Discussion Paper No.361
A Simple Bayesian VAR Analysis of Tourism Demand
for Japan’s Two Major Prefectures in the Kansai Region
Kazuhiko NAKAHIRA
Meikai University

Masahiro YABUTA
Chuo University

December 2021

INSTITUTE OF ECONOMIC RESEARCH
Chuo University
Tokyo, Japan

A Simple Bayesian VAR Analysis of Tourism Demand for Japan’s Two Major Prefectures in the Kansai Region(Preliminary Working Draft: Please do not cite or quote without permission of the authors.)

Kazuhiko NAKAHIRA
Professor, Faculty of Economics, Meikai University
E-mail: nakahira@meikai.ac.jp

Masahiro YABUTA
Professor, Faculty of Economics, Chuo University
E-mail: yabuta@tamacc.chuo-u.ac.jp

Abstract

This paper investigates the influence of economic variables on tourism demand for Japan’s two major cities in westernregion is conducted by utilizing BVAR methodology. In this research, we assume that prior distribution function and theposterior one are in the same distribution family and utilize one of the conjugate priors － Litterman or Minnesota prior.
The cumulative impulse response of Kyoto are consistent with the conventional belief. However, the estimated responses
of tourism demand in Osaka to the several economic shocks seem to be inconsistent with the conventional assumption.

Keywords : Bayesian VAR, Litterman or Minnesota prior, tourism demand
JEL classification : C11, O20, Z30

11. Introduction
As is well known, VAR (vector autoregression) methodology has been broadly utilized to analyse social change since
the pioneering work of Sims (1980). Especially, SVAR (structural vector autoregression) or identified VAR model iswidely applied to macro-economic research. For example, Sims (1992) puts stress on the role of short-term market interest
rate as the factor for monetary policy with recursive identification frameworks of SVAR. Blanchard and Watson (1986),
Gali (1992), Gordon and Leeper (1994), and Lastrapes and Selgin (1995) apply a non-recursive approach to impose
contemporaneous restrictions for identification. In addition, Bernanke and Mihov (1998) adopt the block-recursive
approach to identify the shocks to monetary policy.
On the other hand, the BVAR (Bayesian vector autoregression) model has been used as the Bayesian-flavored VAR
specification for empirical analysis, which connects priors with information incorporated in sample. BVAR decreases therisk of over-parameterization by the imposition of special restrictions on the parameters in VAR process (the so-called“shrinking parameters”) through their prior probability distribution functions. The prior probability distribution function
contains the prior which include the mean and variance of the distribution. The prior probability distribution function
describes the range of uncertainty of the prior mean, and it revised by sample information if underlying distribution
significantly differs from the prior. Furthermore, the posterior distribution function for parameter in BVAR model can begiven from the combination of the prior distribution function and the distribution of the sample data. One difficult problem
is whether the prior distribution function and the posterior are in the same distribution family. In this research, we assume
that they are in the same distribution family and utilize one of the conjugate priors － Litterman or Minnesota prior. Taking
the above features into account, the empirical analysis utilizing BVAR methodology to investigate the influence ofeconomic variables on tourism demand for Japan’s two major cities in western region is conducted in this study.
The reminder of this paper is organized as follows. Section 2 highlights the characteristics of the Bayesian econometricanalysis with the Litterman or Minnesota Prior. Section 3 is for data set. Section 4 describes the empirical study utilizing
the BVAR, and Section 5 presents the concluding remarks.

2. Bayesian Econometric Analysis with the Litterman or Minnesota Prior
Vector autoregression (autoregressive) (VAR) models have been widely used as a tool for empirical multivariate
economic analysis since the 1980s. However, it is said that VAR models include the so-called “overparameterization
problem” when it applied in large models with many parameters. We have at least two kinds of coping methods for thisproblem – “structural vector autoregression model” (SVAR: way of application of theoretical constraints) and “Bayesian
vector autoregression model” (BVAR: way of application of Bayesian theory).

2

Generally, a VAR models for our estimation are inclined to have many parameters, and some of them might besignificant only by coincidence. In this kind of situation, they do not have substantive information if estimated. In thiscontext, the BVAR approach deals with this kind of topic by defining the prior for parameters.
Bayesian statistical flamework connect the distribution properties of the prior distribution, likelihood, posterior
distribution based on the assumption that the parameters can be regarded as random variable. The “prior” expresses theexternal distributional information derived from the “belief” on the parameters. The “likelihood” means the informationof the sample probability distribution function. By the “Bayes’ Theorem”, the “prior distribution” is related to the data
likelihood results in the “posterior distribution”.
If we denote the data by 𝑦 , the parameters of interest by 𝜃 = (𝛽, 𝛴), the prior distribution by 𝜋(𝜃), the likelihood by𝑙(𝑦|𝜃), we can express 𝜋(𝜃|𝑦), “posterior distribution”, as𝜋(𝜃|𝑦) =𝜋(𝜃)𝑙(𝑦|𝜃 )(1)∫ 𝜋(𝜃)𝑙(𝑦|𝜃 )𝑑𝜃where the denominator describes a normalizing constant without randomness. Therefore, the posterior is proportional tothe product of 𝑙(𝑦|𝜃) and the 𝜋(𝜃):𝜋(𝜃|𝑦) ∝ 𝜋(𝜃)𝑙(𝑦|𝜃).

(2)

The theoretical connection between this specification and BVAR approach requires the following the basic VAR(𝑝)model𝑝𝑦𝑡 = 𝑎0 + ∑𝑗=1 𝑎𝑗 𝑦𝑡−𝑗 + 𝜖𝑡(3)where 𝑦𝑡 (for 𝑡 = 1,∙∙∙, 𝑇) is an 𝑚 × 1 vector with observations on 𝑚 different series. 𝜖𝑡 is an 𝑚 × 1 vector of errors
where 𝜖𝑡 ~𝑁(0, 𝛴𝜖 ), 𝑖. 𝑖. 𝑑..
For simplicity, this equation can be written as:
𝑌 = 𝑋𝐴 + 𝐸(4)or
𝑦𝑡 = (𝐼𝑚 ○×𝑋)𝜃 + 𝑒(5)′′where 𝑌 and 𝐸 are 𝑇 × 𝑚 matrices, 𝑋 = (𝑥1 ,∙∙∙, 𝑥𝑡 )′ is a 𝑇 × (𝑚𝑝 + 1) matrix for 𝑥𝑡 = (1, 𝑦𝑡−1,∙∙∙, 𝑦𝑡−𝑞), 𝐼𝑚

is the 𝑚-dimension identity matrix, 𝜃 = 𝑣𝑒𝑥(𝑥), and 𝑒~𝑁(0, 𝛴𝜖 ○×𝐼𝑇 ).
By applying equation (5), the likelihood function is written as the following form.
1
2

−

1

−1

′

𝑙(𝜃, 𝛴𝜖 ) ∝ |𝛴𝜖 ×○𝐼𝑇 | 𝑒𝑥𝑝 {− (𝑦 − (𝐼𝑚 ○×𝑋)𝜃) (𝛴𝜖 ×○𝐼𝑇 ) (𝑦 − (𝐼𝑚 ○×𝑋)𝜃)}
2(6)

Assuming that 𝛴𝜖 is known and a multivariate normal prior for 𝜃 to explain the derivation of the posterior moments:

3

1

1
2

∏(𝜃) ∝ |𝑉0 |−2 𝑒𝑥𝑝 {− (𝜃 − 𝜃0 )′ 𝑉0−1 (𝜃 − 𝜃0 )}(7)

where 𝜃0 is the mean of prior and 𝑉0 is the covariance of the prior. The posterior density is expressed by the following
form as a multivariate normal probability density function if we combine equation (6) and (7):
′
1
1
1
−
−
1
2
𝜋(𝜃|𝑦) = 𝑒𝑥𝑝 {− 2 (((𝑉0 (𝜃 − 𝜃0 )) (𝑉0 2 (𝜃 − 𝜃0 ))) + {(𝛴𝜖 −2 ○×𝐼𝑇 ) 𝑦 −

′

1

1

1

(𝛴𝜖 −2 ○×𝑋) 𝜃} {(𝛴𝜖 −2 ○×𝐼𝑇 ) 𝑦 − (𝛴𝜖 −2 ○×𝑋) 𝜃})}.

(8)

Defining 𝜔 and 𝑊 as−1−

𝑉0 2 𝜃0

1

𝑉0 2

𝜔≡[
] and 𝑊 ≡ [
],
1
1
−
−
2
2
(𝛴𝜖 ○
×X)
(𝛴𝜖 ○
×X)

(9)

we get the exponential part in equation (8) is described as11∏(𝜃|𝑦) ∝ 𝑒𝑥𝑝 {− (𝑊 − 𝑊𝜃)′ (𝑊 − 𝑊𝜃)} ∝ 𝑒𝑥𝑝 {− (𝜃 − 𝜃̅ )′ 𝑊 ′ 𝑊(𝜃 − 𝜃̅ ) + (𝜔 − 𝑊𝜃̅ )′ (𝜔 −2𝑊𝜃̅ )}

2(10)

where the mean value of the posterior, 𝜃̅, has the specification:𝜃̅ = (𝑊 ′ 𝑊)−1 𝑊 ′ 𝜔 = [𝑉0−1 + (𝛴𝜖 −1 ○×X ′ X)]−1′×X) 𝑦][𝑉0−1 𝜃0 + (𝛴𝜖 −1 ○(11)

If the 𝛴𝜖 is known, the 𝜃̅ in equation (10) does not include randomness. In this context, the posterior distribution may
be simply described by the form:
1
1∏(𝜃|𝑦) ∝ 𝑒𝑥𝑝 {− (𝜃 − 𝜃̅ )′ 𝑊 ′ 𝑊(𝜃 − 𝜃̅ )} = 𝑒𝑥𝑝 {− (𝜃 − 𝜃̅ )′ 𝑉̅ −1 (𝜃 − 𝜃̅ )}
2

2

(12)

where the covariance of posterior, 𝑉̅, is𝑉̅ = [𝑉0−1 + (𝛴𝜖 −1 ○×𝑋 ′ 𝑋)]−1(13)

In the Bayesian econometric flamework, the prior distribution function of the parameter for estimation is constituted
based on the “belief” of the researcher to reflect the prior information. One of the important problems is whether the priordistribution function and the posterior are in the same distribution family. If they are in the same distribution family, thenwe can conduct the simple analytical estimation process of the Bayesian VAR by using some conjugate priors. If not, weshould implement some kinds of simulation-based inference like the Markov Chain Monte Charlo (MCMC) method, theGibbs Sampling, and so on.1 In the case of this study dealing with tourism behavior, our research might be in the former

1

See Chan, Koop, Poirier, and Tobias (2019) for details of the Markov Chain Monte Charlo (MCMC) method, the Gibbs Sampling.

4one, and we could select some applicable prior, for example, the so-called “Litterman or Minnesota prior”, “The NormalWishart Prior”, “The Sims-Zha normal-Wishart prior”, and “The Sims-Zha normal-flat prior”. Concretely, we apply the“Litterman or Minnesota prior” for our estimation, which assumes a normal prior on 𝜃, the prior, with fixed 𝛴𝜖 in VAR
process. This prior was initially developed by, for instance, Litterman (1986) and Doan, Litterman, and Sims (1984). Thiŝ𝜖 . In general, there are three options
prior treats 𝛴𝜖 is fixed or known. Therefore, 𝛴𝜖 should be replaced by the estimated 𝛴̂𝜖 － (1) Univariate AR estimate, (2) Diagonal VAR estimate, (3) Full VAR estimate. In this sense, we
for estimating 𝛴̂𝜖 . Usually, the Litterman or Minnesota prior assumes thatshould specify a prior for 𝜃 because we estimate 𝛴𝜃~𝑁(𝜃0 , 𝑉0 ). The hyper-parameter 𝜇1 = 0 derives 𝜃0 = 0 (a zero-mean model). But the prior covariance should not
be zero, 𝑉0 ≠ 0. The 𝜃0 = 0 case could lessen the risk of over-fitting.
The explanatory variables in any equation of the VAR model is divided into own lags of dependent variable, lags of theother dependent variables, and any exogenous variables, including constant term. The factors of 𝑉0 corresponding toexogenous variables are set to infinity. It means that no information of the exogenous variables is included in the prior.
𝑖
The remainder of 𝑉0 is a diagonal matrix that includes diagonal elements 𝜐𝑖𝑗
for 𝑙 = 1,∙∙∙, 𝑝2

𝝀𝑙( 𝝀1𝟑 )for (𝑖 ≠ 𝑗)

𝑖
𝜐𝑖𝑗
=

(14)
𝝀1 𝝀2𝜎( 𝑙𝝀𝟑 𝜎 𝑖 )𝑗2for (𝑖 ≠ 𝑗)where 𝜎𝑖 2 is the i-th diagonal element of 𝛴𝜖 . This setting simplifies the selection of the specification of all the elements of
𝑉0 into the choice of the scalars, the hyper-parameters, 𝜆1 , 𝜆2 , and 𝜆3 . The 𝜆1 and 𝜆2 are overall tightness and relative
cross-variable weight, respectively. The 𝜆3 is the lag decay and the coefficients are increasingly shrunk toward zero as lag
length increases. These hyper-parameter scalar values may lead to smaller or larger variances of coefficients － tightening
or loosing the prior. The setting of the values of these scalars depends on the empirical estimation.2
After the selection of prior, the posterior for 𝜃 takes the following specification:
𝜃~𝑁(𝜃̅ , 𝑉̅ )

(15)

where
−1

̂𝜖 −1 ○
𝑉̅ = [𝑉0−1 + (𝛴×X ′ X)]

(16)

and
′

̂𝜖 −1 ○
𝜃̅ = 𝑉̅ [𝑉0−1 𝜃0 + (𝛴×X) 𝑦]

2(17)

Litterman (1986) proposes the other type of explanation with respect to this problem.

5

3. The Data
This section describes the data set used in the empirical analysis utilizing BVAR methodology to investigate theinfluence of economic variables on tourism demand for Japan’s two major prefectures in western region － Kyoto andOsaka－ is conducted in this study. Our estimations are conducted utilizing monthly data spanning the period 2013:
January to 2021: August, and our data set is constructed by the following variables.3
V: approximate total number of overnight guests; prefectural data (Kyoto, Osaka), monthly, data listed in Table 9 in resultof the survey “Overnight Travel Statistics,” second preliminary estimate, issued by the Japan Tourism Agency, Ministryof Land, Infrastructure, Transport, and Tourism.
C: heavy fuel oil for industry, type A (for heavy loaded lorry), regional basis (Kinki region), monthly, unit: Yen / Litter,excluding consumption tax, in result of the survey of oil marketing products, issued by the Agency for Natural Resources
and Energy - Ministry of Economy, Trade and Industry.
I: indices of industrial production, prefectural data (Kyoto, Osaka), monthly, original index, manufacturing (Item Number:
20000000 for Kyoto and 21000011 for Osaka), base year = 2015, issued by each prefectural government office and theMinistry of Economy, Trade, and Industry.
P: consumer price index, data for major cities (City of Kyoto and City of Osaka), monthly, original index, all items, baseyear = 2020, issued by the Ministry of Internal Affairs and Communications.
Our empirical analysis casts a spotlight on the Japan’s two major areas in western region, or on the Kyoto and Osaka.
concretely. the variables, “V” and “I” reflect the prefectural-level data that were observed by several local governmental
offices, while “P” in our estimation is city-level (municipality) data as the proxy variable for the prefectural one since thedata on Kyoto and Osaka prefectures are not available. Similarly, because prefectural data on the heavy fuel oil for industry
also are not available, regional basis data for Kinki area (that includes Kyoto and Osaka) on the heavy fuel oil “C” is3

The data on “approximate total number of overnight guests” can be retrieved from the website of the Japan Tourism Agency, Ministryof Land, Infrastructure, Transport, and Tourism (https://www.mlit.go.jp/kankocho/siryou/toukei/shukuhakutoukei.html). The “heavy
fuel oil for industry, type A (for heavy loaded lorry), regional basis (Kinki area)” is obtained from the Agency for Natural Resources
and Energy’s website (https://www.enecho.meti.go.jp/statistics/petroleum_and_lpgas/pl007/results.html). The “consumer price index”
is available from the “e-stat” website (https://www.e-stat.go.jp/stat-search/files?page=1&toukei=00200573). The data on “Indices ofIndustrial Production (prefectural data)” can be retrieved from the website of the Ministry of Economy, Trade, and Industry(https://www.meti.go.jp/statistics/tyo/iip/chiiki/index.html).

6adopted. “V” and “C” work as the proxy variables for tourism demand and transportation cost of the tourism in ourconsideration, respectively. “I” and “P” are the proxy variables for vitality of regional economy and regional price level.
In this study, Logarithmic transformation (natural logarithm) is performed on all the variables listed above, and a firstdifferences of them are taken for the (monthly) rate of change. Namely, 𝐷𝑉 = 𝑙𝑛𝑉𝑡 − 𝑙𝑛𝑉𝑡−1, 𝐷𝐶 = 𝑙𝑛C − 𝑙𝑛𝐶𝑡−1,
𝐷𝑃 = 𝑙𝑛𝑃𝑡 − 𝑙𝑛𝑃𝑡−1, and 𝐷𝐼 = 𝑙𝑛𝐼𝑡 − 𝑙𝑛𝐼𝑡−1 . ("𝑙𝑛" means the natural logarithm)

4. Empirical Result
This section is constructed to investigate the tourism demand for Japan’s two major prefectures in the Kansai region,
namely, Kyoto and Osaka. The empirical estimations by utilizing BVAR (Bayesian vector autoregression) model basedon the Litterman or Minnesota Prior with the variables explained in the former section for Kyoto and Osaka are conducted.
The following specifications are applied in our estimation.
𝐷𝑉𝑡 = 𝛼1,1 𝐷𝑉𝑡−1 + 𝛼1,2 𝐷𝑉𝑡−2 +∙∙∙ +𝛼1,12 𝐷𝑉𝑡−12+𝛼2,1 𝐷𝐶𝑡−1 + 𝛼2,2 𝐷𝐶𝑡−2 +∙∙∙ +𝛼2,12 𝐷𝐶𝑡−12+𝛼3,1 𝐷𝑃𝑡−1 + 𝛼3,2 𝐷𝑃𝑡−2 +∙∙∙ +𝛼3,12 𝐷𝑃𝑡−12+𝛼4,1 𝐷𝐼𝑡−1 + 𝛼4,2 𝐷𝐼𝑡−2 +∙∙∙ +𝛼4,12 𝐷𝐼𝑡−12+𝑐1 + 𝜀1𝑡(18)

𝐷𝐶𝑡 = 𝛼1,1 𝐷𝑉𝑡−1 + 𝛼1,2 𝐷𝑉𝑡−2 +∙∙∙ +𝛼1,12 𝐷𝑉𝑡−12+𝛼2,1 𝐷𝐶𝑡−1 + 𝛼2,2 𝐷𝐶𝑡−2 +∙∙∙ +𝛼2,12 𝐷𝐶𝑡−12+𝛼3,1 𝐷𝑃𝑡−1 + 𝛼3,2 𝐷𝑃𝑡−2 +∙∙∙ +𝛼3,12 𝐷𝑃𝑡−12+𝛼4,1 𝐷𝐼𝑡−1 + 𝛼4,2 𝐷𝐼𝑡−2 +∙∙∙ +𝛼4,12 𝐷𝐼𝑡−12+𝑐2 + 𝜀2𝑡(19)

𝐷𝐼𝑡 = 𝛼1,1 𝐷𝑉𝑡−1 + 𝛼1,2 𝐷𝑉𝑡−2 +∙∙∙ +𝛼1,12 𝐷𝑉𝑡−12+𝛼2,1 𝐷𝐶𝑡−1 + 𝛼2,2 𝐷𝐶𝑡−2 +∙∙∙ +𝛼2,12 𝐷𝐶𝑡−12+𝛼3,1 𝐷𝑃𝑡−1 + 𝛼3,2 𝐷𝑃𝑡−2 +∙∙∙ +𝛼3,12 𝐷𝑃𝑡−12+𝛼4,1 𝐷𝐼𝑡−1 + 𝛼4,2 𝐷𝐼𝑡−2 +∙∙∙ +𝛼4,12 𝐷𝐼𝑡−12+𝑐4 + 𝜀4𝑡(20)

𝐷𝑃𝑡 = 𝛼1,1 𝐷𝑉𝑡−1 + 𝛼1,2 𝐷𝑉𝑡−2 +∙∙∙ +𝛼1,12 𝐷𝑉𝑡−12+𝛼2,1 𝐷𝐶𝑡−1 + 𝛼2,2 𝐷𝐶𝑡−2 +∙∙∙ +𝛼2,12 𝐷𝐶𝑡−12+𝛼3,1 𝐷𝑃𝑡−1 + 𝛼3,2 𝐷𝑃𝑡−2 +∙∙∙ +𝛼3,12 𝐷𝑃𝑡−12+𝛼4,1 𝐷𝐼𝑡−1 + 𝛼4,2 𝐷𝐼𝑡−2 +∙∙∙ +𝛼4,12 𝐷𝐼𝑡−127

+𝑐3 + 𝜀3𝑡(21)Considering the fact that we use the monthly data set, the lag length for each estimation is set as 12. With respect to the
BVAR process with Litterman or Minnesota Prior, some conditions explained in section 2 should be settled before
estimation. First, initial residual covariance matrix is obtained by the full-VAR estimation in this study. Second, the hyperparameters, 𝜇1 , 𝜆1 , 𝜆2 , and 𝜆3 have to be determined as scalar values. The 𝜇1 , the AR(1) coefficient is set as 0 in ourestimation that describes the zero-mean model. The 𝜆1 is the overall tightness on the variance of the first lag, and thisparameter decides the relative importance of sample and prior information. In our estimation, it is set as 𝜆1 = 0.1. The
𝜆2 represents relative tightness of the variance of other variables, and we set it as 𝜆2 = 0.99. The 𝜆3 (> 0) shows is therelative tightness of the variance of lags, and it is set as 𝜆3 = 1.
As is widely known, VAR-type model provides impulse response analysis as a tool for grasping the marginal effects of
the assumed shock with respect to one of the variables on the current and future levels of other endogenous variables.4 In
this context, the analysis by utilizing impulse response is applied in this study. Our impulse response is based on a one
standard deviation shock and Cholesky decomposition with degrees of freedom correction.
Figure 1 indicates the estimated cumulative impulse responses of Kyoto. (The the estimated coefficients of thespecification described by the equations (18), (19), (20), and (21) for Kyoto are shown in the appendix 1.) Our cumulative
impulse responses capture the marginal effects for 24 periods (24 months) after the one-time shock considering one of thevariables on the present and future values of other endogenous variables. The most important result to investigate theinfluence of economic variables on tourism demand is shown in the first row. With respect to the shock to “DC”
(transportation cost of the tourism) described in the second column of the first row, it can be seen that the response of “DV”
(tourism demand) is consistent with the usual assumption, that is, a rise in transportation cost is followed by a decline intourism demand in the long term. The response of tourism demand to “DI” (vitality of regional economy) indicated in thethird column of the first row is persistently positive although it is not on a large level. Concerning the shock to “DP”
(regional price level) displayed in the fourth column, it is followed by cumulative negative response of tourism demand.
These responses of Kyoto are consistent with the conventional belief.
Figure 2 reports the cumulative impulse responses of Osaka (The the estimated coefficients of the specification
described by the equations (18), (19), (20), and (21) for Osaka are shown in the appendix 2.) The responses do not always
indicate the same patterns of behavior as Kyoto. With respect to the first row, the cumulative impulse response for theshock to transportation cost in the second column does not coincides with the usual assumption. A positive shock to

4

See Koop (2013) for details.

8Figure 1: Cumulative Impulse Responses of Kyoto by utilizing BVAR model

Accumulated Response to Cholesky One S.D. Innovations
Accumulated Response of DLVKYOTO to DLVKYOTO

Accumulated Response of DLVKYOTO to DLPPKINKI

Accumulated Response of DLVKYOTO to DLIOKYOTO

Accumulated Response of DLVKYOTO to DLPOKYOTO

.5

.5

.5

.5

.4

.4

.4

.4

.3

.3

.3

.3

.2

.2

.2

.2

.1

.1

.1

.1

.0

.0

.0

.0

-.1

-.1

-.1

-.1

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of DLPPKINKI to DLVKYOTO

Accumulated Response of DLPPKINKI to DLPPKINKI

Accumulated Response of DLPPKINKI to DLIOKYOTO

Accumulated Response of DLPPKINKI to DLPOKYOTO

.08

.08

.08

.08

.06

.06

.06

.06

.04

.04

.04

.04

.02

.02

.02

.02

.00

.00

.00

.00

-.02

-.02

-.02

-.02

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of DLIOKYOTO to DLVKYOTO

Accumulated Response of DLIOKYOTO to DLPPKINKI

Accumulated Response of DLIOKYOTO to DLIOKYOTO Accumulated Response of DLIOKYOTO to DLPOKYOTO

.10

.10

.10

.10

.08

.08

.08

.08

.06

.06

.06

.06

.04

.04

.04

.04

.02

.02

.02

.02

.00

.00

.00

.00

-.02

2 4 6 8 10 12 14 16 18 20 22 24-.02
2 4 6 8 10 12 14 16 18 20 22 24-.02
2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24-.02
2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of DLPOKYOTO to DLVKYOTO Accumulated Response of DLPOKYOTO to DLPPKINKI Accumulated Response of DLPOKYOTO to DLIOKYOTO Accumulated Response of DLPOKYOTO to DLPOKYOTO
.003

.003

.003

.003

.002

.002

.002

.002

.001

.001

.001

.001

.000

.000

.000

.000

-.001

-.001
2 4 6 8 10 12 14 16 18 20 22 24-.001
2 4 6 8 10 12 14 16 18 20 22 24-.001
2 4 6 8 10 12 14 16 18 20 22 249

2 4 6 8 10 12 14 16 18 20 22 24

Figure 2: Cumulative Impulse Responses of Osaka by utilizing BVAR model

Accumulated Response to Cholesky One S.D. Innovations
Accumulated Response of DLVOSAKA to DLVOSAKA

Accumulated Response of DLVOSAKA to DLPPKINKI

Accumulated Response of DLVOSAKA to DLIOOSAKA

Accumulated Response of DLVOSAKA to DLPOOSAKA

.4

.4

.4

.4

.3

.3

.3

.3

.2

.2

.2

.2

.1

.1

.1

.1

.0

.0

.0

.0

-.1

-.1

-.1

-.1

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of DLPPKINKI to DLVOSAKA

Accumulated Response of DLPPKINKI to DLPPKINKI

Accumulated Response of DLPPKINKI to DLIOOSAKA

Accumulated Response of DLPPKINKI to DLPOOSAKA

.08

.08

.08

.08

.06

.06

.06

.06

.04

.04

.04

.04

.02

.02

.02

.02

.00

.00

.00

.00

-.02

-.02

-.02

-.02

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of DLIOOSAKA to DLVOSAKA

Accumulated Response of DLIOOSAKA to DLPPKINKI

Accumulated Response of DLIOOSAKA to DLIOOSAKA

Accumulated Response of DLIOOSAKA to DLPOOSAKA

.10

.10

.10

.10

.08

.08

.08

.08

.06

.06

.06

.06

.04

.04

.04

.04

.02

.02

.02

.02

.00

.00

.00

.00

-.02

-.02

-.02

-.02

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

Accumulated Response of DLPOOSAKA to DLVOSAKA

Accumulated Response of DLPOOSAKA to DLPPKINKI

Accumulated Response of DLPOOSAKA to DLIOOSAKA

Accumulated Response of DLPOOSAKA to DLPOOSAKA

.002

.002

.002

.002

.001

.001

.001

.001

.000

.000

.000

.000

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 24

2 4 6 8 10 12 14 16 18 20 22 2410

2 4 6 8 10 12 14 16 18 20 22 24

transportation cost is followed by a small positive response of tourism demand. The shock to vitality of regional economy(in the third column) is not consistent with the standard supposition since it gets negative response in the long run. Only
the shock to regional price level (displayed in the fourth column) brings the understandable result. Namely, a rise in pricelevel derives the cumulative negative response of tourism demand. Overall, the estimated responses of tourism demandin Osaka to the several economic shocks seem to be inconsistent with the conventional assumption.

5. Concluding Remarks
The BVAR (Bayesian vector autoregression) model has been used as the Bayesian-flavored VAR specification for
empirical analysis, which connects priors with information incorporated in sample. BVAR decreases the risk of overparameterization by the imposition of special restrictions on the parameters in VAR process through their prior probability
distribution functions.
In this research, we assume that prior distribution function and the posterior one are in the same distribution family andutilize one of the conjugate priors － Litterman or Minnesota prior. Taking the features of BVAR into account, theempirical analysis to investigate the influence of economic variables on tourism demand for Japan’s two major cities inwestern region is conducted in this study.
With respect to the estimated cumulative impulse responses of Kyoto, the shock to transportation cost of the tourism isconsistent with the usual assumption, that is, a rise in transportation cost is followed by a decline in tourism demand in thelong term. The response of tourism demand to vitality of regional economy is persistently positive although it is not on alarge level. Concerning the shock to regional price level, it is followed by cumulative negative response of tourism demand.
These responses of Kyoto are consistent with the conventional belief.
With respect to the estimated result of Osaka The cumulative impulse response for the shock to transportation cost does
not coincides with the usual assumption. A positive shock to transportation cost is followed by a small positive responseof tourism demand. The shock to vitality of regional economy is not consistent with the standard supposition since it gets
negative response in the long run. Only the shock to regional price level brings the understandable result. Namely, a risein price level derives the cumulative negative response of tourism demand. Overall, the estimated responses of tourism
demand in Osaka to the several economic shocks seem to be inconsistent with the conventional assumption.
Totally, a further research with more sophisticated estimation is required since the empirical analysis in this paper has
some unfavorable results.

11

Acknowledgment
This research was supported by the Ministry of Education's Scientific Research Fund (Grant-in-Aid for Scientific
Research (C), No.17K02127, 2017/04 - 2020/03.

References
Bernanke, Ben S., and Ilian Mihov (1998), “Measuring Monetary Policy,” Quarterly Journal of Economics, Vol.113,
No.3, pp.869-902.
Blanchard, Olivier Jean, and Mark W. Watson (1986), “Are Business Cycles All Alike?,” in Gordon, Robert J. (ed.),American Business Cycles: Continuity and Change, Chicago: University of Chicago Press, pp.123-156.
Chan, Joshua, Koop, Gary, Poirier, Dale J., and Tobias, Justin L. (2019) Bayesian Econometric Methods (2nd Edition),
Cambridge.
Doan, Tomas, Litterman, Robert, B., and Sims, Christopher A. (1984) “Forecasting and conditional projection using
realistic prior distributions,” Econometric Reviews, Volume 3, Issue 1, pp.1-100.
Gali, Jordi (1992), “How Well Does the IS-LM Model Fit Postwar U.S. Data?,” Quarterly Journal of Economics, Vol.107,
No.2, pp.709-738.
Gordon, David, B., and Eric M. Leeper (1994), “The Dynamic Impacts of Monetary Policy: An Exercise in Tentative
Identification,” Journal of Political Economy, Vol.102, No.6, pp.1228-1247.
Koop, Gary. M. (2013) “Forecasting with Medium and Large Bayesian VARs,” Journal of Applied Econometrics, vol.28,
pp.177-203.
Lastrapes, William D., and Geoge Selgin (1995), “The Liquidity Effect: Identifying Short-Run Interest Rate Dynamics
Using Long-Run Restriction,” Journal of Macroeconomics, Vol.17, No.3, pp.387-404.
Litterman, Robert, B., (1986) “Forecasting with Bayesian Vector Autoregressions: Five Years of Experience,” Journal ofBusiness & Economic Statistics, Vol.4, No.1., pp.25-38.
Lutkepohl, Helmut (2006), New Introduction to Multiple Time Series Analysis, Springer Berlin Heidelberg.
Sims, Christopher A. (1980), “Macroeconomics and Reality,” Econometrica, Vol.48, No.1, pp.1-48.
Sims, Christopher A. (1992), “Interpreting the Time Series Facts: The Effects of Monetary Policy,” European Economic
Review, Vol.6, No.5, pp.975-1011.

12

Appendix 1: estimated coefficients for Kyoto
Sample (adjusted): 2014M02 2021M08
Included observations: 91 after adjustments
Prior type: Litterman/Minnesota
Initial residual covariance: Full VAR
Standard errors in ( ) & t-statistics in [ ]DLVKYOTO DLPPKINKI DLIOKYOTO DLPOKYOTODLVKYOTO(-1)

0.049518(0.06469)[ 0.76542]

0.006402(0.00993)[ 0.64480]

0.043665(0.01359)[ 3.21334]

0.000620(0.00055)[ 1.13468]

DLVKYOTO(-2)-0.101026(0.04227)[-2.39014]

2.18E-05(0.00647)[ 0.00337]-0.012783(0.00885)[-1.44423]

1.89E-05(0.00035)[ 0.05327]

DLVKYOTO(-3)

0.005756(0.03092)[ 0.18616]-0.002061(0.00472)[-0.43663]

0.006388(0.00646)[ 0.98884]

0.000134(0.00026)[ 0.52194]

DLVKYOTO(-4)-0.003201(0.02385)[-0.13423]-0.001583(0.00364)[-0.43519]

0.009306(0.00498)[ 1.86896]

0.000161(0.00020)[ 0.81243]

DLVKYOTO(-5)-0.004984(0.01942)[-0.25661]

0.000323(0.00296)[ 0.10921]-0.003794(0.00405)[-0.93625]-2.24E-05(0.00016)[-0.13882]

DLVKYOTO(-6)-0.010939(0.01634)[-0.66927]

0.001184(0.00249)[ 0.47515]-0.002424(0.00341)[-0.71098]-4.82E-05(0.00014)[-0.35581]

DLVKYOTO(-7)-0.003895(0.01409)[-0.27645]

0.000712(0.00215)[ 0.33162]

0.000492(0.00294)[ 0.16747]-4.42E-07(0.00012)[-0.00379]

DLVKYOTO(-8)

0.002428(0.01238)[ 0.19612]-0.000199(0.00189)[-0.10557]

0.000126(0.00258)[ 0.04878]-2.66E-06(0.00010)[-0.02594]

DLVKYOTO(-9)

0.005369(0.01102)[ 0.48710]-0.000401(0.00168)[-0.23847]-0.000937(0.00230)[-0.40766]-2.23E-05(9.1E-05)[-0.24439]

DLVKYOTO(-10)-4.90E-05(0.00994)[-0.00493]-5.71E-05(0.00151)[-0.03769]-0.000650(0.00207)[-0.31379]-1.27E-05(8.2E-05)[-0.15483]

DLVKYOTO(-11)-0.001364(0.00904)[-0.15085]-8.64E-05(0.00138)[-0.06273]

0.000529(0.00189)[ 0.28056]

3.10E-06(7.5E-05)[ 0.04142]

DLVKYOTO(-12)

0.003278-0.000221

0.000235

1.13E-0513

(0.00830)[ 0.39515](0.00126)[-0.17476](0.00173)[ 0.13577](6.9E-05)[ 0.16417]

DLPPKINKI(-1)

0.019373(0.39413)[ 0.04915]

0.408110(0.06094)[ 6.69684]

0.015794(0.08307)[ 0.19012]

0.001472(0.00334)[ 0.44117]

DLPPKINKI(-2)-0.071927(0.27370)[-0.26280]-0.036107(0.04248)[-0.85004]

0.015487(0.05770)[ 0.26840]

0.000568(0.00231)[ 0.24615]

DLPPKINKI(-3)-0.086301(0.19471)[-0.44322]-0.023603(0.03024)[-0.78059]

0.040253(0.04104)[ 0.98084]

0.001484(0.00164)[ 0.90684]

DLPPKINKI(-4)-0.095544(0.15132)[-0.63140]-0.003953(0.02351)[-0.16816]

0.020719(0.03189)[ 0.64974]

0.000232(0.00127)[ 0.18296]

DLPPKINKI(-5)-0.027233(0.12335)[-0.22077]

0.006594(0.01917)[ 0.34406]-0.007507(0.02599)[-0.28885]

2.02E-05(0.00103)[ 0.01952]

DLPPKINKI(-6)-0.037416(0.10400)[-0.35976]

0.012352(0.01616)[ 0.76430]-0.019177(0.02191)[-0.87522]-0.000241(0.00087)[-0.27639]

DLPPKINKI(-7)-0.030258(0.08991)[-0.33653]

0.008072(0.01397)[ 0.57774]-0.015224(0.01894)[-0.80382]-0.000150(0.00075)[-0.19887]

DLPPKINKI(-8)

0.026712(0.07912)[ 0.33764]

9.99E-05(0.01229)[ 0.00812]-0.006694(0.01666)[-0.40168]-0.000213(0.00066)[-0.32164]

DLPPKINKI(-9)

0.030610(0.07053)[ 0.43398]-0.001208(0.01096)[-0.11022]

0.001233(0.01486)[ 0.08299]-5.72E-05(0.00059)[-0.09698]

DLPPKINKI(-10)

0.010944(0.06364)[ 0.17196]-0.001611(0.00989)[-0.16293]-0.000796(0.01340)[-0.05938]-4.00E-06(0.00053)[-0.00752]

DLPPKINKI(-11)-8.96E-05(0.05795)[-0.00155]-0.001385(0.00901)[-0.15374]

0.001260(0.01220)[ 0.10327]

3.31E-07(0.00048)[ 0.00068]

DLPPKINKI(-12)

0.003858(0.05318)[ 0.07255]-0.001880(0.00827)[-0.22746]

0.003184(0.01120)[ 0.28430]

0.000105(0.00044)[ 0.23741]

DLIOKYOTO(-1)

0.217011(0.23060)[ 0.94106]-0.054284(0.03550)[-1.52906]-0.302360(0.04876)[-6.20147]-0.001838(0.00195)[-0.94409]

14

DLIOKYOTO(-2)-0.032771(0.17368)[-0.18869]

0.021043(0.02675)[ 0.78665]-0.285583(0.03684)[-7.75217]-0.001865(0.00147)[-1.27065]

DLIOKYOTO(-3)-0.087833(0.13621)[-0.64484]

0.003505(0.02098)[ 0.16710]

0.071515(0.02895)[ 2.47061]

0.000664(0.00115)[ 0.57886]

DLIOKYOTO(-4)-0.089775(0.10737)[-0.83609]

0.009585(0.01653)[ 0.57967]

0.010466(0.02283)[ 0.45847]

5.78E-05(0.00090)[ 0.06406]

DLIOKYOTO(-5)

0.066837(0.08785)[ 0.76080]-0.004408(0.01353)[-0.32587]-0.012566(0.01868)[-0.67268]

5.49E-05(0.00074)[ 0.07442]

DLIOKYOTO(-6)-0.018618(0.07444)[-0.25011]

0.000458(0.01146)[ 0.03999]

0.008037(0.01583)[ 0.50766]

7.93E-05(0.00062)[ 0.12703]

DLIOKYOTO(-7)-0.053440(0.06445)[-0.82915]

0.004457(0.00992)[ 0.44923]-0.016888(0.01371)[-1.23206]-0.000388(0.00054)[-0.71920]

DLIOKYOTO(-8)

0.058756(0.05710)[ 1.02895]-0.002740(0.00879)[-0.31179]

0.002594(0.01214)[ 0.21359]

9.08E-05(0.00048)[ 0.19000]

DLIOKYOTO(-9)-0.008379(0.05105)[-0.16413]-0.001184(0.00786)[-0.15064]

0.015850(0.01086)[ 1.45969]

0.000214(0.00043)[ 0.50222]

DLIOKYOTO(-10)-0.015805(0.04618)[-0.34225]

0.000414(0.00711)[ 0.05829]-0.013466(0.00982)[-1.37101]-0.000199(0.00039)[-0.51472]

DLIOKYOTO(-11)

0.019362(0.04218)[ 0.45906]

0.000400(0.00649)[ 0.06170]-0.009702(0.00897)[-1.08148]-9.89E-05(0.00035)[-0.28048]

DLIOKYOTO(-12)-0.001287(0.03874)[-0.03322]-0.001875(0.00596)[-0.31443]

0.017111(0.00824)[ 2.07634]

0.000256(0.00032)[ 0.79092]

DLPOKYOTO(-1)-5.038650(8.18172)[-0.61584]-2.294251(1.26068)[-1.81986]-0.474045(1.72618)[-0.27462]-0.216693(0.06982)[-3.10378]

DLPOKYOTO(-2)-4.569193(5.26687)[-0.86754]-0.307321(0.81136)[-0.37877]-0.202250(1.11070)[-0.18209]-0.018459(0.04475)[-0.41247]

DLPOKYOTO(-3)-0.299711(3.72063)[-0.08055]-0.036790(0.57291)[-0.06422]

0.099422(0.78420)[ 0.12678]-0.002113(0.03152)[-0.06704]

15

DLPOKYOTO(-4)

0.401954(2.85795)[ 0.14064]

0.054049(0.43997)[ 0.12285]

0.219989(0.60220)[ 0.36531]

0.005410(0.02417)[ 0.22379]

DLPOKYOTO(-5)

0.382919(2.31536)[ 0.16538]

0.108976(0.35639)[ 0.30578]-0.460406(0.48778)[-0.94389]-0.010245(0.01957)[-0.52362]

DLPOKYOTO(-6)-0.846982(1.94432)[-0.43562]

0.091857(0.29924)[ 0.30697]

0.018241(0.40955)[ 0.04454]-0.000497(0.01642)[-0.03030]

DLPOKYOTO(-7)

0.640848(1.67369)[ 0.38290]-0.003131(0.25757)[-0.01216]

0.050525(0.35252)[ 0.14333]-0.000564(0.01413)[-0.03995]

DLPOKYOTO(-8)

0.174204(1.46908)[ 0.11858]

0.044278(0.22607)[ 0.19586]-0.029626(0.30940)[-0.09575]-0.000889(0.01240)[-0.07174]

DLPOKYOTO(-9)-0.059693(1.30800)[-0.04564]-0.058834(0.20128)[-0.29230]

0.031148(0.27547)[ 0.11307]

0.002024(0.01104)[ 0.18339]

DLPOKYOTO(-10)-0.023293(1.17899)[-0.01976]-0.005431(0.18142)[-0.02993]-0.023528(0.24829)[-0.09476]-0.001633(0.00995)[-0.16413]

DLPOKYOTO(-11)-0.118222(1.07281)[-0.11020]-0.024065(0.16508)[-0.14578]

0.059780(0.22593)[ 0.26460]

0.002264(0.00905)[ 0.25011]

DLPOKYOTO(-12)

0.057376(0.98427)[ 0.05829]

0.029581(0.15145)[ 0.19531]-0.017443(0.20728)[-0.08415]-0.000330(0.00830)[-0.03969]

C-0.004946(0.02233)[-0.22149]-0.001069(0.00344)[-0.31114]-0.003082(0.00470)[-0.65547]

3.21E-05(0.00019)[ 0.17213]

R-squared
Adj. R-squared
Sum sq. resids
S.E. equation
F-statistic
Mean dependent
S.D. dependent

0.170624-0.777235
6.021211
0.378632
0.180010-0.003723
0.284017

0.381696-0.324938
0.137453
0.057207
0.540161-0.001621
0.049700

0.508568-0.053069
0.406940
0.098433
0.905510-0.002875
0.095921

0.157707-0.804914
0.000271
0.002540
0.163831
2.20E-05
0.001890

16

Appendix 2: estimated coefficients for Osaka
Sample (adjusted): 2014M02 2021M08
Included observations: 91 after adjustments
Prior type: Litterman/Minnesota
Initial residual covariance: Full VAR
Standard errors in ( ) & t-statistics in [ ]DLVOSAKA DLPPKINKI DLIOOSAKA DLPOOSAKADLVOSAKA(-1)

0.098139(0.06201)[ 1.58271]

0.013327(0.01775)[ 0.75097]

0.019361(0.01536)[ 1.26043]

0.000511(0.00058)[ 0.88356]

DLVOSAKA(-2)-0.073294(0.04146)[-1.76801]

0.004746(0.01183)[ 0.40112]-0.006455(0.01020)[-0.63253]-0.000211(0.00038)[-0.54849]

DLVOSAKA(-3)-0.005463(0.03054)[-0.17891]-0.001798(0.00871)[-0.20639]

0.008157(0.00744)[ 1.09573]-7.02E-05(0.00028)[-0.24974]

DLVOSAKA(-4)

0.004019(0.02373)[ 0.16940]-0.002708(0.00677)[-0.39989]

0.002651(0.00576)[ 0.46051]

5.53E-05(0.00022)[ 0.25415]

DLVOSAKA(-5)

0.003605(0.01932)[ 0.18662]-0.001924(0.00551)[-0.34909]-0.003871(0.00467)[-0.82833]

6.31E-05(0.00018)[ 0.35725]

DLVOSAKA(-6)-0.021710(0.01630)[-1.33223]

0.003285(0.00465)[ 0.70628]-0.001257(0.00393)[-0.31941]-3.13E-05(0.00015)[-0.21021]

DLVOSAKA(-7)-0.004186(0.01408)[-0.29739]

0.001452(0.00402)[ 0.36132]

0.001091(0.00339)[ 0.32159]-6.34E-07(0.00013)[-0.00494]

DLVOSAKA(-8)

0.003883(0.01235)[ 0.31433]-0.000332(0.00353)[-0.09411]

0.001171(0.00298)[ 0.39354]-3.36E-06(0.00011)[-0.02984]

DLVOSAKA(-9)

0.005541(0.01101)[ 0.50343]-0.001112(0.00314)[-0.35390]-8.32E-05(0.00265)[-0.03138]-7.80E-06(0.00010)[-0.07784]

DLVOSAKA(-10)-0.000179(0.00993)[-0.01799]-0.000540(0.00283)[-0.19072]-0.001264(0.00239)[-0.52924]

5.35E-06(9.0E-05)[ 0.05924]

DLVOSAKA(-11)-0.001498(0.00904)[-0.16578]

7.20E-05(0.00258)[ 0.02791]

0.000319(0.00217)[ 0.14673]-1.61E-05(8.2E-05)[-0.19553]

DLVOSAKA(-12)

0.003631-0.000667-0.000178

1.12E-0517

(0.00829)[ 0.43790](0.00237)[-0.28170](0.00199)[-0.08899](7.5E-05)[ 0.14848]

DLPPKINKI(-1)

0.173497(0.23842)[ 0.72769]

0.317986(0.06878)[ 4.62304]

0.136463(0.05924)[ 2.30371]-0.000267(0.00223)[-0.11956]

DLPPKINKI(-2)-0.018977(0.15349)[-0.12364]-0.019872(0.04452)[-0.44632]-0.031618(0.03774)[-0.83787]

0.001038(0.00142)[ 0.72892]

DLPPKINKI(-3)

0.032307(0.10739)[ 0.30083]-0.023028(0.03120)[-0.73812]

0.007619(0.02630)[ 0.28966]

0.000331(0.00099)[ 0.33354]

DLPPKINKI(-4)-0.031994(0.08246)[-0.38800]-0.000719(0.02397)[-0.03001]

0.005435(0.02014)[ 0.26977]-0.000254(0.00076)[-0.33349]

DLPPKINKI(-5)-0.029826(0.06683)[-0.44628]

0.007380(0.01944)[ 0.37957]-0.001178(0.01630)[-0.07226]-0.000219(0.00062)[-0.35614]

DLPPKINKI(-6)-0.031942(0.05614)[-0.56902]

0.009161(0.01634)[ 0.56077]-0.003388(0.01367)[-0.24778]-6.42E-05(0.00052)[-0.12421]

DLPPKINKI(-7)-0.011195(0.04837)[-0.23145]

0.003587(0.01408)[ 0.25476]-0.003294(0.01177)[-0.27980]

8.95E-05(0.00045)[ 0.20119]

DLPPKINKI(-8)

0.008953(0.04246)[ 0.21085]-0.000370(0.01236)[-0.02991]

0.000233(0.01033)[ 0.02253]-4.79E-06(0.00039)[-0.01226]

DLPPKINKI(-9)

0.014035(0.03782)[ 0.37111]-0.000360(0.01101)[-0.03268]

0.002390(0.00920)[ 0.25993]-9.71E-05(0.00035)[-0.27931]

DLPPKINKI(-10)

0.002013(0.03410)[ 0.05902]-0.000747(0.00993)[-0.07519]-0.000793(0.00829)[-0.09568]-2.65E-05(0.00031)[-0.08446]

DLPPKINKI(-11)-0.005040(0.03103)[-0.16243]

2.63E-05(0.00904)[ 0.00291]-0.001003(0.00754)[-0.13302]-3.30E-05(0.00029)[-0.11559]

DLPPKINKI(-12)

0.002194(0.02847)[ 0.07708]-0.001311(0.00829)[-0.15808]

0.000152(0.00692)[ 0.02194]

4.80E-05(0.00026)[ 0.18329]

DLIOOSAKA(-1)

0.005059(0.19193)[ 0.02636]-0.061256(0.05519)[-1.10999]-0.313010(0.04752)[-6.58686]

0.000759(0.00179)[ 0.42448]

18

DLIOOSAKA(-2)-0.276097(0.14776)[-1.86855]-0.018442(0.04245)[-0.43440]-0.290129(0.03685)[-7.87284]

9.55E-05(0.00138)[ 0.06919]

DLIOOSAKA(-3)-0.007259(0.11722)[-0.06192]

0.007183(0.03372)[ 0.21303]

0.039847(0.02912)[ 1.36856]

5.83E-05(0.00109)[ 0.05352]

DLIOOSAKA(-4)

0.028752(0.09242)[ 0.31109]-0.003012(0.02660)[-0.11325]

0.003989(0.02291)[ 0.17415]-4.70E-05(0.00086)[-0.05488]

DLIOOSAKA(-5)

0.014930(0.07586)[ 0.19682]-0.001054(0.02184)[-0.04825]

0.003519(0.01877)[ 0.18750]

0.000247(0.00070)[ 0.35172]

DLIOOSAKA(-6)-0.013617(0.06434)[-0.21164]

0.004172(0.01853)[ 0.22517]-0.001358(0.01589)[-0.08542]-0.000135(0.00059)[-0.22703]

DLIOOSAKA(-7)-0.059255(0.05580)[-1.06188]

0.004354(0.01607)[ 0.27086]-0.009974(0.01377)[-0.72436]-0.000160(0.00052)[-0.31026]

DLIOOSAKA(-8)

0.037384(0.04936)[ 0.75734]-0.000447(0.01422)[-0.03140]

0.004702(0.01216)[ 0.38659]

0.000123(0.00046)[ 0.26944]

DLIOOSAKA(-9)

0.023184(0.04416)[ 0.52493]-0.002484(0.01273)[-0.19517]

0.015510(0.01087)[ 1.42647]-6.86E-05(0.00041)[-0.16843]

DLIOOSAKA(-10)-0.019358(0.04000)[-0.48401]-0.001960(0.01153)[-0.17005]-0.015917(0.00984)[-1.61801]

6.26E-05(0.00037)[ 0.16991]

DLIOOSAKA(-11)

0.000247(0.03657)[ 0.00675]-0.000204(0.01054)[-0.01938]-0.007719(0.00899)[-0.85887]

7.05E-05(0.00034)[ 0.20942]

DLIOOSAKA(-12)

0.006302(0.03358)[ 0.18770]

0.001136(0.00968)[ 0.11738]

0.013256(0.00825)[ 1.60717]-0.000103(0.00031)[-0.33251]

DLPOOSAKA(-1)-8.508390(6.85303)[-1.24155]

1.344986(1.96783)[ 0.68349]

0.099986(1.70519)[ 0.05864]-0.266644(0.06451)[-4.13324]

DLPOOSAKA(-2)

2.102019(4.61462)[ 0.45551]-0.888017(1.32627)[-0.66956]

0.362231(1.14194)[ 0.31721]-0.024913(0.04338)[-0.57422]

DLPOOSAKA(-3)-1.111590(3.30902)[-0.33593]

0.139274(0.95218)[ 0.14627]

0.079360(0.81336)[ 0.09757]-0.009023(0.03097)[-0.29137]

19

DLPOOSAKA(-4)

0.715225(2.56223)[ 0.27914]

0.304186(0.73778)[ 0.41230]

0.531880(0.62748)[ 0.84765]-0.015106(0.02392)[-0.63157]

DLPOOSAKA(-5)

0.366975(2.08600)[ 0.17592]-0.070594(0.60093)[-0.11747]-0.277698(0.50948)[-0.54506]

0.004130(0.01943)[ 0.21252]

DLPOOSAKA(-6)-0.842069(1.75293)[-0.48038]

0.185999(0.50511)[ 0.36824]

0.110321(0.42756)[ 0.25803]-0.002760(0.01632)[-0.16915]

DLPOOSAKA(-7)

0.122714(1.51216)[ 0.08115]-0.032895(0.43581)[-0.07548]-0.140910(0.36840)[-0.38249]

0.001842(0.01406)[ 0.13095]

DLPOOSAKA(-8)

0.164823(1.32909)[ 0.12401]-0.056861(0.38311)[-0.14842]

0.042804(0.32353)[ 0.13230]

0.001528(0.01235)[ 0.12374]

DLPOOSAKA(-9)-0.238755(1.18427)[-0.20161]

0.039815(0.34139)[ 0.11663]

0.040551(0.28815)[ 0.14073]-0.002563(0.01100)[-0.23296]

DLPOOSAKA(-10)-0.196507(1.06764)[-0.18406]

0.003541(0.30779)[ 0.01150]-0.030875(0.25969)[-0.11889]

0.001375(0.00992)[ 0.13862]

DLPOOSAKA(-11)-0.145225(0.97230)[-0.14936]-0.009187(0.28032)[-0.03277]-0.029438(0.23642)[-0.12451]

0.000532(0.00903)[ 0.05888]

DLPOOSAKA(-12)

0.180836(0.89219)[ 0.20269]-0.009838(0.25723)[-0.03824]

0.004424(0.21690)[ 0.02040]-0.000454(0.00828)[-0.05479]

C-0.004548(0.01534)[-0.29656]-0.001114(0.00442)[-0.25186]-0.000705(0.00372)[-0.18930]-1.28E-05(0.00014)[-0.09110]

R-squared
Adj. R-squared
Sum sq. resids
S.E. equation
F-statistic
Mean dependent
S.D. dependent

0.173495-0.771083
3.189437
0.275570
0.183674-0.004376
0.207068

0.322212-0.452403
0.150676
0.059896
0.415964-0.001621
0.049700

0.432861-0.215298
0.314223
0.086496
0.667831-0.001110
0.078461

0.197096-0.720509
0.000210
0.002236
0.214794-5.44E-06
0.00170520