Estimating financial conditions indices for Switzerland : time varying aggregation vs. generic PCA approaches

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Estimating Financial Conditions Indices

for Switzerland:

Time Varying Aggregation vs.

Generic PCA Approaches

Monica Mihaela Pop

Master Thesis in Economics

Monetary Policy, Banking and Regulation

Universiteit van Amsterdam

Submitted by: Monica Mihaela Pop, 11087900

Supervisors: Dr. W.E. Romp and Dr. C.A. Stoltenberg

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List of Figures

1 Sch¨uler (4 series) and Sch¨uler (2 series) . . . 26

2 Hatzius (4 series) retaining all PC with E > 1 and Hatzius (4 series)a -retaining one PC . . . 28

3 Hatzius (17 series) retaining all PC with E > 1 and Hatzius (17 series)a -retaining one PC . . . 30

4 Hatzius (2 series) vs. Sch¨uler (2 series) . . . 33

5 Hatzius (4 series) vs. Sch¨uler (4 series) . . . 34

6 Hatzius (4 series)a vs. Sch¨uler (4 series) . . . 35

7 Hatzius (17 series) and Hatzius (17 series)a vs. Sch¨uler (17 series) . . . 36

8 Sch¨uler (2 variables) and Sch¨uler (2 variables) filtered . . . 38

9 Sch¨uler (2 variables) for Romania’s financial cycle. Variables: total credit to the non-gov. sector and real estate and construction gross value added. Estimation completed at the NBR, July 2016. . . 40

A.10 DATASET 1: Normalised variables - ECDF normalization . . . 43

A.11 DATASET 1: Standardized variables - zero mean,unit variance . . . 44

A.12 Switzerland Household Debt-to-GDP . . . 44

A.13 DATASET 2: Standardized variables - zero mean,unit variance . . . 45

A.14 DATASET 2, cont’d: Standardized variables - zero mean,unit variance . . 46

A.15 DATASET 2, cont’d: Standardized variables - zero mean,unit variance . . 47

A.16 DATASET 2: Normalized variables - ECDF . . . 48

A.17 DATASET 2: Normalized variables - ECDF . . . 49

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List of Tables

1 DATASET 1: Variables and their transformations . . . 16

2 DATASET 2: Variables and their transformations . . . 16

3 Hatzius (4 series): Variables, principal components and aggregation weights, retaining all PC with E > 1 . . . 29 4 Hatzius (4 series)a: Variables, principal components and aggregation weights,

retaining one PC . . . 29 5 Hatzius (17 series): Variables, principal components and aggregation weights,

retaining all PC with E > 1 . . . 31 6 Hatzius (17 series)a: Variables, principal components and aggregation weights,

retaining one PC . . . 32

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1 Introduction 2

1 Introduction

The interest in the estimation of financial conditions indices (FCI) has regained momen-tum in the aftermath of the Financial Crisis of 2007/2008, spurred by the conviction that dire developments in financial conditions presage future adverse developments in macroe-conomic activity. Traditionally, macroemacroe-conomic models featured the interest rate, as a straightforward depiction of financial conditions. But it is especially during periods of great financial distress, that interest rate changes may not be sufficient to represent the whole interaction that is present between financial markets and the real economy. Aside from the interest rate, choosing additional financial variables such as credit aggregates, asset prices or survey questions can all considerably add to the information quality of fi-nancial conditions. The academic literature as well as practitioners in research institutes and financial institutions have brought forth a large spectrum of indicators that serve this purpose – from the perspective of different methodologies.

In light of the vast supply of approaches to the construction of financial indicators, this work aims for the provision and scrutiny of two types of FCI that can be obtained from the pool of the methodological literature. Firstly, a particular type of FCI is constructed by implementing the procedures according to Hatzius et al. (2010), who obtain FCIs based on weights estimated with principal component analysis (PCA), a method which reduces large datasets to a smaller dimensionality, obtaining their informational essence. Secondly, a competing methodology is implemented, represented by the recent contribution to the financial cycle literature by Hiebert et al. (2015), who propose a differentiated approach to the aggregation of financial variables into an FCI. Due to the fact that both methodologies share the correlation structure of the input dataset as a common starting point, while at the same time exhibiting a few methodological particularities, a comparison between the two could prove interesting. Should both methodologies aggregate variables in a way that would result in highly coordinated FCI - it would increase the robustness of indicators obtained with both methodologies. At the same time, where differences in the two methodologies might lead to discrepancies in the indicators they are aiming to estimate, this constitutes a valuable opportunity to assess the mechanisms responsible for these discrepancies. Thus, both methodologies are implemented using two different datasets, which are detailed in the respective data section.

The contribution of this work to the existing literature consists of expanding the geo-graphical coverage of recent models like Hiebert et al. (2015) while at the same time testing them in parallel to alternative methods with whom they share common features, as well

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2 The current state of the literature 3

as differences.

The thesis is structured as follows: Section two provides an overview of the financial conditions and financial cycle literature, to position both methodologies within their areas of literature contribution. Section three details the employed datasets and their transfor-mations. Section four formally details the methodological aspects of principal component analysis and the alternative methodology, represented under the denomination of ”time varying aggregation”. Section five provides the presentation of results, the ten obtained financial conditions indicators, together with a comparison of both methodologies. Section six concludes.

2 The current state of the literature

2.1 Theory

Understanding the role of FCIs as instruments of prediction for macroeconomic activity re-quires a closer look at the theoretical underpinnings that define them. Financial conditions indices (FCIs) are synthetic measures which, through the aggregation of a large array of relevant financial variables, indicate the contemporary state of financial conditions. Their usefulness lies in the predictive power of financial conditions for future economic activ-ity, where financial conditions can be defined as ”the current state of financial variables that influence economic behavior and thereby the future state of the economy”(Hatzius, Hooper, Mishkin, Schoenholtz & Watson 2010). Underlying this definition is, of course, the assumption of the existence of one or more transmission mechanisms, describing how changes in financial conditions actually translate into effects on the real economy. For this, the theoretical literature provides a vast array of frameworks.

A starting point for the theory behind the workings of FCIs is the monetary transmission mechanism. Intuitively, explaining FCIs from the perspective of monetary transmission is attributed to the fact that monetary policy – represented, for instance, by the management of the short term interest rate, impacts the real economy by managing economic conditions affecting economic behaviour. Similarly, an FCI summarizes those variations in financial conditions attributable to exogenous changes (shocks) in financial variables that emerge either in conjunction with monetary policy changes or over and above them (Hatzius, Hooper, Mishkin, Schoenholtz & Watson 2010). According to Boivin, Kiley & Mishkin (2010), the monetary transmission mechanism may be explained out of the perspective of two separate transmission channels: neoclassical and non-neoclassical.

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2.1 Theory 4

Neoclassical channels summarize more traditional types of monetary transmission ef-fects which are based in the core models describing investment, consumption and interna-tional trade behavior that were elaborated starting with the middle of the 20th century. Seminal contributions here include the models of investment by Jorgenson (1963) and To-bin (1969), the lifecycle models of consumption in Brumberg & Modigliani (1954), Ando & Modigliani (1963), and Friedman (1957), as well as, in the case of international trade, the open economy IS/LM type of frameworks present in Mundell (1969) and Fleming (1962). Non-neoclassical channels for the monetary transmission mechanism devote their atten-tion to market imperfecatten-tions, most notably to imperfecatten-tions in credit markets, a reason for which this literature runs under the overarching name of the credit view. The credit channel literature thus attributes an important role to credit market imperfections in propagating the effects of monetary policy on the real economy. Noteworthy channels include the credit rationing channel, bank based channels such as the bank lending and bank capital channels and lastly, the balance sheet channel. The credit rationing channel played a central role in the macro-econometric models in the era up to the 1980s (for e.g. the MPS model in Bray-ton & Mauskopf (1985)). This channel features imperfections in the supply of credit that is attributable to government interventionism. Bank based channels summarize the effects of monetary policy on bank lending. With respect to the bank lending channel, monetary policy is seen as an important determinant of lending resources available to banks. Re-strictive monetary policy limits lending resources available to lenders, while expansionary policy spurs bank loan provision and consequently investment and consumption spend-ing by bank-dependent borrowers.((Bernanke & Blinder 1988) and (Bernanke & Blinder 1992), Oliner & Rudebusch (1995)). Bank capital channels emphasize the importance of the state of banks balance sheet for monetary transmission. Here, interest rate declines are theorized to increase banks net margins, enabling higher bank profits and, over time, an improved state of balance sheets. The monetary transmission mechanism also involves effects on asset prices. Expansionary policy facilitates asset price increases accompanied by bank capital improvement and subsequent expansion in bank lending. Conversely, asset price declines may ensue from a reduction in credit quality (reduced willingness/possibility of borrowers to pay) potentially leading to an erosion of bank capital and a contraction in bank lending, - a situation that actually materialized in the Financial Crisis of 2007/2008. The bank lending and bank capital channels have received increased attention in the after-math of the Financial Crisis of 2007/2008, with comments from, inter alia, Mishkin (2008) and Wessel (2009). Lastly, this group of non-neoclassical channels also involves the balance

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2.2 Practice - Financial Conditions Indices 5

sheet channel. This channel is determined by the existence of asymmetric information in credit markets, in which agents with falling net worth create adverse selection problems and where their increased propensity to higher risk taking behavior impose moral hazard issues for lenders. In light of this information asymmetry, lenders face higher cautiousness with their credit provision, either by rationing the quantity of credit or through higher risk premia requirements that exclude part of the borrowers from credit, both ultimately leading to rationing in lending. Representative of this particular channel is the financial accelerator framework present in Bernanke & Gertler (1995) and Bernanke, Gertler & Gilchrist (1999).

Concluding, as a binding element between the neoclassical and non-neoclassical chan-nels of monetary transmission, the observation has to be made that both types of transmis-sion channels permit a variable link between monetary policy (the policy instrument) and the economic behavior that determines the future state of the economy. While neoclassical channels imply changes to financial conditions more directly connected to the policy in-strument, non-neoclassical channels include changes in financial conditions more related to factors that represent”virtually everything else” affecting these conditions (Boivin, Kiley & Mishkin 2010). In other words, shocks to financial conditions can be seen as emerging as a result of monetary policy, or from other factors that are over and above it. After dealing with the theory underpinning FCIs, the next section is devoted to their implementation in practice. The next sections are devoted to two types of such indicators financial condi-tions indices on the one hand, and measures representing the financial cycle, on the other, explaining their construction as well as detailing their employment by practitioners.

2.2 Practice - Financial Conditions Indices

2.2.1 Origins

FCIs have their origin in the pursuit by economic research to find reliable predictors of economic activity. Historical examples of such indicators predating FCIs include single indicators such as the slope of the yield curve (Estrella & Hardouvelis (1991); Harvey (1988); Laurent (1989); Stock & Watson (1989)), the spread between the Fed funds rate and the 10yr. treasury yield (a key component of the Conference Boards index of leading indicators since 1996) or stock market variables (which have been present in leading indices since the 1950s, see Zarnowitz (1992)).

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Index(MCI), proposed by the Bank of Canada(BOC) in the mid-1990s (Freedman 1994). Additionally to the monetary policy rate, this MCI considered the exchange rate as an important variable such that the index consisted of a weighted average of the two, with the weight structure being estimated through macro models designed to estimate the impact of a change in these variables on GDP. The index proved particularly useful for evaluating the necessary adjustment in the policy rate that was required to commensurately offset a certain change in the exchange rate, that is, to estimate the needed adjustment in the pol-icy rate to keep monetary conditions steady after an exchange rate shock. Unfortunately, MCIs suffer from an important pitfall: a MCI is as good as the underlying model from which the variable weights are drawn from. A noteworthy criticism of MCIs can be found in Eika, Ericsson & Nymoen (1996), which illustrate that weights based on estimated coef-ficients may carry a reasonably substantial level of uncertainty. Eika, Ericsson & Nymoen (1996) thus identify five areas in which deviations from model assumptions may affect the operational usefulness of MCIs: these are dynamics, data non-stationarity, instrument exogeneity, parameter constancy and omitted variables1_.

Still, MCIs paved the way for the development of FCIs, in which the variable set to explain monetary policy effects was broadened to include, among others, long term in-terest rates, residential prices and equity prices, aiming to represent a more complete picture of monetary transmission. FCI are presently employed by a large group of organi-zations(central banks, policymakers, international organizations).

The construction of FCIs can be divided into two broad categories: a weighted-sum approach and a principal components approach, which details the mode of aggregation for constructing a FCI. The next sections deal with their representation.

1_{Specifically, the authors criticize that data dynamics may render the estimated weights to be} time-frame dependent, so the parameter constancy assumption might be violated. Further, the strong as-sumption of instrument exogeneity may be violated as well, leading to a biased estimation in the weights (omitted variable bias). The authors also note problems emerging from the potential non-stationarity of the data, perturbing statistical inference through an alteration of the error term distributions.

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2.2.2 Weighted sum approaches

The overarching procedure in the weighted-sum approach consists of the estimation of weights to be assigned to financial variables prior to their aggregation into the FCI. The most elementary vintage of this approach is represented by simple weighted averaging. Bloomberg proposes its Bloomberg U.S. FCI based on this approach, by aggregating the underlying, standardized variables into the final index through a preliminary distribution of indicators into three index subgroups (through simple averaging of indicators), there-after aggregating the obtained sub-indices into the FCI again performed through simple averaging. A more discriminate application of indicator weights is present in FCIs that as-sign weights in concordance with indicator variance, these approaches employing so-called variance-weighted averaging in aggregation, a vintage of this type of FCI being represented by IMFs Financial Stress Index (Lall, Cardarelli & Elekdag 2009).

More advanced versions of the weighted sum approach employ an array of estimation methods to generate the aggregation weights, by quantifying the relative impacts of the underlying indicators on GDP. The generation of weight estimates emerges from either reduced-form demand equations, through simulations of large scale macroeconomic mod-els, or implementation of vector autoregression (VAR) models. While these approaches are more complex than simple or variance-based averaging, the estimation of indicator weights using structural models or VAR- based estimations often implies imposing a cer-tain structure for the individual importance of each indicator, which is model dependent. Representative implementations of these weighting methods include Dudley & Hatzius (2000), Goodhart & Hofmann (2002), Mayes & Viren (2001), and Gauthier, Graham & Liu (2016).

2.2.3 Principal component analysis

A separate class of FCI employs the method of principal component analysis (PCA) to estimate the weights that are used to aggregate individual indicators into a composite index. This methodology has the advantage over weight estimations based on structural or reduced form models, in that it does not impose a model-based structure for deriving the relative importance of the variable input.

Using aggregation weights to obtain a FCI can be formulated according to equation (1):

F CIt=

X

i=1

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With:

F CIt: the value of the FCI at time t

λi : the aggregation weight for each variable xi

xi,t : the value of each variable xi at time t

2

Principal component analysis (PCA) is, to detail the estimation, an empirical procedure by which a large set of potentially correlated variables is reduced to a smaller set of (artifi-cial) variables which are linearly uncorrelated, called principal components. This variable reduction process has a practical reason: Where the visualization of high-dimensional (mul-tivariate) datasets is simply less useful for analysis, PCA can be thought of providing a projection of such datasets in a lower-dimension picture, while aiming to keep most of the information of the initial dataset. Principal component analysis thus aims at finding an optimal level for this trade-off (information content vs. dimension size).

Technically, PCA is performed in the following steps: a first step involves the computa-tion of a covariance matrix, for the purpose of identifying groups of variables where there is a high degree of correlation. Then, principal components are extracted with the help of the eigenvalue decomposition of the observed covariance matrix. Equation (2) exemplifies this procedure from the perspective of an elementary dataset of two variables, x1 and x2.

" x1x1 x2x1 x1x2 x2x2 # | {z } A ∗ci = Ei∗ ci (2) With: ci : the 2x1 eigenvectors

Ei : the corresponding Eigenvalues

A : the covariance matrix containing variances and covariances of x1 and x2

A decision has to be made upon the number of components to be extracted. At most, the number of components is equal to the initial number of variables in the dataset.3 _Supposing

2_{Note that the choice of the variable input into the FCI, x}

i depends on the researchers approach. See Hatzius, Hooper, Mishkin, Schoenholtz & Watson (2010), who empirically purge their financial variables of past macroeconomic influences

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that two components are retained, the components matrix, C, is calculated (equation (3), containing the eigenvectors from (2)), ranked according to the corresponding eigenvalues. In equation (3), cx1,1 is to be understood as the loading of the component with the highest

eigenvalue, concerning variable x1, while the other elements are to be read analogously.

C = " cx1,1 cx1,2 cx2,1 cx2,2 # (3) The elements of the component matrix are finally used in the estimation of λi, the weighted

loading corresponding to each variable i = x1, x2. This is formally attained through

equa-tion (4). Note that the components are, themselves weighted by αk, which is the amount

of variance explained by each corresponding component, according to αk = Ek/i, with i,

the number of variables in the dataset and k, the index of components, for k = 1 to i.

λi = α1ci1+ α2ci2 (4)

For example, both loadings, cx1,1 and cx1,2 are used to compute the weighted loading of

variable x1, according to λx1 = α1cx1,1 + α2cx1,2. Finally, the FCI can be computed, in

accordance to equation (1), after successfully estimating λi, the weighted loading for each

financial variable to input into the index.

Noteworthy studies employing PCA in the weight estimation for their FCI are An-gelopoulou, Balfoussia & Gibson (2014) and Hatzius, Hooper, Mishkin, Schoenholtz & Watson (2010). Angelopoulou, Balfoussia & Gibson (2014) construct FCIs for the euro area as a whole, as well as for individual countries, considering the period 2003 – 2011. They include, as input variables, a wide range of prices, quantities, several spreads as well as data from surveys, apart from considering variables representing monetary policy. Their application of PCA involves a particularity, which consists in the decision of setting the threshold for the ratio of explained variance to 70%, a rule which results in selecting the three highest eigenvalues for their FCI. At this imposed ratio, the aim is to safeguard the majority of the information contained in the dataset and strike a compromise with regard to the number of components to retain.

In another noteworthy contribution, Hatzius, Hooper, Mishkin, Schoenholtz & Wat-son (2010) construct their FCI based on weight estimation through PCA,their approach includes some improvements relative to the FCI literature. Firstly, they consider a broad number of variables (45), innovating the data selection process especially through adding a range of quantitative and survey-based data to their index. Secondly, all financial variables

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2.3 Practice - Financial Cycle Estimation 10

are purged by the influence of macroeconomic fundamentals, proxied by GDP and infla-tion, motivated by the belief that ”true financial shocks should be distinguished from the endogenous reflection or embodiment in financial variables of past economic activity that itself predicts future activity”(Hatzius, Hooper, Mishkin, Schoenholtz & Watson 2010). This purging is performed with a regression of the each of the financial variables on lagged values of GDP and inflation, respectively, retaining the obtained error terms of the regres-sion. These are then used as proxies for the exogenous variation in the financial variables, to be used as input into their FCI, although imposing a strong assumption on their exogene-ity. In performing PCA, the authors conclude that retaining only one principal component leads to similar performance than with retaining a larger amount of components. Finally, this study manages to improve the predictive power of FCI by expanding the data history and data coverage and especially through the procedure of separating financial conditions from macroeconomic fundamentals.

2.2.4 Dynamic factor models

One of the drawbacks of PCA lies in the fact that resulting weights, λi, remain constant over

the whole period for which the FCI is to be obtained. A separate strand of the literature has thus tasked itself with providing a way to allow the importance of financial indicators for the FCI to vary over time. Most notably, this can be performed through dynamic factor analysis, where weights in aggregation are estimated through methods other than PCA. Studies pertaining to this strand are Montagnoli & Napolitano (2006), Swiston (2008), and Gumata, Ndou & Klein (2012).

2.3 Practice - Financial Cycle Estimation

2.3.1 Origins

The literature concerned with the empirical estimation of financial cycle measures is still in its incipient years, but its theoretical roots can be traced back to a well-established liter-ature strand, dealing with systematic boom and bust patterns in the financial system and their potential subsequent macroeconomic impact. Some of the most prominent examples of early literature in this field feature the works by Fisher (1933), Kindleberger (1978), Minsky (1986) and Minsky (1992).

Given these theoretical views, a significant array of works has dedicated itself to their empirical scrutiny. Central to these empirical studies is the identification of stylized facts

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about how the dynamics of credit and asset prices could be linked to financial distress and ultimately, to macroeconomic activity, with the overarching perspective revolving around how excessive growth rates in credit and asset prices are reflected in a build-up of financial imbalances that can potentially become very disruptive to financial conditions and, in the end, to macroeconomic activity. Relevant works include Borio & Lowe (2002), Detken & Smets (2004), Goodhart & Hofmann (2008), Gerdesmeier, Reimers & Roffia (2010), Agnello & Schuknecht (2011), Alessi & Detken (2011), Schularick & Taylor (2012) and Taylor (2015).

Borio & Lowe (2002) empirically analyze the relationship between the dynamics in asset prices and the conduct of monetary policy for a large group of industrialized economies, dating back to the 1970s. They point to the potential vulnerability encountered with low inflation environments in facilitating a build-up of financial imbalances. Thus, a specific combination of asset price increases, credit easing and overall optimistic assessments of risk taken altogether, could be construed as indicators presaging financial instability.

Detken & Smets (2004) lend support to these findings, by deriving stylized facts for a set of financial, real and monetary variables during 38 episodes of asset price booms and busts, identified since the 1970s for a number of 18 OECD economies. They similarly point to the existence of so–called ”high cost” asset price busts in terms of their negative effect for economic activity. Their work is followed up in Alessi & Detken (2011), who similarly uncover ”costly” asset price boom and bust cycles in 18 OECD countries and propose a host of real and financial variables to serve as early warning indicators for their identification. Particularly variables representing global measures of liquidity, as the global private credit gap, are found to display high forecasting power and are proposed as instruments for policy makers interested in appropriate and timely reactions to growing financial imbalances. Further, in a fixed effects panel VAR model comprising 17 industrial economies for the period 1970–2006, Goodhart & Hofmann (2008) provide evidence in support of the thesis of a ”significant and multidirectional” causality between house prices, broad money, private credit, interest rates and GDP growth. Most noteworthy are the results from Granger causality tests which reveal a statistically significant effect of house prices, money and credit on GDP growth.

Performing a pooled probit analysis on a sample of 17 OECD industrialized countries and the euro area over the period 1969–2008, Gerdesmeier, Reimers & Roffia (2010) corrob-orate a set of indicators that bare high relevance for the forecasting of financial imbalances build-up. They find that credit aggregates, changes in nominal long-term interest rates and

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the investment-to-GDP ratio that are combined with either indicators denoting residential or stock prices emerge as the best choice indicators to facilitate the forecast of asset price busts up to 8 quarters ahead. The results from this research thus grant further emphasis to the potential usefulness of indicators representing e.g. credit developments to stand as early warning indicators for the accumulation of financial imbalances.

In a random effects panel probit model applied to a sample of 18 industrialized countries for the period 1980–2007, Agnello & Schuknecht (2011) study the occurrence of real estate price boom and bust cycles. Their findings underline that more recent real estate booms in the data have been more persistent and of a significant magnitude. Further, they corroborate a strong correlation between the persistence and magnitude of booms with subsequent busts. Importantly, the authors conclude that the economic costs, in terms of GDP losses accrued during the post-boom phase, are highly dependent on the magnitude and duration of the boom. Moreover, a number of policy variables representing money and credit developments as well as the level of mortgage market deregulation are found to significantly affect the probability of the occurrence of booms and bust cycles.

Looking back at a long-run historical dataset comprising 14 developed countries over almost 140 years (1870–2008), Schularick & Taylor (2012) uncover that episodes of financial instability have, to a large extent, been the result of credit booms gone dire, precipitated by faults in the operation and regulation of the financial system. The authors reveal a profound structural shift in the relationship between money, credit and output, whereas a pre WW2 period is identified, where money growth and credit growth go approximately hand in hand and a post WW2 period, where loans and assets are seen as embarking on a secular uptrend relative to broad money. The authors assert a paradigm change, that what happens in financial markets – borrowing conditions, the state of liquidity, market confidence, starts to matter a lot for credit creation as well as for financial stability, ultimately amplifying the pro-cyclicality of financing in a major fashion. Similarly, Taylor (2015) observes a continuous increase in bank lending – as percentage of GDP looking as far back as 1870, for all the countries in their dataset.

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2.3.2 Estimation

While the theoretical literature has come up with an array of stylized facts about financial cycles, still few approaches have been aimed at actually estimating the financial cycle em-pirically. Methodologically, this literature contains approaches employing the analysis of turning points (Claessens, Kose & Terrones (2011), Claessens, Kose & Terrones (2012)), ap-proaches using frequency based filters (Aikman, Haldane & Nelson (2015), Hiebert, Sch¨uler & Peltonen (2015)) and lastly, approaches turning to unobserved component time series models (Lucas & Koopman (2005), Galati, Hindrayanto, Koopman & Vlekke (2016)).

For works employing the turning point analysis, this approach goes back to an already established literature on the measurement of business cycles, through the identification of upturns and downturns, which ca be found in Burns & Mitchell (1946). Notably, Claessens, Kose & Terrones (2011) adapt this methodology for a detailed cross–country empirical analysis (for 21 advanced OECD economies within the period 1960–2007) with the purpose of documenting the main features of financial cycles. They represent financial cycles in terms of identified peaks and troughs for the case of three individual indicators, namely credit, residential prices and equity prices, providing an extensive chronology of about 470 financial cycles. Claessens, Kose & Terrones (2012) employ the turning point analysis to detect particularities in the interaction between financial and business cycles. For a dataset comprising 44 countries spanning 1960–2010, the authors conclude that both the duration and amplitude of recessions seem to be shaped by how financial and business cycles interact. Financial cycles are, the authors find, generally longer and more ample than business cycles.

A second strand of the literature resorts to the employment of frequency based filters for estimating financial cycles. Most relevant examples include the Hodrick–Prescott filter as well as the band-pass filters proposed by Christiano & Fitzgerald (2003) and by Baxter & King (1999). A common feature of these filters is the requirement for the user to pre-specify, exogenously, a frequency rule at which these filters should operate, when filtering the data to represent the financial cycle. Aikman, Haldane & Nelson (2015) make use of the bandpass filter methodology proposed by Christiano & Fitzgerald (2003) to analyze the interconnection between the credit and the business cycle. They take to comprise fluctuations within the 8–20 years range, which they apply to the filter rule.

A third strand of the empirical literature is based on the usage of unobserved component time series models to estimate financial cycles, a methodological overview of which can be found in Durbin & Koopman (2012). This methodology is linked to an already established

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tradition of estimating the business cycle, featuring works such as Valle e Azevedo, Koop-man & Rua (2006) and Creal, KoopKoop-man & Zivot (2010). In the case of financial cycles, applications of this methodology are still scarce. Lucas & Koopman (2005) provide an estimation of financial cycles for the United States based on the usage of indicators such as credit spreads, business failure rates and the real GDP. A more recent contribution per-taining to this literature strand can be found in Galati, Hindrayanto, Koopman & Vlekke (2016), who follow up on the research of Lucas & Koopman (2005), employing a multivari-ate model-based filter (Kalman filter) for financial variables such as credit, credit-to GDP ratio and residential prices in the case of the US, Germany, Italy, France and the Nether-lands between 1970–2013. An advantage of this method comprises, most importantly, in endogenously estimating the parameters for the Kalman filter vs. exogenously imposing them, which is performed through the estimation of an unobserved component model in application of a maximum likelihood approach. The authors are able to extract univariate cycles for the underlying financial variables, the duration of financial cycles in this research spanning from 8–25 years, which is in tandem with previous research (most notably, with Drehmann, Borio & Tsatsaronis (2012)).

To improve on robustness properties, recent works combine more than one of the above mentioned methodologies. Among those is a seminal paper by Drehmann, Borio & Tsat-saronis (2012), who in their methodology combine both the turning point analysis, as well as an employment of the bandpass filter of Christiano & Fitzgerald (2003). Looking at a set of financial variables (credit, credit to GDP ratio, residential prices, equity prices as well as an aggregate asset price index) from a group of advanced economies over the period of 1960–2011, a very important finding of this contribution lies in the identification of financial cycles lasting between 8–30 years, with an average duration of 16 years.

A particular study by Hiebert, Sch¨uler & Peltonen (2015) proposes a novel approach for estimating financial cycles, which they apply to 13 European Union countries and to a synthetic Euro Area aggregate, for a time span between 1970–2013. Their methodology comprises two parts. One consists of a time-varying aggregation of quarterly growth rates for four main variables (total credit to the private sector, property prices, equity prices and 10y government bond spreads) into a composite index. This is performed through considering the dynamics in the pairwise correlation between the variables and allowing for aggregation weights to fluctuate with these correlations. Specifically, it is intended that variables which correlate more strongly across time, should receive a higher weight in aggregation, with the intent to capture developments in the financial sector which are

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systemic in nature .

A second part of their methodology aims at innovating the estimation of financial cycles through the identification of common cycle frequencies through a procedure they call power cohesion. Essentially, power cohesion is employed for the endogenous estimation of finan-cial cycle frequencies, which are to be applied as inputs to known filters such as the band pass filter in Christiano & Fitzgerald (2003). This study aims at addressing a drawback in the financial cycle literature, the fact that many studies employed a filtering of their data by setting frequencies required by generic filter rules exogenously, that is, inspired either by the business cycle literature or by findings about cycle length corroborated from related literature. Due to the fact that the case is still out about financial cycle length across economies, this method provides one alternative to estimate these lengths endogenously. Thus, additionally to a raw FCI, Hiebert, Sch¨uler & Peltonen (2015) provide – through fre-quencies obtained through power cohesion, a filtered estimate of the financial cycle. Their results, represented by a composite index of the financial cycle, are found to outperform the credit-to-GDP gap in the prediction of systemic crises for a horizon of up to three years. As it represents one of the methodologies chosen in this paper, a formal representation of the approach in Hiebert, Sch¨uler & Peltonen (2015) is performed in section 4.

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3 Data 16

3 Data

VARIABLE SOURCE TRANSFORMATIONS 10y-government bond yields OECD quarterly pp. changes Equity Price Index Federal Reserve Bank of St. Louis Log q-o-q

Residential Price Index BIS Log q-o-q Total credit to the private sector Federal Reserve Bank of St. Louis Log q-o-q

Table 1: DATASET 1: Variables and their transformations

VARIABLE SOURCE TRANSFORMATIONS 1. 3MLIBOR, CHF St. Louis Fed Level

2. 10y government bond yields Bloomberg Level

3. SMI Index Bloomberg First log difference 4. Forex Reserves, in CHF SNB First log difference 5. Residential Price Index BIS First log difference 6. M1 SNB First log difference 7. M2 SNB First log difference 8. Market capitalization SNB First log difference 9. REER BIS First difference 10. Mortgage interest rates SNB Level

11. Mortgage rate spread SNB First difference 12. Total credit to the private sector SNB First log difference 13. Stock market turnover SNB First log difference 14. VIX St.Louis Fed First difference 15. Survey,borrower creditworthiness, companies KOF/ETH Z¨urich Level

16. Survey, borrower creditworthiness, households KOF/ETH Z¨urich Level

17. Consumer sentiment survey OECD First difference

Table 2: DATASET 2: Variables and their transformations

Dataset 1 is based on a quarterly set of four variables that encompasses total credit to the private sector, as well as prices representing the main asset-market segments, namely residential prices, equity prices and benchmark government bond yields. All series are measured in real terms, whereas real residential prices are obtained directly from the BIS

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3 Data 17

database, total credit and equity prices are deflated by the CPI, while 10y government bond yields are adjusted by the inflation rate to reflect real long term yields. Furthermore, credit, equity and residential prices are transformed to reflect log q-o-q, i.e. percentage changes, whereas government bond yields are transformed to reflect q-o-q, i.e. percentage point changes. Further, note that 10y government bond yields are pre-multiplied by (−1), with the aim that each variable’s increase should reflect an improvement in financial conditions. As such, growth in the long term yields reflects a worsening of financial conditions as it increases the government cost of financing, whereas its pre-multiplication calibrates the yields to reflect an improvement in financial conditions. The quarter on quarter differencing of the series represents an adaptation of the established NBER methodology that is used for the identification of peaks and troughs of the business cycle, which is based on q-o-q changes in GDP. This set of series represents the direct replication of the variable choice in Hiebert, Sch¨uler & Peltonen (2015), who produce financial cycle estimates based on indicator quarterly growth rates.

Dataset 2 represents a broader choice of financial variables, with the purpose of selecting the most representative indicators that are relevant for the Swiss financial market. Firstly, the dataset includes quantities such as total credit to the private sector, market capital-ization and turnover. Foreign exchange reserves and the monetary aggregates M1 an M2 reflect liquidity in the financial market. They are important for the management of the ex-change rate, which is especially relevant for a small open economy like Switzerland. Thus, the real effective exchange rate is chosen to reflect the perception of investors upon the value of the Swiss currency, as well as to include trade balance effects from the currencies’ real appreciation or depreciation.

Asset prices such as equity and residential prices are also considered, as they are closely connected to wealth effects. In fact, Swiss property prices score among the highest by international standards, supported by favourable interest rate conditions, easy access to mortgage credit, high degree of job security, to name a few factors. The deductibility of interest rate payments on mortgages from taxable income further incentivize the incurring of large debts towards home ownership in Switzerland. As a result, credit granted to Swiss households, frequently scores above 100% of GDP, with this value never been undercut since 2001 (Fig. A.12 Appendix). Furthermore, the Swiss debt market is traditionally highly collateralized by real estate assets. In 1993, after the bursting of the real estate bubble, 73% of total credit to the private sector has been found to be backed by residential collateral Borio (1995). These arguments underline the importance of real estate prices

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4 Methodology 18

for the wealth of households and the vulnerability of the banking system to real estate

price shocks. Further, the 3MLIBOR represents the monetary policy target rate and

reflects monetary conditions. Average mortgage rates reflect the cost of financing of home ownership while the spread between the mortgage rate and the deposit rate are indicative of the tension between demand and supply of funds, i.e. of the scarcity of financing funds. As mortgage credit constitutes about 2/3 of Swiss aggregate credit to the private sector, these rates are most relevant. VIX represents a measure for the implied volatility of S&P 500 index options, which is calculated by the Chicago Board Options Exchange (CBOE). The VIX, also called the ”fear index”, portrays investor’s expectations of stock market volatility over the next 30-day period. Lastly, survey data completes the dataset. Two survey questions obtained from the KOF Institute in Z¨urich are meant to proxy the perception of financial institutions about borrower creditworthiness, including household and corporate borrowers, while creditworthiness should highlight the willingness of financial institutions to give out funds, in connection to the established credit standards. A consumer sentiment survey is included to proxy consumer’s perception of the overall state of the economy and of the state of the individual financial health.

Prior to implementation, the variable set is tested for stationarity via the Augmented Dickey-Fuller statistic, testing the H0 of an unit root against the H1 that the series is stationary. Failing to reject the H0 leads to the necessity of data transformations, to achieve stationarity. Table (2) summarizes the implemented transformations which enabled stationarity in the data, i.e. the H0 to be rejected at 5% significance level. Note that further transformations were not required for dataset 1, as all indicators directly result as stationary from the perspective of the ADF-test.

4 Methodology

The construction of financial conditions indices for the case of Switzerland is performed using two methodologies, which are presented, in detail, in the sections that follow. The purpose of providing two competing methodologies for the estimation of FCIs lies in the scrutiny of their similarities, differences and, importantly, in the ensuing implications for practitioners employing financial conditions indices estimated through these procedures.

First, a set of Swiss FCIs is provided through the methodology in Hiebert, Sch¨uler & Peltonen (2015). Closely following the author’s implementation of FCI estimation for 13 Euro Area countries and a EA synthetic aggregate, two Swiss FCIs are provided. Sch¨uler

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4.1 Sch¨uler’s (2015) time varying aggregation 19

(4 series), which is presented in the results section, is estimated using a quarterly set of four financial variables, namely, total credit to the private sector, residential prices, equity prices and finally, benchmark 10y–government bond yields. Schüler (2 series) is the parsimonious version of Schüler (4 series), using as data input the variables total credit to the non–financial sector and residential prices. A detailed representation of the dataset, the sources and transformations is summarized in Table (1). The same dataset is, thereafter, used for the estimation of Hatzius (4 series) and Hatzius (4 series)a, the FCIs resulting from the implementation of principal component analysis, as the alternative methodology to Hiebert, Schüler & Peltonen (2015). Note that indices that are marked with the letter ”a” are obtained from PCA at retaining one PC, while the other indices are obtained from retaining all PC with an Eigenvalue > 1. A formal description of PCA is comprised in section (4.2).

Second, another group of FCIs is obtained from a larger dataset of 17 variables, for which an overview, the sources and performed transformations are summarized in Table (2). From this dataset, two indicators are obtained through PCA – Hatzius (17 series) and Hatzius (17 series)a and one through time varying aggregation – Sch¨uler (17 series).

Using both datasets within both methodologies, a comparison of the resulting indices ensues in section 5.2.1. The indicators are scrutinized in terms of their correlation, to assess weather identical datasets lead to similar results. Finally, Sch¨uler (2 series) features the FCI in filtered form, obtained from the implementation of power cohesion, the procedure put forth by Hiebert, Sch¨uler & Peltonen (2015) for endogenously estimating the frequency interval that will serve as a parameter input to the asymmetric band-pass filter of Christiano & Fitzgerald (2003), towards filtering the FCI of idiosyncratic noise. The result of this procedure can be seen under Figure (8).

4.1 Sch¨

uler’s (2015) time varying aggregation

4.1.1 A composite index for the financial cycle

The starting point of the fist part of this methodology is a dataset constituting of i = 1, . . . , M stationary variables xi,t. Denoting (xi,[1], xi,[2], ..., xi,[T ]) as the ordered sample of

each variable xi,t, all indicators are standardized according to equation (5), resulting in

variables yi,t. These represent the values of the empirical cumulative distribution function

at points xi,t.

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value and provides a position index, r, which is then divided by the total number of variables, T , to obtain each corresponding value yi,t. The variable at the top of the order

statistic naturally receives the value T/T = 1, which is the upper threshold value of the ecdf function, Fi,T. Per construction, the transformed variables, yi,t will thus adopt values

in the unit free ordinal scale (0, 1].

yi,t = Fi,T(xi,t) =

 



r/T for xi,[r] ≥ xi,t < xi,[r+1], r = 1,2,...,T-1

1 for xi,t ≤ xi,[T ]

(5)

With:

yi,t : the transformed variables xi,t

Fi,T : the empirical cumulative distribution function

Fi,T(xi,t) : the value of the ecdf function at points xi,t, which is equivalent to yi,t

The procedure by which Hiebert, Sch¨uler & Peltonen (2015) propose the aggregation of financial indicators into a composite FCI, is represented in equation (6).

ζt=

1 ιCtι0

· ιCtYt0 (6)

With:

ζt : the scalar value of the FCI at time t

ι : a vector of ones, dimension (1xM ) Ct : the time varying cross-correlation matrix

Yt : the row vector (y1,t, y2,t, ..., yM,t)

Precisely, Ct, the cross-correlation matrix of dimensions (M xM ), is constituted of generic

elements, ci,j, which are computed anew, for each period t, which is ultimately the source

of the ”time varying” aspect of the aggregation procedure. That is, each element ci,j is

rep-resented by the time-varying correlation coefficient ρij,t, which is computed in accordance

to equations (7) and (8). ρij,t= σij,t √ σii,tσjj,t (7)

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σij,t= λσij,t−1+ (1 − λ)(yi,t− 0.5)(yj,t− 0.5) (8)

Here, equation (8) implies the recursive calculation of time-varying covariances, σij,t and

variances σii,tand σjj,t, which are the inputs for the time–varying correlation coefficients,ρij,t

determining the changing structure in the covariance matrix Ct. Two steps are required

towards obtaining the values for σij,t. Firstly, an initialization of covariances is required.

This means that a portion of the input dataset is used to obtain an estimative value for the first covariance, σij,t−1. This procedure is performed using up a total of 8 quarters of

data, which is a compromise between a sufficiently accurate estimation of initial covariance conditions and data loss due to the estimation procedure. Secondly, the application of a decay factor, λ, a constant parameter, which is used to weigh the values of past covari-ances against the contemporaneous values in the data yi,t and yj,t and their deviations from

historical average, proxied by the median value 0.5. Specifically, the choice is made for λ = 0.89, which is the value proposed by Hiebert, Sch¨uler & Peltonen (2015) for the case of quarterly datasets. 4

Equation (6) represents the aggregation of all these steps into the final FCI, ζt, which

weighs the transformed variables, summarized in the transposed vector (y1,t, y2,t, ..., yM,t)

with the time-varying correlation structure presented above. Per mathematical construc-tion of the formula for ζt, the FCI obtained through this methodology encompasses itself

values in the interval (0, 1].

4.1.2 Estimating cycle frequencies through power cohesion

In a second part of this methodology, the procedure called power cohesion is detailed, by which Hiebert, Sch¨uler & Peltonen (2015) obtain their filtered version of the FCI. Specifically, the goal of this procedure is to determine, endogenously, thresholds to be specified to the band-pass filter of Christiano & Fitzgerald (2003), which is thereafter employed to remove very high and very low frequencies from the data.

Formally, the estimation of the frequency interval, [ω1, ω2] is realized by solving the

following optimization problem: For a dataset X comprising M stationary time series of

4_{Hollo, Kremer & Lo Duca (2012), who employ a similar procedure in the estimation of CISS, a financial} stress indicator, employ a decay factor λ = 0.93, which they apply to monthly data. For smaller values of λ, initial conditions fade faster, i.e. the value of initialized covariances matter less compared to the present common movement of variables relative to their historical averages.

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length T, find [ω1, ω2] that solves:

min ω2− ω1 s.t. Rω2 ω1 P COHX(ω)dω Rπ 0 P COHX(ω)dω ≥ p with p = 2/3 0 ≤ ω1 ≤ ω2 ≤ 2π/5. (9)

Intuitively, what the minimization strives to achieve is to search for the smallest possible frequency window that is able to capture a predetermined percentage of all fluctuations – denoted here by the choice of p = 2/3. Beforehand, frequencies are restricted to be smaller or equal to 2π/5 5, while frequencies are not restricted on the lower side. This allows for the consideration of all cycle lengths starting with 5 quarters in this optimization problem, even if stationarization of the data removed long term trends. The minimization problem uses the measure of PCOH – power cohesion as an input into the optimization constraint. This requires further detailing of what power cohesion stands for.

Formally, Hiebert, Sch¨uler & Peltonen (2015) define power cohesion as:

P COHX(ω) = 1 (M − 1)M X i6=j |fxixj(ω)| (10)

with fxixj(ω) being the normalized cross-spectral density defined according to equation

(11), where sxixj(ω) is the cross–spectrum of xi and xj, while σx denotes the standard

deviation of series xi and xj, respectively.

fxixj(ω) =

sxixj(ω)

σxiσxj

(11) The cross spectrum of xi and xj, sxixj is formally defined by equation (12).

sxixj(ω) = 1 2π ∞ X k=−∞

cov(xi,t, xj,t+k)e−ikω (12)

The cross spectrum can be understood as a ”translation” of the cross–autocovariance, cov(xi,t, xj,t+k) from the time-series domain, into the frequency domain. In other words,

the cross spectrum is the so-called Fourier-transform of the cross-autocovariance, where the Fourier transform separates a time function or a signal expressed in the time dimen-sion into the frequencies that constitute it.6 Note that the cross–spectrum is a complex

5_{this is the equivalent of a cycle length of 5 quarters}

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4.2 Principal component analysis 23

number, constituting of a real component, cxixj, called the co–spectrum and an imaginary

component, qxixj, called the quadrature spectrum. Also, per definition, the absolute value

of the cross–spectrum is written as |s| = c2_{+ q}2_.

In order to obtain an expression for PCOH, which is more practical in terms of implemen-tation, equations (10) - (12) are combined, resulting in equation (13):

P COHX(ω) = 1 (M − 1)M 1 2π X i6=j ∞ X k=−∞ cov(xi,t, xj,t+k) σxiσxj e−ikω (13)

Lastly, equation (13) can be simplified to (14), considering ρxixj,k =

cov(xi,t,xj,t+k) σ_xiσ_xj , with

ρxixj,k being the cross–autocorrelation for variables xi and xj, computed for k lags.

Denot-ing the maximum number of lags with ¯k, PCOH can now be written as:

P COHX(ω) = 1 (M − 1)M 1 2π X i6=j ¯ k X k=−¯k ρxixj,ke −ikω (14) Power cohesion now functionally represents the importance of common fluctuations across all cycle frequencies ω, over the input set of indicators and, as the cross-autocorrelations, ρxixj,k, can be computed in advance, P COHX(ω) is a function dependent only on the

vari-able ω. Going back to the minimization problem, the functional form of P COHX(ω) can

be introduced into the optimization constraint, which ultimately results in the estimation of the searched–for frequency window, [ω1, ω2].

4.2 Principal component analysis

This section details the procedure by which a separate class of FCI can be estimated, employing the method of principal components analysis. As discussed in the literature section, principal component analysis is a methodology aimed at reducing a large dataset to a small group of variables (principal components) that separate the common movement in the data from information characterized as idiosyncratic noise. Principal components are linear combinations of the initial variables, they are orthogonal and the amount of variance each PC explains is distributed decreasingly.

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First off, FCIs constructed with this methodology are in accordance to equation (15).

F CIt=

X

i=1

λiυi,t (15)

With:

F CIt: the value of the FCI at time t

λi : the aggregation weight for each variable υi

υi,t : ”purged” financial indicators, see (16)

The construction of this type of FCI closely follows the proposition by Hatzius, Hooper, Mishkin, Schoenholtz & Watson (2010), who purge their financial indicators of past macroe-conomic influences, which is performed in accordance with equation (16).

Xi,t = αi+ 3 X j=0 βj,iYt−j+ 3 X j=0 γj,iΠt−j+ υi,t (16)

Here, the financial variables from Table (2) are regressed on lagged values of GDP, Y , and inflation, Π, picking up the residuals of this regression, υi,t as proxies for the exogenous

variation in financial conditions.7 _{The choice for this methodological approach is motivated}

by the intent to capture ”true” financial shocks, which are to be ”distinguished from the endogenous reflection in financial variables of past economic activity that in itself predicts future activity”(Hatzius, Hooper, Mishkin, Schoenholtz & Watson 2010).

Secondly, the estimation of the aggregation weights, λi is detailed. Starting from the

eigenvalue decomposition of the covariance matrix, a number of p principal components can be extracted. The literature review already exemplifies this procedure from the perspective of an elementary dataset of two variables, in equations (2)-(4).

For a general set of i variables, the eigenvalue decomposition COV ∗ ci = Ei∗ cifeatures

a covariance matrix, COV , that is of dimensions ixi. The corresponding components matrix contains eigenvectors ci, ranked according to the corresponding eigenvalues. Finally,

7_{note that the exogeneity assumption for the error terms is a strong one, as other factors than inflation} and GDP might still be influencing Xi,t. Still, there are studies which conclude that macroeconomic variance is sufficiently proxied by inflation and GDP, see Brave & Butters (2011).

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aggregation weights for each variable, υi,t are estimated according to (17).

λi = α1ci1+ α2ci2+ ... + αkcik (17)

With:

λi : aggregation weights for each variable υi

α1to αk : amount of variance explained by components 1 to k

ci1to cik : component loadings 1 to k, where 1 is the component with the highest E, for variable i

Due to the fact that the maximum number of PC retainable is equal to the size of the dataset, the question arises about how many PC to extract optimally. Thus, in line with propositions from the literature, FCIs are constructed in this paper, by extracting firstly, all components for which the eigenvalue is > 1, following Rencher (1995), and secondly, only one PC, in accordance to the proposition by Hatzius, Hooper, Mishkin, Schoenholtz & Watson (2010).

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5 Results 26

5 Results

5.1 FCIs estimated with Sch¨

uler’s (2015) time varying

aggrega-tion

Figure 1: Sch¨uler (4 series) and Sch¨uler (2 series)

Schüler (4 series) and Schüler (2 series) feature indices obtained through time varying aggregation in accordance to Hiebert, Schüler & Peltonen (2015). The former represents the dataset of 4 variables that is present in Table (1), namely total credit to the private sector, residential prices, equity prices and lastly, benchmark long term government bond yields. This composite indicator represents the closest replication of the author’s implementation

for 13 EA countries and an EA synthetic aggregate. The index depicts deviations of

financial conditions from historical average (= 0.5 on the vertical scale), where an increase in the index represents an improvement of financial conditions. Sch¨uler (2 series) is the parsimonious representation of Sch¨uler (4 series), as two of the variables from Table (1), namely total credit to the private sector and residential prices, are used for this index. This version of an FCI can be seen as depicting the most elementary representation of the financial cycle.

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5.1 FCIs estimated with Sch¨uler’s (2015) time varying aggregation 27

As can be construed from Figure (1), three main observations can be made. Firstly,

a strong deviation of financial conditions of almost 0.5 from historical median can be observed in 1974-Q4. Most plausibly, this period of worsening in financial conditions can be attributed to the oil crisis that entered the scene in October 1973, when members of the OPEC proclaimed an oil embargo, which lasted until March 1974, with the oil price having increased from 3 USD, to about 12 USD per barrel, globally. To what extent the oil crisis might have individually affected the four variables constituting Schüler (4 series), this is dependent on the transmission of oil prices to these variables. Certainly an increase in the oil price, by affecting economic activity, corporate earnings, inflation and monetary policy, has implications for asset prices and financial markets. Secondly, both indices reveal a sharp decline in financial conditions in the 90’s period, with a downward culmination in Q4-1990, which coincides with the bursting of the residential price bubble in Switzerland. Note that Schüler (2 series), which is comprised only of the variables residential prices and total credit to the private sector, feature a more dramatic decline in financial conditions compared to Schüler (4 series). Thirdly and notably, compared to previous episodes of financial conditions worsening, Switzerland does not feature a very sharp decline in financial conditions, in the period of the Financial Crisis of 2008, albeit the evident volatility in both indices in the second half of the 2000s.

Finally, comparing Schüler (4 series) with Schüler (2 series), it becomes evident that in a small number of periods, the two indices seem to deviate from each other. This becomes visible, among others, at Q2–1992. Firstly, the two indices emerge from two different datasets, this would provide the trivial explanation. But as the two FCI do share half (two) of the variables, this divergence deserves clarification. The explanation of this divergence is due to Hiebert, Schüler & Peltonen (2015), who suggest that as their weights in aggregation are a direct result of the evolution of correlations between variables over time, the final position of the FCI will emulate the historical position of those variables, which exhibit positive correlations over time, while indicators which are negatively related are subdued.

8

Turning to the variables in both FCIs, it can be concluded that periods when the two indices deviate from each other are a result of Sch¨uler (4 series) reflecting a ”weighted” position between equity prices, government bond yields, house prices and credit (with the

8_{To exemplify, suppose two of the indicators remain above (below) historic average for a prolonged} period of time, while a third one is located below (above) historical average. This implies, according to equation (8) that the two variables correlate positively over time, while the third series is negatively related. Per aggregation methodology, the final position of the FCI at time t will come to reflect the historical position of the former two series.

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5.2 FCIs obtained with PCA 28

”net” position of the FCI reflecting more closely the position of equity prices and bond yields), while, obviously, Sch¨uler (2 series), reflects the position of credit and house prices. An indication of this can be additionally construed from the descriptive statistics of the normalized variables in Fig (10) of the appendix, with equity and bond yields being far above historic average and credit and house prices below average, but to a lesser amount, in the period around Q2–1992, which is an example of when the indices diverge.

5.2 FCIs obtained with PCA

Figure 2: Hatzius (4 series) - retaining all PC with E > 1 and Hatzius (4 series)a - retaining one PC

Hatzius (4 series) and Hatzius (4 series)a are obtained through implementation of principal component analysis on the variable set in Table(1), the former, through the retention of all PC for which E > 1, the latter through the retention of a singular PC. The stationary variables are purged of the past macroeconomic influences, as discussed in the methodology section and standardized to have a mean of zero and unit standard deviation. Further, ex-tracting all PC with an Eigenvalue > 1 results in the extraction of two PC. These, together with the estimated weights, λi are summarized in the report of Table (3). Furthermore,

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grant residential prices and total credit the highest weights in aggregation, while the other two variables receive either almost neutral weights (Hatzius (4 series)a) or considerable negative weights (Hatzius (4 series)). Both indices emphasize the importance of residen-tial prices and aggregate credit to the private sector for Swiss financial conditions, while granting different weights for the other two variables.

Variable

PC1

PC2

Weights

10y-government bond yields

0.018028108

-0.749327747

-0.203310381

Equity prices

-0.280954437

-0.6307011

-0.273053237

Residential prices

0.684971071

-0.046273494

0.222832555

Total credit to the private sector

0.671977845

-0.196425086

0.176377085

Table 3: Hatzius (4 series): Variables, principal components and aggregation weights, retaining all PC with E > 1

Variable PC1 Weights

10y-government bond yields 0.0180 0.0062

Equity prices -0.2810 -0.0967

Residential prices 0.6850 0.2358

Total credit to the private sector 0.6720 0.2313

Table 4: Hatzius (4 series)a: Variables, principal components and aggregation weights, retaining one PC

Finally, Hatzius (17 series) and Hatzius (17 series)a are obtained through the implementa-tion of principal component analysis on the variable set in Table(2), the former, through the retention of all PC for which E > 1, the latter through the retention of a singular PC. Again, the stationary variables were purged of the past macroeconomic influences and standardized to have a mean of zero and unit standard deviation. For the case of Hatzius (17 series), extracting all PC with an Eigenvalue > 1 results in the extraction of 6 PC. These, together with the estimated weights, λi are summarized in the report of Table (5).

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Figure 3: Hatzius (17 series) retaining all PC with E > 1 and Hatzius (17 series)a -retaining one PC

The FCIs estimated with PCA employing the 17-variable dataset feature a prolonged period of below-average financial conditions, in Switzerland, between 2005-Q1 and 2007-Q3. Coinciding with the start ot the Financial Crisis of 2007/2008, a mild worsening of financial conditions is visible, followed by a prolonged period of above-average conditions. A prolonged period of financial conditions going strongly above average - with a peak of over one standard deviation above historical average is to be noted between 2011-Q2 and 2014-Q4. This period marks the debut of the European Debt Crisis, a period that was accompanied by a flight away from the crisis ridden euro, to the Swiss Franc, as a safe haven currency. To protect the CHF from the imminent appreciation in the Swiss Franc, the SNB famously introduced a ceiling on the exchange rate, on the 6th of September 2011, limiting it to 1.20 CHF/EUR. In order to keep this ceiling, a myriad of measures were put in place, to provide the Swiss financial market with high liquidity, inter alia, the SNB used foreign exchange swaps and repo agreements for this purpose. Notably, the money supply started to appreciate considerably in the post 2008 timeline. As money supply received one of the highest weights in aggregation for Hatzius (17 series)a, a source of financial conditions improvement in the aforementioned period can be followed back to

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the increased liquidity in the Swiss financial market, as a measure to preserve the exchange rate at the decided ceiling.

Variable PC1 PC2 PC3 PC4 PC5 PC6 Weights

3MLIBOR, CHF 0.0035 -0.1633 0.1287 0.0551 0.6807 0.1777 0.0604

10y government bond yields 0.3592 -0.0711 0.2191 0.3308 0.1811 -0.0839 0.1384

SMI Index -0.0697 0.4880 -0.2630 0.2231 -0.0270 -0.0429 0.0432

Forex Reserves, in CHF 0.2661 0.0362 0.0790 -0.3678 -0.0940 -0.1955 0.0261

Residential Price Index 0.3104 0.1397 0.2178 0.1487 0.1447 -0.0689 0.1409

M1 0.3937 -0.0088 -0.2584 -0.0328 -0.2133 0.0189 0.0458

M2 0.4207 0.0204 -0.1855 -0.0118 -0.2526 0.0186 0.0637

Market capitalization -0.0865 0.5340 -0.1411 0.1758 -0.0101 -0.0135 0.0590

REER 0.0641 -0.0973 0.3072 -0.0742 -0.4777 0.3485 0.0132

Mortgage interest 0.3978 -0.0817 0.1259 0.3545 -0.0099 -0.0348 0.1257

Mortgage rate spread -0.0699 0.2180 0.5664 -0.0463 -0.0516 -0.0419 0.0696

Total credit to the private sector 0.0951 0.1945 -0.3024 -0.0748 0.2012 0.5299 0.0619

Stock market turnover -0.0951 0.0420 0.2459 0.1329 -0.1457 0.5934 0.0495

VIX -0.0013 -0.4489 -0.2613 -0.1724 0.0417 0.0081 -0.1099

Survey, company creditworthiness -0.3703 -0.0876 0.0623 0.0282 -0.1560 -0.1540 -0.1153

Survey, household creditworthiness -0.1742 -0.1833 -0.0666 0.5493 -0.1779 -0.2479 -0.0590

Consumer sentiment survey 0.0814 0.2784 0.1784 -0.3993 0.1161 -0.2705 0.0390

Table 5: Hatzius (17 series): Variables, principal components and aggregation weights, retaining all PC with E > 1

According to the reports on estimated weights, the three variables which receive most emphasis in Hatzius (17 series) are: residential prices, 10y government bond yields and mortgage interest rates. In the case of Hatzius (17 series)a, where one PC is retained, the same variables represent the group with the most weighting in the index, accompanied by M1, which ranks highest alongside the weighting of mortgage interest.

Estimating financial conditions indices for Switzerland : time varying aggregation vs. generic PCA approaches