Scuola Superiore di Studi Universitari e di Perfezionamento
Sant’Anna
Master of Science in Economics
Monetary Policy Effectiveness
in a Low-Interest Environment
Evidence from a Factor-Augmented
VAR
Supervisor: Candidate:
Prof. Alessio MONETA Omar Pietro Carnevale
Nominal and real interest rates started declining in the eighties, with the Great Fi-nancial Crisis deepening the already declining trajectory. As conventional monetary policy transmission mechanisms rely on interest-rate management, it is of utmost importance to characterize the reasons for this unusual dynamic. From a policy perspective, one may also ask whether monetary policy exerts a lower effectiveness when interest rate are persistently low.
The aim of the present work is twofold. On the one hand, it presents a thorough survey of the literature accounting for the observed declining trajectory of the last forty years. On the other, it provides fresh evidence from a FAVAR estimated on two subsamples, corroborating the provision that lower-for-long interest rates impinge upon monetary policy effectiveness. To uncover the responsible causal mechanisms, a FAVAR estimated on a single sample ascertains the operation of a risk-taking channel of monetary policy.
This work would have not seen the light without the precious supervision of Professor Moneta, to whom I reserve my sincere gratitude.
I dedicate this work to my family, my deepest source of joy and happiness. Nothing of the little steps I achieved would have been possible, if not were for their relentless support.
Last but not least, I dedicate this work to whom I deem to be more than friends–sisters, brothers, comrades– that every day gave me reason for smiling, and for keeping the stakes high. I shared with you the most beautiful days of my life, and I owe you more than you can imagine.
List of Figures 7
List of Tables 8
1 Introduction 9
2 Low interest-rate environment 12
2.1 The natural interest rate . . . 14
2.2 Secular Stagnation Hypothesis . . . 15
2.3 Controversies on the natural rate of interest . . . 17
2.3.1 Methodological issues . . . 17
2.3.2 Theoretical issues . . . 19
2.4 Financial-drag hypothesis . . . 21
2.4.1 The financial cycle . . . 22
2.4.2 Asymmetrical monetary policy responses . . . 25
2.6 Concluding remarks . . . 29
3 Monetary policy effectiveness in a low-interest environment 30 3.1 Literature review . . . 34
3.2 Empirical methodology . . . 35
3.2.1 Framework . . . 38
3.2.2 Application: the dynamic effects of monetary policy . . . 39
3.2.3 Estimation . . . 39
3.2.4 Identification . . . 41
3.3 Data . . . 42
3.4 Results . . . 43
3.4.1 Impulse-response analysis . . . 45
3.4.2 Forecast Error Variance Decomposition . . . 47
3.5 The risk-taking channel of monetary policy . . . 49
3.6 Literature review . . . 52
3.7 Data and identification strategy . . . 54
3.8 Results . . . 56
3.8.1 Impulse-response analysis . . . 56
3.8.2 Variance decomposition . . . 59
3.9 Concluding remarks . . . 59
A Data transformation 66
2.1 Nominal and real interest rates in the main advanced countries: 1980-2020 . . . 13
2.2 Financial and business cycles in the United states . . . 24
3.1 Scree-plot of factors extracted for the first sample and second sample 44
3.2 Estimated Impulse Responses of selected time series to 100-basis-point positive innovation in the short-term interest rate . . . 46
3.3 Lending Standards and Lending Margin in the Euro Area . . . 55
3.4 Estimated Impulse Responses of selected time series to 100-basis-point positive innovation in EONIA . . . 57
3.5 Estimated Impulse Responses of selected time series to 100-basis-point positive innovation in SHADOW RATE . . . 58
3.1 Summary statistics of extracted principal components . . . 45 3.2 Contribution of the policy shock to variance of the common component . . . 48 3.3 Contribution of the policy shock to variance of the common component- Risk Taking 59
Introduction
The global financial crises proved to be a defining moment in the history of the economic discipline, as it questioned the deep analytical foundations that years of tranquillity cemented and never challenged. Standard equilibrium models repre-sented economies as inherently stable, only temporarily getting off track. As a matter of fact, the analytical approach was concerned with stable states perturbed by limited external shocks; the intrinsic recurrent boom-and-bust dynamics charac-terizing economic systems were completely ruled out (Colander et al., 2009). The financial crises posed an enormous challenge also for policy institutions as they had to prevent the system’s implosion. Central banks found themselves reaching well beyond interest-rate policies, as severe distrust emerged in financial markets and liquidity provisions were needed for averting further distress. With policy mak-ers’ great surprise, the following years did not witness the rise of a new normality. Interest rates were stuck at zero, and monetary policy makers enriched their toolbox as conventional measures would not be operational within the zero-lower bound. Balance-sheet policies –asset purchase programmes of private and public bonds– were deployed with the view of counteracting the feared deflationary spiral. Sadly, feebler inflation dynamics and anemic growth turned to be defining characteristics of mature economies rather than temporary deviations sparked by the financial cri-sis. Other than immense bewilderment, these observations spurred research on the
long-term causes ushering in the great financial crisis. There is no more disagree-ment that the seeds of the global financial crisis were sown during the the Great Moderation (Borio, 2014a). But what specific mechanisms drove the upswing of the financial cycle, other than the deregulation wave initiated in the eighties? Did mon-etary policy regimes focused on price stability contribute increasing the fragility of the system? Should central banks incorporate financial developments when setting the monetary policy stance? The ample heterogeneity one may find in these answers mirrors the wide analytical disagreement of the causal explanations at hand.
The present work scrutinizes some implications for monetary policy effectiveness when central banks operate in crisis-prone environments where financial stability is not properly addressed. In particular, are low-interest rates here to stay? What are the consequences for monetary policy transmission mechanisms?
Chapter 2 reviews two competing theories enquiring the structural reasons of the observed interest rates dynamics, and stresses the different policy prescriptions im-plied by their respective analyses. The adopted explanation provisions that interest rates declined because of a perverse interplay between asymmetrical monetary policy responses and unfavourable financial developments. The main policy prescription is that central banks should systematically take into financial developments when setting the policy stance.
Chapter 3 reviews the factors accounting for lower monetary policy effectiveness in a low-interest environment. To add evidence and contribute to the dedicated lit-erature, a factor-augmented VAR (FAVAR) for the Euro Area is estimated, in two specific subsamples. Impulse response analyses and forecast error variance decom-position confirm that an expansionary monetary policy has a lower impact when interest rates trend down. In accordance with the proposed theoretical account, the found lower effectiveness is partly ascribed to the operation of a risk-taking channel of monetary policy. Results from a FAVAR estimated in the period 2003-2017 add evidence to expansionary monetary policy negatively influencing banks’ risk taking. The intuition is that central banks unwittingly contribute encouraging risk taking when aggressively easing in the bust phase of a balance-sheet recession. In other
words, asymmetrical monetary policy responses may undermine their own effective-ness.
Low interest-rate environment
Over the last forty years, both nominal and real interest rates witnessed a down-ward trend, with the Great Financial Crisis deepening the already declining trajec-tory (figure 2.1). This stylized fact spurred debate among economists on the most plausible theoretical account for explaining the observed phenomenon. Though nu-merous conjectures have been put forward, it is possible to classify the different theoretical explanations on the basis of a simple principle: whether or not they accept the existence of an equilibrium rate guiding the monetary policy stance in setting the relevant policy rates. In particular, authors believing in the existence of an interest rate equating ex-ante savings with ex-ante investments believe that observed interest declined because its equilibrium counterpart did; money is a veil that improves over barter. On the other hand, skeptics would reject the idea of a central banker mimicking passively the evolution of a purported equilibrium rate; they recognize instead that monetary policy may have long-lasting effects onto the wider economy.
Figure 2.1
Nominal and real interest rates in the main advanced countries: 1980-2020
Source: European Commission, AMECO
In what follows, we present the two main explanation one may find in the literature. (see for example Ferrero and Neri, 2017). Even though they are often considered not mutually exclusive in nature, we believe the two offer contrasting views for the phenomenon at stake. Before of analyzing each in turn, in section 1 we describe the major source of contention between the two theoretical accounts: the employ-ment of the natural rate of interest in explaining real interest rates decline. In section 2 we will document how the Secular Stagnation Hypothesis as put forward by Summers (2016, 2018) is closely linked with the natural interest rate development, while section 3 thoroughly discusses the theoretical and methodological controver-sies surrounding this equilibrium rate; this will enable us to consider in section 4 the alternative Financial-Drag hypothesis developed by researchers at the Bank of International Settlements (BIS) (cfr. Borio, 2017). In section 5 we derive testable implications and spell out relevant policy prescriptions. Section 6 presents our
con-cluding remarks.
2.1
The natural interest rate
The theoretical underpinning of the natural rate of interest is rooted in the neoclas-sical tradition, with the former being conceived as the intersection point between the supply and demand of loanable funds. (Levrero, 2019).
In particular, the supply of funds is modeled as the result of the optimal saving plan of a representative households that maximizes the present value of her utility sub-ject to a budget constraint. The saving schedule is represented as an upward-sloping curve with respect to the level of the interest rate (the substitution effect outweighs the wealth effect). 1
The demand of funds is determined by the amount of investment that maximizes profits of a firm for a given technology. Since interest rates constitute a cost in the firm-specific maximization problem, higher levels of interest reduce the demand of funds. As a result, the latter depends negatively on nominal interest rates deflated by future inflation. In this framework, ”productivity and thrift” set the natural or normal rate of interest, which equates the supply and demand of funds when the available resources are full employed (cf. Wicksell, 1936, 2013).
Even though it is admitted that the market rate might differ from its natural coun-terpart, the resulting deviations are at most temporary. The idea is that, with no frictions and rigidities in real markets, the joint operation of perfect competition and price movements will ensure that every factor of production is fully employed. For this reason, any attempt of the central banker to steer the policy rate in any di-rection will cause undesired price movements. In any case, in the long-run monetary ’disturbances’ are believed not to influence real quantities, as rigidities are phased out. Therefore, in the neoclassical tradition there exists a dichotomy between real
1The optimal saving due to variations of the interest rate depends on the relative strength of
two contrasting forces: the relative convenience to anticipate (postpone) consumption with respect future periods (substitution effect), and by the decreased (increased) wealth in the current period (wealth effect). If the substitution effects is supposed to always offset the wealth effect, one finds a positive relationship between the supply of funds and the interest rate.
and monetary variables: the quantity of money or the interest rates affect only mon-etary variables such us prices, while real variables are affected only by real factors. It is within the boundaries of this theoretical account that the Secular Stagnation Hypothesis finds its major arguments.
2.2
Secular Stagnation Hypothesis
In the Fall of 2013, Summers (2015) invoked the idea of secular stagnation, led by the observation that growth in advanced economies had been slower for longer than could be plausibly explained by the eruption of the Great Financial Crisis. In do-ing so, he revived the homonym conjecture put forward by Hansen after the Great Depression, according to which the essence of secular stagnation is ”sick recoveries which die in their infancy and depressions which feed on themselves and leave a hard and seemingly immovable core of unemployment” (Hansen, 1939, pag. 4). The core of the argument can be summarized in the following three propositions. First, the exogenous factors determining the position of both the saving and the investment schedules triggered an ongoing downward trend of the equilibrium rate. Second, in accordance with the neoclassical tradition, monetary policy influences are ruled out in the medium term. It follows that the observed real interest rate is supposed to follow passively its equilibrium counterpart. Third, the market rate being above the natural one can account for sluggish growth, low inflation, and an impaired financial system. The idea is that an higher-than-natural rate holds down aggregate demand, thereby causing both a slower output growth and a feebler infla-tion dynamics. Moreover, financial stability is hindered because a looser monetary policy (due to the central banker mimicking the natural interest) creates easy money that inflates asset prices and contributes reducing credit standards.
Before of thoroughly analyzing the soundness of the theoretical reasoning, it might be instructive to consider the factors affecting the saving-investment balance.
Funds are mainly used for financing investments; to this end, IMF (2014) documents an ongoing decline in the investment-to-GDP ratio in advanced economies that dates back the eighties. Two factors might account for this trend: a lower price of investment, and a lower investment profitability. The former contributes the most in explaining the observed downward trend, due to its declining trajectory exhibited during the last forty years; on the other hand, there is no sign of significant impaired investment profitability up to the financial crisis.
Shifts in saving
IMF (2014) also reports an increasing global saving-ratio since the 2000, which can be explained by an increasing saving-to-GDP ratio in emerging market economies. In particular, higher oil prices in oil exports countries partly account for this trend (as households become wealthier); moreover, demographic factors, financial con-straints, erosion of safety nets, and higher growth are other plausible explanations. In addition, higher global inequality as documented by Piketty (2013) fosters higher savings, since richer households have lower marginal propensity to consume.
It is worth analyzing the plausibility of this type of explanation for describing the declining trend of observed real rates. While leaving to the next section the careful assessment of the adequacy of the natural interest rate, we now highlight contro-versies surrounding the empirical analysis being conducted to support the Secular Stagnation Hypothesis. In particular, existing studies are carried out with the pur-pose of providing estimates of the factors determining the saving-investment balance, linking observable factors (e.g higher life expectancy) with an unobservable variable (the natural interest rate). In particular, once the existence of an equilibrium rate is assumed, the empirical exercises are content with finding correlation in line with theory, so that (e.g.) higher inequality might serve the purpose of explaining a shift in the saving curve, hence purportedly documenting a lower real rate (maintaining that the natural rate exists and influences the observed rates). As a matter of fact, these studies never test the maintained hypotheses of the plausibility that interest rates are determined in the market of loanable funds.
To the best of our knowledge, Borio et al. (2017) is the only study that system-atically examines the empirical link between real interests rates and the posited determinants, not only since the 1980s but also back in history. The authors find a tenuous link between real interest rates and observable proxies for the main saving-investment determinants once a longer sample is considered, thereby casting doubt on the reliability of the saving-investment framework for explaining the observed real rates development. Their account of the observed interest rates dynamic relies on the notion that monetary policy regimes, defined by the central banks’ inter-est rate-setting behaviour, play a central role in steering long-run real rates. This conjecture constitutes the backbone of the financial-drag hypothesis (see section 4).
2.3
Controversies on the natural rate of interest
The previous section brings evidence on the saving-investment framework not sur-viving a severe test linking its posited determinants with the observed trend of real interest rates. However, there are deeper reasons that cast doubts over the Secular Stagnation Hypothesis, and they are related to the specific notion of the natural interest rate. A critique assessment can be carried out on a methodological level, questioning the different techniques used for tracing its evolution over time. But more importantly, it is possible to challenge the theoretical notion of an interest rate determined in the market of loanable funds, with monetary policy not exerting any real effect. We address each critique in turn.
2.3.1
Methodological issues
Estimation procedures of the natural interest rate can be grouped in three main categories. In particular, one can distinguish time-series approaches, fully-fledged dynamic equilibrium models, or semi-structural econometric models (Levrero, 2019).
cycle component as a negligible disturbance that can be ignored over the long-run. To ascertain these trends, statistical tools encompass moving average of realized rates over the length of a business cycle, filtering techniques, and other weighting schemes. This class of methods share several weaknesses, the most relevant being the fact that the averaging of observed rates yields smooth time-series that can hardly be reconciled with the theoretical interpretation of its natural counterpart. In particular, if the natural interest is as an average, it cannot be subject to ample and sizeable variations corresponding to the shift that underlies the saving-investment relationship (see the previous section). All in all, no relevant estimate can be gauged from these data-driven methods.
In model-based estimates of the natural rate, a micro-founded structural model specifies all the relevant relationships characterizing the artificial economy, thereby representing all the real factors affecting interest rates. The natural rate is the result of an indirect estimation, obtained by the interaction of the relationships embedded in the model. In particular, counterfactual exercises allow the modeler to charac-terize sequences of equilibria where all real variables are at their natural level; the natural rate is derived in this way as a function technology and preference shocks. (Smets and Wouters, 2003; Barksy et al., 2014; C´urdia et al., 2015; Giammarioli and Valla, 2003). The most serious weakness of this approach is the high sensitiv-ity of the natural interest rate on the specific hypothesis underlying the structural relationships. The problem is compounded by the complexity of the model, so that the corresponding estimates of parameters and unobservable variables are hardly reliable for policy analysis.
Semi-structural approaches try to lower the risk that estimates of the natural rate are influenced by structural parameters of badly specified relations. This approach relies on parsimonious specifications of structural models. The natural rate is con-sidered a latent variable that is estimated via the Kalman filter, together with the other relevant parameters (see for instance Benati and Vitale, 2007; Laubach and Williams, 2003). While this method is less arbitrary with respect to the former, the same critique applies: the specifications of the model render the natural rate highly
dependant on the behavioral relationships the modeler envisages, even though there are less restrictions with respect to fully-fledged equilibrium models.
2.3.2
Theoretical issues
The sheer existence of a natural rate of interest determined by ”productivity and thrift” has been questioned since the publication of Keynes’s General Theory (Keynes, 1936). In particular, he argued that savings equalize investment by income changes, with the interest rate being determined in the money market. A preliminary assess-ment of his methodological modeling approach is needed for grasping the relevance of his analysis. To be specific, he never formulated relationships between variables as an interdependent system of simultaneous equations, where ’everything depends on everything else’. On the contrary, his analysis was more of a ’causal-type’, whereby the economic theorist specifies which variables are sufficiently interdependent for being represented as simultaneous relationships, and which instead show an over-whelming dependence on one side so as to be best represented as one-way relations (Pasinetti, 1974). With respect to the relationships between savings and invest-ments, he argued that the absence of any interdependence between the two curves prevents the determination of the level of interest for any given level of income. His alternative theoretical account presupposes that investments are obtained by relating expected profitability with levels of observed interest rates, with the latter being determined as the intersection point between liquidity preference and money supply. Once investments are determined, it possible to compute income, being it the sum of investments and consumption. It is only then that savings appear in to the picture as income not spent. A crucial result is that investments cause savings, because the former are determined prior to the latter.
Mainstream authors recognized that investments might not be interdependent of decisions to save, but only if one assumes that income is not at its potential level. Indeed, as Keynes also admitted, if the economy is at its full capacity, one may consider investments and savings being equal in correspondence of a specific level of the interest rate (the natural rate) (cf. Keynes, 1936, chap. 14). Even though
Keynes considered the full employment a special case, mainstream authors’ de-scribed Keynes’s analysis as ’The Economics of Depressions’, thus rehabilitating the neoclassical theory of the interest rate (cf. Hicks, 1937, p. 155)2. It took several decades for Post-Keynesians authors to provide better ground to an interest rate determination not embedded in the the saving-investment framework, thus showing the logical fallacies of mainstream analysis.
Keynes’s insights were downsized because of his willingness to accept some of the marginalist postulates. To support this claim, it is instructive to represent the neo-classical theory of interest as comprising two propositions.
Firstly, there is an inverse relation between the volume of planned investment and the rate of interest. Secondly, the latter is sufficiently sensitive so as to equilibrate possible divergences between investment and savings decisions.
Keynes’s different account of the rate of interest undermines the latter proposition, while accepting instead the more fundamental inverse relation between the rate of interest and planned investments.3 Admittedly, it is the acceptance of this postu-late that paved the way toward the rehabilitation of the neoclassical theory of the interest rate (Garegnani, 1979).
A more foundational critique questioned the possibility of drawing a downward slop-ing investment curve, thus pointslop-ing to some prior logical fallacies in the neoclassical notion of capital as ’factor of production’. In particular, capital is defined as a com-posite commodity of different capital goods; theory then postulates that in order to produce a given quantity of output, it is possible to employ capital and labour in different proportions, thus assuming a form of continuous substitutability between these factors of production. Consequently, given the marginal productivity of cap-ital, a lower interest rates favours a more capital-intensive production, since the
2Mainstream authors maintain that scarce resources are optimally employed if nothing prevents
perfect competition from operating. Admittedly, it is believed that Keynes’s analysis is valid only if some form of rigidity is assumed. However, Keynes showed that his analysis bears the same conclusions even without assuming specific frictions (cf. Keynes, 1936, chap. 19).
3In Keynes’s theoretical account, the determination of the rate of interest is heavily influenced
by agents’ expectation over the course of future interest rates development ; this renders the interest rate a highly conventional variable, deprived of its purported stabilization role with respect to savings and investments.
relative price of capital diminishes. A negatively sloped curve between the invest-ment curve and the interest rate is thus obtained. However, it has been shown that the dependence of the value of capital on prices and thus on the rate of interest inhibits the possibility to treating capital as a datum of the theory when determin-ing relative prices (cf. Sraffa, 1960). Hence, it is impossible to draw a a decreasdetermin-ing investment curve for any given level of capital (Garegnani, 1970).
Motivated by empirical, methodological and theoretical issues, we review a different theoretical account not relying on the employment of an equilibrium interest rate.
2.4
Financial-drag hypothesis
The provision according to which the decline of interest rates reflects only the struc-tural evolution of the economy would be satisfactory only in a real economy, where money exists only for allowing exchange to proceed costlessly and smoothly, assur-ing perfect coordination among trades (Borio and Disyatat, 2010). However, the recognition that our economies are monetary in nature permits a more realistic de-scription for the phenomenon of interest.
In a monetary economy, the banking system does not transfer savings from house-holds to firms, but rather generates nominal purchasing power. As a matter of fact, deposits are not needed for generating loan: loan formation precedes deposit cre-ation. The fact that a plethora of financial institutions might generate purchasing power is a fundamental characteristic of capitalist economies, since it enables an endogenous credit creation.4 While acting it as the oil for the economic machine,
money creation is also a major source of financial instability, since it might be poorly pinned down by loose perception of value and risks (Borio, 2014b). Since financial imbalances resulting from unanchored loans formation might severely damage the real economy, it is relevant to characterize which are the factors influencing financial
4If money creation were exogenous, as the quantity theory of money presupposes, credit would
be constrained by the the high-powered money the central bank is willing to inject in a specific moment.
institutions’ behaviour when extending credit. To that end, monetary policy plays a crucial role, since short-term interest rates decision establishes the cost of leverage for a currency area (Drehmann et al., 2012).
According to the financial drag hypothesis, the decline of observed interest rate is the result of a series of financial booms gone wrong, together with asymmetrical policy responses (Borio, 2017). The argument is that financial imbalances became more frequent since the 1980s, thereby requiring an accommodating policy stance for avoiding a major depression in the aftermath of the bust phase. However, since policies did not target financial imbalances development, further financial disrup-tions occurred and policy rates were pushed into a declining trajectory. This created a perverse loop between policy responses and financial imbalances, increasing the fragility of the economic system. To better assess these claims we introduce the concept of financial cycle, and we also highlight what monetary policy might have done differently for addressing the issues at hand.
2.4.1
The financial cycle
While no unique definition of financial cycle exists, we denote the term as represent-ing the ’self-reinforcrepresent-ing interactions between perceptions of value and risk, attitudes toward risk and financial constraints, which translate into booms followed by busts’ (Borio, 2014b, pag. 183, emphasis added ). For the purpose at hand it is necessary to understand the nature of these interactions as well as their feedback rules; prior to that, we need to characterize the core features defining the financial cycle.
Feature 1
There is wide agreement on the procyclical nature of the financial system, meaning its tendency to follow the development of the business cycle and to amplify the lat-ter’s fluctuations (Adrian and Shin, 2010; Borio et al., 2001; Brunnermeier et al., 2009; Danıelsson et al., 2004; Kashyap et al., 2004). An explanation of the pro-cycicality underlines the information asymmetries existing between borrowers and
lenders, and it is known as ’financial accelerator’ hypothesis (cf. Bernanke et al., 1999). The intuition is that in a depressed economic environment, where collat-eral value is low, even agents with profitable investment projects might find diffi-culties in obtaining funding. On the contrary, prosperous conditions lull financial intermediaries thereby allowing firms to get easier access to external finance, quite independently of projects profitability considerations. The financial cycle might be procyclical also because financial market participants react inappropriately to change in risk over time. This might be due to measurement difficulties in the time dimension of risk, so that the latter is underestimated in booms and overestimated in recessions (Borio et al., 2001).
Feature 2
The financial cycle is described by the co-movement of medium-term cycles in credit and property prices, and not by asset prices as sometimes stated (Drehmann et al., 2012). These variables co-vary closely with each other, underlining the importance of credit in financing the construction and purchase of property. These variables adequately represents the interactions between financing constraints (credit) and perceptions of value and risks (property prices), thereby constituting a relevant information content for the financial cycle (Borio, 2014b).
Feature 3
The financial cycle has a lower frequency than the traditional business cycle. For the latter, statistical filters indicate frequencies from 1 to 8 years when distinguishing cyclical from trend components of GDP. By contrast, the average length of the financial cycle is around 16 years (Drehmann et al., 2012). Figure 2.2 illustrates this point for the United States. The blue line measures the financial cycle as obtained by a statistical filter considering both credit and property prices. The red line traces the business cycle in GDP as obtained by the corresponding statistical filter that targets frequencies up to 8 years. It clearly appears that the financial cycle has a greater amplitude.
By further inspecting this figure it emerges that peaks in financial cycle are closely associated with financial crises. Indeed, all the financial crises with domestic origin
Figure 2.2
Financial and business cycles in the United states
Source: Borio et al. (2018)
are close to the peak of the financial cycle. As a matter of fact, it is possible to measure the build up of financial crises in real time with fairly good accuracy (Borio, 2014b).
Feature 4
The amplitude, length, and disruptive force of the financial cycle depend on the financial, monetary, and real-economy regime that are in place in a specific moment (Borio and Lowe, 2002). Let us consider each in turn.
Figure 2.2 highlights that the length and amplitude of the financial cycle has in-creased from the mid-1980s, which is a good approximation for the start of the financial liberalisation phase in advanced economies (Borio and White, 2004). Fi-nancial arrangements in the late 1970s restricted the free play of market forces. For instance, on the liability side of banks’ balance sheets, these constraints implied ceil-ings on deposit rates; on the asset side, quantitative interest rate controls were often in place. By the early 1990s, many of these constraints had been undermined by market developments. The main result of the liberalisation process was a major rise in competitive pressures and hence easier access to external funding. In addition,
liberalisation led to a much richer spectrum of tradable instruments.
As for the real-economy regime, and its influence to the lengthening of the financial cycle, globalisation represented a major positive supply side development; it con-tributed raising growth potential and increasing the scope for credit and asset prices booms.
Moreover, the early 1980s marked the beginning of a monetary policy regime where central banks enshrined price stability as the main objective to be pursued. Policy-makers’ focus was on equity prices and standard business cycle measures, thereby downplaying the role of monetary and credit aggregate development. This drove them to loose sight of deep-seated forces that contribute to the upswing of the fi-nancial cycle. Indeed, disruptive fifi-nancial imbalances build up even alongside low and stable inflation.
In the next subsection we enquire how an inflation-targeted monetary policy might have increased the fragility of the financial regime, thereby contributing in imparting a downward trend to observed policy rates.
2.4.2
Asymmetrical monetary policy responses
Financial cycle downswings may usher in severe and prolonged recessions. While not all of them are born equal, most recent recessions in mature economies share features of balance-sheet recessions, which are characterized by the burst of an asset bubble financed by debt. In the aftermath of the collapse, non-financial firms seek to repay their excessive burden, thereby shifting their priorities from profit maximization to debt minimization (Koo, 2014). When evaluating the appropriateness of monetary policy responses, it is necessary to distinguish two phases following a financial bust: a crisis management and a crisis resolution phase (Borio, 2014a; Caruana, 2018).
In the crisis management phase, policy responses seek to prevent that an implosion of the financial system cause severe damages to the the real economy. Instances
of such policies include lender-of-last-resort provisions and aggressive cuts in policy rates.
On the contrary, in the crisis resolution phase, the priority is balance-sheet repaire-ment. Policy actions should include a comprehensive loss recognition, the recapital-ization of those institution that incurred in losses, and the careful management of bad assets (e.g non-performing loans). The key point is that in the crisis resolution phase, central banks needs to avoid that stock problems have lasting consequences for income and production flows. To that end, it is important to underline that monetary policy influences economic activity by encouraging greater indebtedness, boosting asset prices, and facilitating risk taking. However, a balance sheet recession emerge precisely because of too much debt, excessively high asset prices, and ex-treme risk taking (Caruana, 2018). Since current monetary policy regimes overlook financial developments, policymakers tend to overreact to short-term developments and thus loose sight of troubles that might originate by aggressively policy easing. To document this asymmetric response, consider the action of lowering policy rates following the collapse of asset prices. Since the latter are not a reliable indicator of the financial cycle, the initial slump might usher in slowdown in economic growth or even recessions; this happens because policy actions contribute worsening credit and property price booms that causes serious financial disruptions and damages to the real economy (remembering that these indicators actually characterize the financial cycle). Global stock market crashes of 1987 and 2001 are instances of this situa-tion, which are also termed as ’unfinished recessions’ for underlining the unintended consequences that wrong policy actions might exert by deepening the initial slump (Borio and Lowe, 2002).
The downward bias of observed interest rates reflects a combination of factors. On the one hand, financialisation increased the amplitude of the financial cycle, thereby rendering busts more frequent and severe. On the other, central banks’ focus on tight inflation objectives unwittingly allowed the build-up of further financial im-balances.
might have played a role for explaining the phenomenon at stake. Low aggregate demand resulting from heightened inequality and low investment rates influence cen-tral bank’s behaviour when determining the policy stance (however, they play an indirect role). Admittedly, interest rate are pinned down by the interplay between central bank’s reaction function, private sector expectation, and preferences as ex-pressed in financial markets. The short end of the maturity spectrum is set largely by monetary policy, while the rest of the term structure reflects market expectations of future short rates plus a term premium (Borio and Disyatat, 2010).
2.5
Analytical implications and policy
prescrip-tions
From previous analyses it emerges that unsustainable booms in credit and asset markets might develop against the backdrop of low and declining inflation. As a matter of fact, imbalances in the financial system dot not necessarily put upward pressure on goods and services prices. It follows that inflation is not a reliable signal for the emergence of financial distress. However, monetary policies that target price inflation result in aggressive easing in the bust phase of the recession, thereby failing to promote the necessary adjustment. Before of advancing policy proposals for amending the current monetary regime, it might be instructive to list the factors explaining the coexistence of subdued inflation and financial distress.
A first factor reflect supply side developments stemming from technological advance-ments and structural reforms influencing factors productivity. On the one hand, these developments generate optimism about the future and contribute increasing corporate profitability, thereby inflating asset prices; on the other, prices of goods and services might trend downward because of reduced unit labour costs (Borio and Lowe, 2002).
A second factor accounting for both subdued inflation and financial imbalances is monetary policy credibility. In particular, credible policy makers anchor inflation
expectations to a particular target, thereby reducing the degree with which inflation responds to demand pressures. In a strong demand growth environment, a lower inflation sensitivity makes costs and prices stickier, thus boosting firms’ profits. By the same token, credible monetary policy contributes reducing uncertainty about the future, thus lowering the probability of future downturns. Reduced uncertainty generate optimism, thus leading to higher asset prices and more willingness of finan-cial institution to extend credit. The end result might be a finanfinan-cial system more susceptible to economic downturns.
It is also worth considering in detail what might be the side-effects of prolonged monetary easing. First, an accommodating stance hides underlying balance-sheet weaknesses, delays the recognition of losses and postpones the implementation of the required policies. Second, extremely low short-term interest rates compress banks’ interest margins and undermine the earning capacity of financial intermediaries (Ra-maswamy, 2012). If also low long-term interest rates prevail, the sustainability of pension funds and insurance business models is jeopardised, and this also impairs non-financial corporations and households’ balance-sheets. Third, the documented compression of banks’ interest margins might change banks’ risk perception or risk-tolerance, thereby leading banks to lower credit standards for extending more credit: the risk-taking channel of monetary policy might be operational. 5. Fourthly, and
relatedly, monetary policy effectiveness might be severely hindered if a low-for-long interest rate policy is pursued. Indeed, if the accommodating policy stance in-creases the probability of financial imbalances ushering in balance-sheet recessions, then monetary policy responses find heightened difficulties in sustaining the recov-ery. As recalled above, in a balance-sheet recession borrowers try to deleverage for reducing the outstanding debt they owe. However, the objective of encouraging the lending process is by definition downsized as demand for loans is scarcer than in normal times (Bech et al., 2014).
Conventional wisdom holds that financial stability can be ensured by appropriate
5(Borio and Zhu, 2012) In the next chapter we conduct an empirical exercise to ascertain its
prudential framework; conversely, monetary stability should be instead assigned to monetary policy. The received theory suggests that in the presence of two goals two instruments needs to be deployed, in accordance with the Tinbergen rule (cf. Tin-bergen, 1952). Admittedly, a prudential framework would allow the building up of buffers during the financial boom that can be purposefully deployed during the bust, with the view of stabilising the system. However, there are reasons to believe that a prudential response cannot be enough for achieving financial stabilisation. Indeed, as financial imbalances may coexist with subdued inflation, policies that are asym-metrical in relation to the financial cycle may accommodate an unsustainable and disruptive boom in the real economy. Therefore, the main amendment concerning the current monetary policy regime involve the inclusion of financial developments into central banks’ reaction function, so that financial factors are systematically taken into account. Moreover, due to the documented amplitude of the financial cycle, a longer horizon is required when setting the policy stance.
2.6
Concluding remarks
The main claim of this chapter is that working with better representations of mone-tary economies helps understanding the evolution of observed interest rates. In par-ticular, unveiling the interlinkages existing between the financial cycle, the economic regime, and the policy regime allows a thorough understanding of the phenomenon at stake.
The aim of the next chapter will be instead to test some implications that followed from our theoretical account. In particular, we will build onto the literature positing that monetary policy effectiveness might be hindered in a low-interest environment. Moreover, we will link this result with the interactions existing with the financial cycle, thus shedding light on the role played by the risk-taking channel of monetary policy.
Monetary policy effectiveness in a
low-interest environment
The aim of this chapter is to assess whether the positive effects of lower interest rates on aggregate demand diminish as policy rates trends downward. There are two conceptual arguments accounting for a purported lower monetary policy effectiveness in this particular scenario (Borio and Hofmann, 2017). Specifically, since low interest rates prevail in the aftermath of balance-sheet recessions, monetary policy ability to influence aggregate demand by encouraging lending is impaired. Hence, this account links reduced monetary policy effectiveness to headwinds coming from the economic context within which the central banker is supposed to operate. The second argument accounting for smaller effects of interest rates on output suggests the presence of nonlinearities, meaning that policy effectiveness might be lower the smaller is the level of observed interest rates; contrary to the first explanation, the presence of a depressed economic environment is neither necessary nor sufficient for explaining the phenomenon at hand. Let us give a bird’s eye on the empirical evidence sustaining these arguments.
Headwinds
re-cession, highlighting that in the immediate bust monetary policy is highly powerful in preventing major disruptions; however, in the resolution phase the central bank needs to address the legacy of the financial boom, where aggressive risk taking, un-sustainable credit expansion, and skyrocketing asset prices tend to prevail. In this scenario, there are different factors blowing against the efforts of the policy maker. A first factor is debt overhang, which hampers policy responses by negatively af-fecting aggregate demand. Indeed, following the bursting of a bubble, asset prices and output drop and the relative debt burden increases, reducing firms and house-holds’ net worth. In order to downsize their financial exposures and restore their wealth, borrowers who have overestimated their income prospects react by reducing their expenditures (Mian and Sufi, 2015; Juselius and Drehmann, 2020). Second, an impaired financial sector may fail to play the pivotal role of generating purchasing power and channeling funds to creditworthy agents. Indeed, financial institutions experiencing losses on loans and other assets find heightened difficulties in raising capital; their reduced lending capacity causes credit supply curtailment.
Third, uncertainty and low confidence about future economic prospects may arise in the aftermath of a balance-sheet recession (Mian and Sufi, 2015). This uncertainty may lower expenditure and boost precautionary savings (Deaton, 1989; Skinner, 1988), as well as reduce investment rates (Dixit, 1992; Bernanke, 1983).
Finally, financial booms may cause shifts of resources into sectors characterized by slow productivity growth (e.g. construction), thereby causing unfavourable sup-ply side developments (Borio et al., 2016). This may happen because during the boom phase interest-sensitive sectors such us construction expands, while shrinking during the contraction. However, an impaired banking system does not favour the reallocation of resources that would be needed. Risk averse banks, unless properly recapitalized, keep extending credit to weaker borrowers, thereby giving rise to the zombie lending phenomenon (Bruche and Llobet, 2014).
Nonlinearities
Persistently low interest rates may endanger monetary policy effectiveness through different channels (independently of whether a financial crisis occurred or not). The
first is concerned with bank profitability.1 Since banks’ core business concerns ma-turity transformation (i.e borrowing short and lending long), their major source of profit is the income resulting from the intermediation activity. As deposits are priced as a markdown on market rates, a persistent diminution of the latter reduce the extent to which banks can apply a lower markdown, thus implying lower profits. This happens because banks cannot reduce deposits rates below zero, as customers would hoard cash instead of paying for placing their money into a bank deposit. The end result of an impaired profitability is the reduction of loan supply.
Another channel through which low interest rates may jeopardise monetary policy effectiveness stems from the intertemporal substitution of consumption and savings. Conventional theory suggests that low interest rates incentives present consumption as it becomes less convenient to save, thereby highlighting an intertemporal substi-tution effect.2 If persistently low interest rates prevail, also an in income effect come into play. To that respect, agents envisaging low returns on their assets may increase precautionary savings for ensuring an adequate standard of living after requirement (White, 2012). Relatedly, persistently low rates may heighten uncertainty and risk perceptions, as agents might interpret this policy stance as signaling bleak economic prospects (cf. Keynes, 1936, chap. 19). This effect could be operational through pension funds and insurance companies, whose business model is endangered by de-clining long term interest rates.
An aggressive accommodating policy stance may also favour a misallocation of re-sources, giving rise to a zombification of the economy; for instance, Caballero et al. (2008) reports this phenomenon for the Japanese recession occurred in the 1990s. This unintended consequence manifest itself because low interest rates numb incen-tives for bank to clean up their balance-sheet, thereby encouraging roll over rather than non-performing charging-off (Borio and Hofmann, 2017). Weak borrowers may be kept afloat thereby crowding out new credit to more productive borrowers.
1There is a documented positive relationship between interest rates and bank profitability (cf.
Flannery, 1981; Samuelson, 1945; Hancock, 1985; English et al., 2002).
2This analytical result stems from the Euler consumption equation, which is an intertemporal
first-order condition describing the optimal choice for the employment of a stream of resources over an infinite time span; it is obtained by equating expected marginal costs to marginal benefits (Parker, 2007).
In this work we aim at providing fresh evidence on the purported lower effective-ness of conventional monetary policy when interest rates are persistently low. To that end, we conduct an empirical investigation involving two main steps. To begin with, we enquire whether monetary policy influence on output, aggregate demand and prices diminished as interest rates declined. For that purpose, we use aggregate time series representing the European economy. After obtaining a result in line with the theoretical accounts we surveyed, in the second step we shed lights on a specific factor that might account for this finding. As recalled above, low interest rates compress banks’ profit as they narrow the interest-net margin; however, an accom-modating policy stance modifies also banks’ risk perception, thereby incentivising a search-for-yields activity that consists in abating credit standards for extending loans to less creditworthy customers. We provide evidence for this situation to oc-cur, thereby establishing a risk taking channel of monetary policy. Its existence may contribute explaining the increased frequency of financial recessions, including the Great Financial Crisis. As a matter of fact, in the aftermath of such depressed economic context headwinds cause lower policy effectiveness.
The chapter is organized as follows. In section 1 we briefly review the literature studying whether transmission mechanisms of monetary policy changed over the last decades. Section 2 presents the proposed macro-econometric methodology em-ployed throughout the empirical investigation; as for the first step of the analysis, data description and results obtained are presented in section 3 and 4, respectively. In section 5 we thoroughly present the risk-taking channel of monetary policy, sum-marizing existing evidence in section 6. Section 7 describes the database employed as well as the proposed identification strategy; results will be presented in section 8. Finally, section 9 summarizes the main arguments.
3.1
Literature review
This section presents a brief survey of the studies adopting an empirical model for measuring changes in the transmission mechanisms of monetary policy. To pursue this objective, three strategies have been followed in the literature, and concerned (Boivin et al., 2010): (1) the estimation of an empirical model over different sub-samples; (2) the estimation of an empirical model with time-varying parameters; (3) the estimation of a regime-switch empirical model where parameters can stochasti-cally switch between different, regime-dependent, values.
Boivin and Giannoni (2002, 2006) estimate a small VAR using U.S. data from 1960 to 2001, where identification is achieved using a recursive scheme. They split the sample with the view of characterizing a pand post-Volcker period. Findings re-veal that in the post-Volcker period monetary policy has a lower effects on output and inflation. However, they do not regard this finding as convincing evidence of a reduced monetary policy effectiveness; indeed, they speculate that a diminished estimated response of output and inflation to monetary policy shocks may reflect a greater attention of the central bank to output and inflation stabilization. In other words, monetary policy might have increased its effects. However, as they also admit, it is not possible to ascertain this claim within an unrestricted macro-econometric model.
Primiceri (2006), Canova and Gambetti (2009), and Gal´ı and Gambetti (2009) iden-tify policy shocks with a time-varying coefficients VAR, allowing for a richer evolu-tion of the transmission of monetary policy. Primiceri (2006) identifies the model recursively, and reports negligible changes in the transmission of monetary policy over the last fifty years; relatedly, Canova and Gambetti (2009) using sign restric-tions obtain a similar result, with the additional finding that real output becomes even more responsive to monetary shocks.
The ambiguity one may find in the literature about the changing role of the transmis-sion mechanisms is partly due to the different identification procedures informing the empirical models. More than that, since these studies employ a handful of
macroeconomic variables for the purpose of not incurring in the curse of dimension-ality, inferential analysis may be unreliable due to the possible omission of relevant variables. To address this specific drawback, Boivin et al. (2010) estimate a FAVAR over two subsamples: 1962:1-1979:9 and 1984:1-2008:12. The model includes 181 macroeconomic indicators, comprising mainly real activity, price and interest mea-sures. They employ a recursive identification scheme, where monetary policy is assumed to respond contemporaneously to real GDP, the price deflator, and un-employment rate. Results suggest that in the post-1984Q1 period monetary policy shocks exert a lower effect on real GDP and the price deflator, even tough responses in the later period appear more delayed and persistent. To disentangle the sources of these changes, the authors inspect the working of two specific transmission mech-anisms. On the one hand, they find a reduction in the effect of monetary policy shock on expected inflation, relating this result to a better anchoring of inflation during the post-1984 period. Relatedly, they also find a reduced monetary policy effectiveness by inspecting the balance-sheet channel; the authors rationalize this result considering that the institutional changes occured in the structure of credit markets in the late 1980s (i.e. the emergence of shadow banking) may have altered the relative strength of bank-related transmission mechanisms.
Our analysis follows Boivin et al. (2010) in that we estimate a FAVAR over two sample using European data. Differently to their study and because of data un-availability, we do not compare over time the changes of a specific transmission mechanism. However, we provide evidence for the emergence of a risk-taking chan-nel that, at least partially, can account for a reduced monetary policy effectiveness. In the next section we thoroughly describes the proposed empirical methodology.
3.2
Empirical methodology
How to measure the effect of monetary policy on a variable of interest? To bet-ter grasp the state-of-the-art methodologies meant to address policy questions, it is instructive to consider the macroeconometrics practices when the discipline was
at its early stages. Back in the day, practitioners relied on macroeconomic linear models comprising hundreds of equations, where variables were classified as endoge-nous or exogeendoge-nous, and random shocks were appended to account for omission of relevant variables, specification and measurement errors, etc. Prior to conducting policy analysis, researchers posed restrictions for identifying the empirical model; these further assumptions were to be found on the prevailing economic theory, that at the time was Keynes’s macroeconomics filtered by the neoclassical synthesis. In his fundamental contribution, Sims (1980) argued that the employed identifying re-strictions were incredible, meaning that no theory could convincingly restrict the statistical model without relying on ad hoc assumptions. His key insight was that policy analysis could be performed by examining the moving average representation relating macroeconomic reality (observed variables of interest) to the structural eco-nomic shocks (Stock and Watson, 2005). To that end, he introduced unrestricted reduced-form vector autoregression, that is a system of equations estimated by re-gressing each model variable on lags of its own as well as lags of the other model variables (Kilian and L¨utkepohl, 2017). However, reduced-form equations do not permit to focus on a particular dynamic response function, thereby preventing any meaningful policy analysis: the variables of interest cannot be perturbed separately.3
As a matter of fact, Sims’ empirical strategy is not immune from the identification problem, which is instead a pervasive feature that philosophers of science call the problem of ’underdetermination of theory by data’. 4 According to their proponents, SVARs are more reliable for conducting policy analysis since they require only struc-tural economic shocks identification, while leaving unrestricted both the number of
3To understand why policy analysis cannot be performed, let us first denote with u
tthe vector
of var innovations, and with Ytthe vector of the variables of interest. The reason why one needs
to recover the structural counterpart of the reduced form VAR is that ut is the one-step ahead
forecast error of Yt. In general, each element of ut reflects the effects of all the fundamental
economic shocks contained in Yt. There is no reason to believe that any element of utcorresponds
to a particular shock, unless some other assumption is made (Christiano et al., 1999).
4Rival theories making reference to unobservable features of the world might all be compatible
with available data (Moneta, 2007); some form of background knowledge is always required for discriminating between equivalent empirical observations and for conducting structural analysis (Heckman, 2000).
variables and the number of lags to be included in the model.5 Practically speaking, identification of structural shocks is achieved by placing enough restrictions only on the structure of the contemporaneous orderings.
The correct mapping between reduced-form innovations and structural shocks re-quires that every variable containing information about a structural economic shock is included in the VAR. Omitting that variable means that VAR innovations cannot in general span the space of the structural shocks, with the end result of undermin-ing any causal effect captured by a purported structural impulse-response analysis (Stock and Watson, 2005). This problem impinges upon the fundamentalness of the VAR process (cf. Alessi et al., 2011). To key to addressing omitted-variable bias is to increase the information set of the model, thereby including all the relevant variables into the VAR. However, there is a dilemma facing the analyst when setting-up the empirical model (cf. Kilian and L¨utkepohl, 2017, chap. 16). On the one hand, since the number of estimated parameters increases with the square of the number of ob-served variables, one should prefer parsimonious models so as to preserve estimation precision. On the contrary, the omitted-variable bias makes it desirable to consider a greater number of variable for correctly describing the DGP. Techniques developed for increasing the information content comprise factor-augmented VAR (FAVAR), Bayesian VAR models, panel VAR models, global VAR models, and spatial VAR models (Kilian and L¨utkepohl, 2017).
Bernanke et al. (2005) proposed the FAVAR as a way to combine standard VAR with factor analysis for addressing the trade-off concerning information deficiency and degree-of-freedom. The intuition is the following: if there is a small number of factors summarizing large amounts of information about the economy, then a VAR augmented by these factors would increase the information set upon which the econometricians bases her analysis. In the next subsection we present in detail this methodology.
5To leave them unrestricted means that they are not specified a priori. However, the
cor-rect representation of the data-generating process (DGP) restrict the discretion of the modeler in choosing both the number of variables and the number of lags, in that in principle there is only one true DGP.
3.2.1
Framework
Let Yt be a M × 1 vector of observable economic variables driving the evolution of
the economy. In the monetary VAR literature, Yt usually comprises real GDP, a
policy indicator, and some measure of inflation. To summarize additional economic information not captured by Yt, suppose that that there exist a K × 1 vector of
unobserved factors Ft, with K ’small’. We may interpret these factors as forces
affecting many economic variables, that we may call ”informational” time series. Formally, let Xt be a N × 1 vector of informational time series, where N may be
greater than T, the time periods; it is also customary to assume that N is greater than the number of factors and observed variables (K + M N ).
The factor-augmented VAR (FAVAR) is defined as the following transition equation characterizing the joint dynamics of (Ft, Yt):
Ft Yt = Φ(L) Ft−1 Yt−1 + vt (1)
where Φ(L) is a conformable lag polynomial of finite order d, which may contain restrictions on the contemporaneous orderings. The error term vt is a vector with
mean zero and covariance matrix Q. Note that if the terms of Φ(L) that relate Yt
with Ft−1 are all zero, then equation (1) collapses to a VAR in Yt.
Equation (1) cannot be estimated because the factors Ftare unobservable; however,
we may suppose that these factors are related to the informational time series Xt
by an observation equation of the form,
Xt = ΛfFt+ ΛyYt+ et, (2)
where Λf is an N × K matrix of factor loadings, Λy is an N × M matrix of
coeffi-cients, and et is a N × 1 vector of error terms with mean zero and with at most a
time series N goes to infinity6. ΛfFt is also called the common component of Xt.
Equation (2) is referred as dynamic factor model7.
3.2.2
Application: the dynamic effects of monetary policy
Central banks routinely monitor and analyze hundreds of data series for the process of policy formulations. Thus, the FAVAR may bear fruitful results for monetary policy analysis, since it allows the researcher to condition her information set on a longer list of information variables, thereby strengthening causal inference analysis. Throughout this work, following Bernanke et al. (2005), we assume that both the econometrician and the central bank observe only the policy instrument, as well as a large set of (noisy) macroeconomic indicators Xt. It amounts to say that Yt ≡ Rt,
where Rt is the nominal interest rate controlled by the central bank. The reasons
for assuming such information structure boil down to the concept of measurement error. In particular, measures of inflation and output envisaged in theoretical models are likely to differ from actual observations. They would be best thought as latent measures of economic activity rather than specific data series such us real GDP or CPI (Bernanke et al., 2005). For this reason, these and other variables will be treated as unobserved factors to be extracted from the large pool of informational times series.
3.2.3
Estimation
Bernanke et al. (2005) proposed to estimate (1)-(2) either with a two-step proce-dure based on principal component analysis or by likelihood-based Gibbs sampling techniques. Following the publication of this article, other estimations techniques have been developed (cf. Boivin and Giannoni, 2008; Bai et al., 2016). In this work
6The vector e
t may exhibit some mild correlation only if factors are extracted by principal
component analysis (Stock and Watson, 2002).
7The fact that in equation (2) X
tdoes not depend on lagged values of Ftis not restrictive, in
we employ the two-step procedure based on principal component analysis as imple-mented by Bernanke et al. (2005), being aware that Oulirias et al. (2014) showed that this procedure should be slightly modified for yielding consistent estimators of the impulse responses.
The two step principal component approach is a non-parametric procedure for un-covering the common space spanned by the factors of Xt, that we may denote as
C(Ft, Yt). In the first step, common static factors ˆC(Ft, Yt) are estimated
us-ing the first K + M principal components of all the times series vector Xt (for a
formal treatment of principal component analysis see Stock and Watson, 2002). In the second step, one would be tempted to insert directly the estimated factors
ˆ
C(Ft, Yt) into (1). However, note that ˆC(Ft, Yt) recovers K + M linear
combina-tions of Xt and Ft, meaning that extracted factors are linearly influenced by the
variables included in Yt (where in our case Yt ≡ Rt). It would be incorrect to
estimate the VAR model in ˆC(Ft, Yt) and Rtwhile identifying the monetary policy
shock recursively8. Therefore, the estimated principal components ˆC(F
t, Yt) need
to be corrected for accounting the direct influence of the observable variable Rt.
To this end, one could split up the variables Xt into fast-moving and slow-moving,
where the distinction depends on whether or not variables react contemporaneously to the monetary policy shock. Then, a new vector ˆFs
t of principal components is
extracted from the slow-moving series. Since these new factors are by construction not contemporaneously correlated with Rt, the influence of Rt can be ascertained
on the basis of the following regression:
ˆ
C(Ft, Yt) = βsFˆst+ βrRˆt+ t, (3)
where βsis the coefficient matrix of estimated factors ˆFs
t, βr is the coefficient vector
of the observed variable Rt, and tis a vector of random variable with mean zero and
8Even if the VAR model is not recursively identified, the direct influence of Y
t on Ft needs
to be somehow addressed. The reason is that dynamic shocks could not be individually identified if linear dependence exists among the variables included in the model. The specific procedure by means of which the ”purging” is achieved depends on the proposed identifying assumption (Bernanke et al., 2005; Oulirias et al., 2014)
covariance matrix Σ. The unobservable factors, cleaned by the direct dependence
of ˆC(Ft, Yt) on Rt, can be calculated by subtracting βrRˆt from ˆC(Ft, Yt).
In the second step of the analysis, estimated factors ˆFt can be treated as data and
inserted into equation (1), that in turn can be estimated using standard methods.
3.2.4
Identification
The system (1)-(2) requires two different sets of restrictions. On the one hand, the dynamic factor model estimated via principal component analysis is not uniquely identified, hence some form or normalization is required. It is customary to as-sume that C0C/T = I, where C0 = [C(F1, Y1), . . . , C(F1, Y1)]. This implies that
ˆ
C =√TˆZ, where the ˆZ are the eigenvectors corresponding to the K largest eigenval-ues of XX0, sorted in descending order. (Stock and Watson, 1998, 2002; Bernanke et al., 2005). On the other hand, structural shocks identification from transition equation (1) requires the retrievement of the matrix embedding the true contem-poraneous orderings of the variables included in the model. Since we assume to observe only the policy interest rate, our matrix contains only the latter plus the unobserved factors. We impose a recursive ordering where the unobserved factors do not respond to monetary policy innovations within the period. Practically speak-ing, in the contemporaneous relations matrix the policy interest rate is ordered last. In general, structural impulse response analysis is not independent from the cho-sen causal orderings (Christiano et al., 1999). However, the proposed estimation procedure reduces the degree of arbitrariness in choosing a particular triangular-ization of the variance-covariance matrix of the reduced-form innovations. To see why, consider that factors have been extracted from the informational time series that purportedly do not react to the monetary policy shock within the period. As a matter of fact, it is safe to order ’slow’ factors first in the contemporaneous relations matrix. However, the controversial identifying assumption regards the splitting up of informational time series between slow-moving and fast moving. The credibility of the proposed identification strategy should be assessed by considering this choice.
3.3
Data
The data set consists of 47 quarterly macroeconomic time series for the euro area from 1970:Q1 to 2017:Q4. The series are taken from the Aria Wide Model (AWM) data set, which is an up-to-date data set managed by the Euro Area Business Cycle Network.9 Since many times series are officially released for specific countries of the Euro Area, available data require aggregation. The main source from which data are collected is Eurostat, complemented by the OECD National Accounts, the OECD Main economic indicators, the BIS and the AMECO databases. Data are aggregated by using the ”Index method”10. The log-level index for any series X is defined as follows:
ln Xz=
X
z
wiln Xi,
where wi is the weight of Xi in the aggregate Xz. This method is used for nominal
and real accounts variables, as well as for GDP income variables. For other vari-ables like employment and unemployment, the aggregate is calculated as a weighted sum of the variables. The weights used in aggregating individual country series are constant GDP at market prices for the euro area for 1995.
In the following analysis we estimate the FAVAR in two samples, namely: 1970:Q1-1989Q4 and 1990-2007:Q4. According to the AIC criterion, two lags are chosen for both samples. The break-date is somewhat chosen arbitrary, and reflect the need of having two samples with a comparable number of observations. However, the idea of comparing two different sample addresses the research question of spotting changes in monetary policy effectiveness in a declining-interest environment. As a matter of fact, the second sample in characterized by low levels of both real and nominal interest rates. The second sample ends in the last quarter of 2007 because the Great Financial Crisis brought interest rates to a negative territory. Indeed, a VAR cannot be estimated when an endogenous variable is constant and equal to zero.11. Prior of
9Data can be downloaded from the dedicated website https://eabcn.org/page/
area-wide-model.
10For a thorough description of this aggregation method, see Fagan and Henry (1998) 11Rossi (2019) surveys the identification procedures developed for addressing this problem.
