Instrumental Variable Estimation of Tourism Demand: Comparing Level versus Change-rate Models

Transcription

1 Inernaional Review of Business Research Papers Vol. 9. No. 3. March 203 Issue. Pp Insrumenal Variable Esimaion of Tourism Demand: Comparing Level versus Change-rae Models Chung-ki Min Tourism demand is highly sensiive o economic flucuaions. If variables are subjec o such ime-specific effecs, lagged variables in dynamic models can cause he OLS esimaion o be biased. This sudy esimaes ourism demand wih conrolling for imespecific effecs using insrumenal variables. The empirical resuls show ha he models of change rae variables produce more significan and reliable esimaes han he ones of level variables. I is because he level variables are nonsaionary and also because he insrumenal variables consruced by he level variables are no exogenous and canno solve he endogeneiy problem caused by he ime specific effecs. Field of Research: Economerics. Inroducion Tourism demand is highly sensiive o economic flucuaions, in paricular during global economic crisis. If variables are subjec o such ime-specific effecs, heir lagged variables can bias esimaion of dynamic models; dynamic relaions are a key componen in causaliy ess and are also included in modeling ourism demand. Since he imespecific effecs are no observable and canno be separaed from observed variables, we need o employ appropriae esimaion mehods o conrol for hem. Treaing he lagged ime-specific effecs as measuremen errors in explanaory variables, his sudy uses insrumenal variables from he lieraure on measuremen errors. In modeling ourism demand many sudies in he lieraure use change-rae variables o accoun for nonsaionariy in ime-series. Esimaion could be negaively affeced if nonsaionary level-variables are included in a model. Afer we examine wheher he level variables are nonsaionary, we evaluae he level-variable models versus he changerae models. This sudy repors ha he models of change-rae variables produce more significan and reliable resuls han he ones of level variables because he level-variables are nonsaionary. Anoher reason for he poor level-variable resuls is ha he insrumenal variables consruced by he level variables are no exogenous and canno solve he endogeneiy problem caused by he lagged ime specific effecs. The empirical resuls also show ha he generalied mehod of momens (GMM) esimaion produces more Deparmen of Economics, Hankuk Universiy of Foreign Sudies, Seoul, Korea. cmin@hufs.ac.kr. This work was suppored by he Hankuk Universiy of Foreign Sudies Research Fund.

2 significan esimaes for ourism demand han he wo-sage-leas-squares mehod (2SLS). I is because here are several oulying observaions. The 2SLS mehod assumes homoscedasic disurbances and hus applies equal weighs o all observaions. In conras, he GMM accouns for heeroscedasiciy and can reduce he effecs of hose oulying observaions. The following secion formulaes a model for ourism demand and explains an insrumenal variable esimaion which can correc a possible bias in he Grangercausaliy es. Secion 3 repors he esimaion resuls for annual and quarerly daa. Conclusions are presened in secion Models and Mehodology 2. Dynamic Models and Time-Specific Effecs The Granger-causaliy is defined as a relaionship beween a variable and he lagged values of oher variables. Thus, he causaliy es uses an auoregressive model which is a reduced-form equaion of srucural equaions. There are many sudies in he ourism lieraure which es he causaliy beween ourism demand and economic growh. Nowak e.al. (2007) analye ime series daa for Spain, Bonham e al. (2009) for Hawaii, Drisakis (2004) for Greece, Kaircioglu (2009) for Turkey, Mishra e al. (20) for India, among ohers. These sudies repor empirical resuls supporing he ourism-led economic growh hypohesis for each seleced counry. To esimae he ourism demand, his sudy employs a dynamic model wih focusing on a causaliy from economic growh o ourism demand. For such case of wo variables, an auoregressive model of order one is expressed as % ARR % GDP % ARR u () 2 where % ARR, a measure of ourism demand, is he (percenage) change rae of foreign ouris arrivals during ime period, and % GDP is he (percenage) GDP change rae and is used as a measure of economic growh. A null hypohesis of 0 implies ha he economic growh (% GDP ) does no Granger-cause he ourism demand (% ARR ). The OLS mehod is ofen used for esimaing he auoregressive models, bu he OLS esimaors become biased if any of he lagged variables on he righ-hand side are correlaed wih he disurbances, called he endogeneiy problem. Every ime period he economy experiences unexpeced changes and almos all economic variables are influenced by he changes. The effecs on economic variables of he changes in each period, called ime-specific effecs, are merged ino he variables % ARR and % GDP in Eq.(). A problem arises in esimaing Eq.() since neiher hese ime-specific effecs nor he underlying variables % ARR and % GDP are 5

3 A G observed. Leing and denoe he ime-specific effecs for % ARR and % GDP, respecively, we can observe only he sum of he laen variables and heir corresponding ime-specific effecs. % ARR % GDP % ARR % GDP A G (2) As changes in each period are unexpeced, heir ime-specific effecs are independen beween periods. Therefore, hey are no associaed wih any dynamic relaionship. Insead, he dynamic relaionship holds only for he laen variables. Since ARR and % GDP % are no observable, however, we need o ransform Eq.() ino equaions expressed in observable variables. Subsiuing Eq.(2) for Eq.(), we obain % ARR and % GDP in % ARR u (3) % GDPx 2 % ARR where A G A 2 ; his is a funcion of curren and lagged ime-specific effecs. Noice ha he lagged ime-specific effecs are included no only in bu also in G A % ARR and % GDP. Thus, ignoring (or and ) biases he OLS esimaors due o he endogeneiy. This resuling bias belongs o he problem of measuremen errors in explanaory variables. This indicaes ha lagged ime-specific effecs need o be conrolled for in he esimaion of he dynamic model. If here are muliple observaions in each ime period, he ime-specific effecs can be conrolled for by he wihin-period ransformaion. However, his approach canno be applied o he single ime series in his sudy. Alernaively, we employ an insrumenal variable (IV) esimaion mehod. 2.2 Insrumenal Variable Esimaion Dagenais and Dagenais (997) propose an insrumenal variable esimaor for linear regression models wih errors in explanaory variables. This esimaor uses insrumenal variables obained from sample momens of order wo and hree. The momens are consruced by he endogenous explanaory variables which conain measuremen errors bu do no require any exraneous informaion. Such IVs are conemporaneous wih he endogenous explanaory. Consider he following regression model for ime-series observaions from period o T. Y X (4) where X is a T K marix of explanaory variables measured wih error. Since X is no observable, we use observable variables X which include measuremen errors V. u 6

4 Y X ( u V ) X (5) T T where X X V. The higher momen esimaor for (, ' ) is derived using he following insrumenal variables. Z (,,, ), T x x, 2 7 x y, x x x 3x[ E( x' x / T ) I x x y 2x[ E( x' y / T ) I x y y x[ E( y' y / T ) I y y y 3y[ E( y' y / T )] 3 y y, K K K ], ] y{ [ E( x' x / T ) I K ] 2y[ E( y' x / T )], K ]}, (6) where he symbol designaes he Hadamard elemen-by-elemen marix muliplicaion operaor and ( x, y) corresponds o ( X, Y) in a mean deviaion form. As Z is orhogonal o as proven in Dagenais and Dagenais (997), we use Z as insrumen variables in he nex secion. These IVs are conemporaneous wih he endogenous variables. Using simulaed daa, Min (202) shows ha hese IVs correc a bias in a Granger-causaliy es. When here are exogenous explanaory variables, Lewbel (997) develops IVs which are higher momens of he endogenous variables and funcions of he exogenous variables. These IVs are also conemporaneous wih he endogenous variables. In addiion, Griliches and Hausman (986) sugges use of appropriaely lagged values of he relevan variables as insrumens, assuming ha he measuremen errors are serially uncorrelaed. 2.3 A Model for Tourism Demand Tourism demand is obviously influenced by many oher facors, no jus by lagged values of he variables included in he Granger-causaliy es. They include he cos of ravel, he cos of living of ouriss in he desinaion counry relaive o he origin counries, he cos of ravel o he compeing desinaions, he economic condiion in he origin and desinaion counries, ourism infrasrucure and poliical sabiliy, ec (Garin-Muno, 2006; Naude and Saayman, 2005; Song e al., 2003, among ohers). In his applicaion we focus on he cos of ravel among many possible facors. An exended model for ourism demand is where counry during period, and % ARR % GDPx % ARR % CPI % OIL (7) % CPI is he % change rae of consumer price index (CPI) in he desinaion % OIL is he % change rae of he crude oil price during period. Since hese added facors are measured in period, hey are no correlaed wih he lagged ime-specific effecs which cause a bias in he causaliy es. Thus, hese can be reaed as exogenous variables. 2 7

5 3. Daa and Esimaion Resuls 3. Daa The models in his sudy are esimaed using annual and quarerly daa abou he Hong Kong ourism. The daa period is from he firs quarer of 985 unil he fourh quarer of The arrival daa are colleced from Visior Arrival Saisics (published monhly) via hp://parnerne.hkb.com/; hese are used as a measure of ourism demand for Hong Kong. The daa on Hong Kong GDP and CPI are colleced from he IMF daabase and he daa on he crude oil price are from Energy Informaion Adminisraion. Table : ADF Tes of Non-Saionariy for he Level Variables Annual daa Variable ADF saisic p-value log ARR log GDP logcpi logoil Quarerly daa log ARR log GDP logcpi logoil The null hypohesis of he Augmened Dickey-Fuller (ADF) es is ha he variable concerned is non-saionary. This ADF es uses an auoregressive order of for he annual daa and 4 for he quarerly daa. 3.2 Change-Rae versus Level Variables We firs examine he saionariy of he variables. If a regression model includes nonsaionary variables, is esimaion resuls could be wrong. In Table he augmened Dickey-Fuller (ADF) es shows ha all of he four level variables are nonsaionary as he null of nonsaionariy is no rejeced wih large p-values. Figure also confirms he nonsaionariy wih growing rends. In conras, as shown in Figure 2, he firs-differenced variables of logarr and loggdp become saionary. In addiion, he change raes are free from quarerly effecs in he quarerly daa as he change raes are calculaed over he same quarer of he previous year. Therefore, our main models for he causaliy es and ourism demand use he firs-differences of logarihmic values, i.e., change-raes. 3 8

6 log(arrivals) log(gdp) Figure Plos of Level Variables (annual daa) %Ch(Arr). %Ch(GDP). Figure 2: Plos of Change-rae Variables (annual daa) The nonsaionariy is an asympoic issue and hus causes an esimaion problem for infiniely long ime series. However, he daa periods are 25 for he annual daa (985~2009) and 00 for he quarerly daa (985.I~2009.IV). Given hese finie-sied ime series he esimaion in his sudy migh no have he nonsaionariy problem of spurious resuls. One advanage of using level variables is ha level variables can keep he variaions in hem while change-rae variables lose much of he variaions because hey are calculaed as differences beween wo consecuive periods. If so, he levelvariable models can be esimaed more precisely wih smaller sandard errors. For comparison purpose his sudy also uses he level variables for esing he causaliy and esimaing ourism demand. 3.3 Esimaion Resuls: Annual Daa For he annual daa we have seleced he lag order of one afer applying a sequenial es; we sar wih a sufficienly large lag (e.g., 5) and es down o he righ lag order unil we rejec a null hypohesis ha he coefficiens on he las lag are joinly ero. For a 9

7 robusness check of he seleced lag order, we have also applied he Pormaneau es o examine wheher he residuals are auocorrelaed; his es suppors he seleced lag order by concluding ha he residuals are no auocorrelaed. Table 2 shows he esimaion resuls for he models wihou and wih exogenous variables, % CPI and % OIL. For he endogenous lagged variables % GDP and % ARR, heir higher momens suggesed by Dagenais and Dagenais (997) are used as insrumens. According o Griliches and Hausman (986), heir lag-wo variables (% GDP 2 and % ARR 2 ) can also be used as IVs. However, since he change rae variables are weakly auocorrelaed, he relevance of such lag-wo IVs is oo weak o produce reliable esimaes. In conras, he higher momens are conemporaneous wih he endogenous explanaory variables and are herefore more relevan as IVs. For boh models he GMM esimaes have smaller sandard errors han he OLS and 2SLS ones. I is because here are several oulying observaions, paricularly on he change rae of ouris arrivals (% ARR ) ; Figure 2 shows such observaions during years 988, 996, 997, 2003 and The OLS and 2SLS mehods assume homoscedasic disurbances and hus apply equal weighs o all observaions. In conras, he GMM accouns for heeroscedasiciy and can reduce he effecs of hose oulying observaions. As a resul, he Granger causaliy from % GDP o % ARR is significan only by he GMM esimaion. Table 3 shows he esimaion resuls for he models of he level variables. The sandard errors of he coefficien esimaes are smaller for he level-variable GMM han for he change-rae variable GMM in Table 2. I is because he level variables can keep he variaions in hem while he change-rae variables lose much of he wihin variaions because change raes are calculaed as differences beween wo consecuive periods. However, he higher-momen IVs of he level variables (log GDP and log ARR ) have a problem in heir exogeneiy. The over-idenifying resricions es rejecs he null hypohesis ha he higher-momen IVs are exogenous; he p-values are and Therefore, he esimaes for he level variables are inconsisen. 20

8 Table 2: Esimaion Resuls Using Change-rae Variables of Annual Daa % ARR 0 % GDP 2% ARR 3% CPI 4% OIL u Insrumenal Variables Higher momens of (% GDP, ARR ) % Higher momens of and Exogenous a) % CPI % OIL Esimaion mehod OLS 2SLS GMM OLS 2SLS GMM Coefficien for % GDP (0.590) (0.679) (0.300) (0.809) (.84) (0.987) % ARR (0.287) (0.296) (0.25) (0.349) (0.353) (0.307) Granger causaliy es b) Exogeneiy es c) % CPI (0.359) (0.446) (0.357) % OIL (0.55) (0.62) (0.40) p-value p-value a) I is assumed ha % CPI and % OIL are exogenous and do no need any insrumenal variables. b) This Granger-causaliy from % GDP o % ARR ess he null of H 0 : 0. c) This is o es wheher he IVs are exogenous (i.e., orhogonal o he srucural disurbances) and called an over-idenifying resricions es when he number of IVs exceeds he number of endogenous regressors. As he null hypohesis here is ha all IVs are exogenous, large p- values canno rejec he null. The symbols of, and aached o he coefficien esimaes indicae ha is coefficien is significanly differen from ero a he %, 5% and 0% levels, respecively. 2

9 Table 3: Esimaion Resuls Using Level Variables of Annual Daa log ARR 0 loggdp 2 log ARR 3 logcpi 4 logoil u Insrumenal Variables Higher momens of (% GDP, ARR ) % Higher momens of and Exogenous % CPI % OIL Esimaion mehod OLS 2SLS GMM OLS 2SLS GMM Coefficien for GDP log (0.545) (0.697) (0.327) (0.76) (0.950) (0.286) log ARR (0.27) (0.346) (0.55) (0.35) (0.390) (0.66) Granger causaliy es a) Exogeneiy es b) log CPI (0.258) (0.336) (0.02) log OIL (0.08) (0.30) (0.056) p-value <0.000 p-value a) This Granger-causaliy from loggdp o logarr ess he null of H0 : 0. c) This is o es wheher he IVs are exogenous (i.e., orhogonal o he srucural disurbances) and called an over-idenifying resricions es when he number of IVs exceeds he number of endogenous regressors. As he null hypohesis here is ha all IVs are exogenous, large p-values canno rejec he null. The symbols of, and aached o he coefficien esimaes indicae ha is coefficien is significanly differen from ero a he %, 5% and 0% levels, respecively. 3.4 Esimaion Resuls: Quarerly Daa For he quarerly daa he lag order of four has been seleced by a sequenial es. The lag order of four is expeced o accoun for he quarerly seasonal effecs. The Pormaneau es confirms ha he residuals from he lag order of four are no auocorrelaed. 22

10 Table 4: Esimaion Resuls Using Change-rae Variables of Quarerly Daa % ARR % GDP Insrumenal Variables % ARR 0 % GDP % ARR % GDP % ARR Higher momens of (% GDP S, % ARR S ) 3 % ARR 4 % GDP CPI % CPI OIL % OIL u Higher momens of and Exogenous % CPI % OIL Esimaion mehod OLS 2SLS GMM OLS 2SLS GMM Coefficien for GDP % % 2 (0.996) (.023) (0.46) (.052) (.092) (0.52) GDP % 3 (.447) (.467) (0.203) (.444) (.468) (0.20) GDP (.46) (.468) (0.257) (.459) (.472) (0.239) GDP (0.946 (0.945) (0.43) (0.983) (0.984) (0.33) % 4 % ARR (0.) (0.2) (0.038) (0.0) (0.2) (0.043) ARR % 2 (0.5) (0.6) (0.00) (0.5) (0.6) (0.00) ARR % 3 (0.20) (0.20) (0.02) (0.20) (0.2) (0.0) ARR % 4 (0.) (0.2) (0.035) (0.) (0.3) (0.040) % CPI (0.389) (0.388) (0.080) % OIL (0.067) (0.068) (0.00) Granger causaliy es b) p-value < <0.000 a) This Granger-causaliy from % GDP o % ARR ess he null of H 0 : The symbols of, and aached o he coefficien esimaes indicae ha is coefficien is significanly differen from ero a he %, 5% and 0% levels, respecively. 23

11 Table 5: Esimaion Resuls Using Level Variables of Quarerly Daa log ARR loggdp log ARR 3 Insrumenal Variables Esimaion mehod 0 3 log ARR 4 loggdp CPI loggdp 3 logcpi Higher momens of (% GDP S, % ARR S ) OIL 3 loggdp 4 4 log ARR logoil (quarer dummies) u log ARR Higher momens of and Exogenous logcpi logoil OLS 2SLS GMM OLS 2SLS GMM Coefficien for GDP log (0.909) (.346) (0.247) (0.923) (.64) (0.447) loggdp (.286) (.95) (0.347) (.260) (.68) (0.564) loggdp (.268) (.972) (0.44) (.239) (.632) (0.522) log 4 GDP (0.762) (.96) (0.244) (0.780) (.00) (0.329) 2 2 log ARR (0.28) (0.70) (0.048) (0.29) (0.50) (0.064) log 2 ARR (0.30) (0.7) (0.09) (0.30) (0.5) (0.064) ARR log 3 (0.28) (0.68) (0.022) (0.28) (0.47) (0.029) ARR log 4 (0.099) (0.58) (0.043) (0.24) (0.45) (0.052) log CPI (0.68) (0.24) (0.063) log OIL (0.073) (0.087) (0.030) Granger causaliy es a) p-value < <0.000 Noe: The quarer dummy variables are included for all models, bu heir coefficien esimaes are no repored in his able. The symbols of, and aached o he coefficien esimaes indicae ha is coefficien is significanly differen from ero a he %, 5% and 0% levels, respecively. a) This Granger-causaliy from loggdp o logarr ess he null of H 0. 0 : Similarly o he annual daa, Tables 4 and 5 show ha he GMM produces more significan esimaes wih smaller sandard errors han he OLS and 2SLS. Therefore, he GMM suppors he causaliy from GDP o ARR more significanly. 24

12 The sandard errors are bigger for he level-variable models han he change-rae models. This is because he level variables are highly auocorrelaed (i.e., nonsaionary) and he variance of he disurbance grows as he ime period increases. This growing variance will inflae he sandard errors, more for he quarerly daa as here are four imes as many ime periods. This inflaing effec has overridden he decreasing effec by more variaions conained in he level variables han in he change-rae variables. 4. Summary and Conclusions This sudy esimaes ourism demand wih conrolling for ime-specific effecs. If variables are subjec o ime-specific effecs, heir lagged variables can bias dynamic relaions in esing a causaliy and esimaing ourism demand. Since he ime-specific effecs are no observable and canno be separaed from observed variables, hey have o be accouned for by appropriae esimaion mehods. Treaing he lagged ime-specific effecs as measuremen errors in explanaory variables, his sudy uses insrumenal variables. The empirical resuls suppor use of he change rae variables because he level variables in his sudy are nonsaionary and heir resuls are affeced by he nonsionariy. In addiion, he insrumenal variables consruced by he level variables are no exogenous and canno solve he endogeneiy problem caused by he lagged ime specific effecs. The discussion in his sudy will be useful for esing causaliy of economic variables and for esimaing dynamic relaions, paricularly when he variables involved are sensiive o ime-specific effecs. In addiion, regarding a search for insrumenal variables, Lewbel (997) develops an alernaive se of insrumenal variables using higher momens of endogenous variables and funcions of exogenous variables. Use of hese insrumenal variables is planned for fuure work. Endnoes If he order of auoregressive models is no large enough, he disurbances will be auocorrelaed, leading o inconsisen esimaes. In his sudy we es for auocorrelaion of he disurbances as a way of supporing he chosen lag order. 2 When we rea % CPI and % OIL as endogenous variables and use IVs of heir higher momens, he esimaion resuls are qualiaively unchanged and are no repored in he following ables. 3 The quarerly variables show he same resuls abou he nonsaionariy es and heir firs-differences are hus used for he main models. References Bonham, C, Gangnes, B and Zhou, T 2009, Modeling ourism: a fully idenified VECM approach, Inernaional Journal of Forecasing, Vol. 25, pp Dagenais, M and Dagenais, DL 997, Higher momen esimaors for linear regression models wih errors in he variables, Journal of Economerics, Vol. 76, pp

13 Drisakis, N 2004, Tourism as a long-run economic growh facor: an empirical invesigaion for Greece using causaliy analysis, Tourism Economics, Vol. 0, No. 3, pp Garin-Muno, T 2006, Inbound inernaional ourism o Canary Islands: a dynamic panel daa model, Tourism managemen, Vol. 27, pp Griliches, Z and Hausman, JA 986, Errors in variables in panel daa, Journal of Economerics, Vol. 3, pp Kaircioglu, ST 2009, Revisiing he ourism-led-growh hypohesis for Turkey using he bounds es and Johansen approach for coinegraion, Tourism Managemen, Vol. 30, pp Lewbel, A 997, Consrucing insrumens for regressions wih measuremen error when no addiional daa are available, wih an applicaion o paens and R&D, Economerica, Vol. 65(5), pp Min, C 202, Time-specific effecs and a bias in he Granger-causaliy es, World Review of Business Research, Vo. 2(3), pp Mishra, PK, Rou, HB and Mohapara, SS 20, Causaliy beween ourism and economic growh: evidence from India, European Journal of Social Sciences, Vol. 8 (4), pp Naude, WA and Saayman, A 2005, Deerminans of ouriss arrivals in Africa: a panel daa regression analysis, Tourism Economics, Vol., No. 3, pp Nowak, JJ, Sahli, M and Cores-Jimene, I 2007 Tourism, capial good impors and economic growh: heory and evidence for Spain, Tourism Economics, Vol. 3, pp Oh, CO 2005, The conribuion of ourism developmen o economic growh in he Korean economy, Tourism Managemen, 26, Song, H, Wong, KKF and Chon, KKS 2003, Modeling and forecasing he demand for Hong Kong ourism, Hospialiy Managemen, Vol. 22, pp