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RIVISTA BANCARIA
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ISTITUTO DI CULTURA BANCARIA «FRANCESCO PARRILLO»
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Comitato Accettazione Saggi e Contributi:
GIORGIO DI GIORGIO (editor in chief) - Domenico Curcio (co-editor)
Alberto Pozzolo (co-editor) - Mario Stella Richter (co-editor)
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ISTITUTO DI CULTURA BANCARIA
«FRANCESCO PARRILLO»
PRESIDENTE
CLAUDIO CHIACCHIERINI
VICE PRESIDENTI
MARIO CATALDO - GIOVANNI PARRILLO
CONSIGLIO
TANCREDI BIANCHI, FABRIZIO D’ASCENZO, GIAN GIACOMO FAVERIO, ANTONIO FAZIO,
GIUSEPPE GUARINO, PAOLA LEONE, ANTONIO MARZANO, FRANCESCO MINOTTI,
PINA MURÈ, FULVIO MILANO, ERCOLE P. PELLICANO’,
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In copertina: “Un banchiere e sua moglie” (1514) di Quentin Metsys (Lovanio, 1466 - Anversa, 1530), Museo del Louvre - Parigi.RIVISTA BANCARIA
MINERVA BANCARIA
ANNO LXXVI (NUOVA SERIE) GENNAIO-APRILE 2020 N. 1-2
SOMMARIO
Editoriale
G. DI GIORGIO La politica monetaria nella pandemia. Ci salverà l’elicottero? ... 3
Saggi
R. COCOZZA
D. CURCIO
A. PACIFICO Do Global Markets Imply Common Fear? ............................. 7
Le piccole e medie imprese italiane nella riflessione
G. GAROFALO di Francesco Parrillo e nel contesto dell’economia italiana
G. GUARINI del III millennio: un percorso di ricerca sul capitalismo
C. CHIACCHIERINI italiano con una verifica empirica .......................................... 47
Saggi - Sezione Giovani
G. CHIORAZZO Dismissione di NPL tramite iniziative di sistema
(bad-bank): un modello contabile per la simulazione
degli effetti sui bilanci delle banche italiane ........................... 77
E. GABRIELE Tips for Financial Risk Managers During
QE Enforcement: Evidence from EU-Core Countries ......... 129
Rubriche
Valutazioni giuridiche sull’impatto della Mifid II
(A. Fittante) .................................................................................................................... 171
L’incertezza frena le imprese. Nel 2019 calano le richieste di credito
(E. Mazzotti) .................................................................................................................. 183
Bankpedia ...................................................................................................................... 189
Assicurazione dei depositi in Italia e nella UE
(C. Oldani)
La nuova Via della Seta - Belt and Road Initiative
(C. Oldani)
Recensioni
F. Capriglione, A. Sacco Ginevri, Metamorfosi della governance bancaria
(Marina Brogi)................................................................................................................ 203
A. Dell’Atti, F. Miglietta e A. P. Iannuzzi, Il sistema bancario e la crisi finanziaria
(S. Sylos Labini) .............................................................................................................. 206
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Istituto di Cultura Bancaria “Francesco Parrillo”
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dalle maggiori banche dell’epoca allo scopo di diffondere la cultura bancaria e di provvedere alla
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un altro trentennio da Francesco Parrillo, fino al 2003. In questo secondo periodo, accanto alla trat-
tazione scientifica dei problemi finanziari e monetari, la rivista ha rafforzato il suo ruolo di osserva-
torio attento e indipendente della complessa evoluzione economica e finanziaria del Paese. Giuseppe
Murè, subentrato come direttore dal 2003 al 2008, ha posto particolare accento anche sui problemi
organizzativi e sull’evoluzione strategica delle banche. Nel 2003, l’Istituto di Cultura Bancaria è stato
dedicato alla memoria di Francesco Parrillo, alla cui eredità culturale esso si ispira.
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Segui Editrice Minerva Bancaria su:DO GLOBAL MARKETS
IMPLY
COMMON FEAR?
ROSA COCOZZA
DOMENICO CURCIO
ANTONIO PACIFICO
Abstract
This research investigates the relations of the US VIX and the European
VSTOXX, on the one hand, and their main determinants, on the other hand.
In line with prior studies, US and European stock and volatility markets ex-
hibit a contemporaneous negative relationship. Furthermore, the increase of
VIX and VSTOXX associated with a fall in stock prices is larger than the
decrease that the two indices experience when stock prices rise. During the
great financial crisis, the negative relation between volatility indices and stock
market indices weakens for both financial markets; the asymmetric reaction
to changes in stock market returns becomes stronger for the VSTOXX index
and decreases for the VIX.
The analysis of the dynamic interaction between volatility indices and main
financial and macroeconomic variables based on a Structural Panel Bayesian
VAR shows that the US monetary policy rate is an important driver of both
the US and European volatility indices’ behavior, thus hugely affecting not
only the domestic financial market, but also the European one. Moreover, the
presence of consistent co-movements and interdependencies among volatil-
ity indices prove that international spillovers are mainly linked via financial
markets.
Department of Economics, Management, Institutions, University of Naples “Federico II”, Via Cinthia, Com-
plesso Monte S. Angelo, Napoli (NA) 80126, Italy, E-mail: rosa.cocozza@unina.it
Corresponding author. Department of Economics, Management, Institutions, University of Naples “Federico
II” Via Cinthia, Complesso Monte S. Angelo, Napoli (NA) 80126, Italy, E-mail: domenico.curcio@unina.it
Department of Political Science, LUISS Guido Carli, Viale Romania 32, Roma (RM) 00197, E-mail: apacifi-
co@luiss.it
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 7ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
Mercati globali implicano comune paura? – Sintesi
Questa ricerca analizza le relazioni tra gli indici di volatilità VIX e VSTOXX,
da una parte, e le loro principali determinanti, dall’altra. In linea con la prece-
dente letteratura, gli indici dei mercati azionari statunitensi ed europei mostrano
una relazione negativa con i corrispondenti indici di volatilità. Inoltre, l’aumento
del VIX e del VSTOXX, associato ad un calo dei prezzi azionari nei rispettivi
mercati, è maggiore della riduzione che i due indici di volatilità subiscono quan-
do, invece, i prezzi aumentano. Durante la grande crisi finanziaria, la relazione
negativa tra gli indici di volatilità e gli indici azionari si indebolisce per entrambi
i mercati finanziari; la reazione asimmetrica alle variazioni dei rendimenti azio-
nari diventa più forte per il VSTOXX e si attenua per il VIX.
L’analisi dell’interazione dinamica tra gli indici di volatilità e le principali
variabili finanziarie e macroeconomiche, basata su un modello di tipo Structural
Panel Bayesian VAR, mostra che il tasso di politica monetaria degli Stati Uniti
è un driver importante del comportamento di entrambi gli indici di volatilità, in
grado di influenzare, quindi, in maniera significativa, non solo il mercato finan-
ziario domestico, ma anche quello europeo. Inoltre, lo studio mostra la presenza
di co-movimenti e interdipendenze tra gli indici di volatilità, che dimostrano che
fenomeni di spillover a livello internazionale sono interrelati per il tramite dei
mercati finanziari.
Parole chiave: Indici di Volatilità; Indici Azionari; Politica Monetaria; Tassi di Interesse.
Codici JEL: E44; F30; F44.
Keywords: Volatility Indices; Stock Indices; Monetary Policy; Interest Rates
8 SAGGIDO GLOBAL MARKETS IMPLY COMMON FEAR? 1. Introduction According to a growing body of literature, risky asset prices around the globe and international capital flows do have a strong common component (see, among the others, Calvo et al., 1996, Bekaert et al., 2012, Miranda Agrippino and Rey, 2012). Cycles in the real interest rates and in the growth rate of advanced economies have been identified as important “push” factors for capital flows. Several studies have found that movements in the VIX, the Chicago Board Options Exchange (CBOE) market volatility index, and in other indices of “market fear” (Forbes and Warnock, 2012) are strongly and negatively associated with capital flows. Bruno and Shin (2015) emphasize the surge in international capital flows caused by the lowering of the VIX. Furthermore, even financial intermediaries’ leverage and leverage growth are negatively correlated with the VIX (Rey, 2016). Within such a financially globalized world, monetary conditions of the center country (the US) have an impact on changes in aggregate risk aversion and volatility, capital flows and the leverage of the financial sector in many parts of the international financial system (Miranda Agrippino and Rey, 2012). While seeing a lot of co-movement in asset prices and capital flows worldwide may just reflect financial markets integration, the fact that these co-movements are to some extent caused by US monetary policy is important and we believe that shedding more light on the role played by volatility indi- ces is crucial to get a comprehensive knowledge of how financial globalization works. On the other hand, empirical evidence shows a strong and persistent correlation among main volatility indices, which is much higher than the correlation among the corresponding stock market indices (Aussenegg et al., 2013). Global financial market integration may not be the only reason to ex- plain such strong and persistent co-movements in the volatility indices, given the structural differences between the reference stock markets. By focusing on the VIX and the VSTOXX volatility indices, we observe a stable and very high positive correlation since their introduction. The correla- tion of the two volatility indices is much higher than the correlation between the two corresponding stock market indices, the S&P 500 and Euro Stoxx 50, that are different because of a number of factors, among which the liquidity RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 9
ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
of their reference markets, the economic sectors respectively represented in
the two stock indices and the leverage of the companies included in each of
them. By accounting for these issues and the post-crisis financial markets con-
ditions, detecting the factors determining market volatility indices is a timely
and key research area.
Since, to the best of our knowledge, there is no prior literature specifically
investigating the joint dynamics of volatility indices, this research aims to
fill this gap and investigate the causes of what we define “common fear” of
global markets. In particular, in order to address the issues associated with the
main determinants of the volatility indices, this research contributes to prior
literature by: i) shedding light on the link between the volatility indices and
the risk-free interest rates that are used in their calculation; ii) adding new evi-
dence, particularly referred to the great financial crisis period, on the relation-
ship between the volatility indices and the corresponding stock indices, with a
special focus on the great financial crisis; and iii) providing new insights about
the importance of monetary policy actions in determining market implied
volatility from an international standpoint.
From a methodological perspective, we first examine how market fear in-
dices are built in order to detect potential drawbacks in their construction
models. Based on an analytic approach, we show how stock market indices
and interest rates included in the VIX and VSTOXX formulas contribute to
the level and dynamics of the two fear indices themselves. Then, based on the
analysis of the time series of daily market data, in order to further investigate
the determinants of these two indices, we study their sensitivity to both global
and local financial market variables, such as US and Euro Area monetary pol-
icy rates and stock market indices. Finally, the adoption of a Structural Panel
Bayesian Vector Autoregressive (SPBVAR) framework allows us to compre-
hensively capture the interdependencies among the fear indices and the other
financial variables included in our analysis as well as their dynamic behavior.
Our main findings are: i) US and European stock and volatility markets
exhibit a contemporaneous negative relationship, which is slightly less pro-
nounced for the European market; ii) the reaction of VIX and VSTOXX to
changes in stock prices is asymmetric in the sense that the increase of volatil-
ity indices when stock prices go down is larger than the decrease caused by a
10 SAGGIDO GLOBAL MARKETS IMPLY COMMON FEAR?
rise in stock prices; iii) during the great financial crisis, the negative relation
between volatility indices and stock market indices weakens for both financial
markets, whereas the asymmetric reaction to changes in stock market returns
becomes stronger for the VSTOXX index and less intense for the VIX; iv)
the US monetary policy rate appears to be an important driver of the US and
European volatility indices’ behavior.
The rest of the paper is organized as follows: section 2 presents the fear
indices we are interested in and focuses on their calculation methodology,
interpretation and potential benefits for investors; in section 3 we discuss
the relationship between the volatility indices and their main determinants,
namely the underlying stock market indices and interest rates; in section 4 we
present the empirical evidence resulting from static OLS regression models
and from a Structural Panel Bayesian Vector Autoregressive (SPBVAR) model
analysis; section 5 contains some concluding remarks.
2. The VIX and VSTOXX indices: calculation methodology, interpreta-
tion and benefits for investors
The Chicago Board Options Exchange (CBOE) volatility index (VIX) is a
forward-looking measure of the future market volatility that investors expect
to see over the next 30 calendar days and is implied by the current prices of
the S&P500 index (SPX index) options. In particular, to calculate the VIX,
near- and next-term put and call options with more than 23 days and less
than 37 days to expiration are taken into account. The VIX was introduced in
1993 in order to provide, on the one hand, a benchmark for expected short-
term market volatility and, on the other hand, an index upon which futures
and options contracts could be written.
The VIX was initially designed to measure the market’s expectation of 30-
day volatility implied by at-the-money S&P100 index (OEX index) option
prices. Later, in 2003, the CBOE introduced a more detailed methodology to
calculate the VIX, which is based on the S&P500 index and estimated expect-
ed volatility by averaging the weighted prices of S&P500 puts and calls over a
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 11ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
wide range of strike prices1. Finally, in 2014, the CBOE enhanced the VIX to
include series of SPX Weeklys, allowing to calculate the index with S&P500
index option series that most precisely match the 30-day target timeframe for
expected volatility that the VIX aims to represent2.
VIX calculation employs rules for selecting component options and the
following, generalized formula to calculate the index values:
2 | 3K i RT 1: F D
2
VIX = 100 # T i K 2i e Q ( K i) - T K0 - 1 (1)
where:
T = Time to expiration;
F = forward SPX level desired from index option prices. It is determined
by identifying the strike price at which absolute difference between
the call and put prices is smallest;
K0 = First strike below the forward index level F;
K i = Strike price for the i th out-of-the-money option; a call if K i > K 0 ,
and a put if K i < K 0 , both put and call if K i = K 0;
3K i = interval between strike prices, half the difference between the strike
Ki+1 - Ki-1
on either side of K i: 3 K i = 2 ;
Q (K i) = the midpoint of the bid-ask spread for each option with stike ;
R = risk free interest rate to expiration.
The VIX is quoted in percentage points and represents the expected range
of movement in the S&P500 index over the next year, at a 68% confidence
level (i.e. one standard deviation of the normal probability curve). For exam-
ple, a VIX equal to 15 represents an expected annualized change, with a 68%
probability, of less than 15% up or down.
Based on the same methodology, European stock exchanges also created
volatility indices for several European stock markets. In particular, Eurex in-
troduced the Euro STOXX 50 volatility index (VSTOXX) to measure the im-
1 In particular, the new methodology is based on Carr and Madan (1998) and Demeterfi et al. (1999) work on
pricing variance swaps.
2 Using SPX options with more than 23 days and less than 37 days to expiration ensures that the VIX will always
reflect an interpolation of two points along the S&P500 volatility term structure.
12 SAGGIDO GLOBAL MARKETS IMPLY COMMON FEAR?
plied volatility of the EURO STOXX 50 index (ESTOXX), i.e., to indicate,
in percentage points, which volatility is to be expected for the EURO STOXX
50 index over the coming 30 days. The index is based on a basket of EURO
STOXX 50 index options quoted at-the-money or out-the-money.
VIX and VSTOXX are measures of the overall market perceived volatility,
both upwards and downwards. Therefore, high values of the index do not
necessarily represent negative predictions for stocks movements, since inves-
tors can become nervous even during market rallies. For example, Panel A
of Figure 1 shows that the VIX spikes during periods of market turmoil, as
it happened right after the Lehman Brothers’ collapse on September 2008,
but the volatility index might also rise when the level of the S&P 500 index
increases.
Figure 1 - Volatility and stock market indices (January 1st, 2002 – December 31st,
2015; daily observations)
Panel A - VIX (black line and right scale in % per year) and S&P 500 (grey line and
left scale in points)
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 13ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
Panel B - VSTOXX (black line and right scale in % per year) and Euro Stoxx 50
(grey line and left scale in points)
Source: our elaborations on data from DatastreamTM.
As concerns the interpretation of the values and trends of the volatility
indices, if investors expect great upside volatility, they will sell upside stock
call options only if they obtain a large premium. On the other hand, option
buyers will pay such high premiums only if they similarly anticipate a large
upside movement. Due to the resulting aggregate of increase in upside stock
call option prices, the volatility index will raise. Similarly, the index will raise
in the case of an aggregate growth in downside stock put option premiums
that would occur when both option buyers and sellers expect a sharp down-
ward movement. When investors perceive neither significant downside risk
nor significant upside potential, the volatility index will be low. By focusing
on stock prices, the behavior of volatility indices can be explained as follows:
if expected market volatility increases (decreases), investors demand higher
(lower) rates of return on stocks, so stock prices fall (rise) (Whaley, 2009).
Prior literature has investigated both the contribution of VIX and other
volatility indices to investors’ portfolio management and how well the im-
plied volatility forecasts future realized volatility. From a portfolio manage-
ment perspective, since they are tradeable via swaps, futures, options and
exchange traded notes, volatility indices can help to get a desired level of
portfolio diversification and can provide investors with easy access to strate-
gies involving hedging of equity risk by taking positions in implied volatility.
14 SAGGIDO GLOBAL MARKETS IMPLY COMMON FEAR?
For example, when equity markets become highly volatile and the portfolio
tracking error and the rebalancing costs increase, using volatility futures helps
to hedge against these frictional costs. On the other hand, investors may also
use volatility index derivatives to enrich the set of potential speculative di-
rectional positions. Szado (2009) and Rhoads (2011) highlight the potential
benefits of adding volatility derivatives to equity index portfolios. Similarly,
Chen et al. (2011) demonstrate that adding VIX futures contracts can im-
prove the mean-variance investment frontier, while Daigler and Rossi (2006)
find significant diversification benefits from adding a long VIX position to an
S&P500 portfolio.
The question of how well the implied volatility forecasts future realized
volatility has received a great deal of attention in the financial literature. The
general conclusion of prior studies is that implied volatility outperforms the
well-known volatility measures based on historical data: see, among the oth-
ers, Blair et al. (2001), Corrado and Miller (2005) as well as Carr and Wu
(2006), who show that VIX outperforms GARCH volatility estimated from
the S&P500 index returns. However, Becker et al. (2006) find that VIX is
not an efficient forecaster of future realized volatility, and that other volatility
estimates based on historical data can be superior to VIX alone.
3. Analyzing the determinants of volatility indices: stock market indices
and interest rates
Equation (1) shows that volatility indices are functions of a wide set of
variables. In order to address the issues associated with the main determinants
of the volatility indices, this research contributes to prior literature by: i) add-
ing new evidence on the relationship between the volatility indices (VIt) and
stock indices (SIt), that, in addition to prior literature, we examine during the
great financial crisis, ii) shedding light on the link between the volatility indi-
ces, the risk-free interest rates (IRt) that are used to calculate the US VIX and
European VSTOXX, and iii) providing new insights about the importance of
monetary policy actions in determining market implied volatility.
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 15ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
3.1. Volatility and stock indices
According to prior literature, the negative relationship between stock re-
turn and implied volatility can be justified by either firm fundamentals or by
the behavior of market participants. Within the former group of studies, ac-
cording to the “leverage hypothesis”, the increase in leverage, which is caused
by a decrease in stock prices, determines the increase in the equity volatil-
ity and the associated risk of equity holders (Black, 1976; Christie, 1982;
Schwert, 1989). Based on the “feedback hypothesis”, due to a rise in volatility,
investors raise the future rates of stock returns they ask for, thus determining
a fall in stock prices (French et al., 1987; Bekaert and Wu, 2000; Wu, 2001;
Kim et al., 2004). As concerns the studies accounting for the behavior of mar-
ket participants, investors believe that good investments are characterized by
low risk and high return and associate larger negative (positive) returns with
larger (smaller) volatility (Hibbert et al., 2008; Low, 2004).
From a methodological perspective, we start our analysis by regressing the
daily log returns of all sample stock indices on the corresponding volatility
index log returns, based on the following regression model:
3VI t = c + b 1 3 SI t + f t (2)
where: 3VI t is the log return of the i - th volatility index (either the VIX or
the VSTOXX), 3SI t is the log return of the corresponding i - th stock mar-
ket index (either the S&P500 or the EURO STOXX 50) and f t represents a
normally distributed error term.
Early studies also investigate for a potential asymmetric relation between
volatility and stock market indices, but evidence is not conclusive. For ex-
ample, Giot (2005) finds not only that the relation between the S&P100’s
returns and the changes in VXO (the “old VIX”) is asymmetric, but also that
it tends to differ in periods of low and high volatility. The increase in implied
volatility (when negative stock index returns occur) is lower in high-volatility
periods than in low-volatility periods. Fleming et al. (1995) also find a statis-
tically significant asymmetric relation between the old VIX and S&P returns,
16 SAGGIDO GLOBAL MARKETS IMPLY COMMON FEAR?
whereas Simon (2003)’s results show a statistically significant asymmetric re-
lation between VIX, VNX (the technology sector based on the Nasdaq 100
implied volatility) and their respective equity indices. Siriopoulos and Fassas
(2009) and Whaley (2000) do not find evidence for strong asymmetric re-
lation between VIX, RVX (the CBOE Russell 2000 Volatility Index), VNX
and their respective stock market indices. Alexander (2008) and Siriopoulos
and Fassas (2012) both show an asymmetric negative relation for VFTSE (the
FTSE volatility index) and FTSE whilst Gonzalez and Novales (2009) report
lack of asymmetric negative relation between VDAX (the German DAX vola-
tility index), VSMI (the Swiss SMI volatility index), and their corresponding
stock market indices.
In order to detect any potential asymmetric relation between each of the
two volatility indices and the underlying stock indices, following Whaley
(2009), we use a slightly modified version of the previous model, that can be
written as follows:
3VI t = b 0 + b 1 3 SI t + b 2 3 SI -t + f t (3)
where 3SI -t is the log return of the stock market index conditional on the
market going down and 0 otherwise. Should both the slope coefficients be
negative and statistically sgnificant, we would find support not only to the in-
verse relation between stock market index and volatility, but also to its asym-
metric nature.
3.2. Volatility indices and interest rates
VIX and VSTOXX are calculated as risk-neutral expectations of volatility
for near- and next-term options via a linear interpolation. The risk-free in-
terest rates for the expectations referred to the near- and next-term options,
respectively R 1 and R 2, are the bond-equivalent yields of the US T-bill matur-
ing closest to the expiration dates of relevant SPX options for the US volatility
index and the corresponding Euribor rate for the European one.
The risk-free interest rate is also relevant to determine the option price
Q (K i) and the forward level of stock index, F, as shown by the following
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 17ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
equation (CBOE, 2009):
F = Strike Price + e RT # ^ Call Price - Put Price h (4)
Therefore, based on equation (4), volatility indices react to the risk-free
interest rate according to the following sensitivity index, which is obtained by
calculating the derivative of the volatility function with respect to the risk-free
rate:
2R = 50 E 6 v 2@ # ' T | Q (K i) + T | 2 i e RT t i + 1
2VI 1 2 3K i RT 2 3K
2 Te
i Ki i Ki
- T : K - 1D; K Te RT E 1
2 F ( c - p) (5)
0 0
where t i measures the sensitivity of an option to a change in interest rate, c is
the call price and p is the put price. The derivative of the volatility index with
respect to the risk-free rate shown in equation (5) is not always positive. The
sign of this sensitivity index depends on the difference in brackets and on the
of the options included in the portfolio taken into account to calculate the
volatility index. In particular, the sign is positive if:
^c - ph
2 ti $ T # ( :F D 2
3K i 3K i
| i Ki K 0 # K 0 - 1 - | i K 2i Q (K i) (6)
As a result, it is first the construction mechanism of the volatility indices to
determine the final relationship of VIX and VSTOXX with interest rates. In
particular, the sign of the t of the options portfolio in equation 6 depends on
the relative weight of the call and put options included in the portfolio itself.
The impact of a rise in interest rates on the value of a generic option de-
pends on the combination of the two following effects: due to an increase in
interest rates, on the one hand, the expected stock return required by inves-
tors tends to rise, and, on the other hand, the present value of any future cash
flow received by the holder of a certain option decreases. Ceteris paribus, the
combination of these two effects leads to an increase in the value of a generic
call option t call > 0 and to a decrease in the value of a generic put option
18 SAGGIDO GLOBAL MARKETS IMPLY COMMON FEAR?
(t put < 0).
Finally, there is one last channel to consider to get a comprehensive view
of the impact of interest rates movements on volatility indices. Consider the
companies whose stocks are included in the stock index underlying the op-
tions used to calculate the volatility index. If these companies pay dividends,
by affecting their stock prices, interest rate movements also affect the value
of the stock index and, eventually, the value of the options included in the
volatility index.
By accounting also for the risk-free interest rates, equation (3) can be writ-
ten as follows:
3VI t = b 0 + b 1 3 SI t + b 2 3 SI -t + b 3 3 IR t + f t (7)
where 3IR t is the percentage change in the risk-free rate used in the formula
of each of the two volatility indices.
This research also aims to shed light on the relationship between the
volatility indices and the monetary policy decisions taken by the two most
important central banks, namely the US Federal Reserve and the European
Central Bank. By changing their policy rates, monetary authorities affect in-
vestors’ decisions and expectations and can contribute to explain volatility
indices behavior.
In order to test for the impact of monetary policy actions on volatility
indices, we introduce a new variable 3MPR t , i.e., the change in the mone-
tary policy rate, in equation (7). Therefore, our final regression model can be
formalized as follows:
3VI t = b 0 + b 1 3 SI t + b 2 3 SI -t + b 3 3 IR t + b 4 3 MPR t + f t (8)
The global financial turmoil erupted in June 2007 occurred during the
time-span we examine and the Chow test confirms the presence of a structur-
al break in our time series. Therefore, to detect whether the events of those
years of financial turbulences do affect the relationships we are interested in,
we introduce into equations (2), (3), (7) and (8) a dummy variable CRISIS,
that takes the value of 1 for the observations referred to the crisis period, and
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 19ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
0 otherwise, together with its interaction with the regressors specified in each
of the models previously defined.
The final version of the regression equations that we estimate in the empir-
ical section are as follows:
3VI t = b 0 + b 1 3 SI t + b 2 CRISIS + b 3 CRISIS ) 3SI t + f t (9)
3VI t = b 0 + b 1 3 SI t + b 2 CRISIS + b 3 CRISIS ) 3SI t +
+b 4 3 SI -t + b 5 CRISIS ) 3SI -t + f t (10)
3VI t = b 0 + b 1 3 SI t + b 2 CRISIS + b 3 CRISIS ) 3SI t +
+b 4 3 SI -t + b 5 CRISIS ) 3SI -t + b 6 3 IR t +
+b 7 CRISIS ) 3IR t + f t (11)
3VI t = b 0 + b 1 3 SI t + b 2 CRISIS + b 3 CRISIS ) 3SI t +
+b 4 3 SI -t + b 5 CRISIS ) 3SI -t + b 6 3 IR t +
+b 7 CRISIS ) 3IR t + b 8 3 MPR t +
+b 9 CRISIS ) 3MPR t + f t (12)
4. Empirical analysis
4.1. Data
The data used in our empirical analysis are taken from DatastreamTM and
refer to the period ranging from January 1st, 2002 to December 31st, 2015,
for a total of 3,653 daily observations. The main descriptive statistics of the
volatility indices time series are presented in Panel A of Table 1. Our sample
is characterized by wide ranging levels of volatility: the highest single value,
equal to 87.5, was reached by VSTOXX on October 16th, 2008 while the
minimum of 9.9 was recorded by the VIX on January 24th, 2007. The daily
mean and median volatility log returns are close to zero, reflecting the absence
of a deterministic growth trend in volatility, and confirming that volatili-
20 SAGGIDO GLOBAL MARKETS IMPLY COMMON FEAR?
ty follows a mean-reverting process (Allen et al., 2006). We find significant
positive skewness in both the levels and the log returns of the indices. The
Shapiro-Francia statistics reject the hypothesis of a normal distribution in
all cases at the 1% significance level, which implies a higher probability of
extreme movements.
The negative relationship between equity and volatility markets is con-
firmed by the correlation matrix presented in Panel B of Table 1. The daily
log returns of stock markets and volatility indices are negatively correlated at
the 1% level: we observe a negative correlation of 74.5% between the VIX
and S&P500 and of 74.6% between the VSTOXX and the EURO STOXX
50 index. The correlation between the levels of VIX and VSTOXX stands at
an impressive value of 91.9%. The correlation between S&P500 and EURO
STOXX 50 is also positive, but it is much lower than the correlation between
the two volatility indices, being equal to 42.4%.
We calculate the correlations between the volatility indices, on the one
hand, and the stock market indices, on the other hand, for three different
sub-periods, namely the last 10 years, the last 5 years and the last year of
our sample period, respectively (Figure 2). Correlation between VIX and VS-
TOXX ranges from 95%, if calculated over the last 10 years of the time hori-
zon under analysis, to 80%, if referred to the 2015 year only. The correlation
between SPX and ESTOXX stands at 36.1% if calculated over the 2006-2015
period, whereas it raises to 88.3% over the last five years of the sample period
and 77.9% for the last 12 months.
Figure 2 - Evolution of the correlation between VIX and VSTOXX and between
SPX and Euro Stoxx 50 (daily observations).
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 21ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
Source: our elaborations on data from DatastreamTM.
The time horizon we investigate covers periods with different stock market
conditions. For example, Panel B of Figure 1 depicts the evolution of the
EuroStoxx 50 and VSTOXX. After a minor market correction in the first half
of 2004 a tight range of volatility lasted until early 2006 when the closure of
a majority of Ameriquest’s branches announced the imminent credit crises3.
Although low-volatility conditions lasted for several months, implied volatil-
ity rose to 35% in the last quarter of 2007, when some of Bear Stearns hedge
funds bankrupted.
In order to detect the relation between the volatility indices and risk-free
interest rates used in equation (1), we use the 4-week T-Bill interest rate for
the US market and the 1-month Euribor for the European market. Panel B
of Table 1 includes the pairwise correlation coefficients between the changes
in these interest rates and the volatility indices. In particular, the log return
of the VIX index is negatively correlated with the percentage change in the
1-month T-Bill rate at the 1% confidence level, whereas the correlation co-
efficient between the log return of the VSTOXX index and the percentage
change in the 1-month Euribor is positive but neither economically, nor sta-
tistically significant.
As concerns the impact of monetary policy on volatility indices, we rep-
resent the monetary policy stance through the percentage changes in the Fed
Funds rate (FFR) for the VIX and in the Euro Overnight Deposit rate (EU-
RDEPRATE) for the VSTOXX. The change in FFR (∆FFR) is positively and
statistically correlated with both the level of the VIX index and its log returns
at the 1% confidence level, with two correlation coefficients approximately
equal to 6% and 4%. The correlation coefficients of the change in the Euro
Overnight Deposit rate (∆EURDEPRATE) with the level of the VSTOXX
index and its log returns are -1.1% and 0.6%, respectively. Nevertheless, nei-
ther of them is statistically significant.
3 Ameriquest was one of the largest mortgage lenders in North America.
22 SAGGIDO GLOBAL MARKETS IMPLY COMMON FEAR? Table 1 - Volatility indices, stock market indices and interest rates (January 1st, 2002 – December 31st, 2015; daily observations). VIX is the CBOE volatility index, based on the S&P 500 index; VSTOXX is the Euro Stoxx 50 volatility index; ∆VIX is the log return of the VIX index; ∆VSTOXX is the log return of the VSTOXX index; SPX is the S&P 500 stock market index; ESTOXX is the Euro Stoxx 50 stock market index; ∆SPX is the log return of the S&P 500 stock market index; ∆ESTOXX is the log return of the Euro Stoxx 50 stock index; ∆TBILL is the percentage change in the 1-month T-Bill interest rate; ∆EURI- BOR is the percentage change in the 1-month Euribor rate; ∆FFR is the percentage change in the US Fed Funds Rate used as a proxy of the Federal Reserve’s monetary policy stance; ∆EURDEPRATE is the percentage change in the Euro Overnight Deposit rate, taken as a proxy of the monetary policy rate of the European Central Bank. RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 23
SAGGI
Panel A - Descriptive statistics of VIX and VSTOXX
Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Shapiro Francial normality test
VIX 0.201 0.175 0.809 0.099 0.092 2.21** 9.92** 0.798***
VSTOXX 0.248 0.222 0.875 0.116 0.103 1.63** 6.10** 0.856***
ΔVIX 0.000 -0.002 0.496 -0.351 0.066 0.70** 7.25** 0.948***
ΔVSTOXX 0.000 -0.003 0.328 -0.249 0.058 0.71** 5.81** 0.961***
Panel B - Correlation matrix of volatility indices, stock indices and interest rates
ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
VIX VSTOXX SPX ESTOXX ΔVIX ΔVSTOXX ΔSPX ΔESTOXX ΔTBILL ΔEURIBOR ΔFFR ΔEURDEPRATE
VIX 1
VSTOXX 0.919*** 1
SPX -0.507*** -0.474*** 1
ESTOXX -0.430*** -0.520*** 0.424*** 1
ΔVIX 0.084*** 0.022 -0.004 0.01 1
ΔVSTOXX 0.071*** 0.080*** -0.004 -0.006 0.534*** 1
ΔSPX -0.130*** -0.062*** 0.029* 0.001 -0.745*** -0.445*** 1
ΔESTOXX -0.115*** -0.115*** 0.029* 0.033** -0.469*** -0.746*** 0.597*** 1
ΔTBILL 0.015 0.005 0.030* -0.008 -0.054*** -0.029* 0.071*** 0.043*** 1
ΔEURIBOR -0.041** -0.037** 0.019 0.048*** 0.014 0.005 -0.019 -0.01 0.030* 1
ΔFFR 0.060*** 0.037** -0.001 -0.003 0.039*** 0.006 -0.078*** -0.029* -0.02 -0.005 1
ΔEURDEPRATE -0.016 -0.011 0.004 -0.023 -0.016 0.006 0.012 0.009 0.004 0.006 -0.026 1
24
***, ** and * denote significance at the 1%, 5% and 10% level, respectively.
Source: our elaborations on data from DatastreamTM.DO GLOBAL MARKETS IMPLY COMMON FEAR?
4.2. The determinants of the volatility indices: results of the OLS regressions
Table 2 presents the results of our OLS estimates of equations (9)-(12), re-
ferred to both the VIX (columns 1-4 in Panel A) and VSTOXX (columns 5-8
in Panel B). The negative and statistically significant coefficients of the rate of
change in the stock indices 3SI t confirm, for both the European and US mar-
ket, the negative correlations between changes in implied volatility indices and
underlying stock market returns that we have discussed in the previous section,
and are consistent with, among the others, Whaley (2000) and Giot (2005).
Positive stock returns correspond to declining implied volatility levels, while neg-
ative returns are associated with increasing implied volatility levels. The negative
relationship appears much less pronounced for the European market. During the
crisis period, the negative relationship between stock indices returns and implied
volatility seems to be less negative, since the coefficients of interaction terms
CRISIS ) 3SI t are positive and statistically significant in all the specifications
reported in Table 2.
Since the coefficients of the variable 3SI -t are negative for both the VIX and
VSTOXX regressions, our empirical evidence supports the hypothesis of an
asymmetric relation between the two volatility indices and the respective stock
market indices. VIX and VSTOXX show wider changes when stock prices go
down, relative to the case in which stock prices rise. For example (see column 1
in Panel A), if, during the non-crisis years, the S&P500 index rises by 100 basis
points, the VIX will fall by almost 4.9%. Should the S&P500 fall by 100 basis
points, the VIX will experience an increase of circa 5.16%.
Consistently with prior literature, the volatility indices appear to be measures
of investors’ fear of the downside risk more than indicators of investors’ excite-
ment in a market rally i.e., downward volatility seems to be higher than the up-
ward one. According to Giot (2005), the increase in implied volatility is lower in
high-volatility periods than in low-volatility periods. In line with this result, we
find that, during the years of the great financial crisis, when volatility is higher
than that referred to ordinary market conditions, the asymmetric nature of the
relation is weaker for the US market: the coefficients of the interaction terms
CRISIS ) 3SI -t are all positive and statistically significant at the 1% confidence
level. Results are opposite for the European market, where we observe that the
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 25ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
coefficients of the interaction terms CRISIS ) 3SI -t are always negative and sta-
tistically significant at the 5% confidence level, thus supporting the hypothesis
that the asymmetric behavior of the VSTOXX is even stronger during the finan-
cial turmoil.
The coefficients of the changes in risk-free interest rates are positive for the
American market and negative for the European one, respectively, but they are
not statistically significant in none of the two cases. The effect of risk-free rates
becomes statistically significant during the crisis period with a negative sign for
the VIX-S&P 500 relation (see column 4 in Panel A), and a positive sign for the
European market (see column 8 in Panel B).
As to the impact of monetary policy stance, the coefficient of 3MPR t is neg-
ative and statistically significant at the 1% confidence level in the case of the VIX
regression (see column 4 in Panel A), which means that VIX decreases when the
monetary policy rate increases. Therefore, a restrictive monetary policy is associ-
ated with a contemporaneous decrease in implied volatility for the US market.
This negative relation, which is consistent with what we would expect to see
during periods of ordinary economic and financial conditions, becomes much
weaker during the crisis period since the interaction term CRISIS ) 3MPR t is
positive and statistically significant at the 1% confidence level. On the contrary,
the coefficient of the change in the Euro overnight deposit rate is positive but
neither statistically nor economically significant (see column 8 in Panel B), and
its interaction term with the dummy CRISIS is negative but significant at only
10% confidence level.
26 SAGGITable 2 - OLS regression results
This table presents the results of OLS regressions of volatility indices returns on returns of their respective stock market indices, risk-free interest and money market rates. Columns labeled with 1, 2, 3 and 4
in Panel A exhibit results for equations (9), (10), (11) and (12), respectively, when the dependent variable is the log return of the VIX index ); columns labeled with 5, 6, 7 and 8 in Panel B exhibit results for
equations (9), (10), (11) and (12), respectively, when the dependent variable is the log return of the VSTOXX index ). is the log return of the stock market indices (S&P 500 for Panel A and EuroStoxx50 for
CRISIS
Panel B, respectively) and
) 3SI -t is the log return of stock market indices conditional on the market going down andCRISIS
0 otherwise.
) 3IR t is the percentage change in the 4-week T-Bill interest rate for regressions
in Panel A, and the percentage change in the 1-month Euribor for regressions in Panel B. 3MPR t is the percentage change in the Fed Funds Rate for regressions in Panel A, and the percentage change in the
European overnight deposit rate for regressions in Panel B. CRISIS )is 3 a dummy
SI -t variable taking the value of 1 for the observations referred to the crisis years (i.e., from June 2007 onward).
Panel A: Dependent variable: 3VIX t Panel B: Dependent variable: 3VSTOXX t
1 2 3 4 5 6 7 8
0.0014* -0.0048*** -0.0048*** -0.0047*** 0.0002 -0.0056*** -0.0056*** -0.0056***
Intercept
(1.92) (-4.62) (-4.64) (-4.59) (0.29) (-5.91) (-5.92) (-5.96)
-5.0216*** -4.0987*** -4.0986*** -4.0905*** -3.0548*** -2.4451*** -2.4450*** -2.4448***
CRISIS ) 3SI t
(-65.80) (-31.38) (-31.39) (-31.32) (-61.08) (-28.65) (-28.65) (-28.66)
-0.0028 -0.0009 -0.0012 -0.0012 -0.0019 -0.0077*** -0.0074** -0.0073***
CRISIS ) 3SI -t
(-1.42) (-0.34) (-0.44) (-0.44) (-1.05) (-3.22) (-3.06) (-3.03)
2.2389*** 1.6404*** 1.7172*** 1.7031*** 0.5787*** 0.8430*** 0.8696*** 0.8855***
CRISIS ) 3SI t
(19.74) (8.37) (8.66) (8.58) (6.11) (5.23) (5.37) (5.46)
- -1.8163*** -1.8180*** -1.8284*** - -1.2034*** -1.2043*** -1.2056***
CRISIS ) 3SI -t
- ( -8.66) (-8.67) (-8.72) - (-8.74) (-8.74) (-8.76)
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020
- 1.2098*** 1.1174*** 1.1567*** - -0.4793** -0.5265** -0.5385**
CRISIS ) 3SI -t - (3.94) (3.61) (3.71) - (-1.88) (-2.05) (-2.10)
- - 0.0008 0.0010 - - -0.0064 -0.0065
CRISIS ) 3IR t
- - (0.44) (0.50) - - (-0.47) (-0.48)
- - -0.0059** -0.0059** - - 0.2316 0.2746**
CRISIS ) 3IR t
- - (-2.10) (-2.10) - - (1.77) (2.06)
- - - -0.0062*** - - - 0.0004
3MPR t
- - - (-2.88) - - - (1.29)
- - - 0.0056** - - - -0.0301*
CRISIS ) 3MPR t
- - - (2.42) - - - (-1.72)
Adjusted R2 0.5978 0.6064 0.6069 0.6071 0.5614 0.5772 0.5773 0.5776
F-statistics 1810.00*** 1126.33*** 806.34*** 627.93*** 1559.33*** 997.97*** 713.54*** 555.86
# of obs. 3,653 3,653 3,653 3,653 3,653 3,653 3,653 3,653
T-statistics are reported in parentheses.
27
DO GLOBAL MARKETS IMPLY COMMON FEAR?
*** and * denote significance at the 1% and 5% level, respectively.
Source: our elaborations on data from DatastreamTM.ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
5. The determinants of the volatility indices: a SPBVAR evidence
5.1. Econometric Methodology and Specifications
The above OLS approach is highly sensitive to departures from normal dis-
tribution and suffers from significant limits in jointly analyzing the dynamic
of potentially endogenous variables, like the financial variables we are inter-
ested in. Therefore, to better investigate the interaction between VIX, VS-
TOXX and their drivers, here we use a vector autoregressive model (VAR)4.
VAR models are among the best suited approaches to analyze multivariate
time series and are typically used to describe the dynamic behavior of eco-
nomic and financial variables.
A general VAR model has many parameters that may be difficult to inter-
pret due to the complex interactions and feedback between the variables in
the model. Consequently, in this section, we propose a time-varying Structur-
al Panel Bayesian VAR (SPBVAR) model of the form:
Y mi,t = U i,0 + | j = 1 U mit,l (B) Y mi,t - j + f i,t
p
(13)
where the subscripts i, l = 1, 2, ..., N are country indices, t = 1, 2, ..., T denotes
time, B stands for the lag operator, U i,0 is an NM ) 1 vector of intercepts for
each i, U it,l is an NM ) NM matrix of coefficients for each pair of countries
(i, l) for a given m, Yi,t - j is an NM ) 1 vector of lagged variables of inter-
est for each i for a given m, and f i,t + i.i.d.N (0, | t) is an NM ) 1 vector
of disturbance terms. The subscripts j = 1, 2, ..., p are lags for each of the
m = 1, 2, ..., M endogenous variables.
The model (13) would correspond to a simplified version of the time-vary-
ing multicountry SPBVAR model proposed in Pacifico (2019a,b,c). To be more
precise, in this analysis, we only consider two country indices (N = 2) and a
set of five lagged endogenous variables ( M = 5). Moreover, in this study, in
order to examin the dynamic interaction between volatility indices and main
financial and macroeconomic variables in US and European stock and volatil-
ity markets, we assume the variance-covariance matrix of the vector of errors
4 For applications of VAR models to financial data, see Hamilton (1994) and Campbell, Lo and MacKinlay
(1997).
28 SAGGIDO GLOBAL MARKETS IMPLY COMMON FEAR?
| diag (exp (t
t
), exp (t 2t)), where t it = (t 1t, t 2t) denotes the time-varying
1t
log-volatilities evolving over time according to the following random walk:
t t = t t - 1 + r t with r + N (0, | t) (14)
where | t is a block diagonal matrix and t 0 denotes the initial conditions to
be estimated.
The random-walk assumption in (14) is very common in the time-varying
VAR literature and has the advantage of focusing on permanent shifts and
reducing the number of parameters in the estimation procedure. Moreover,
with the hierarchical strategy used to construct the time-varying SPBVAR
in (13), one would be able to investigate any type of coefficient factors via
their interactions. The variance in f i,t is allowed to be time-variant and it is
a way of modelling time-varying conditional second moments to provide an
alternative to the stochastic volatility specification. The main difference is that
volatility changes are replaced by coefficient changes and the computational
costs involved in using this specification are moderate since the high dimen-
sionality is avoided via Bayesian inference and Markov Chain Monte Carlo
(MCMC) integrations.
The variables included in our SPBVAR model are: (i) the natural logarithm
of the volatility indices, respectively labeled as logVIX and logVSTOXX, (ii)
the US monetary policy interest rate (FFR), (iii) the EU monetary policy
interest rate (EURDEPRATE), (iv) the natural logarithm of the underlying
stock indices, labeled as logSPX and logESTOXX50, (v) the 18-month for-
ward exchange rate. Here, all variables in the system are endogenous and
time-varying.
The estimation sample covers daily data for the period 2002-2015 and
all time-series have persistent memory, but the partial autocorrelation func-
tion of each variable is not statistically different from zero over lag 4. Based
on conventional Akaike (AIC), Schwarz-Bayesian (BIC) and Hannan-Quinn
(HQ) information criteria, we use one lag in our VAR models both for VIX
and VSTOXX. The gray shaded areas correspond to 95 percent confidence
interval. Generally, the volatility indices have same dynamic reactions to the
RIVISTA BANCARIA - MINERVA BANCARIA N. 1 - 2 / 2020 29ROSA COCOZZA, DOMENICO CURCIO, ANTONIO PACIFICO
shocks of all the variables taken into account.
In equation (13), the dynamic relationships are allowed to be unit-spe-
cific, and all coefficients vary over time. Moreover, if the elements of U t (L)
are stacked over i, it is possible to obtain a matrix that is not block-diagonal
for at least some p. Thus, cross-unit lagged interdependencies matter, and
dynamic feedback and interactions among volatility indices and macroeco-
nomic-financial variables are possible. Nevertheless, even if this feature adds
flexibility to the specification, it is very costly since the number of coefficients
is increased by 6^ N ) M h ) p@ factors.
To avoid the curse of dimensionality, by following the framework of Pacifico
(2019a,b), a 1 ) k vector X t = (I, Y l mi,t - 1, Y l mi,t - 2, ..., Y l mi,t - p)l can be defined con-
taining all lagged variables in the system for each i, where k = 6^ N ) M h ) p@ is
the number of all matrix coefficients in each equation of the SPBVAR model for
the two country indices. Then, we define an 6 NMk ) 1@ vector c itk ,l = vec (g itk ,l)
containing all columns, stacked into a vector5, of the matrix U t (L) for the
two country indices for a given k, with g itk ,l = ^ Uli,0 , Ul it1 ,l, Ul it2 ,l, ..., Ul itM,l hl , and
c t = ^ cl1t , cl2t hl denoting the time-varying coefficient vectors, stacked for i, for
each country-variable pair. With these specifications, we are able to express
the model (13) in a simultaneous-equation form:
Yt = ^ I NM 7 X t h c t + E t (15)
where Yt = (Y l 1mt, Y l 2mt)l and E t = (fl1t , fl2t )l are [NM ) 1] vectors containing
the observable variables of interest and the random disturbances of the model
for each i for a given m, respectively. In model (15), there is no subscript i
since all lagged variables in the system are stacked in X t .
Now, because the coefficient vectors in c t vary in different time periods for
each country-variable pair and there are more coefficients than data points,
it is impossible to eliminate c t . To be more precise, each equation of the
time-varying SPBVAR in equation (13) has k = (2 ) 5) p = 10 coefficients,
and there are 4,400 equations in the system. Thus, to cope with the problem
of dimensionality, we assume that c t has the following factor structure:
5 The vec operator transforms a matrix into a vectorby stacking the columns of the matrix, one underneath the
other.
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