AIDS Models for Tourism Demand Modelling and

ForecastingGang Li

Reader in Tourism EconomicsSchool 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 single-equation 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 TVP-EC-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

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:

x/P: real total expenditure,

ui~N(0,2): the normal disturbance term.

(1) )/log(log ij

ijijii uPxbpaw

(2) loglog2

1loglog 0

i i jjiijii pppaP

Linear Approximation--LAIDS

• Replacing the price index P with Stone’s (geometric) price index (P*):

• Static LAIDS:

(3) log*log i

ii pwP

(4) *)/log(log ij

ijijii uPxbpaw

Theoretical Restrictions

• Adding-up:

– It implies all budge shares sum to unity.

• Homogeneity:

– It implies he absence of money illusion: a proportional change in all prices and expenditure does not affect the quantities purchased.

and ,01

n

iij

n

iib

1

0

0, ijj

i

Theoretical Restrictions

• Symmetry:

– 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.

, ,ij ji i j

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:

• Uncompensated price elasticity: given total expenditure (x) and any other prices held constant

• Compensated price elasticity: assuming real expenditure (x/P) keeps constant

where =1 for i=j; =0 for ij.

(6) ji

i

i

ijijij w

w

b

w

(7) *j

i

ijij wwij

ij

(5) 1i

iix w

b

ij

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 short-

run 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

is the estimated residual term from the static (long-run) AIDS model.

(8) *)/log(log 1 iitj

ijijii uPxbpaw

1jt

Fixed-Parameter vs Time-Varying-Parameter LAIDS Models

•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).

(8) *)/log(log 1 iitj

ijijii uPxbpaw

Methodological Developments:TVP-EC-LAIDS

• The system is specified in a state space form:

- Signal equation:

(9) *

loglog ,,,,1,,, tit

tti

jtjtijtittiti P

xbpaw

- State equations (specified as random walks):

ttiti aa 1,, , ttt 1 , ttijtij 1,, , (10) 1,, ttiti bb

- 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 PortugalSource: 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)

Others30.5%

Spain29.1%

Portugal4.3%

Italy7.2%

Greece8.0%

France21.0%

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-EC-

LAIDS

Key Findings: Substituion

• Substitution pairs:– France and Spain – France and Portugal – Portugal and Italy – Portugal and Greece

• Less substitutable Less substitutable more competitive! more competitive!

Key Findings: Forecasting Performance

Forecasted Variable

MeasureU-FP-LR-

LAIDSH&S-FP-

LR-LAIDSU-FP-EC-

LAIDSH&S-FP-

EC-LAIDSU-TVP-LR-

LAIDSU-TVP-EC-

LAIDS

Level variables

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)

Differenced variables

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)

Average ranking 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.

Table 1. Overall Ex Post Forecast Accuracy of LAIDS Models

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

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

UK USA Australia Japan Singapore Korea Taiwan MainlandChina

Shopping Hotels Meals

Expenditure Elasticities

Cross-Price Elasticities: Substitution Effects

Source Market Shopping-Hotels Hotels-Meals UK X X USA X Australia X Japan X X Singapore X Korea X Taiwan X Mainland China 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-LAIDSReference: Song, Li and Cao (2011)

Key Findings: Substitution between Hong Kong and Its Competitors

  Australia China Japan Taiwan UK USA  

Macau-Hong Kong 1.842*** 3.107**  

Singapore-Hong Kong 0.396**  

Korea-Hong Kong 0.279*** 0.336** 0.305*** 0.133*  

Short-Run Cross-Price Elasticities

• 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