Nonstationary panel data methods applied on a winter tourism demand model

8/8/2019 Nonstationary panel data methods applied on a winter tourism demand model

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Nonstationary panel data methods

applied on a winter tourism demand model

Franz Eigner

August 2009

University of Vienna

UK Advanced Econometrics

with Prof. Costantini

Table of contents

1. Introduction.........................................................................................................................................................................1

2. Winter tourism demand model...................................................................................................................................1

3. Panel cointegration tests and estimations .............................................................................................................2

3.1. Preliminary considerations..................................................................................................................................2

3.2. Panel unit root tests ................................................................................................................................................2

3.3. Cointegration tests...................................................................................................................................................3

3.4. Estimation table ........................................................................................................................................................4

4. Concluding remarks.........................................................................................................................................................4

5. References............................................................................................................................................................................5


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1. IntroductionIn this report, methods for nonstationary panel data are applied on a winter tourism demand model for Austrian ski

destinations. Assuming crosssection independence, cointegrating relationships are employed and estimated by OLS,fully modified OLS (FMOLS) and dynamic OLS (DOLS). Panel cointegration analyses are made with the statistical

software GAUSS (Aptech Systems, 2001), using the packages Coint 2.0 by Ouliaris and Phillips, NPT 1.3 (Kao/Chiang,

2002) and CNPT by Hlouskova and Wagner.

2. Winter tourism demand model

The winter tourism demand model is applied for N=20 ski destinations in Austria for the period 19732006 (T=34). 1

Winter tourism demand is measured by the number of overnight stays (NIGHTS), which is assumed to depend on

relative purchasing power (PP) and income (GDP) of the tourist countries and on the climate variable snow (SNOW),

measuring the number of days of snow cover. Thus, the tourism demand model follows a typical neoclassical demand

function, using prices and income variables, together with a climate variable. NIGHTS, GDP and PP enter the equation

with their natural logarithm. Due to the loglog specification, coefficients of GDP and PP can be interpreted as income

elasticity and price elasticity respectively. Panel time series are plotted in Figure 1 using STATA (StataCorp, 2007).

Figure 1: Paneldata line plots for panel time series.

1 The original dataset is described in Toeglhofer and Prettenthaler (2009). It consists of a crosssection panel with 185 ski

destinations for the period 19732006. The original dataset could not pass nonstationarity tests for panels. In order to findnonstationarity for all time series in the panel variables, the dataset was reduced to the 20 largest ski destinations in Austria. Smallerdataset of 5, 6 or 10 destinations were also considered. They fulfilled nonstationarity assumptions, but no cointegratingrelationships could be detected.


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3. Panel cointegration tests and estimations

3.1. Preliminary considerations

Regressions based on nonstationary time series typically suffer i.a. from potential spurious regression problems.

Instead of differencing the data set to make them stationary, hence losing longterm information of the data, one could

improve estimation results by making use of cointegration relationships, for the case they exist.

Three estimators for nonstationary panel regressions are applied in this study. These are OLS, fully modified OLS (FM

OLS) and dynamic OLS (DOLS). Whereas OLS estimates are generally biased due to endogeneity in variables, FMOLS

accounts for both serial correlation and endogeneity in the regressors that results from the existence of a cointegrating

relationship. It corrects the dependent variable using the longrun covariance matrices for the purpose of removing

the nuisance parameters and applies the usual OLS estimation method to the corrected variables. (Kao/Chiang/Chen,1999). The DOLS estimator also corrects for the nuisance parameter, but with including lead and lag terms. Despite

super consistency of FMOLS, DOLS and also for OLS estimators, Kao and Chiang (1998) found that a substantial

estimation bias might remain for moderate sample sizes. However they suggest that DOLS estimations should be most

promising in estimating cointegrated panel regressions.

Before univariate unit root tests are applied, their weaknesses should be reminded in advance. Due to their low power

in general, they are not able to distinguish a unit root from a near unit root process. Moreover they may erroneously

identify a trend stationary process as a unit root, especially in the case where the stochastic portion of the trend

stationary process has sufficient variance. This problem may be relevant in this study due to the usage of GDP, which istypically considered as trendstationary. However one can increase the power of univariate unit root tests substantially

by using a longer data span, e.g. annual data as in this study.

3.2. Panel unit root tests

At first (independent) unit root tests have to be applied on each panel variable. All unit root tests were examined with

two lagged first difference terms in the ADF equation, including a constant and a trend. Obtained pvalues are given in

table 1.

Table 1: Panel unit root tests.

LLC IPS MW

log(NIGHTS) 1.00 0.03 0.12

SNOW 0.85


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All three unit root tests check the null hypothesis of panel time series integrated of order one against the alternative of

stationarity. This paper will follow unit root tests with homogenous alternative hypothesis, which are LLC and MW.

Even though the ones with heterogenous alternative hypothesis like IPS are more flexible, their results may contrast

with the homogenous alternative hypothesis in the panel cointegration test, assuming a common cointegrating vector

for all destinations.

As can be seen in table 1, the null hypothesis is not rejected for log(NIGHTS) and log(PP). The rejection of the null

hypothesis for SNOW may indicate that at least some of its time series are stationary, making SNOW inadequate for

cointegration analyses. Surprisingly, the null hypothesis of log(GDP) is also rejected according to MW 2. This results

contradicts with the graphical analysis in figure 1, which strongly supports GDP to be integrated of order one, therefore

consisting of a unit root. Examining unit root tests with the untransformed levels of GDP (not taking the logarithm), one

actually obtains the result of GDP being integrated of order one. Nonetheless, the logarithm of GDP will be used in

further analyses due to interpretation reasons.

A disadvantage of these panel tests is that they do not provide explicit guidance concerning the size of the fraction of

(non)stationary time series. At least the data set for this study has a moderately large time dimension over a long

(annual) time period, which should lead to unit root tests with higher power than for data sets containing observations

over a short time period. However one should bear in mind that independence between the unit roots is assumed in

order to keep analyses simple, although this assumption may be implausible.

3.3. Cointegration tests

Cointegration tests are conducted on three estimation equations, consisting of either one of the independent variables

(GDP/PP) or both. For instance, equation (1), using both independent variables as regressors, is given as:

log( NIGHTS ) it = 1 log(GDP ) it + 2 log( PP ) it + i + it (1)

where

it denotes the white noise disturbance term. Individual fixed effects are included by

i , capturing

heterogeneity between the destinations.

The presence of cointegration of log(NIGHTS) with log(GDP), log(PP) or both is confirmed by testing for a unit root in

the residuals of the LSDV regression for each of the three equations. Two homogenous tests suggested by Kao (1999),

which are the Dickey Fuller (DF) panel cointegration test and its augmented version (ADF), are assessed. Obtained p

values of the latter are given in Table 2.

Table 2: ADF panel cointegration test table for all three equations.

Equation number Regressors p-value

(1) log(GDP), log(PP) 0.01(2) log(GDP) 0.03(3) log(PP)


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With the null hypothesis of no cointegration, test results suggest the presence of cointegration at a significance level of

5% for all equations. Consequently panel regressions can be estimated accounting for these cointegration relationships.

3.4. Estimation table

Table 3: Estimation table for log(NIGHTS) using OLS, FMOLS and DOLS.

OLS FM-OLS DOLS(1) (2) (3) (1) (2) (3) (1) (2) (3)

log(GDP) 0.39(10.6)

0.39(10.3)

- 0.38(9.4)

0.38(9.2)

- 0.31(6.5)

0.34(7.1)

-

log(PP) 0.37(5.2)

- 0.50(4.5)

0.39(12.6)

- 0.54(11.2)

0.06(1.8)

- 0.86(15.6)

adjusted R_squared 0.63 0.61 0.03 0.61 0.58 0.04 0.24 0.27 0.11

Notes:N=20, T=34; estimated cointegration equation include fixed effectst-statistics are given in parenthesesFM-OLS with averaged correction factors (Kao and Chiang, 2000)DOLS (Mark and Sul, 2001); 2 lags and leads for all variables were chosen

Given the superiority of the DOLS over the FMOLS as suggested by Kao and Chiang, one obtains an income elasticity of

0.31, and a price elasticity of 0.06. Price elasticity is therefore inelastic and has an unexpected positive sign. However

purchasing power probably should not be considered as an important component in winter tourism demand in Austria.

Not only due to statistical considerations, which indicate that the coefficient is small and only significant at the 10

percent significant level, but also due to economic reasons, concerning the high amount of German tourists in the data,

having in common a similar price evolution and a fixed exchange rate regime. Though one can assume that theinfluence of this variable will increase in the future, due to the increasing amount of Eastern European tourists. The

estimated inelastic income elasticity also does not correspond with the expectations of tourism demand as a luxury

good and emphasizes the need for extensions for the current model.

4. Concluding remarks

Extensions of this study should definitely cope with crosssection dependence in the panel time series, which is likely to

be present due to the common economic area for the ski destinations. Accounting for crosssection dependence will

necessarily consider the possibility of cointegration between the panel variables within groups as well as across

groups, due to unobserved I(1) common factors, affecting some or all the variables in the panel.

One could further follow Phillips (1993), who provides a general framework which makes it possible to study the

asymptotic behaviour of FMOLS in models with full rank I(1) regressors, models with I(1) and I(0) regressors, models

with unit roots, and models with only stationary regressors. Such a framework would enable to consider the use of

FM regression in the context of vector autoregressions (VAR's) with some unit roots and some cointegrating relations,

which is therefore a multivariate extension, accounting for the underlying structure between the time series.


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5. References

Chiang, MH. and Kao C. (2002). Nonstationary Panel Time Series Using NPT 1.3 A User Guide, Center for Policy

Research, Syracuse University.

Im, Kyung So, Pesaran, M. Hashem, Shin and Yongcheol. (2003). Testing for Unit Roots in Heterogeneous Panels. Journal

of Econometrics, 115, 5374. Earlier version available as unpublished Working Paper, Dept. of Applied

Economics, University of Cambridge, Dec. 1997.

Kao, C., Chiang, M.H., (1998). On the Estimation and Inference of a Cointegrated Regression in Panel Data, Working

Paper, Center for Policy Research, Syracuse University.

Kao, C. (1999). Spurious regression and residualbased tests for cointegration in panel data, Journal of Econometrics 90,

pp. 144.

Kao, C., Chiang, M.H. and Chen, B. (1999). International R&D Spillovers: An Application of Estimation and Inference in

Panel Cointegration, Center for Policy Research Working Papers 4, Center for Policy Research, Maxwell School,

Syracuse University.

Kao, C. and Chiang, M.H. (2000), On the estimation and inference of a cointegrated regression in panel data, in Baltagi,

B.H. (Ed.) Nonstationary Panels, Panel Cointegration and Dynamic Panels, pp. 179222, Elsevier, Amsterdam.

Levin, Andrew, Lin, ChienFu and ChiaShang James Chu. (2002). Unit Root Tests in Panel Data: Asymptotic and Finite

Sample Properties. Journal of Econometrics, 108, 124.

Maddala, G.S. and Wu, Shaowen. (1999). A Comparative Study of Unit Root Tests With Panel Data and A New Simple

Test', Oxford Bulletin of Economics and Statistics 61, 631652.

Mark, Nelson C. and Sul, Donggyu, (2001). Nominal exchange rates and monetary fundamentals: Evidence from a small

postBretton woods panel, Journal of International Economics, Elsevier, vol. 53(1), pages 2952, Febr.

Phillips, Peter C.B. (1993). Fully Modified Least Squares and Vector Autoregression, Cowles Foundation Discussion

Papers 1047, Cowles Foundation, Yale University.

StataCorp. (2007). Stata Statistical Software: Release 10. College Station, TX: StataCorp LP.

Toeglhofer, C. and Prettenthaler, F. (2009). Estimating climatic and economic impacts on tourism demand in Austrian

skiing areas. Graz: Wegener Center for Climate and Global Change.

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Nonstationary panel data methods applied on a winter tourism demand model