact (K=1, baseline model); in the second, restrictions are imposed on impact as well as on one period after that (K=1&2); in the third, restrictions are imposed on impact as well as on …rst two periods after that (K=1&2&3); and in the fourth restrictions are imposed on impact as well as on subsequent three periods after that (K=1&2&3&4). 3 It can be noticed that results are very similar in all cases across these four sets of restrictions. Chart 17 shows that counterfactuals are also very similar for all variables for all economic area across the four scenarios. Very similar results are found also for average variance decompositions and series of structural shocks to loan supply, with notable spikes in the same periods as discussed above (not shown but available upon request).
As regards the second sensitivity exercise, Chart 18 shows the average impulse responses (with 68% percentiles) for two cases: i) model with …ve variables and restrictions imposed only on impact (baseline model); ii) model with four variables (i.e. excluding the short-term interest rate) and restrictions imposed only on impact. Also in this case the shape, magnitude and uncertainty bands of impulse responses are very similar across the two cases. The main di¤erence is that the short-term response of in ‡ation is more markedly negative in the case of the model with four variables in all three cases. Similarly, as shown in Chart 19, also the counterfactuals are barely distinguishable across the two sets of models. An exception as regards the latter is represented by the counterfactual for loan growth for the US, with the model with four variables pointing to a bigger contribution of loan supply shocks to the decline in loan growth between 2007 and 2009, by about 50% instead of only by about 30% as the counterfactual based on the baseline model suggests. By contrast, the counterfactuals for the Euro Area and the United Kingdom for loan growth are very similar, with only minor di¤erences emerging between the baseline case and the 4-variables model case.
As regards the third sensitivity exercise, Chart 20 shows the average impulse responses (with 68% percentiles) for two cases: i) model with …ve variables and restrictions imposed only on impact (baseline model); ii) model with four variables, but in contrast to the second sensitivity exercise with the spread between the lending rate and the short-term interest rate instead of the lending rate, and restrictions imposed only on impact. In this case some di¤erences emerge. First, the response of in ‡ation based on the smaller model becomes markedly positive in the short term for all three economic areas. Second, the responses of loans appears to be stronger in the short run in the case of the smaller model for all three economies. However, overall, the responses of real GDP and loans seem very similar across the two models. Similarly, Chart 21 shows that the counterfactuals based on the two models are in most cases very similar, with few exceptions. The latter include a stronger contribution of loan supply shocks to the decline in loan growth between 2007 and 2009 in the euro area, mildly so, and especially the United States, by about 45% instead of only by about 30% as the counterfactual based on the baseline model suggests. Moreover, in the case of the United Kingdom the impact of loan supply shocks on the decline of in ‡ation in 2009 seems much smaller in the case the 4-variables model than the baseline model.
As regards the fourth sensitivity exercise, we estimate in both cases the baseline model with the same …ve variables but identify in the alternative case also a fourth shock, a standard monetary policy shock. For this purpose, in the alternative model with four shocks some changes in the identi…cation scheme are needed. As shown in Table 3, the standard monetary policy shock is identi…ed by assuming that on impact an expansionary monetary policy shock would be associated with a decrease in the shortterm policy rate and increases in real GDP in ‡ation and loan volumes (presumably driven by higher loan demand). By contrast, no assumption is imposed on the response of the lending rate as it is not needed and it might be uncertain, with the decline in the policy rate possibly implying some pass-through to the lending rate (although it sometimes takes more time for banks to pass-through such changes) but the implied increase in loan demand possibly implying some upward pressure on the lending rate. In order to di¤erentiate the aggregate demand shock from the standard monetary policy shock, we assume that the former leads to an increase in interest rates on impact in the case of an expansionary shock, as presumably the central bank would respond to an expansionary (non-monetary policy) demand shock by tightening interest rate due to the in ‡ationary pressures emerging from such shock. In order to identify loan supply shocks, and in particular to di¤erentiate them from standard monetary policy shocks, we assume that they have the same e¤ects as in the baseline model with three shocks, except that the short-term impact on in ‡ation is negative, a choice driven by the results presented above which indicate that this tends to be the case in all three economies. Chart 22 suggests that the average impact of the loan supply shock based on the two models is very similar, with the main exception being the stronger negative response of in ‡ation on impact in all three economic areas in the case of the model with four shocks, which of course is a consequence of the identi…cation scheme adopted. Chart 23 shows that the counterfactuals based on the two models are in most cases very similar, with possibly only a slightly stronger contribution of loan supply shocks to the decline in loan growth between 2007 and 2009 in the Euro Area in the case of the model with four identi…ed shocks, now closer to 50% instead of only about 40% as the counterfactual based on the baseline model suggests.
Overall, the various sensitivity exercises carried out suggest clearly that the impact of loan supply shocks appears to be robust to a number of modi…cations in the baseline model and identi…cation scheme assumed, thus reinforcing the credibility of the results presented in the previous sub-sections.

Conclusions
This paper provides some evidence that loan supply shocks have played an important role in business cycle ‡uctuations in the Euro Area, the United Kingdom and the United States over the past three decades. The model adopted, a time-varying parameters VAR with stochastic volatility, seems to be particularly useful to capture the role of these shocks over the business cycle, as evidence can be found that this role has changed over time. The main results of the empirical analysis are the following. First, loan supply shocks appear to have a signi…cant e¤ect on economic activity and credit markets, but to some extent also in ‡ation, in all three economic areas. At the same time, some di¤erences across geographic areas can also be uncovered. For example, the short-term impact on real GDP and loan volumes appears to be stronger in the United States and, especially for loan growth, in the United Kingdom, than in the Euro Area. Second, the impact of these shocks may have changed over time, as for example the short-term impact of these shocks on real GDP and loans seems to have increased in all three economic areas over the past few years. Third, it appears that the contribution of loan supply shocks is particulary important during slowdowns. For example, the contribution of these shocks can explain about one half of the decline in annual real GDP growth during 2008 and 2009 in the Euro Area and the United States and possibly about three fourths of that observed in the United Kingdom. Finally, the contribution of loan supply shocks to the decline in the annual growth rate of loans observed from the peaks of 2007 to the troughs of 2009/2010 was slightly less than half of the total decline in all three economic areas considered.

Appendix A -Estimation
Estimation is done using Bayesian methods. To draw from the joint posterior distribution of model parameters we use a Gibbs sampling algorithm along the lines described in Primiceri (2005). The basic idea of the algorithm is to draw sets of coe¢ cients from known conditional posterior distributions. The algorithm is initialized at some values and, under some regularity conditions, the draws converge to a draw from the joint posterior after a burn in period. Let z be (q 1) vector, we denote z T the sequence

Gibbs sampling algorithm
Step 1: sample from p( T jy T ; T ; T ; ; ; ; s T ) To draw T we use the algorithm of Kim, Shephard and Chibb (KSC) (1998). Consider the system of equations y t F 1 t (y t X 0 t t ) = D 1=2 t u t , where u t N (0; I), X t = (I n x 0 t ), and x t = [1 n ; y t 1 :::y t p ]. Conditional on y T ; T , and T , y t is observable. Squaring and taking the logarithm, we obtain where y i;t = log((y i;t ) 2 + 0:001) -the constant (0.001) is added to make estimation more robusti;t = log(u 2 i;t ) and r t = log i;t . Since, the innovation in (7) is distributed as log 2 (1), we use, following KSC, a mixture of 7 normal densities with component probabilities q j , means m j 1:2704, and variances v 2 j (j=1,...,7) to transform the system in a Gaussian one, where fq j ; m j ; v 2 j g are chosen to match the moments of the log 2 (1) distribution. The values are: Let s T = [s 1 ; :::; s T ] 0 be a matrix of indicators selecting the member of the mixture to be used for each element of t at each point in time. Conditional on s T , ( i;t js i;t = j) N (m j 1:2704; v 2 j ). Therefore we can use the algorithm of Carter and Kohn (1994) to draw r t (t=1,...,T) from N (r tjt+1 ; R tjt+1 ), where r tjt+1 = E(r t jr t+1 ; y t ; T ; T ; ; ; ; s T ; ) and R tjt+1 = V ar(r t jr t+1 ; y t ; T ; T ; ; ; ; s T ).
Step 2: sample from p(s T jy T ; T ; T ; T ; ; ; ) Conditional on y i;t and r T , we independently sample each s i;t from the discrete density de…ned by P r(s i;t = jjy i;t ; r i;t ) / f N (y i;t j2r i;t + m j 1:2704; v 2 j ), where f N (yj ; 2 ) denotes a normal density with mean and variance 2 .
Step 3: sample from p( T jy T ; T ; T ; ; ; ; s T ) Consider again the system of equations F 1 t (y t X 0 t t ) = F 1 tŷ t = D 1=2 t u t . Conditional on T ,ŷ t is observable. Since F 1 t is lower triangular with ones in the main diagonal, each equation in the above system can be written aŝ y 1;t = 1;t u 1;t (9) y i;t = ŷ [1;i 1];t i;t + i;t u i;t i = 2; :::; n where i;t and u i;t are the ith elements of t and u t respectively,ŷ [1;i 1];t = [ŷ 1;t ; :::;ŷ i 1;t ].
Step 4: sample from p( T jy T ; T ; T ; ; ; ; s T ) Conditional on all other parameters and the observables we have Draws for t can be obtained from a N ( tjt+1 ; P tjt+1 ), where tjt+1 = E( t j t+1 ; y T ; T ; T ; ; ; ) and P tjt+1 = V ar( t j t+1 ; y T ; T ; T ; ; ; ) are obtained with the algorithm of Carter and Kohn (1994).
Step 5: sample from p( jy T ; T ; T ; T ; ; ; s T ) Conditional on the other coe¢ cients and the data, has an Inverse-Wishart posterior density with scale matrix 1 1 = ( 0 + P T t=1 t ( t ) 0 ) 1 and degrees of freedom df 1 = df 0 + T , where 1 0 is the prior scale matrix, df 0 are the prior degrees of freedom and T is length of the sample use for estimation. To draw a realization for make df 1 independent draws z i (i=1,...,df 1 ) from N (0; 1 1 ) and compute = ( Gelman et. al., 1995).
Step 6: sample from p( i;i jy T ; T ; T ; T ; ; ; s T ) Conditional the other coe¢ cients and the data, has an Inverse-Wishart posterior density with scale matrix log t ( log t ) 0 ) 1 and degrees of freedom df 1 = df 0 +T where 1 0 is the prior scale matrix and df 0 the prior degrees of freedom. Draws are obtained as in step 5.
Step 7: sample from p( jy T ; T ; T ; T ; ; ; s T ). Conditional on the other coe¢ cients and the data, i has an Inverse-Wishart posterior density with scale matrix 1 i;1 = ( i;0 + P T t=1 i;t ( i;t ) 0 ) 1 and degrees of freedom df i;1 = df i;0 + T where 1 i;0 is the prior scale matrix and df i;0 the prior degrees of freedom. Draws are obtained as in step 5 for all i.
We make 15000 repetitions discarding the …rst 10000 and collecting one out of …ve draws.
to households (Flow of Funds de…nitions and codes: "Households and nonpro…t organizations; credit market instruments; liability" FL154104005.q minus "Nonpro…t organizations; municipal securities and loans; liability" FL163162005.q) and loans to non-…nancial corporations (Flow of Funds de…nitions and codes: "Non…nancial business; credit market instruments; liability" FL144104005.q minus "Nonfarm non…nancial corporate business; commercial paper; liability" FL103169100.q, "Nonfarm non…nancial corporate business; municipal securities and loans; liability" FL103163003.q and "Nonfarm non…nancial corporate business; corporate bonds; liability" FL103162005.q). Downloaded from www.federalreserve.gov/releases/z1/ current/. Sources: Flow of Funds Accounts of the United States, Board of Governors of the Federal Reserve System.

Composite lending rates
Euro area: Composite lending rate, derived as weighted average of interest rates charged on loans to households and loans to non-…nancial corporations, with weights based on the nominal outstanding amounts (or, if not available, ‡ows) of loans to households and to non-…nancial corporations. Sources: Own calculations based on data from the European Central Bank.
United Kingdom: Composite lending rate, derived as weighted average of interest rates charged on loans to households and loans to non-…nancial corporations, with weights based on the nominal outstanding amounts of loans to households and to non-…nancial corporations. Composite lending rate for non-…nancial corporations derived from quarterly average of UK resident monetary …nancial institutions' (excl. Central Bank) sterling weighted average interest rate on other loans, new advances to private non-…nancial corporations (in percent), not seasonally adjusted (Bank of England Statistical Interactive Database code: CFMBJ82, see www.bankofengland.co.uk/ mfsd/iadb/NewIntermed.asp) from 2004Q1 onwards; extended backwards to 1999Q1 using the (…rst di¤erence of) quarterly average of UK resident monetary …nancial institutions' (excl. Central Bank) sterling weighted average interest rate, other loans to private non-…nancial corporations (in percent), not seasonally adjusted (Bank of England Statistical Interactive Database code: CFMHSDC, see www.bankofengland.co.uk/ mfsd/iadb/NewIntermed.asp); extended backwards using Bank of England estimates for corporate bond rate. Composite lending rate for households derived as composite of lending rate of mortgage rate (IUMTLMV, see www.bankofengland.co.uk/ mfsd/iadb/ NewIntermed.asp, from 1995Q1 onwards, extended back using di¤erences in BIS data -average of mortgage rates by building societies and retail banks-until 1985Q1, extended back using di¤erences in Council of Mortgage Lenders, CML, building societies basic mortgage rate), personal loan rate (IUMHPTL, see www.bankofengland.co.uk/ mfsd/iadb/NewIntermed.asp, from 1995Q1 onwards, extended back using di¤erences in Bank of England estimates for personal loan rates data) and credit card rate (IUMCCTL, see www.bankofengland.co.uk/ mfsd/iadb/NewIntermed.asp, from 1995Q1 onwards, extended back using di¤erences in Bank of England estimates for credit card rates data), with weights based on outstanding amounts of corresponding loan categories. Sources: Own calculations based on data from the Bank of England.
United States: Composite lending rate, derived as weighted average of interest rates charged on loans to households and loans to non-…nancial corporations, with weights based on the nominal outstanding amounts of loans to households and to non-…nancial corporations. Composite lending rate for non-…nancial corporations derived as average of bank prime loan rate prime rate on short-term business loans (Fred II: MPRIME, see http:// research.stlouisfed.org/fred2/) and commercial and industrial loan rate ( (2005), since the value of the trace of the prior variancecovariance matrix is smaller that even the 16% percentile, this can be interpreted as evidence pointing to the presence of time variation in the parameters of the VAR (i.e. the sample points towards greater time variation in the parameters than that of the prior selected). Note: Fractions of variances of each variables explained by loan supply shocks at various horizons. "LS" stands for fraction of variance explained by loans supply shocks, while "OTH" stands for fraction of variance explained by other shocks. Note: Counterfactual exercises: evolution of variables in the absence of loan supply shocks. Model with 5 variables includes real GDP growth, inflation, non-financial private sector loan growth, the composite lending rate and the short term interest rate (baseline model). Model with 4 variables includes only the latter first four variables (i.e. the variables on which sign restrictions are imposed). "K" is the number of periods over which the sign restrictions are imposed. K=1 refers to restrictions imposed only on impact (baseline).

Chart 21 -Counterfactual: variables evolution in the absence of loan supply shocks for alternative models
Euro Area United Kingdom United States real GDP growth inflation loan growth Note: Counterfactual exercises: evolution of variables in the absence of loan supply shocks. Model with 5 variables includes real GDP growth, inflation, non-financial private sector loan growth, the composite lending rate and the short term interest rate (baseline model). Model with 4 variables includes real GDP growth, inflation, non-financial private sector loan growth and the spread between the composite lending rate and the short term interest rate. "K" is the number of periods over which the sign restrictions are imposed. K=1 refers to restrictions imposed only on impact (baseline).
Chart 23 -Counterfactual: variables evolution in the absence of loan supply shocks for alternative identification schemes Euro Area United Kingdom United States real GDP growth inflation loan growth lending rate short term interest rate Note: Counterfactual exercises: evolution of variables in the absence of loan supply shocks. "Model 5 variables, 3 shocks" is the baseline model, while "Model 5 variables, 4 shocks" also identifies monetary policy shocks (see text for details). In both cases, K=1.