Museum and monument attendance and tourism flow: A time series analysis approach

Abstract

In this paper, we analyze a discrete-time Markov chain theoretic model of the provision of guided tours to tourists by a private firm. Specifically, we first determine the equilibrium probability distribution of the number of tourists in the guided tour providing firm's waiting room just before this firm begins to match tour guides with tourists. Second, we compute the long run expected number of tourists in this firm's waiting room. Finally, we ascertain the long run expected delay per tourist in the firm's waiting room.

Full text

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File: Cellini-Cuccia(SEASON+CAUSALITY+PRESTUR_MUSMON).doc
MUSEUM & MONUMENT ATTENDANCE AND TOURISM FLOW:
A Time Series Analysis Approach
Roberto Cellini
University of Catania, Italy
Tiziana Cuccia
University of Catania, Italy
Abstract - This paper takes a time series analysis approach to evaluate the directions
of causality between tourism flows, on the one side, and museum and monument
attendance, on the other. We consider Italy as a case study, and analyze monthly data
over the period January 1996 to December 2007. All considered series are seasonally
integrated, and co-integration links emerge. We focus on the error correction
mechanism among co-integrated time series to detect the directional link(s) of
causality. Clear-cut results emerge: generally, the causality runs from tourist flows to
museum and monument attendance. The non-stationary nature of time series, their co-
integration relationships, and the direction of causal links suggest specific implication
for tourism and cultural policies.
Keywords: Tourism, Museum, Seasonal unit root, Co-integration, Causality.
Roberto Cellini - Faculty of Economics, University of Catania (corso Italia, 55 – 95128
Catania, Italy. Email <cellini@unict.it>).
Tiziana Cuccia - Faculty of Economics, University of Catania. (corso Italia, 55 – 95128
Catania, Italy. Email <cucciati@unict.it>).
.

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MUSEUM & MONUMENT ATTENDANCE AND TOURISM FLOW:
A Time Series Analysis Approach
Abstract: This paper takes a time series analysis approach to evaluate the directions
of causality between tourism flows, on the one side, and museum and monument
attendance, on the other. We consider Italy as a case study, and analyze monthly data
over the period January 1996 to December 2007. All considered series are seasonally
integrated, and co-integration links emerge. We focus on the error correction
mechanism among co-integrated time series to detect the directional link(s) of
causality. Clear-cut results emerge: generally, the causality runs from tourist flows to
museum and monument attendance. The non-stationary nature of time series, their co-
integration relationships, and the direction of causal links suggest specific implication
for tourism and cultural policies.
Keywords: Tourism, Museum, Seasonal unit root, Co-integration, Causality.
1. INTRODUCTION
The effectiveness of cultural attractions in enhancing tourism flows is a widely
debated issue, both in cultural economics and in tourism economics. Quite surprisingly,
however, the evidence about the relationships between attendance at cultural attractions and
tourist flows is restricted to specific, albeit interesting, cases, and general analyses are
lacking, to the best of our knowledge. In particular, we did not find any single study
analyzing the relationship at national levels, nor employing aggregate data over long periods
of time. In this paper we show that it is possible to derive clear-cut results from the time
series analysis of monthly time series concerning tourism flows and museum and monument
attendance, taking Italy as a case study. More specifically, we are interested in studying
which is the possible direction of causal links between tourism flows and the attendance at
museums and monuments.
Not surprisingly, time series in the field of both tourism and cultural sites attendance
show a great deal of seasonality; more specifically, all the time series taken into consideration
in the present paper appear to be seasonally integrated. Hence, the techniques related to
integration and co-integration among time series provide a natural language to study the
relationships and, more specifically, the causal links among tourism flows and cultural sites

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attendance. It is worth stressing that, while the presence of seasonal unit roots in time series
related to tourism is not a novelty in the literature, the present paper represents –as far as we
know– the first attempt to investigate the causal direction between tourism flows and
monument attendance, using time series analysis techniques based on seasonal co-integration.
The knowledge of the properties of time series, and their relationships, can shed light
on the sound evaluation of different points: in the case at hand, we can derive implications on
the effectiveness of cultural sites to attract tourism, on the effects of tourism dynamics upon
the attendance at museums and monuments, and on the role of monuments and museums to
lessen seasonality in tourism flows, just to mention the most prominent and obvious ones.
We anticipate that tourist presence as measured by overnight stays (as well as tourist
arrivals and average stay) co-integrate with the attendance at museums and monuments, and a
unidirectional long-run causal link generally does emerge, running from tourism flow
variables to cultural sites attendance. Technically, tourism flows Granger-cause cultural sites
attendance, while the reverse does not hold. Appropriate elasticity coefficients are estimated
at the end. Consistently, it is hard to sustain that cultural attractions can promote tourism in
the long run, at least in the aggregate. On the other hand, the long-run dynamics of visits to
cultural sites is strongly determined by the dynamics of tourism flows. Therefore, we can
guess that the role of cultural sites is limited in lessening seasonality.
There is a wide body of studies, especially in cultural economics, concerning
museums. The largest part of this literature focuses on the microeconomic determinants of
museum visits, on the demand side, and on problems of organization and governance on the
supply side. An update review is provided by Frey and Meier (2006), in their chapter in the
Handbook of Cultural Economics devoted to the economics of museums. Interestingly
enough, however, their review on applied works cannot list any study, in which tourism flow
is considered among the determinants of attendance at museums. In this perspective, our
present exercise can complement the evidence in existing literature. Of course, we are aware
that museums and monuments have values that go far beyond tourism motivation.
Nevertheless, omitting tourism flows from the determinants of cultural visits can lead to
serious mistakes, especially in relation to (here documented) cases of cointegrating
relationships. Similarly, we are also aware that the visits to monuments and museums
represent too strict a measure of cultural tourism, and hence our evidence –that causal links
go from tourism flows to museum visits and not in the reverse sense– cannot justify the
conclusion that “cultural tourism” is not important for enhancing tourism flows.

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2. TOURISM FLOWS AND ATTENDANCE AT MUSEUMS AND MONUMENTS
Tourism studies seem to take for granted that museums and monuments play a
significant role as tourist attractions. The available economic literature on museums, in
particular, can be divided into two lines of research. The first line looks at the museum as an
institution that has a private and a social role: it has to satisfy the present visitors but it has to
improve and preserve the present collection for future generations (Johnson, 2003). The main
issues within this research line concern the organizational form (e.g., Fedeli and Santoni,
2006), the managerial aspects of supplying services and merchandise, along with the
strategies for reducing production costs and fund raising (Kotler and Kotler, 1998). A large
number of empirical studies are devoted to estimating visitors’ willingness to pay and their
price elasticity, with the final scope of evaluating the effect of the introduction of admission
fees, as a new source of revenue (Santagata and Signorello, 2000; Maddison and Foster, 2003;
Lampi and Orth, 2009). The second line of research looks at the economic impact of the
museums and cultural initiatives in the promotion of local economic growth and development.
It considers the indirect use value of museum and cultural attractions, their external effects on
local tourism operators and their multiplier effect in the local economy (see, e.g., Cooke and
Lazzaretti, 2008).
Available analyses, within both research lines, are generally based on case studies, and
the conclusions are difficult to generalize (Bille and Schulze, 2006; Plaza, 2008). In the wake
of the successful cases described, the 1990s saw an increase in the number of museums at the
international level and, consequently, an increase in competition. Competition among local
policy-makers also arose: they were confident that the setting of a museum could easily lead
to increasing tourism flows, with the consequent economic growth of the local area.
However, sound quantitative evidence on this possible nexus is lacking: only few
recent studies present econometric exercises on the relation between cultural tourism
specialization and economic growth at national and regional level (respectively, Arezki et al.,
2009, and Cellini and Torrisi, 2009). Similarly, only few contributions study the relation
between the valorization of cultural attractions and tourist arrivals, from an econometric point
of view; for instance, Yang et al. (2009) test the significance of the inclusion of monuments
and sites in the UNESCO World Heritage List (and in national lists) in attracting international

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tourists to China. The results concerning the effectiveness of such cultural sites in attracting
tourism are mixed.
No specific studies are available, to the best of our knowledge, on the causality
between tourism flows and visit to monuments and museums. More explicitly, we think that it
can be interesting to deal with the following question: is it the presence of cultural attraction
(and specifically, museum and monuments) which attracts tourists, or –on the contrary– does
the existence of tourism flows permit museums to be visited? We try to answer this question,
taking aggregate Italian data into consideration.
3. THE ITALIAN CASE
We analyze Italian data with a monthly frequency over the period January 1996 to
December 2007. Data are from ISTAT, the Italian Central Statistics Office, and they are
easily obtainable from the ISTAT website (and from the website of the Ministry of Cultural
Heritage in the case of time series of visits to museums and monuments).
As far as tourism variables are concerned, we consider tourist presences, measured by
overnights (denoted by PRESTUR), tourist arrivals (ARRIV) and average stays (AVSTAY);
as is well known, arrivals multiplied by average stays give the presences. Official data are
articulated according to the source countries, the region of destination, the accommodation
structure, and so on, but –when not differently stated– we refer to the total datum (the total
presences, or total arrivals, and so on). Figure 1.a represents the pattern of the time series of
overnights, while some descriptive statistics of such series are offered in Table 1 (line a).
Arrivals and stays are described in panel b and c of Figure 1, and their statistical properties
are summarized in Table 1 (lines b, c). Figure 1.d and Table 1 provide information related to
the visits to State museums, monuments and museum networks. Also in this case, more
articulated data are available, but generally we limit ourselves to the aggregate datum
(MUSMONUV). Note that only cultural sites run by the State are considered here: though
questionable, this is a necessary choice, due to the fact that consistent data are not completely
available for monuments or museums run by private subjects or local public administrations;
however, the main cultural sites are run by the State in Italy, and these museums account for
over one third of the visits to museums (as documented, e.g., by Fedeli and Santoni, 2006), so
we believe that our data are sufficiently representative.

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INSERT FIGURE 1 AND TABLE 1
Clearly, monthly data show a great deal of variability and strong seasonal patterns. For
this reason, we report some indices related to seasonality in the time series at hand (Table 2).
Specifically, the Gini index provides information on the month concentration (the higher the
Gini index, the stronger the seasonality concentration). Alternatively, one can decompose the
time series (according to one of the available procedures) into trend-cycle, seasonal and
erratic components, and take a look of the seasonal factors: the higher the variation field of
the seasonal factors (or the higher their standard deviation), the more severe the seasonality.
Again, one can take a look at the correlation between the original series and the seasonally
adjusted series (the higher the correlation, the less important the seasonal component). The
message from Table 2 is simple and clear: all the considered series have a significant seasonal
component, even if seasonality in tourist presences appears to be more severe than the
seasonality in museums and monuments attendance.
INSERT TABLE 2
Quite interestingly, the peak seasons, in tourism variables and in visits to museums
and monuments, do not coincide: August is the peak season for tourism, while April
represents the peak season for visits to museums and monuments; the same non-coincidence
holds for the season with the lowest values, which is November for tourism flow variables
and January for cultural sites’ attendance. Apart from seasonality patterns, it is clear that
arrivals show an upward trend, while the trend of average stay is decreasing; these facts are
consistent with tourist presences which are rather stable in the long run. Visits to museums
and monuments appear to have a slightly positive long-term tendency until 2005, and then a
slight decreasing tendency emerges; so, they appear stable over the whole period sample.
We are interested in establishing which statistical representation is the most adequate
for the data at hand. Not surprisingly, we will find that seasonal unit roots are present. This
result is common to all recent applied analyses of tourism time series, in different countries
and over different periods and frequencies (see, e.g., Lim and McAleer, 2000, 2001, Balaguer
and Cantavella Jordà, 2002, Dritsakis, 2004, 2008, Brida, Carrera and Risso, 2008, on
quarterly data referred to Australia, Spain, Greece and Mexico as destinations, respectively,

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and Goh and Law, 2002, Koc and Altinay, 2007, and de Olivera, 2009, on monthly data
concerning arrivals at different destinations). Thus, we have to take a time series analysis
approach based on seasonal unit root and seasonal integration and co-integration properties.
We provide a methodological note on such techniques below. It is important to stress that the
co-integration analysis will provide a natural way (and straightforward tools) to assess the
direction of causality, which is the core point of interest in the present paper.
4. UNITS ROOTS AND CAUSALITY IN TIME SERIES ANALYSIS
4.1. A methodological note
The issue of unit-root has been introduced into statistics and economic analysis with
reference to annual time series. As is well-known, a time series Xt is said to have a unit root,
if in its autoregressive representation ttt ubXX
+
=
−1 (with t=1,2,...T), parameter b is equal
to 1, and the error term ut is a stationary process.
In order to detect the presence of a unit root in a time series, the procedure first
suggested by Dickey and Fuller (1979) involves subtracting 1−t
X from both sides of the
autoregressive representation, so to obtain ttt ucXX
+
=
Δ
−1 (with 1−
−≡
Δ
ttt XXX and
1−≡ bc ). The presence of the unit root can be tested, by evaluating c=0 and by resorting to
the specific critical values for the t-statistics in this case ((augmented) Dickey-Fuller test). If
only one differentiation makes the series stationary, then the series is integrated of order one.
The statistical properties of an integrated series largely differ from the properties of a
stationary series. In particular, an integrated series has no inherent tendency to return to mean
value (that is, shocks on it have permanent effects) and it has increasing expected variance.
If two time series, each of whom integrated of order one, have a stationary linear
combination, then they are said to be co-integrated. Loosely speaking, co-integration means
that long-run relationship exists, as long as two co-integrated series cannot diverge “too
much” from each other. The stationary linear combination can be interpreted as the long-run
link between the non-stationary series. Operationally, in order to evaluate the presence of co-
integration, a static equation is considered, say Yt =m + nXt +ERRt (t=1,2,...T ). If the error
term et is a stationary process, X and Y are co-integrated, and the residuals ERRt can be

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interpreted as the “error” (or “discrepancy”) of current variable Y with respect to its long-run
equilibrium value dictated by the co-integrating relationship.
According to Granger’s representation theorem (Granger, 1986, Engle and Granger,
1987), if two integrated variables co-integrate, an error correction mechanism is operative,
which means that Y and/or X have to move in order to correct the disequilibrium with respect
to the long-run relationship. This means that (at least) one Granger causal ordering does exist.
Thus, the co-integration analysis offers powerful tools to look at the causality issue. Since we
will use these concepts extensively, let us briefly summarize the idea behind the
representation theorem. Consider the following system representing the dynamics of the co-
integrated variables X and Y, where
Δ
is the first-difference operator and ERR denotes the
error term of the static regression:
[1]
Xt
kktXk
hhtXhtXXt
Yt
kktYk
hhtYhtYYt
eYYERRaX
eXYERRaY
+Δ+Δ++=Δ
+Δ+Δ++=Δ
∑∑
∑
∑
−−−
−−−
φϕγ
φϕγ
1
1
According to equations of system [1], variables X and Y move fro two reasons: (a) to
adjust the long-run disequilibrium (that is,, in response to the term ERR) –this component is
the error correction mechanism; and (b) in response to short-run variations of them (captured
by the terms jt
Y−
Δ and jt
X−
Δ).
The Granger representation theorem assures that at least one error correction
mechanism exists if (and only if) two series are co-integrated. This means that parameter
Y
γ
and/or X
γ
has to be significant (and negative) in at least one of the two equations of
system [1].
The equations of system [1] with error correction mechanism allow us to define
different concepts of causality. The long-run Granger-causality refers to the links between the
levels of Y and X, and more precisely refers to the variable which has to move in order to
adjust the “disequilibrium” with respect to the co-integrating relationship. Specifically, if
Y
γ
(or X
γ
) is significant, it means that variable Y (or X)moves in order to reduce the
disequilibrium with respect to the long-run equilibrium value; clearly, if only one error
correction coefficient is significant, a one-directional causal link is established : if 0
≠
Y
γ
,

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variable Y is Granger-caused (in the long run) by X. If both X
γ
and Y
γ
differ from zero,
bidirectional (long-run) Granger causality exists.
The short-run Granger-causality refers to the differences of Y and X. In each equations
of [1], the components related to jt
Y−
Δ
and jt
X−
Δ
are deemed to capture “short-run”
determinants of ΔX and ΔY. If parameters
{
}
0
=
Y
φ
(which means that lagged values of
t
XΔ do not affect contemporary value of t
Y
Δ
) then t
X
Δ
does not Granger cause t
YΔ, or, Xt
does not Granger-cause Yt in its short run movements. Reversely, if
{
}
0=
X
ϕ
, Yt does not
Granger cause Xt in the short-run components. (Different concepts of causality are reviewed
by Granger, 1988).
Different techniques are available to measure the strength of causal links. For instance,
Pesaran and Shin (2002) suggested the variance decomposition technique: the variable whose
variance is explained by its own past value in the largest part, is the “most exogenous” one.
Granger and Lin (1995), in the framework of co-integration, proposed to measure the strength
of causality of Y on X by means of the following index:
[2] ),(,
)(
)1(
1log 2
2
2
YX
YX
X
XY eecorrC
C
C
M=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
−
+=
→
γγ
γ
Clearly, if X
γ
is not different from zero, then 0
=
→XY
M, i.e., Y does not cause X. This kind
of techniques have been extensively used in applied macroeconomic analysis (especially
during the 1990s), using annual data.
The extension of the integration / co-integration analysis to seasonal series can be
dated back to Dickey, Hasza and Fuller (1984). Fransen (1996) or Ghysels and Osborn (2001)
offer comprehensive reviews of theoretical aspects and applied investigations of seasonal
integration and co-integration.
According to standard definition (see, e.g., Ghysels and Osborn, 2001, Def. 3.1) the
non-stationary stochastic process Yt, observed at s equally spaced time interval, is said to be
seasonally integrated of order one if sttts YYY −
−
=
Δ
is stationary. The symbol s
Δ–often
called the “seasonal differencing filter”– denotes the first-difference of lag s (in monthly
data, s=12). In other words, tsYΔ denotes the difference of the realization in any given season
with respect to the realization of the variable in the same season of the previous year. The

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simplest case of a seasonally integrated process is a season random walk, which is described
by the data generating process tts Y
ε
=
Δ, that is, tstt YY
ε
+
=
− , with t
ε
denoting a white
noise process. More generally, seasonally integrated processes can possess drift(s), i.e., a
constant term, or different constant terms for different seasons; they can possess a
deterministic trend or a stationary ARMA structure of the error term. For the specific purpose
of the data at hand, we consider monthly data, and we will consider an equation of type
[3] ttt vYaY
+
+= −12
ρ
or, subtracting Yt-12 from both sides,
[4] ttt vYaY ++=Δ −1212
α
with 1−=
ρ
α
.We are interested in evaluating whether 1
=
ρ
, i.e., 0=
α
; if such a
hypothesis is accepted (rejected), the series is “seasonally integrated” (“seasonally
stationary”).
Prior to the decision about seasonal stationarity, however, we have to take decisions
about three different points. Firstly, we have to evaluate whether 12 different constant terms
are appropriate (one for each season) instead of one constant term; in such a case, a has to be
interpreted as
{}
121=
=i
i
aa . Operationally, we evaluate whether 11 additional seasonal dummy
variables beyond a constant are significant (see also Fransen and Kunst, 1999 on this point);
generally, the inclusion of seasonal dummies turns out to be appropriate in our present cases.
Secondly, we have to evaluate if a deterministic trend (T) is appropriate. Generally, the
deterministic trend is significant in our data; the inclusion of a trend makes the test less
powerful, but we anticipate that our conclusions are robust to the omission of the time trend.
Thirdly, we evaluate whether to introduce a number of autoregressive terms of t
Y
12
Δ in order
to have white noise regression residuals; in most cases, the 1st, 2nd and 12th lags of the
dependent variable are statistically significant and sufficient to make white noise residuals,
and hence they are inserted in the regression.
In sum, the following regression equation is considered in the applied analysis:

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[5] t
jjtjt
iit YYTaY
εβατ
+Δ+++=Δ
∑
∑−−
=1212
12
1
12
For testing for the presence of the seasonal unit root, we look at the significance of the
coefficient
α
. Also in this case, the distribution of estimated standard error, and the Student–t
statistics, are non standard, and specific tabulations of critical values are necessary. The
tabulation of critical values is provided by Dickey, Hasza and Fuller (1984). Different Tables
are appropriate, depending on whether no-constant, or a unique constant or different s
constant terms are introduced. Dickey, Hasza and Fuller label these models as “zero-mean
model”, “one mean model”, and “seasonal means model”, respectively.
If the null of seasonal unit root is not rejected (i.e., 0
=
α
or equivalently 1=
ρ
), the
series is seasonally integrated. The substantial meaning of such a conclusion is very
important. Seasonally integrated series possess s unit root processes (one for each of the s
seasons), none of which has a tendency to return to a deterministic path.
Two seasonally integrated time series Xt and Yt are seasonally co-integrated, if a linear
combination exists which is seasonally stationary. Operationally this means that the residuals
from a regression involving Xt and Yt (and possibly other deterministic components, like time
trend and seasonal dummies) have to be seasonally stationary. In concrete terms, we have to
run a regression (called “static co-integrating regression”) of Yt on Xt (or Xt on Yt), and then
we consider the regression residuals and perform the seasonal integration tests on them: if the
null hypothesis of seasonal integration in the residuals is rejected, then X and Y are seasonally
co-integrated. This test perfectly corresponds to the Augmented Dickey Fuller test, and
critical values are provided by Dickey, Hasza and Fuller, as already mentioned.
In concrete terms, provided that Xt and Yt are seasonally integrated, we will run the
(static) regression
[6] tt
iit emXTaY ,1
12
1+++= ∑=
τ
from which we save the fitted series e1,t; in order to evaluate its seasonal stationarity, we run
a regression similar to [4], and specifically:
[7] tttt ee
ε
α
+=Δ −12,1112

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(possibly augmented by lagged terms of t
e,112
Δ
, to render residual t
ε
stationary, but without
the constant term, the mean of regression residuals being zero) and we look at the Student-t of
coefficient
α
. If stationary, the series e1,t can be interpreted as the linear combination which
represents the “error” or the discrepancy with respect to the co-integrating relationship. (We
also will consider the regression of X on Y, and perform the same test of seasonal stationarity
on the residuals from this equation (e2,t). The conclusions about co-integration of time series
have to coincide –and this happens, in fact, in all the cases considered below).
Also in this case, the Granger representation theorem can apply: if two seasonally
integrated series co-integrate, at least one error-correction mechanism is operative, and the
causal link can be detected, in the sense that it is possible to establish if X or Y (or both) move
over time to correct the discrepancy with respect to the co-integrating relationship equilibrium
values. If the series co-integrate, the error correction mechanism has to be operative,
according to the lines of the Granger representation theorem. Thus, we will consider the two
equations :
[8]
Xt
kktXk
hhtXhtXXt
Yt
kktYk
hhtYhtYYt
eXYERRaX
eXYERRaY
+Δ+Δ++=Δ
+Δ+Δ++=Δ
∑∑
∑
∑
−−−
−−−
θϑγ
θϑγ
12,212
12,112
and we will look at the coefficients XY
γ
γ
, to derive conclusions about the long-run Granger
causality, and at the coefficients
{}
{
}
YkYh
θ
ϑ
, to study the short-run causality.
4.2 Evidence: tourist presences, and the attendance at monuments and museums
We aim to test the presence of seasonal unit root in the time series of tourists’ presence
and cultural sites’ attendance in Italy. Relevant regression results are reported in Table 3.
Specifically, we report the results for equations specified as in [5]. In all the cases at hand, we
find what follows. First, the introduction of different seasonal dummies is appropriate (see
Column (2): test F on the significance of additional 11 dummies beyond a constant term
always leads to the conclusion that different additional dummies are different from zero).
Second, a deterministic time trend is significant, and it is inserted; however, since the power
of unit root test is low when a time trend is inserted, we preferred to check also the results
from the specification without the deterministic trend: the conclusion about the presence of

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the seasonal unit root was the same, so that we can conclude that our results are robust to the
choice of including the deterministic time trend or not. Third, different numbers of lags in the
short-term dynamics of the equation are appropriate: with reference to specification [5], j may
vary across different equations; however, for the series at hand, the significant lags are 2 and
12. Last but not least, the presence of the seasonal unit root at periodicity 12 cannot be
rejected: the Student-t statistics of the estimated
α
is -3.90 and -3.68 for PRESTUR and
MUSMONUV, respectively. These figures are smaller –in absolute value– than the critical
level -5.86, tabulated by Dickey, Hasza and Fuller for the usual 95% significance level; (in
the absence of the deterministic trend, the Student-t of estimated alpha, would be -2.72 and -
3.68, respectively, leading to the same conclusion of seasonal integration.)
INSERT TABLE 3
Thus, the conclusion that the series at hand are seasonally integrated is out of any
doubt. The same conclusion holds for alternative –though not advisable– specifications of the
regression equation, considering alternative design of the deterministic components, like time
trend which assume one value for each year. It is interesting, hence, to establish whether co-
integration links exist. In advance, it is advisable to take a look at the pattern of the two series
in Figure 2: panel (a) shows the raw data, panel (b) normalizes the data to have the same
adjusted mean; panel (c) provides the scatter-plot, and the existence of different seasons is
clear.
INSERT FIGURE 2
In order to establish the possible existence of co-integration, we consider the
relationships corresponding to [6], with tourist presence or, alternatively, the cultural site
attendance as the dependent variable; we save the regression residuals and perform the
seasonal stationarity test on them. Table 4 shows that, in any case, the regression residuals are
stationary, leading to the conclusion that tourists presence and cultural sites attendance co-
integrate. This result is also consistent with the evidence coming from the estimation of the
equations containing the error correction mechanism. In particular, we estimate system [7]
with museum and monuments attendance in the place of Y and tourist presences in the place
of X. The results are provided in Table 5

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INSERT TABLE 4 AND TABLE 5
It is clear that the error correction term is significant in both equations –the equation
explaining the visits to cultural sites, and the equation concerning tourist presence– leading
to the conclusion that bi-directional long-run causal links are present. In other words, we find
that the tourist presences Granger-cause the visits to museums and monuments, and the visits
to museums and monuments Granger-cause the tourist presences, in the long run. However,
the coefficient is larger in absolute value in the case of visits to cultural sites, suggesting that
this variable is more reactive to long-run disequilibria.
As to the short-run Granger-causality, the conclusion is sharper, in the sense that the
causality links run from (variation of) presence to (variation of) visits to cultural sites. This is
clear from the Student-t statistics of single coefficient (in Table 5), and can be confirmed by
F type tests on the significance of multiple coefficients: a test on the significance of lags 1
and 12 of D12PRESTUR in the equation of D12MUSMONUV provides F=3.47 (p=0.034),
while a test on the significance of lags 1, 2, and 12 of D12MUSMONUV in the equation of
D12PRESTUR gives F=0.86 (p=0.460).
As already mentioned, for discerning the endogenous/exogenous nature of variables,
including in the context of co-integration analysis, some authors apply the “generalized
variance decomposition” technique (Pesaran and Shin, 2002 ; see also Masih et al., 2009 for a
very recent application): the relative exogeneity or endogeneity of a variable can be detected
by the proportion of the variance explained by its own past. The variable which is explained
mostly by its own shocks is the «most exogenous». The conclusion in the present case (see
Table 6) is very clear: it is tourist presence that leads (rather than lags) visits to cultural sites.
The same conclusion emerges, based on the computation of the Granger Lin causality
strength index: the strength of causality from tourist presence to site visits is log(1.50), while
the strength of causality from visits to presence is log(1.37).
INSERT TABLE 6

-15-
4.3 Tourist arrivals and stays
We can continue to employ the co-integration analysis approach to investigate the
links of tourist arrivals and average stays, on the one side, with the visits to cultural sites on
the other side (Italy, January 1996 – December 2007). This makes sense since the monthly
time series of arrivals and stays –like tourist presences– possess a seasonal unit root at
periodicity 12, as shown in Table 7 (where we report only the estimates of the specification
with the deterministic trend; however, the conclusion on the presence of the seasonal unit root
is the same, even if we omit the deterministic trend); other information on the time series
were already provided in Tables 1 and 2.
INSERT TABLE 7
Even in the cases of arrivals and stays, we find that each of such tourism series co-integrates
with the series of cultural sites’ visits, as documented by Table 8.
The Table reports the results from the static co-integrating regression (along the lines
of equation specification [6]) and the results from the dynamic specification like [8]. In the
static regression, twelve seasonal dummies are introduced, since additional dummies for
seasons are significant; in the dynamic equation for evaluating the error correction
mechanism, an appropriate number of lags of the dependent variable is introduced, following
a specification strategy from the general to the particular, which started considering the lags
of order, 1,2, 3, 4, 12, 24 and maintained only the significant ones (95% significance level).
INSERT TABLE 8
The evidence concerning the causality links over the long run is very clear. Arrivals
and visits to museums and monuments Granger-cause each other; however, like in the case of
presences, the quantitative dimension of the error correction coefficient suggests that cultural
visits adjust to arrivals in a larger extent than the reverse. As far as stays are concerned, one
can see that stays Granger-cause one-directionally visits to monuments and museums in the
long run (the error correction is significant only in the equation explaining the dynamics of
cultural site visits). The Granger and Lin causality index lead to the same substantial
conclusion: the stronger causal link goes from arrivals and stays to visits to museums and

-16-
monuments; a similar conclusion is provided by the variance decomposition technique, which
suggest that arrivals and stays are “more exogenous”. In the short-run dynamics, arrivals and
visits to cultural sites cause each other, while a one-directional link emerges as far as stays are
concerned: stays do not cause visits, while visits cause stays.
These pieces of evidence lend themselves to some considerations. Loosely speaking,
the long-run dynamics have to do with the long-term decisions of people. It is the dynamics of
visits to cultural sites that adjust to the dynamics of tourism flows. Thus, it is hard to sustain
that cultural site visits play a long-run promoting role with respect to tourism flows:
provocatively stated, it is false that tourists plan to come and stay in Italy in order to visit
cultural sites; rather, people visit museums and monuments just because they decided to
arrive and stay in Italy. However, in the short run, some significant causal effect of the visit of
cultural sites emerges upon the average stays. Just to give a simple and intuitive explanation,
imagine that people have planned the holiday; the presence of cultural sites has been
ineffective at that stage; however, if the weather is bad (short-term shock), the presence of
cultural attractions can be effective in convincing people to remain rather than to go home in
advance. More seriously, the presence of cultural attractions is ineffective in determining
long-run dynamics, but can be effective in the short-run decisions of people.
We are in a position now to provide estimates of the elasticity of cultural site visits to
tourist variables. These elasticities are shown in Table 9, which considers both the
unconditional elasticity estimates, and the estimates from the model with multiple seasonal
dummies. The values, however, are rather similar. All estimates are statistically significant.
Elasticity of visits to museums and monuments with respect to tourist presence is around
0.86; a test of equality of such a value to 1 rejects this hypothesis; the elasticity with respect
to arrivals is around 0.9: also in this case such a value turns out to be statistically different
from 1. Elasticity with respect to stay is about 10: a 1% increase in average stay entails a
10% increase in visits to museums and monuments.
INSERT TABLE 9

-17-
5. DISCUSSION, IMPLICATIONS AND CONCLUSIONS
The effectiveness of cultural attractions in enhancing tourism is a point of interest not
only for academics, but also for private subjects and policy-makers. In several cases, the
presence of cultural attractions is deemed to act as an engine for attracting tourism flows, or
qualifying the tourism. Nevertheless, the empirical evidence on the relationships between
cultural attraction attendance and tourism flows is limited to interesting but specific cases.
The present paper has aimed to fill this absence, providing an analysis on aggregate data.
We have taken Italy as a case study, and have analyzed monthly data over more than a
decade, referring to tourist overnights, arrivals, and average stays, on the one hand, and visits
to museums and monuments on the other. We have proved that all series possess a seasonal
unit root, i.e., they are seasonally integrated. Strong evidence of co-integration between
tourism flows and museum and monument attendance has emerged. This means that long-
term relationships exist between these variables. More importantly, Granger causality analysis
has permitted to conclude that a one-way direction of causality generally emerges, and
tourism flows Granger-cause the attendance to cultural sites, in the long run.
The conclusion about the causality nexus, running from tourism flows to museum
attendance, is the core result of the present research, and lends itself to two comments. First,
from a substantial point of view, we can state that museums cannot be requested, on average,
to play a role as major tourism attractors. The available literature on specific successful cases
(generally superstar museums, which represent a minority among museums) has perhaps
generated the misleading idea that museums can be primary engines for tourism and hence for
growth. We rather believe that, in general, museums can be the “icing on the cake” in a
destination in which a bundle of several material and immaterial structures are the roots of
tourism attraction: museum and monument visits could be able to determine longer average
stays, rather than larger arrivals. Second, from a methodological point of view (even if one
has to be aware that museums and monuments play roles that go well beyond tourism
attraction), omitting the tourism variables from the set of the determinants of the attendance at
museums and monuments can be seriously misleading, in the presence of documented co-
integrating relationships.
Other conclusions are possible, concerning the role of cultural attractions as a means
to reduce seasonality in tourism flows. Schematically, the idea could be as follows: provided
that the visits to cultural sites show a lower degree of “overall” seasonality than tourism

-18-
arrivals or presences (as documented also in our Table 2 for the Italian case), and provided
that peaks of cultural visits are in spring months, rather than in summer, the promotion of
cultural tourism should help in reducing tourism seasonality and hence congestion.
Unfortunately, our analysis clearly shows that cultural visits follow, rather than lead, tourism
presences and arrivals. Provocatively, visits to cultural sites are perceived by most tourists as
a by-product of a holiday stay, rather than the main goal. Consistently, cultural heritage
attractions seem to be effective tools to differentiate tourism products; their effectiveness in
reducing tourism seasonality appears to be more questionable.
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TABLES
Table 1 – Descriptive statistics on variables
Variable Average Min – Max
(date)- (date) St. Dev.
a) PRESTUR (million) 27.850557 8.529030-78.026590
(Nov. 1997)-(Aug. 2007) 19.481268
b) ARRIV (million) 6.773693 3.141226-13.110528
(Nov. 1997)-(Aug. 2007) 2.709173
c) AVSTAY (days) 3.762 2.670-6.619
(Nov. 1998)-(Aug. 2001) 1.118
d) MUSMONUV (million) 2.505890 0.770116-4.598806
(Jan. 1997)-(Apr. 2006) 1.002944
Table 2 – Descriptive statistics on seasonality in data
Variable Gini index Seasonal
Factors:
St. Dev.
Seasonal Factors:
Min - Max
(date)- (date)
Corr
(Raw Series,
Seas-Adjust
Series)
PRESTUR 0.367
0.693 0.356-2.710
(Nov. 1996)-(Aug. 1996) 0.124
ARRIV 0.227
0.385 0.542-1.764
(Nov. 1997)-(Aug. 1996) 0.257
AVSTAY 0.154
0.296 0.714-1.696
(Nov. 1996)-(Aug. 1997) 0.089
MUSMONUV 0.254 0.385 0.415-1.774
(Jan. 2002)-(Apr. 1996) 0.300
Notes: Column (1) reports the Gini index on monthly data of the raw series. Columns(2) to (4) take
into account the seasonal adjustment computed with Census X-12-Arima adjustment programme:
Column (2) and (3) report the standard deviation and the Min-Max values of the seasonal factors,
while Column (4) reports the correlation between the original and the seasonally adjusted series.

-22-
Table 3 – Seasonal unit root – Regression Equation [5]
(1)
Estimated
coefficient
α
(t)
(2)
Seasonal
dummies
(3)
Determ
time trend
(4)
Lags of the
dependent
variable
(5)
R2
DW
PRESTUR -0.25
(-3.90) YES
F11,104=4.03
[p=0.000]
13791.7
(2.68) 2;12 0.41
1.94
MUSMONUV -0.21
(-3.68) YES
F11,118=4.51
[p=0.000]
210.4
(2.71) 2;12 0.41
1.82
Notes: Column (1) reports the estimate of coefficient
α
in specification [5] and its Student-t statistics.
The value of Student-t statistics has to be compared to the critical values reported in Table 5 or 7 in
Dickey-Hasza and Fuller (1984); critical value is -5,86 in the case where different seasonal dummies
are inserted in the regression. Column (2) states whether seasonal dummies are introduced, and
presents a F test (and its p-value in squared brackets) on the significance of additional 11 dummies
added to the constant term. Column (3) reports the estimate of the deterministic trend coefficient, if
inserted. Column (4) lists the lags of the dependent variable inserted in the regression to render
residuals white noise: we started by considering lags 1,2,3,4,12 and decide to insert only the
significant lags. Column (5) reports the R-squared and the DW statistics.
Table 4- Unit root test on the cointegrating regression residuals
Residuals from :
Visits on Presences Residuals from :
Presences on Visits
Estimated coefficient
α
(Student-t) -0.64
(-8.11) -0.59
(-7.61)
Lags of Dependent variables to
have white noise errors 1; 2. 1; 2.
Notes: the 12th difference of the fitted residuals from the static regression equations is regressed
against the 12th lag of the residual levels, according to eq. [10]. No constant term is inserted. Critical
value at the 95% significance level for the Student-t is -1.77 (Dickey, Hasza, Fuller, 1984, Table 3).

-23-
Table 5 – Models with error correction mechanism – Estimation of Equations [8]
Dependent variable :
D12MUSMONUV Dependent variable :
D12PRESTUR
CONSTANT 84328
(4.51) 401518
(3.22)
ERR(-12) -0.33
(-3.17) -0.29
(-4.67)
D12MUSMONUV(-1) Ns Ns
D12MUSMONUV(-2) 0.20
(2.58) Ns
D12MUSMONUV(-12) -0.26
(-2.72) Ns
D12PRESTUR(-1) 0.02
(1.90) Ns
D12PRESTUR(-2) Ns 0.38
(5.08)
D12PRESTUR(-12) -0.03
(-2.83) Ns
R2 0.379 0.315
F 14.04 [p=0.0000] 29.17 [p=0.0000]
Residuals autocorrelation: DW 1.63 1.85
Residuals autocorrelation: F test F=1.34 [p=0.257] F=0.37 [p=0.572]
Notes: Ns denotes “non-significant” (and hence the regressor is omitted from the chosen
specification); Student-t statistics in parenthesis; autocorrelation F test is Breusch- Godfrey Serial
Correlation LM test, with 4 lags.
Table 6 – Variance decomposition analysis
TOURIST PRESENCE MUSEUM ATTENDANCE
Lags 1,2
Lags 1,2,3,4
Lags 1,2,3,4,12
24.6%
26.3%
33.5%
11.3%
11.7%
32.4%
Notes: The Table reports the percentage of variance of 12
Δ
PRESTUR and 12
ΔMUSMONUV
explained by their own lagged values (a regression model is considered with seasonal dummies, but
the conclusions do not change in the present of a single constant or no constant)

-24-
Table 7- Seasonal Unit root in the series of tourist arrivals and average stays
(1)
Estimated
coefficinet
α
(t)
(2)
Seasonal
dummies
(3)
Determin
time trend
(4)
Lags of the
dependent
variable
R2
DW
ARRIV -0.21
(-3.21) YES
F11,104=2.86
[p=0.002]
45856.6
(3.26) 2; 0.23
2.38
AVSTAY -0.03
(-1.41) YES
F11,104=3.36
[p=0.001]
-0.003
(-1.37) 2; 0.12
2.01
Notes: Columns are like in Table 3.
Table 8 – Cointegration Analysis for Tourist Arrivals and Stays with Cultural sites’ visits
X : Arrivals
Y : Cultural sites’ visits
X : Stays
Y : Cultural sites’ visits
Regression of X on Y (i.e., X=f(Y))
Static regression results
• Unit root in residuals: ADF (t)
Dynamic regression with ECM
• EC Coefficient (and its t)
• Significant lags of
X
Δ
• Significant lags of
Y
Δ
(-8.42)
-0.22 (-2.38)
2
1
(-7.27)
-0.03 (-1.20)
2;12
1;2
Regression of Y on X(i.e., Y=f(X))
Static regression results
• Unit root in residuals (t)
Dynamic regression with ECM
• EC Coefficient (and its t)
• Significant lags of
X
Δ
• Significant lags of
Y
Δ
(-9.01)
-0.58 (-4.36)
1;2;12
2;12
(-2.85)
-0.28 (-4.71)
Ns
2;12

-25-
Table 9- Estimates of Elasticity of cultural sites’ visit (Y) w.r.t. tourism variables (X)
Unconditional Elasticity Elasticity conditional on
seasonal means
EY,X : X=presences 0.864 0.855
EY,X : X=arrivals 0.935 0.924
EY,X : X=stays 10.93 10.98
Notes: Column (1) reports the estimate of the coefficient of regressor ln(X), against regressand ln(Y);
in Column(2) seasonal dummies are inserted as additional regressors.

-26-
FIGURES
0.0E+00
1.0E+07
2.0E+07
3.0E+07
4.0E+07
5.0E+07
6.0E+07
7.0E+07
8.0E+07
96 97 98 99 00 01 02 03 04 05 06 07 08
2.00E+06
4.00E+06
6.00E+06
8.00E+06
1.00E+07
1.20E+07
1.40E+07
96 97 98 99 00 01 02 03 04 05 06 07 08
PRESTUR ARRIV
2
3
4
5
6
7
96 97 98 99 00 01 02 03 04 05 06 07 08
0
1000000
2000000
3000000
4000000
5000000
96 97 98 99 00 01 02 03 04 05 06 07 08
AVSTAY MUSMONUV
Figure 1 – Patterns of variables

-27-
0.0E+00
1.0E+07
2.0E+07
3.0E+07
4.0E+07
5.0E+07
6.0E+07
96 97 98 99 00 01 02 03 04 05 06 07
-2
-1
0
1
2
3
96 97 98 99 00 01 02 03 04 05 06 07
0
1000000
2000000
3000000
4000000
5000000
0.0E+00 2.0E+07 4.0E+07 6.0E+0
7
Figure 2 – Tourist Presences and Attendance to Museums and Monuments (patterns, normalized
patterns, and scatter)