AIDS Models for Tourism Demand
Modelling and Forecasting
Gang Li
Reader in Tourism Economics
School of Hospitality and
Tourism Management
Outline
•
•
•
•
Introduction
Methodological developments
Tourism applications
Further research directions
Introduction
• Econometric modelling and forecasting of tourism
demand is important for informing tourism policy
making and strategic planning.
• Most empirical studies on tourism demand
modelling and forecasting are based on the singleequation approach:
– Convenient to estimate and providing easily
interpretable elasticities;
– Lack of an explicit basis in consumer demand
theory.
Introduction
• The system of equations approach initiated by Stone
(1954) overcomes these limitations.
• The Almost Ideal Demand System (AIDS)
introduced by Deaton and Muellbauer (1980) has
been the most popular system-of-equation method.
• There have been only a handful of applications in
tourism demand studies since the 1980s.
– Earlier studies applied static systems, and
consumers’ short-term behaviour were overlooked.
– More advanced, dynamic AIDS models have been
developed recently: Static AIDS EC-AIDS TVPEC-AIDS
Advantages of AIDS
• It gives an arbitrary first-order approximation to
any demand system.
• It has a functional form which complies with
known household-budget data.
• It is easy to estimate and largely avoids the need
for non-linear estimation.
• The restrictions of homogeneity and symmetry
can be tested explictly.
• It has a flexible functional form and does not
impose any a priori restrictions on elasticities.
Methodological Developments:
Static AIDS
wi  ai    ij log p j  bi log( x / P )  ui
(1)
j
where wi: budget share of the ith good,
pj: price of the jth good,
x: total expenditure on all goods in the system,
P: aggregate price index, defined as:
1
log P  a0  i log pi    ij log pi log p j (2)
2 i j
i
x/P: real total expenditure,
ui~N(0,2): the normal disturbance term.
Linear Approximation--LAIDS
• Replacing the price index P with Stone’s
(geometric) price index (P*):
log P* 
w
i
log pi
(3)
i
• Static LAIDS:
wi  ai    ij log p j  bi log( x / P*)  ui (4)
j
Theoretical Restrictions
• Adding-up:
n

ij
i 1
–
 0, and
n
b
i 1
i
0
It implies all budge shares sum to unity.
• Homogeneity:
  ij
 0, i
j
–
It implies he absence of money illusion: a proportional
change in all prices and expenditure does not affect the
quantities purchased.
Theoretical Restrictions
• Symmetry:
 ij   ji , i, j
–
It implies the consistency of consumers’ choices.
• Negativity:
–
It requires the matrix of substitution effects to be negative
semi-definite, which implies that all compensated own
price elasticities must be negative.
Model Estimation & Restriction Tests
• Three estimation methods: OLS, ML and SUR: delete
an equation and estimate the remaining equations, and
then calculate the parameters in the deleted equation
based on the adding-up restrictions.
• Restriction tests: The Wald (W) test, likelihood ratio
(LR) test and Lagrange multiplier (LM) test.
• Considerable bias towards rejection of the null
hypothesis, especially in large demand systems with
relatively few observations  Sample-size-corrected
statistics (Court,1968 and Deaton, 1974).
Demand Elasticities
• Expenditure elasticity:
bi
 ix  1 
wi
(5)
• Uncompensated price elasticity: given total
expenditure (x) and any other prices held constant
 ij bi
 ij   ij   w j
(6)
wi wi
• Compensated price elasticity: assuming real
expenditure (x/P) keeps constant
   ij 
*
ij
 ij
wi
 wj
where  ij =1 for i=j;  ij =0 for ij.
(7)
Drawbacks of the Static AIDS
• Implicit assumption: no difference between
consumers’ short-run and long-run behaviour
=>always in “equilibrium”.
• It often renders serious misspecification problems
and failures of restriction tests, leading to biased
elasticity estimations.
• It is unlikely to general accurate short-run
forecasts (Chambers and Nowman 1997).
Methodological Developments:
Error Correction LAIDS
• The concept of CI and ECM (Engle and Granger,
1987)
– Both the long-run equilibrium relationship and shortrun dynamics can be examined.
– Spurious regression problem will not occur.
• Applications of EC-LAIDS:
– Cortés-Jiménez et al. (2009), Durbarry & Sinclair
(2003), Li et al. (2004), Mangion et al. (2005), Wu et
al. (2011), etc.
EC-LAIDS Specification
•The ADF test for unit roots
•The Engle-Granger approach for cointegration tests
wi  ai    ij  log p j  bi  log( x / P*)  it1  ui (8)
j
 jt1 is the estimated residual term from the static (long-run)
AIDS model.
Fixed-Parameter vs Time-VaryingParameter LAIDS Models
wi  ai    ij  log p j  bi  log( x / P*)  it1  ui (8)
j
•Estimated coefficients are constant over the sample
period. It indicates that the economic structure
generating the data does not change.
•Structural changes, specification errors, nonlinearities,
proxy variables and aggregation are all sources of
parameter variations.
•As modifications of the environment are transitory or
ambiguous in some situations, changes of coefficients
follows a stochastic process (Lucas, 1976).
Methodological Developments:
TVP-EC-LAIDS
• The system is specified in a state space form:
- Signal equation:
xt
wi ,t  ai ,t  t i ,t 1    ij,t  log p j ,t  bi ,t  log
  i ,t (9)
Pt *
j
- State equations (specified as random walks):
ai ,t  ai ,t 1  t , t  t 1   t ,  ij,t   ij,t 1   t , bi ,t  bi ,t 1   t (10)
- An recursive algorithm “the Kalman filter” is used to
estimate this state space model.
Advantages of TVP-LAIDS
• The evolution of tourists’
consumption behaviour can
be analysed over time via
calculated time-varying
demand elasticities.
• Improved forecasting
performance, especially in
short-run forecasting.
Fig. 1 Kalman filter estimates of
expenditure elasticities of UK
demand for tourism in Portugal
Source: Li et al. (2005)
Applications of AIDS Models
• Tourists’ expenditure allocation among different
destinations
– International destination choices (e.g., Li et al., 2004)
– Destination competitiveness (Song et al., 2011)
– Substitution between domestic and outbound tourism
(Athanasopoulos et al., in progress)
• Tourists’ expenditure allocation among different
goods and services at a given destination
– Inbound tourists (excluding international transport) (e.g.,
Wu et al., 2011; 2012)
– Domestic tourists (including domestic transport) (e.g.,
Divisekera, 2009; 2010)
Application 1: UK Tourist
Expenditure in Western Europe
References: Li, Song and Witt (2004; 2005)
Shares of Spending in Western
European Countries by British Tourists (2000)
Spain
29.1%
Others
30.5%
Portugal
4.3%
Italy
7.2%
Greece
8.0%
France
21.0%
Application 1: UK Tourist
Expenditure in Western Europe
• Objectives:
– To investigate UK tourists’ expenditure in Western
Europe
– To explore the relationships among key
destinations
– To compare forecasting performance among
different AIDS models
• Methods:
– Static LAIDS, EC-LAIDS, TVP-LR-LAIDS, TVP-ECLAIDS
Key Findings: Substituion
• Substitution pairs:
–
–
–
–
France and Spain
France and Portugal
Portugal and Italy
Portugal and Greece
• Less substitutable  more competitive!
Key Findings: Forecasting Performance
Table 1. Overall Ex Post Forecast Accuracy of LAIDS Models
Forecasted
Measure
Variable
Level
variables
Differenced
variables
Average
ranking
U-FP-LRLAIDS
H&S-FPLR-LAIDS
U-FP-ECLAIDS
H&S-FP- U-TVP-LR- U-TVP-ECEC-LAIDS
LAIDS
LAIDS
MAPE
0.140 (5)
0.176 (6)
0.115 (3)
0.119 (4)
0.111 (1)
0.112 (2)
RSMPE
0.202 (5)
0.208 (6)
0.159 (3)
0.162 (4)
0.145 (1)
0.155 (2)
MAE
7.943 (5)
8.507 (6)
4.765 (3)
3.124 (1)
7.696 (4)
3.696 (2)
RSME
9.862 (5)
10.063 (6)
5.812 (3)
4.471 (1)
9.369 (4)
4.950 (2)
5
6
3
2.5
2.5
2
Notes: The upper half of the table refers to the forecasts of levels variables, and the lower
to differenced variables. The unit of the figures in the lower half of the table is 10-3. Values
in brackets are ranks.
Application 2: Hong Kong Tourist
Expenditure Analysis
• Objective
– To analyse and compare different source markets’
tourism consumption behaviours in Hong Kong
• Four tourist expenditure categories:
– Shopping, hotel accommodation, meals outside hotels,
and other items
• Eight main source markets are analysed separately:
– Mainland China, Taiwan, Japan, Singapore, South Korea,
Australia, UK and USA.
• Methods: EC-LAIDS, TVP-EC-LAIDS
References: Wu , Li and Song (2011; 2012)
Tourist Expenditure Distribution
Tourist Expenditure Distribution
Tourist Expenditure Distribution
Expenditure Elasticities
Shopping
1.8
Hotels
Meals
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
UK
USA
Australia
Japan
Singapore
Korea
Taiwan
Mainland
China
Cross-Price Elasticities:
Substitution Effects
Source Market
UK
USA
Australia
Japan
Singapore
Korea
Taiwan
Mainland China
Shopping-Hotels
X
X
X
X
X
X
X
Hotels-Meals
X
X
X
X
Application 3: Hong Kong’s
Destination Competitiveness Analysis
• Objective
– To examine how competitive is Hong Kong in
comparison to its neighbouring competitors as
regarded by various key source markets
• Key competitors of Hong Kong:
– Singapore, Macau, Korea, Japan, Taiwan
• Key source markets:
– Mainland China, Japan, Taiwan, the UK and the
USA
• Method: EC-LAIDS
Reference: Song, Li and Cao (2011)
Key Findings: Substitution between
Hong Kong and Its Competitors
Short-Run Cross-Price Elasticities
Macau-Hong Kong
Australia
China
1.842***
3.107**
Japan
Taiwan
0.336**
0.305***
UK
USA
Singapore-Hong Kong 0.396**
Korea-Hong Kong
0.279***
0.133*
• Hong Kong’s competition with Macau focuses on the
Chinese market
• Stronger competition with Korea; product
diversification is important
• Non-price competition with Singapore
Future Research Directions
• To examine the ex ante forecasting performance
of EC-LAIDS and TVP-EC-LAIDS
• To develop structural time series (STS) LAIDS
and STS-TVP-LAIDS to model seasonal demand
• To develop non-linear dynamic AIDS models and
examine their forecasting performance
• To use time-series micro data (domestic or
international tourist surveys) for AIDS modelling
• To develop tourism price indexes and replace
CPIs to measure tourism prices
Key References
•
•
•
•
•
•
Li, G., H. Song and S. F. Witt (2004). Modelling Tourism Demand: A
Dynamic Linear AIDS Approach. Journal of Travel Research, 43(2):
141-150.
Li, G., H. Song and S.F. Witt (2005). Time Varying Parameter and
Fixed Parameter Linear AIDS: An Application to Tourism Demand
Forecasting. International Journal of Forecasting, 22 (1): 57-71.
Li, G., H. Song, Z. Cao (2011). Evaluating Hong Kong’s
Competitiveness as an International Tourism Destination from the
Economic Policy Perspective. Paper presented at the Advancing the
Social Science of Tourism conference, Guildford, UK.
Song, H., S.F. Witt and G. Li (2009). The Advanced Econometrics of
Tourism Demand. London: Routledge.
Wu, D. C., G. Li and H. Song (2011). Analyzing Tourist
Consumption: A Dynamic System-of-Equations Approach, Journal of
Travel Research, 50(1): 46–56.
Wu D.C., G. Li and H. Song (2012). Economic Analysis of Tourism
Consumption Dynamics: A Time-varying Parameter Demand
System Approach. Annals of Tourism Research, 39 (2): 667-685.
Thank you!
Dr Gang Li
Email: g.li@surrey.ac.uk