< O5 -Economywide Country Studies < O -Economic Development, Technological Change, and Growth, O40

Keywords: Tourism, Economic Growth, Panel Data. JEL Classification: L83, O40, O50

On Average, tourism-specialized countries grow more than others. This is not consistent with the core of modern economic growth theory that suggests that economic growth is linked to sectors with high-tech intensity and large scale. In this paper, we use appropriate panel data methods to study the relationship between tourism and economic growth. In general we show that tourism is a positive determinant of economic growth both in a broad sample of countries and in a sample of poor countries. However, contrary to previous contributions, tourism is not more relevant in small countries than in a general sample.

Introduction

Recently, researchers have been interested in the relationship between tourism specialization and economic growth, empirically supporting a direct effect from the first to the second. However this seems to be an inconsistent fact with economic theory as, in particular, endogenous growth theory suggests that economic growth is linked with: (1) sectors with high intensity in R&D and thus high productivity; (2) large scale. In fact, these features are not shared by tourism-intensive countries. On the contrary, the tourism sector is thought not to be a technologically intensive one and countries specialized in tourism are in general small countries (see for instance Easterly and Kraay, 2000 and [START_REF] Lanza | Why are Tourism Countries Small and Fast Growing[END_REF]. Some explanations have appeared linked to a terms-of-trade effect [START_REF] Brau | How Fast Are The Tourism Countries Growing? The Cross Country Evidence[END_REF][START_REF] Copeland | Tourism, Welfare and De-industrialization in a Small Open Economy[END_REF]) and a natural resources abundance approach (Lanza and[START_REF] Lanza | Why are Tourism Countries Small and Fast Growing[END_REF][START_REF] Sinclair | Tourism and Economic Development: a Survey[END_REF]). The first one supports that a tourism boom tends to increase demand for non-tradable goods and this improves terms of trade which increase growth and welfare. The second argues that tourism is linked with the existence of renewable resources (beaches, mountains, rivers, historical and cultural heritage). Thus countries with relative abundance of natural, cultural or historical resources have comparative advantage in specializing in tourism.

An increasing number of articles have been analyzing the relationship and causality between tourism and the economic growth rate both in specific countries (e.g. [START_REF] Ghali | Tourism and Economic Growth: An Empirical Study[END_REF], for Hawaii; Balaguer and Jordá, 2002, for Spain; [START_REF] Durbarry | Tourism and Economic Growth: the case of Mauritius[END_REF], for Mauritius and Gunduz and Hatemi-J, 2005 for Turkey) and in broader samples (e.g. Eugenio-Martin et al., 2004 for Latin America). The former used standard time-series methods to conclude that tourism had fostered growth in the specific countries studied, while the latter used a dynamic panel data estimator -the differenced GMM from [START_REF] Arellano | Some Tests of Specification for Panel Data: Monte Carlo evidence and an Application to Employment Equations[END_REF] -to provide evidence that the increasing number of tourists per capita caused more economic growth in the low and medium-income countries of Latin America. The test done by [START_REF] Brau | How Fast Are The Tourism Countries Growing? The Cross Country Evidence[END_REF] for a broad cross-section of countries is not robust to the possible existence of endogeneity of tourism. Tourism may be correlated with human capital, geographic or cultural features, for instance, and may not be an independent determinant of growth.

Thus, having data for different countries, panel data methods are the correct approach to deal with possible endogeneity of tourism. However, due to the persistence of the output series, [START_REF] Temple | GMM Estimation of Empirical Growth Models[END_REF] suggest that for a broad cross-section of countries, one should use the System-GMM estimator from [START_REF] Blundell | Initial Conditions and Moment restrictions in Dynamic Panel Data Models[END_REF].

The fact is that, on average, tourism-specialized countries grow more than others.

The next Table shows average growth rates between 1980 and 2002 for all countries for which data are available and for subsets of countries specialized in tourism. Data are from a panel of countries through 5 five-years periods: 1980-84, 1985-89, 1990-94, 1995-99 and 2000-2002 and show that there is a clear positive correlation between tourism specialization and economic growth. as previous contributions argued that these sub-samples of countries should benefit more from tourism than the average country.

In Section 2, we present data, method and variables. In Section 3, we present the results. Section 4 concludes and motivates future research.

2 Data and Methods

Specification and Methods

We have used panel data methods to analyze this issue. The use of panel data allows not only the increase of degrees of freedom and better estimators' large sample properties, but also the reduction of endogeneity, due to the consideration of specific-country effects, omitted variables, reverse causality and measurement error.

1 The use of panel data techniques in empirical economic growth literature began with [START_REF] Islam | Growth Empirics: A Panel Data Approach[END_REF]. 2 This means that we study economic growth empirically through the implementation of a growth regression that evaluates the contribution of different determinants of economic growth. The seminal article from [START_REF] Barro | Economic growth in a cross section of countries[END_REF] began this tradition. We estimate the following equation:

Y i,t = α + β 0 Y i,t-1 + β 1 CS i,t + β 3 tourism i,t + η i + ε i,t (1)
where Y i,t is the natural logarithm of per capita GDP at constant prices, calculated using the chain index, CS i,t is a conditioning set that includes various covariates that previous literature used as determinants of economic growth, tourism i,t is one of three different measures of tourism intensity in logs, η i is an unobserved country-specific effect and ε i,t

is the error term. We have also added time dummies to all regressions. 3We present results for two different estimators: the GMM Blundell and Bond (1998

)
estimator and the corrected Least Square Dummy Variables (LSDVC) or fixed effects approach developed by Bruno (2005a, b). The essential difference is that while the first accounts for time-varying endogenous effects and is more appropriate for large samples (large N), the second accounts for endogeneity due to fixed-effects but is more consistent for samples with a small number of cross-sections.

Under the assumptions that (a) the error term is not serially correlated and (b) the explanatory variables are weakly exogenous (i.e., the explanatory variables are assumed to be uncorrelated with future realizations of the error term), the GMM dynamic panel uses the following moment conditions: E[Y i,t-s ∆ε i,t ] = 0 and E[X i,t-s ∆ε i,t ] = 0, for s ≥ 2; t = 3, ..., T ; i = 1, ..., N, where X is the complete matrix of covariates, which includes CS and tourism. Because we use the system GMM estimator developed by [START_REF] Arellano | Another Look at the Instrumental Variables Estimation of Error-Components Model[END_REF] and [START_REF] Blundell | Initial Conditions and Moment restrictions in Dynamic Panel Data Models[END_REF], there are the following additional moment or fixed-effects estimator as better than GMM ones. In fact, in a panel with small crosssection (due to low availability of data, total sample includes near 90 countries) and small time-series (5 periods), GMM estimators would create many instruments, implying an over-fitting bias. We present here the basic ideas of the estimator developed by [START_REF] Bruno | Estimation and Inference in Dynamic Unbalanced Panel Data Models with a Small Number of Individuals[END_REF]. The departure point is the inconsistency of LSDV in dynamic panel data models [START_REF] Nickel | Biases in Dynamic Models with Fixed Effects[END_REF]. The approximation terms to the bias are all evaluated at the unobserved true parameter values, which are of no direct use for estimation. Thus, to make the approximation terms operational, [START_REF] Kiviet | On Bias, Inconsistency and Efficiency of Various Estimators in Dynamic Panel Data Models[END_REF] suggests replacing the true parameters by the estimates from some consistent estimators. Monte Carlo experiments showed that the resulting bias-corrected LSDV estimator (LSDVC) often outperforms IV-GMM estimators in terms of bias and root mean squared error (RMSE). We use an approximation of

O(N -1 T -2
), which is the best approximation provided in [START_REF] Bruno | Estimation and Inference in Dynamic Unbalanced Panel Data Models with a Small Number of Individuals[END_REF], and we initialize the estimation with the Blundell and Bond (1998) estimator. Results do not change significantly with the choice of the consistent initial estimator, nor with the choice of the approximation. This estimator is suitable for unbalanced panels.

Data, Variables and Conditioning Sets

Data on Tourism Specialization

Data on Tourism Specialization are from the World Development Indicators (World Bank, 2004) from 1980 to 2002, all time lengths available in the source. We have considered 5

five-year periods to avoid measurement errors and the effects of cycles in variables. This is usual in empirical economic growth literature. We have considered a broad sample and two smaller samples: Small Countries (less than an initial level of 5 million inhabitants);

Poor Countries (for which GDP per capita is below average in the majority of periods considered). The three variables used are:

In face of this, for small samples, we present only the corrected LSDV results. who travel to a country other than that where they have their usual residence for a period not exceeding 12 months and whose main purpose in visiting is other than an activity remunerated from within the country visited. This proportion is calculated as a ratio to total population (World Bank, 2004);

Tourism receipts in % of Exports (T R 1 ) -International tourism receipts are expenditures by international inbound visitors, including payments to national carriers for international transport. These receipts should include any other prepayment made for goods or services received in the destination country. They also may include receipts from same-day visitors, except in cases where these are so important as to justify a separate classification. Their share in exports is calculated as a ratio to exports of goods and services (World Bank, 2004);

Tourism receipts in % of GDP (T R 2 ) -the same as the previous one but their share in GDP is calculated using the previous variable and the ratio of exports of goods and services to GDP (World Bank, 2004).

Conditioning Information Sets

To test the significance of tourism in explaining economic growth, we have used several variables that are standard in literature [START_REF] Barro | Economic growth in a cross section of countries[END_REF][START_REF] Barro | Economic growth in a cross section of countries[END_REF][START_REF] Barro | Economic Growth[END_REF] and are related to the main determinants of growth. Thus, we have used Real Gross Domestic Product per capita in the previous period ( Y i,t-1 ) to measure conditional convergence (from which a positive sign is expected with a less-than-unity absolute value)

F

Sample and Descriptive Statistics

The next table presents descriptive statistics for tourism variables. Descriptive statistics for other variables included in the conditioning sets are presented in the Appendix. In the next section we present the results, beginning with results for the whole sample, and then for subsamples of small and poor countries.

Results

In this section we present the main results obtained. The results on the variables in the conditioning information sets are often consistent with previous empirical literature on economic growth. In particular, the investment ratio positively influences growth, while the government expenditures ratio and the black market premium negatively influence growth.

The rate of convergence oscillates around 2.44% in the System GMM estimator - The Influence of Life Expectancy and Schooling is almost always non-significant.

Schooling seems to be negatively related to growth in samples of small and poor countries. This is not inconsistent with previous contributions, as different results have been reported in the literature. We have tested alternative specifications, such as the exclusion of life expectancy and the consideration of other variables for schooling (namely average years above 15 years old -syr15) and these changes did not change results on the significance of the tourism variable. Nevertheless, syr15 proved to be positively related to growth in one specification applied to the broad sample. The impact of the inclusion of tourism in convergence is small and its direction is not obvious, depending on the variable used. Nevertheless, the corrected LSDV estimator predicts even a small convergence rate or no conditional convergence at all, especially in samples of small and poor countries. In general, and in particular in the Corrected LSDV estimations, the introduction of tourism variables acted in order to decrease significance of other covariates, namely the impact of the government share of output (G/Y ) and the impact of the Black Market Premium (BM P ) in poor countries.

Complete regressions are presented in Appendix, and to focus the article, we will only be interested on the tourism effect from now on. To avoid excessive length and to focus the article in its main issue, we are not presenting complete regressions for the conditioning information set 2, when we use the alternative measure of institutions (ICRG). We also present only the benchmark regressions in the small and poor countries case. 8 We also note that the specification tests in GMM indicate that instruments are valid as in general we do not reject the null of the Hansen Test nor the null of the AR(2) test.

Results from All Countries

The next Table shows different estimators of the three variables linked with tourism specialization in a regression with economic growth as a dependent variable. These results indicate that in general tourism specialization is an important determinant of long-run economic growth, implying that a 1% increase in the proportion of tourism returns on GDP (or in exports) accounts for a 0.03% to 0.05% increase in output growth rate. Simultaneously, a 1% increase in the proportion of tourist arrivals tends to increase near 0.1% in economic growth rate. The corrected LSDV approach attributes a greater role to tourism than the System GMM approach. Also, when institutions are measured by black market premium, tourism returns assume a greater role than when institutions are measured by international country risk guide composite indicator. These results seem to indicate that the only measure of tourism intensity that is not particularly affected by the measure of institutions is the number of arrivals as a proportion of popu-13 F o r P e e r R e v i e w lation. Thus, bad institutions (measured as country risk) may affect the effectiveness of returns from tourism but not the effectiveness of tourist arrivals. 9These conclusions confirm for a broad cross-section of countries observed through a time-span of 5 five-year periods between 1980 and 2002 what has been shown for some countries, on their own, and for groups of developing countries in previous contributions.

Results for the Sub-Samples: Small and Poor Countries

In the next Tables we show results for the small samples considered. In these small samples we analyze the Corrected LSDV approach, as when the number of countries to be considered decreases, this is clearly the most appropriate estimator. The first case to be considered is the Small Countries case. We considered a country as small if it had less than 5 million inhabitants in the first period considered. According to the explanation in the literature, we should expect a stronger relationship within this sub-sample than in the broad sample. According to this explanation, small countries are relatively well-endowed with renewable natural resources and consequently benefit more from the specialization in tourism. In general, the effect of tourism decreases when small countries are considered, in the opposite direction of what literature have suggested for these countries. In particular only the number of arrivals as a population proportion continues to have a strong and positive effect in the economic growth rate. 10 This seems to suggest that the explanation linked with the natural resources relative abundance is not confirmed by data.

The next table shows results on a sample of poor countries. We have considered that a country is poor if it spends more time below the average per capita GDP (5969 USD) than above. These results support the idea that tourism is an opportunity for poor countries.

In fact, almost all tourism variables are significantly and positively related to economic growth in all specifications (the exception is proportion of tourism returns on GDP with a positive t-ratio of 1.62). In this group of countries it is clear that the introduction of the specialization in tourism as a determinant of economic growth decreases the influence of the government expenditure and of the Black Market Premium.

Conclusion and Prospects

In general, we support the time-series evidence that has been published for a number of countries, according to which tourism specialization enhances growth performance of countries. We come to this conclusion using two recently developed estimators that complement each other in terms of costs and benefits: the System GMM Blundell-Bond (1998) estimator and the Corrected LSDV estimator developed in [START_REF] Bruno | Estimation and Inference in Dynamic Unbalanced Panel Data Models with a Small Number of Individuals[END_REF] tributions, according to which tourism specialization is important for small countries (as small countries are relatively abundant in Natural Resources) and for poor countries, we reject the first and confirm the second conclusion. In fact, small countries do not seem to benefit from tourism specialization more than does the average country. On the contrary, poor countries always benefit from tourism specialization, both in terms of arrivals and in terms of returns. In addition, it seems that tourism specialization is a good option to promote economic growth in poor countries, as it appears to hinder the negative effects of government and bad institutions.

These results add to previous contributions the consideration of recent empirical methods appropriate to study economic growth. The results are generally in line with previous time-series attempts. 11 However, they question the proposition according to which small countries benefit more from tourism than others. Finally, they emphasize the possible contradiction between empirical results and economic growth theory regarding the relationship between growth and tourism specialization. This opens at least two potentially fruitful research avenues. The first one is to explore the relationship between tourism and the traditional determinants of economic growth, e.g., human capital, both theoretically and empirically. The second one is to explore the determinants of tourism growth and in particular to calculate the productivity within the tourism firms. There is also a significant scope of evolution in constructing models of economic growth that incorporate the positive influence of tourism in economic growth.

It is worth noting that establishing the relationship between tourism and economic growth is essential concerning the importance that policy makers are attributing to this

5

 5

  Tourist Arrivals as Population Proportion (T A) -The number of International inbound tourists over population. International inbound tourists are the number of visitors

16 Page

 16 , and applying them to a broad sample of countries during all the available time periods.When testing for the two most important conclusions brought out by previous con-

  11 A first attempt to use panel data methods applied to this broad sample led to different results due to the presence of the[START_REF] Nickel | Biases in Dynamic Models with Fixed Effects[END_REF] bias in Fixed effects estimations (see[START_REF] Sequeira | International Tourism and Economic Growth: A Panel Data Approach[END_REF].

Table 1 :

 1 Specialization in Tourism and Growth Observations

	g Y

  (simultaneity, omitted variables, country-specific effects and measurement errors) problems and closely follow empirical growth literature to test the influence of tourism variables in economic growth in a broad panel data.1 Adding to previous literature, which often used arrivals of tourists per capita as a proxy for tourism intensity, we also use variables linked to the proportion of tourism in Exports and in GDP. Thus, as far as we know, this is the first attempt to evaluate the worldwide impact of tourism, recurring to dynamic panel data techniques that deal with endogeneity and following the empirical economic growth literature.

	F o
	r
	P
	e e r
		R e v i e w
	T /X ≥ 50%	521	1.5%

Note: T /X measures proportion of Tourism receipts in Exports; g Y is the growth rate of real per capita GDP. Sources: Summers-Heston (2002) and World Development Indicators

(2004)

In this article we employ appropriate panel data techniques that deal with endogeneity 2 Additionally, we consider different sub-samples of countries to test if tourism is more important for economic growth in small and poor countries,

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	Submitted Manuscript
	restrictions for the levels equation: E[∆Y i,t-1 (η i + ε i,t )] = 0 and E[∆X i,t-1 (η i + ε i,t )] = 0,
	for t = 3, ..., T. 4 It is worth noting that these conditions allow for the levels of output to
	be correlated with the unobserved country-specific effects. Thus, we use these moment
	conditions and employ a GMM procedure to generate consistent and efficient parameter
	estimates. Temple et al. (2001) argues that this estimator is appropriate to economic
	growth empirical models.
	Consistency of the GMM estimator depends on the validity of the instruments. To F o r address this issue, we consider two specification tests: the first is the Hansen test of
	over-identifying restrictions, which tests the overall validity of the instruments (the null P is that the instruments are valid); the second is the second-order autocorrelation test e for the error term, which tests the null according to which there is no autocorrelation. e r Overall, both specification tests indicate that the instruments used are valid (see Tables R A.1.1, A.1.2 and A.1.5 in Appendix A). e The Bruno (2005b) estimator has been shown to outperform GMM estimators in v i panels with the features of this one. Monte-Carlo experiments shown in Judson and Owen e w (1999) and in Bruno (2005b) indicate a corrected LSDV (Least Square Dummy Variable)

  As a robustness check, we have included in some regressions two additional variables in the conditioning information set, treating the CS 2 as CS 1 plus the following variables:

	and the following Conditioning Information Set (CS 1 ) of variables:
	Investment-Output ratio (I/Y ) -is used as a proxy for physical capital investment, and
	a positive sign is expected; Exports plus Imports to output ratio (Openness) -is used to measure the impact of
	Government Consumption-Output ratio (G/Y ) -is used to measure long-run crowding-openness of the economy in its growth performance, and a positive sign is expected,
	out and the effect of Government Consumption in long-run growth; a negative effect although this is not consensual in the literature (e.g. Edwards, 1998);
	o is traditionally reported, but a positive effect was shown in panel data estimations o F Inflation (consumer prices) (1 + π) -is used to measure the effect of high inflations in
	r r
	P P
	e e r e e r
	R e v i e w R e v i e w
	International Country Risk Guide (ICRG) -is used as an alternative measure of institu-
	tions; as it is negatively related with country risk, it is expected to have a positive
	relationship; 6

in

[START_REF] Caselli | Re-opening the convergence debate: a new look at cross country growth empirics[END_REF]

; Secondary Years of Schooling above 25 years (Syr) -is used as a proxy for human capital; there is a discussion in the literature about the effect of human capital; there are positive and negative effects reported; Life Expectancy (Lif e) -it is used as a proxy for health, which has been interpreted both as a determinant of productivity and as a determinant of the savings behavior of the households; it usually has a positive effect, but

[START_REF] Caselli | Re-opening the convergence debate: a new look at cross country growth empirics[END_REF]

reported a non-significant effect; Black Market Premium (1 + BM P ) -is used to measure market distortions in the economy and the overall negative impact of institutions; reducing the economic growth rates (e.g.

[START_REF] Levine | Financial Intermediation and Growth: Causality and Causes[END_REF]

.

All variables except the average years of schooling are introduced as log transformations. Output, investment-output ratio, government expenditures ratio and openness are from the Penn World Tables

6

.1. Secondary Years of Schooling above 25 years comes from Barro and Lee (2000). Life Expectancy, International Risk Country Guide, and Inflation (consumer prices) come from the World Development Indicators 2004 (World Bank, 2004). Black Market Premium is taken from the World Development Network Database 2001 (World Bank, 2001).

Table 2 :

 2 Descriptive Statistics Variables Obs. Mean Std. Dev. Min. Max.

	GDP pc 1031 5969	6069	304.3 37689
	T A	705 0.511	1.190	0	13.49
	T R 1	744 12.04	14.84	0.055 85.60
	T R 2	580 4.769	8.216	0.016 66.55

Note: Values for Descriptive Statistics are in levels. 10 Page 10 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table A

 A

.A.1, column 0 -in line with the one obtained by Temple et al. (2001) -2.38%

in their Table

1

, column (v) -and closer to OLS estimates than to the Differenced GMM estimates of

[START_REF] Caselli | Re-opening the convergence debate: a new look at cross country growth empirics[END_REF]

.

7

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	Submitted Manuscript
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8

  Although results do not influence our conclusions, they are obviously available upon request.

			Submitted Manuscript
	Table 3:	Regressions Between Tourism and Growth
			System GMM
	tourism		CS 1	CS 2
	Institutions measure BMP ICRG	BMP	ICRG
	ln(T A)		0.01	-0.02	0.03**	0.00
			(1.05) (-0.82) (2.07)	(0.25)
	ln(T R 1 )		0.04**	0.01	0.05***	0.02
			(2.24) (0.61)	(3.13)	(0.82)
	ln(T R 2 )		0.03*	-0.01 0.03***	0.01
			(1.82) (-0.66) (2.64)	(0.54)
			Corrected FE
	tourism Institutions measure F ln(T A) o r ln(T R 1 )	CS 1 ICRG 0.09*** 0.09*** 0.11*** 0.09*** CS 2 BMP BMP ICRG (4.44) (3.75) (4.14) (2.62) 0.05*** 0.02 0.05*** 0.02
	(3.89) P 0.04** (2.48) e Notes: *** stands for a 1% significance level; ** for 5% and (1.30) (3.32) (1.50) 0.02 0.04*** 0.02 ln(T R 2 ) (1.40) (2.89) (1.53) e * for 10%. Regressions include several controls, constant and r time dummies. Complete Regressions are presented in
	w e i v e R Appendix (see Tables A.1.1 to A.1.6).

12 Page 12 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

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Table 4 :

 4 Regressions Between Tourism and Growth Small Countries -Corrected FE

	tourism	CS 1		CS 2
	Institutions measure	BMP	ICRG	BMP	ICRG
	ln(T A)	0.08*** 0.09*** 0.08*	0.04***
		(2.65)	(2.54) (1.81)	(3.13)
	ln(T R 1 )	0.05*	0.02	0.05	0.04
		(1.87)	(0.71) (1.48)	(1.02)
	ln(T R 2 )	0.06*	0.03	0.06*	0.06
		(1.79)	(0.93) (1.78)	(1.52)
	Notes: *** stands for a 1% significance level; ** for 5% and
	* for 10%. Regressions include several controls, constant and
	time dummies. Complete Regressions are presented in
	Appendix (see Tables A.2.1 to A.2.2).

Page 15 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

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Table 5 :

 5 Regressions Between Tourism and Growth Poor Countries -Corrected FE

	tourism	CS 1	CS 2
	Institutions measure	BMP	ICRG	BMP	ICRG
	ln(T A)	0.09*** 0.08** 0.10***	0.09**
		(3.45)	(2.20)	(3.05)	(2.12)
	ln(T R 1 )	0.06*** 0.03*	0.06**	0.04*
		(3.28)	(1.81)	(2.55)	(1.89)
	ln(T R 2 )	0.05***	0.03	0.05***	0.03*
		(2.73)	(1.62)	(3.00)	(1.85)
	Notes: *** stands for a 1% significance level; ** for 5% and
	* for 10%. Regressions include several controls, constant and
	time dummies. Complete Regressions are presented in
	Appendix (see Tables A.3.1 to A.3.2).

Table A .

 A

	Table A.1.2: Convergence Regressions (System GMM) -CS 2 Table A.1.3: Convergence Regressions (Corrected FE) -CS 1
	Dep Var.: ln(Y i,t ) Dep Var.: ln(Y i,t )	(0)	(0)	(1)	(1)	(2)	(2)	(3)	(3)
	ln(Y i,t-1 ) ln(Y i,t-1 )	0.913*** 0.872*** 0.926*** 0.924*** 1.025*** 0.870*** 1.000*** 0.932***
		(26.49) (17.11)	(17.32) (7.96) (10.34) (21.66)	(20.62) (4.81)
	ln(I/Y ) ln(I/Y )	0.092*** 0.089*** 0.064** 0.092** 0.057* 0.074	0.106** 0.102***
	(3.55) (5.90) 1.1: Convergence Regressions (System GMM) -CS 1 (1.96) (1.34) (2.47) (2.35) (1.82) (3.56) Dep Var.: ln(Y i,t ) (0) (1) (2) ln(G/Y ) -0.029 -0.053 -0.021 -0.050 ln(G/Y ) -0.042** -0.022 -0.004 -0.029 (3) ln(Y i,t-1 ) 0.885*** 0.873*** 0.879*** (-1.08) (-1.51) (-0.47) (-1.20) (-1.99) (-0.81) (-0.13) (-0.65) 0.918*** (29.47) (17.27) (15.33) syr 0.012 0.006 0.024 0.008 syr -0.024 -0.031 -0.029 -0.028 (15.70) ln(I/Y ) 0.104*** 0.112** 0.091 (0.61) (0.26) (0.96) (0.032) (-1.11) (-0.95) (-1.07) (-0.60) 0.089* (3.73) (2.02) (1.43) ln(1 + BM P ) -0.004 0.000 -0.001 0.001 ln(1 + BM P ) -0.015*** 0.001 0.006 -0.000 (1.79) ln(G/Y ) -0.035 -0.067* -0.05 (-0.58) (0.36) (-0.17) (0.26) (-3.27) (0.16) (-0.82) (-0.06) -0.074* (-1.26) (-1.80) (-1.14) (-1.72) syr 0.026 0.016 0.049 0.014 (1.28) (0.58) (1.44) (0.45) ln(1 + BM P ) -0.022*** -0.021** -0.016* -0.022** (-3.22) (-2.55) (-1.71) F o r ln(Lif e) 0.290** 0.313* 0.188 0.173 (2.18) (1.80) (1.08) (0.98) ln(1 + π) -0.033*** -0.034*** -0.028*** -0.035*** (-3.32) (-4.20) (-2.82) (-4.43) ln(open) -0.018 -0.036 -0.006 -0.048* ln(Lif e) 0.163 0.289 0.367* 0.321 (0.96) (1.57) (1.95) (0.61) F T A -0.095*** --o (4.44) r T R 1 --0.049*** -(-2.38) ln(Lif e) 0.284** 0.262 0.151 0.115 (2.21) (1.17) (0.65) (0.49) T A -0.015 --(1.05) T R 1 --0.043** -(2.24) T R 2 ---P e e r (-0.75) (-1.20) (-0.21) (-1.69) T A -0.031** --(2.07) T R 1 --0.048** -(3.13) T R 2 ---0.034*** (2.69) (3.89) T R 2 ---0.042*** P (2.48) e Observations 589 334 350 312 Countries 94 93 93 91 e Notes: *** stands for a 1% significance level; ** for 5% and r * for 10%. t-statistics based on the white heteroscedastic-consistent 0.028* (1.82) AR(1) Test -3.64*** -2.92*** -1.91 -2.98*** (p-value) (0.000) (0.003) (0.056) (0.003) AR(2) Test -0.82 0.15 -0.52 -1.87* (p-value) (0.414) (0.883) (0.602) (0.062) Hansen Test 85.5 53.39 52.47 47.03 (p-value) (0.289) (0.309) (0.305) (0.513) Observations 589 334 350 312 Countries 94 93 93 91 Instruments 92 59 59 59 R e v i e w AR(1) Test (p-value) -3.68*** -2.97*** -2.05** -2.76*** (0.000) (0.003) (0.040) (0.006) AR(2) Test (p-value) -1.23 0.39 -0.09 -1.29 (0.220) (0.698) (0.373) (0.199) Hansen Test (p-value) 83.77 62.46 73.58 64.00 (0.975) (0.601) (0.244) (0.547) Observations 532 321 336 302 Countries 94 92 93 90 Instruments 124 79 79 79 Notes: *** stands for a 1% significance level; ** for 5% and w e i v e R variance-covariance matrix appear in parentheses.
	Notes: *** stands for a 1% significance level; ** for 5% and * for 10%. t-statistics based on the white heteroscedastic-consistent
	* for 10%. t-statistics based on the white heteroscedastic-consistent variance-covariance matrix appear in parentheses.
	variance-covariance matrix appear in parentheses.

Page 24 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  Table A.1.4: Convergence Regressions (Corrected FE) -CS 2 Table A.1.5: Convergence Regressions (System GMM) -CS 1 Table A.1.6: Convergence Regressions (Corrected FE) -CS 1 ** stands for a 1% significance level; ** for 5% and * for 10%. t-statistics based on the white heteroscedastic-consistent variance-covariance matrix appear in parentheses.

		Submitted Manuscript
	Dep Var.: ln(Y i,t ) Alternative Measure of Institutions (ICRG) (0) (1) (2) Dep Var.: ln(Y i,t ) (0) (1) (2)	(3) (3)
	ln(Y i,t-1 ) Dep Var.: ln(Y i,t ) ln(Y i,t-1 )	1.062*** 0.891*** 1.067*** (0) (1) (2) 0.971*** 0.898*** 0.985***	0.954*** (3) 0.959***
	ln(Y i,t-1 )	(27.85) 0.870*** 0.869*** 0.872*** (5.89) (10.12) (6.21) (6.89) (6.42)	(6.30) 0.832*** (5.58)
	ln(I/Y ) ln(I/Y )	0.070*** (16.62) 0.020 0.061** 0.041 (15.03)	0.016 (16.17) 0.015	0.085** (12.95) 0.095***
	ln(I/Y )	(3.56) 0.155** (0.62) (2.11) (1.40) 0.133** (0.45) (0.48) 0.141**	(2.56) 0.119** (2.65)
	ln(G/Y ) ln(G/Y )	-0.026 (2.15) -0.034	-0.017 (2.24) -0.049*		-0.011 (2.16) -0.034	-0.020 (2.16) -0.043
	ln(G/Y )	(-1.19) -0.077 (-084)	(-0.71) -0.103** -0.088** -0.109*** (-0.35) (-0.72) (-1.74) (-0.93) (-1.39)
	syr syr	-0.033* (-1.63) -0.048	-0.034 (-2.66) -0.040	-0.039 (-2.11) -0.040	-0.029 (-2.80) -0.048
	syr	(-1.88) 0.011 (-1.23)	(-1.02) 0.006 (-1.18)	(-1.31) 0.007 (-1.31)	(-0.78) 0.007 (-1.18)
	ln(1 + BM P ) ln(ICRG)	-0.009 (0.40) 0.313***		0.005 (0.26) 0.150* 0.294*** -0.004 (0.29)	0.002 (0.22) 0.190***
	ln(ICRG)	(-1.61) 0.191* (3.78)	(0.63) 0.144 (1.82)		(-0.49) 0.195** (3.83)	(0.26) 0.139 (2.91)
	F o r ln(Lif e) 0.142 (0.92) ln(1 + π) -0.024*** -0.022*** -0.016* 0.312 0.303 (1.45) (1.16) (-3.24) (-3.02) (-1.85) ln(open) -0.030 -0.009 0.005 F o r (1.84) (1.46) (2.11) ln(Lif e) 0.184 0.507** 0.200 (0.84) (2.23) (0.93) T A --0.017 -(-0.82) ln(Lif e) 0.059 0.228 0.119 (0.15) (0.86) (0.32) F T A -0.087*** -o (3.75) 0.021 r T R 1 --(1.30)	0.219 (0.77) -0.015** (-2.14) -0.014 (1.59) 0.605** (2.48) -0.116 (0.33) --
	P e e r R e v i e w (-1.55) (-0.27) (0.17) (-0.32) -0.106*** --(4.14) --0.047*** -(3.32) ---0.041*** (2.98) 532 321 336 302 94 92 93 90 Notes: *** stands for a 1% significance level; ** for 5% and T A T R 1 T R 2 Observations Countries * for 10%. t-statistics based on the white heteroscedastic-consistent variance-covariance matrix appear in parentheses. P e e r R e v i e w T R 1 --0.013 -(0.61) T R 2 ----0.013 (-0.66) AR(1) Test (p-value) -2.15** -3.13*** -1.94* -2.25** (0.031) (0.002) (0.052) (0.025) AR(2) Test (p-value) -0.64 0.15 -0.73 -1.57 (0.564) (0.880) (0.464) (0.115) Hansen Test (p-value) 38.81 40.64 42.73 39.96 (0.478) (0.574) (0.483) (0.604) Observations 330 313 327 290 Countries 87 85 86 83 Instruments 49 54 54 54 Notes: *** stands for a 1% significance level; ** for 5% and * for 10%. t-statistics based on the white heteroscedastic-consistent variance-covariance matrix appear in parentheses. T R 2 --0.021 P (1.40) e Observations 330 313 327 290 Countries 87 85 86 83 e r R e v i e w Notes: *27

Page 27 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	A.2 Small Countries
	F o
	r
	P
	e e r
	R e v i e w

Table A .

 A 2.1: Convergence Regressions (Corrected FE) -CS 1 Dep Var.: ln(Y i,t ) ** stands for a 1% significance level; ** for 5% and * for 10%. t-statistics based on the white heteroscedastic-consistent variance-covariance matrix appear in parentheses.

		(0)	(1)	(2)	(3)
	ln(Y i,t-1 )	1.226*** 1.166*** 1.265***	1.380***
		(30.21)	(12.27)	(16.34)	(12.32)
	ln(I/Y )	0.068**	0.036	0.002	0.080*
		(2.59)	(0.90)	(0.03)	(1.71)
	ln(G/Y )	-0.057**	-0.031	-0.003	-0.032
		(-2.13)	(-0.80)	(-0.07)	(-0.69)
	syr	-0.117*** -0.141*** -0.136**	-0.171***
		(-3.86)	(-2.88)	(-2.57)	(-3.47)
	log(1 + BM P )	-0.010	-0.005	-0.136**	-0.011
		(-1.33)	(-0.53)	(-2.57)	(-0.98)
	ln(Lif e)	0.069	0.086	0.257	-0.025
		(0.41)	(0.43)	(1.08)	(-0.09)
	T A	-	0.077***	-	-
			(2.65)
	T R 1	-	-	0.060*	-
				(1.79)
	T R 2	-	-	-	0.055*
					(1.87)
	Observations	276	159	170	149
	Countries	47	47	47	45
	Notes: *28

Page 28 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	A.3 Poor Countries
	F o
	r
	P
	e e r
	R e v i e w

Table A .

 A 3.1: Convergence Regressions (Corrected FE) -CS 1 Dep Var.: ln(Y i,t ) ** stands for a 1% significance level; ** for 5% and * for 10%. t-statistics based on the white heteroscedastic-consistent variance-covariance matrix appear in parentheses. B Descriptive Statistics for Variables in CS 1 and CS 2 Table B.1: Descriptive Statistics Variables Obs. Mean Std. Dev. Min. Max.

		(0)	(1)		(2)	(3)
	ln(Y i,t-1 )	1.133*** 1.013*** 1.096***	1.052***
		(40.40)	(9.20)	(11.62)	(8.75)
	ln(I/Y )	0.079***	0.054		0.038	0.093***
		(4.45)	(1.54)		(0.94)	(2.79)
	ln(G/Y )	-0.076***	-0.006		0.034	-0.030
		(-3.07)	(-0.11)		(0.67)	(-0.60)
	syr	-0.090*** -0.081*	-0.076	-0.092**
		(-2.99)	(-1.73)	(-1.52)	(-2.03)
	log(1 + BM P )	-0.017***	-0.001	-0.006	0.003
		(-3.00)	(-0.07)	(-0.59)	(0.25)
	ln(Lif e)	0.172	0.220		0.387	0.292
		(1.32)	(0.85)		(1.35)	(0.89)
	T A	-	0.092***	-	-
			(3.45)
	T R 1	-	-	0.063***	-
					(3.28)
	T R 2	-	-		-	0.055***
						(2.73)
	Observations	376	206		222	195
	Countries	59	58		58	58
	Notes: *ln(I/Y )	1039 2.54	0.70	-0.04	3.92
	ln(G/Y )	1039 2.89	0.58	0.96	5.02
	syr	940	1.20	1.13	0.01	5.09
	ln(1 + BM P ) 963	2.16	1.89	-1.05 10.84
	ln(Lif e)	1536 4.09	0.22	3.46	4.40
	ln(Open)	1041 4.00	1.02	-19.26 5.84
	ln(1 + π)	1075 2.24	1.24	-3.80	8.80
	ln(ICRG)	605	4.11	0.26	2.93	4.56
			29

Page 29 of 29 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

In the next sub-section, we discuss the composition of the conditioning set and different measures of tourism intensity.

This estimator is preferable to the difference estimator if the dependent variable is highly persistent, as is the case for output.

To avoid the over-fitting bias that arises from the high number of instruments in System GMM, we restrict the number of lagged instruments to two by variable. These specification options do not change our conclusions. In Tables A.1.1, A.1.2 and A.1.5 in Appendix A, we also present the number of instruments introduced in each regression. According to these numbers, we must be confident in a quite small "overfitting" bias. However, this would not happen in small samples for which we present results.

We note that ICRG is a more general measure for institutions than BM P because it includes 22 different indicators of country risk. Nevertheless, it is less used in previous empirical contributions. Its introduction comes at the expense of a significant number of observations. It is increasingly used in development (see e.g. the influential article of Hall and Jones, 1999).

As in these references, the rate of convergence λ is obtained equating e -λT to 0.885 (in the case of column 0 in Table A.1.1, Appendix A), where T = 5.

Eilat and Einov (2004), in an article on the determinants of international tourism, have discovered that political risk is very important to tourism.

We have also tested a sample of countries with less than 1 million inhabitants. Results showed that tourism specialization never has a positive contribution on economic growth. Results are available upon request.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

* This is a fully modified version of a on Tourism and Sustainable Development -Macro and Micro Issues", supported by the World Bank, Cagliari, Italy. One of the authors also gratefully acknowledge a financial support from the FCT, under the Project POCTI/EGE/60845/2004. The usual disclaimer applies.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript


Dr Steven Cook
email: s.cook@swan.ac.uk.

Dimitrios Vougas

-Statistical Simulation Methods|Monte Carlo Methods < C1 -Econometric and Statistical Methods: General < C -Mathematical and Quantitative Methods

Keywords: Unit roots, Momentum-threshold autoregression, Smooth transition, Structural change, UK house prices Unit roots, Momentum-threshold autoregression, Smooth transition, Structural change, UK house prices

Unit root testing against an ST-MTAR alternative: Finite-sample properties and an application to the UK housing market

S Cook, Dimitrios V

Introduction

Following the seminal study of [START_REF] Perron | The Great Crash, the oil price shock and the unit root hypothesis[END_REF], a large literature has emerged considering the issue of testing the unit root hypothesis in the presence of structural change. In response to Perron's finding that the Dickey-Fuller (1979) (DF) test can exhibit low power when applied to series which are stationary about a deterministic component subject to structural change, a number of authors have examined the issue of unit root testing in the presence of regime shifts. While some authors have followed Perron's seminal study and assumed structural change to be abrupt or instantaneous (see, inter alia, Banerjee et al. 1992; Zivot and Andrews 1992), Leybourne, Newbold and [START_REF] Leybourne | Unit roots and smooth transitions[END_REF] (LNV) suggest an alternative approach which allows for gradual adjustment. Using the logistic smooth transition function, LNV permit testing of the unit root hypothesis against an alternative of stationarity about a non-linear trend which allows for gradual adjustment between two regimes. The resulting smooth transition (ST) unit root tests have an obvious appeal, particularly in the analysis of economics data which frequently exhibit changing patterns of behaviour in their evolution. In more recent research, [START_REF] Sollis | Asymmetric adjustment and smooth transitions: A combination of some unit root tests[END_REF] has extended this approach to incorporate the possibility of asymmetric adjustment about a non-linear trend specified by a logisitic smooth transition. Drawing upon the methods of Enders and Granger (1998), [START_REF] Sollis | Asymmetric adjustment and smooth transitions: A combination of some unit root tests[END_REF] employs threshold autoregression (TAR) to develop a ST-TAR unit root test. In the present paper, the research of [START_REF] Sollis | Asymmetric adjustment and smooth transitions: A combination of some unit root tests[END_REF] is itself extended in two ways. First, an alternative method of capturing asymmetric adjustment is proposed based upon momentum-threshold autoregression (MTAR). The extension of smooth transition unit root tests to consider MTAR adjustment has an obvious appeal as the use of MTAR rather than TAR adjustment has been found to result in higher power when extending the [START_REF] Dickey | Distribution of the estimators for autoregressive time series with a unit root[END_REF] unit root test and Engle-Granger (1986) cointegration test (see [START_REF] Enders | Unit root tests and asymmetric adjustment with an example using the term structure of interest rates[END_REF] and [START_REF] Enders | Cointegration and threshold adjustment[END_REF] respectively). Using Monte Carlo simulation, the present paper derives finite-sample critical values of the resulting ST-MTAR tests and examines their power properties in the presence of stationary alternatives. In addition, the properties of the ST-TAR and ST-MTAR tests are compared under the alternative TAR and MTAR adjustment schemes.

That is, ST-TAR (ST-MTAR) tests are examined in the context of misspecification when the data generation process is actually MTAR (TAR). Following this approach, the results of Cook (2003a) for Enders-Granger asymmetric unit root tests show the MTAR models to outperform TAR models even in the presence of TAR adjustment. These findings provide further justification for analysis of MTAR adjustment in the present context. Second, the analysis is extended to provide asymmetric versions of all existing specifications of the ST unit root test. While [START_REF] Sollis | Asymmetric adjustment and smooth transitions: A combination of some unit root tests[END_REF] This paper proceeds as follows. In section [START_REF] Cook | The properties of asymmetric unit root tests in the presence of mis-specified asymmetry[END_REF], the ST unit root tests of LNV are presented along with the ST-TAR tests of [START_REF] Sollis | Asymmetric adjustment and smooth transitions: A combination of some unit root tests[END_REF] and the newly proposed ST-MTAR tests developed herein.

Section [START_REF] Cook | The convergence of regional house prices in the UK[END_REF] presents critical values for the ST-MTAR tests and an analysis of the empirical powers of the ST, ST-TAR and ST-MTAR tests in the presence of both TAR and MTAR adjustment. An empirical application of the tests to aggregate house price data for the UK is provided in section [START_REF] Dickey | Distribution of the estimators for autoregressive time series with a unit root[END_REF], with section [START_REF] Elliott | Efficient tests for an autoregressive unit root[END_REF] concluding.

Smooth transition unit root tests

To allow the unit root hypothesis to be tested against an alternative of structural change in the form of gradual rather than abrupt adjustment, LNV employ the deterministic logistic smooth transition S t (γ, τ ) which is defined as:

S t (γ, τ ) = [1 + exp{-γ(t -τ T )}] -1 γ > 0 t = 1, ..., T (1)
where T is the sample size, τ is the parameter determining the fraction of the sample at which the transition occurs, while γ determines the speed of transition. LNV propose three smooth transition unit root tests based upon the following models denoted as A, B and C:

Model A :

y t = α 1 + α 2 S t (γ, τ ) + u at (2)
Model B :

y t = α 1 + β 1 t + α 2 S t (γ, τ ) + u bt (3)
Model C : Model D:

y t = α 1 + β 1 t + α 2 S t (γ, τ ) + β 2 tS t (γ, τ ) + u ct (4)
y t = α 1 + β 2 tS t (γ, τ ) + u dt (5)
where u dt is a zero mean I(0) error process. The four proposed tests therefore differ according to deterministic terms included and form of break considered. To test for the presence of a unit root, the null hypothesis of a unit root or unit root with drift is tested against an alternative given by Model A, B, C or D as appropriate: 3), ( 4) or ( 5)

H 0 : y t = µ t , µ t = µ t-1 + ε t H 1 : (2), (
H 0 : y t = µ t , µ t = κ + µ t-1 + ε t H 1 : (3), (4) or (5)
where ε t is an error term. The alternative models therefore permit various gradual changes in either intercept and/or trend, with a fixed intercept (and trend in the cases of Models B and C) also included. To implement the ST test, a two-step approach is followed. 1 In the first step, Models A, B, C and D are estimated using a non-linear least squares (NLS) algorithm with the resulting the residual processes (b u it , i = a, b, c, d) stored. These processes are given as: In the second step, an augmented DF test is performed using the t-ratio of ψ i from the following regression:

Model A : b u at = y t -b α 1 -b α 2 S t (b γ, b τ ) (6) Model B : b u bt = y t -b α 1 -b β 1 t -b α 2 S t (b γ, b τ ) (7) Model C : b u ct = y t -b α 1 -b β 1 t + b α 2 S t (b γ, b τ ) -b β 2 tS t (b γ, b τ ) (8) Model D : b u dt = y t -b α 1 -b β 2 tS t (b γ, b τ ) (9)
∆û it = ψ i ûit-1 + p i X j=1 φ ij ∆û it-j + ε it i = a, b, c, d (10)
The test statistics for testing the unit hypothesis ψ i = 0 in (10) are denoted as s α , s α(β) , s αβ , and s β for Models A to D respectively, with (2), ( 3), ( 4) or ( 5) used as appropriate. Recently, Sollis

I t =    1 if ûit-1 ≥ 0 0 if ûit-1 < 0 (11)
This indicator function is then employed to extend [START_REF] Hayashi | Econometrics[END_REF] as follows:

∆û t = I t ρ 1 ût-1 + (1 -I t ) ρ 2 ût-1 + p X j=1 ψ j ∆û t-j + η t (12)
Asymmetric adjustment is therefore permitted as two adjustment parameters (ρ i ) are now present in [START_REF] Meen | Regional house prices and the ripple effect: A new interpretation[END_REF], as compared to a single parameter (ρ) and speed of adjustment in [START_REF] Hayashi | Econometrics[END_REF]. The unit root null hypothesis is then tested via either via the joint hypothesis H 0 : ρ 1 = ρ 2 = 0 or the more significant t-statistic of H 0 : ρ 1 = 0 or H 0 : ρ 2 = 0. To test the unit root hypothesis against the different alternative hypotheses, Sollis (2004) combines ( 11) and ( 12) with ( 2 The resulting ST-MTAR tests therefore combine ( 12) and ( 13) with either (2), ( 3), ( 4) or [START_REF] Elliott | Efficient tests for an autoregressive unit root[END_REF] depending upon whether the smooth transition is given by Model A, B, C or D. As with the ST-TAR tests, the unit root hypothesis is tested via the joint significance of the adjustment parameters

I t =    1 if ∆y t-1 ≥ 0 0 if ∆y t-1 < 0 (13)
{ρ i }
y t = y t-1 + η t t = 1, ..., T (14)
η t ∼ i.i.d. N (0, 1) (15)
All experiments are performed over 10,000 replications using GAUSS, with the error series {η t } generated via the RNDNS procedure with y 0 = 0. The resulting critical values for the alternative ST-MTAR tests are reported in Table One for a range of sample sizes (T = 50, 100, 250, 500) and levels of significance (10%, 5%, 1%). (2004), with its basic structure given as below:

y t = α 1 + α 2 S t (γ, τ ) + v t ( 16
)
∆b v t = I t ρ 1 b v t-1 + (1 -I t ) ρ 2 b v t-1 + η t ( 17
)
v 0 = 0 η t ∼ NID (0, 1) (18)
The basis of this DGP is therefore provided by the Model A specification given above. To ensure a stationary asymmetric DGP with structural change, the following design parameters are employed:

ρ 1 = -0.1, -0.
3, -0.9; ρ 2 = -0.1, -0.3, -0.9; α 1 = 1; α 2 = 2, 5, 10; γ = 0.5, 5; τ = 0.5. With the exception of the inclusion of an additional break size (α 2 = 5), these values follow [START_REF] Sollis | Asymmetric adjustment and smooth transitions: A combination of some unit root tests[END_REF] and allow varying degrees of asymmetry and stationary to be considered in conjunction with a range of breaks of differing sizes occurring at different times. All possible combinations of the above parameters are considered subject to ρ 1 6 = ρ 2 to ensure asymmetric adjustment about the underlying smooth transition. However, in contrast to [START_REF] Sollis | Asymmetric adjustment and smooth transitions: A combination of some unit root tests[END_REF] where asymmetric adjustment of a TAR form alone is considered, both TAR and MTAR adjustment are considered here. Therefore two sets of experiments are performed. For the first set of experiments, I t is specified as in [START_REF] Leybourne | Unit roots and smooth transitions[END_REF] allowing the properties of the alternative tests to be examined under a DGP where stationary TAR asymmetric adjustment occurs around a trend exhibiting smooth transition. For the second set of experiments, I t is given by ( 13) to permit a similar analysis where asymmetric adjustment is of an MTAR form. Given the above design, the alternative TAR and MTAR tests are based upon the use of Model A with the powers of the s α , ts α , F s α , ts * α and F * α tests calculated at the 5% and 10% nominal levels of significance. Under the ST-TAR DGP, ts α and F s α represent correctly specified tests, while under the ST-MTAR DGP they are clearly mis-specified. Similarly, ts * α and F * α are correctly specified under the ST-MTAR DGP but are mis-specified under the ST-TAR DGP. The experimental design therefore permits a standard analysis of the tests under the assumption of correct specification, while also allowing a form of mis-specification analysis where an investigator employs the incorrect form of asymmetric test. All experiments are conducted over 2,000 replications for a representative sample size of 100 observations. The power results for the ST-TAR DGP are presented in Table Two with the results for the ST-MTAR DGP provided in Table Three. While empirical powers of the tests can be seen to vary across the considered designs, the following points can be made to summarise the results. Under a TAR adjustment scheme, it can be seen that for low levels of asymmetry (and consequently stationarity), the original LNV test can exhibit greater power than the TAR or MTAR tests. This is an intuitive finding as the asymmetric tests involve the estimation of additional parameters and the presence of a reasonable degree of asymmetry may be required to offset this and allow greater power to be observed. Considering the F and t forms of the asymmetric tests, it can be seen that for both TAR and MTAR adjustment, the former is a more powerful form than the latter. Comparing the relative powers of the TAR and MTAR tests, the TAR tests are generally more powerful than the MTAR tests. However, this property does not hold for all experimental designs and the difference in power where it does occur is often very small. This is perhaps a surprising finding as the MTAR tests are mis-specified under the current DGP and therefore might be expected to be dominated by the TAR tests. Turning to the results for the ST-MTAR DGP, the most striking feature of the results is superiority of the MTAR tests. Throughout, it is either the F * α or ts * α test which is the most powerful of all the tests considered. In contrast, the TAR tests which are now mis-specified under this DGP, possess similar power to the LNV test when applied in F -form, but less power when applied t-form. To illustrate the relative powers of the tests, consider the first design where {ρ 1 , ρ 2 , α 2 , γ} = {-0.1, -0.3, 2, 0.5} . For this case, the ts * α test has a power advantage of 4%, 34%, 36% and 57% relative to the F * α , F α , s α and ts α tests respectively. Therefore, while the F * α or ts * α tests are similar in terms of power, they are both substantially more powerful than their rivals.

Tables Two and Three about here [START_REF] Dickey | Distribution of the estimators for autoregressive time series with a unit root[END_REF] Examining the order of integration of UK aggregate house prices

To illustrate the empirical relevance of the proposed ST-MTAR test, the order of integration of aggregate house prices for the UK is examined. The house price data considered are seasonally adjusted, quarterly observations on house prices over the period 1973(4) to 2005(1). 3 The series is analysed in its natural logarithmic form. Before considering the smooth transition based unit root tests detailed above, the unit root hypothesis is tested using commonly employed unit root tests. (1996), shows that the unit root hypothesis cannot be rejected at even the 10% level of significance. However, from closer inspection of Figure One it is apparent that despite a clear upward trend, UK house price have not risen continuously over the sample period. In particular, the well documented recessionary period of the early to mid 1990s is apparent. This change in behaviour and its following gradual or steady recovery would appear to be well suited to modelling by a smooth transition process. In light of this, it is perhaps unsurprising that the above τ τ and τ gls τ tests with their common underlying assumption of a maintained linear trend are unable to reject the unit root hypothesis. To incorporate the structural change depicted in the house price series under investigation, the smooth transition s αβ , F αβ , ts αβ , F * αβ and ts * αβ test statistics are calculated. These tests are performed using equations ( 1), ( 4) and ( 10) for s αβ , ( 1), ( 4), ( 11) and ( 12) for F αβ and ts αβ , and ( 1), ( 4), ( 12) and ( 13 test, it can be seen that incorporation of structural change via a smooth transition allows the unit root null to be rejected at the 5% level of significance. To examine whether the detected reversion to an underlying smooth transition attractor is of an asymmetric nature, the results for the ST-TAR and ST-MTAR tests can be considered. The results for the ST-TAR tests of [START_REF] Sollis | Asymmetric adjustment and smooth transitions: A combination of some unit root tests[END_REF] show that the unit root is again rejected, this time at the 10% level of significance for F αβ , and the 5% level of significance for ts αβ . The results for the ST-MTAR are more significant, with the unit root hypothesis rejected at the 5% level of significance for F * αβ , and the 1% level of significance for ts * αβ . Therefore, while all of the smooth transition tests are able to reject the null of a unit root, the most significant rejection (at the 1% level) results from application of the newly proposed ST-MTAR test. To investigate further the relative performances of the tests, the AIC for each of the smooth transition tests is reported in Table Four. These results provide additional support for the ST-MTAR test, with this specification delivering the minimum AIC. Considering the estimated asymmetric adjustment parameters of the ST-TAR and ST-MTAR tests, it can be seen that two very similar values are obtained under the former test with (ρ 1 , ρ 2 ) = (-0.150, -0.156), while the estimated values of the two adjustment parameters under MTAR adjustment differ with (ρ 1 , ρ 2 ) = (-0.186, -0.094). This latter finding indicates that the speed of adjustment is much faster for positive changes in the lagged residual in [START_REF] Perron | The Great Crash, the oil price shock and the unit root hypothesis[END_REF], than for negative changes.

Figures One and Two about here Table Four about here 5 Conclusion

In this paper, recent developments in the testing of the unit root hypothesis have been extended with a class of ST-MTAR tests proposed and examined. Via simulation analysis, the ST-MTAR tests have been shown to possess some advantages relative to the existing ST-TAR tests of [START_REF] Sollis | Asymmetric adjustment and smooth transitions: A combination of some unit root tests[END_REF]. However, the ST-MTAR tests have not been developed with the intention of encompassing or dominating the ST-TAR tests, but are instead viewed as an alternative which might prove more appropriate in the presence of a differing asymmetric adjustment scheme. To illustrate the empirical relevance of the newly proposed tests, an empirical application to aggregate UK house prices was undertaken. In contrast to previous results in the literature which have concluded house prices in the UK to be I(1), application of ST, ST-TAR and ST-MTAR tests resulted rejection of the unit root null in the direction of asymmetric stationarity about a smooth transition. In particular, it was found that the presence of a unit root could be rejected beyond the 1% level of significance using the ST-MTAR test which was seen to provide the most significant results of all tests considered. 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 UK ST-trend

  considered ST-TAR testing based upon the Models A, B and C of LNV, a further testing specification denoted by[START_REF] Vougas | Unit roots and (deterministic) smooth transitions II[END_REF] which has since been proposed, was not considered. In the present paper, all four specifications are extended to provide alternative ST-MTAR tests which allow for the inclusion of alternative deterministic terms and breaks. To illustrate the empirical relevance of the ST-MTAR testing procedure, an application to aggregate UK house price data is presented.Over recent years a large literature has emerged examining UK house prices. A feature of this literature is the inference that the UK aggregate house price series is a unit root process (see, inter alia, Cook 2003b,[START_REF] Meen | Regional house prices and the ripple effect: A new interpretation[END_REF][START_REF] Peterson | Further Work on an Economic Model of the Demand for Social Housing, Report to the Department of the Environment, Transport and the Regions[END_REF]. The application of smooth transition unit root tests overturns this inference, with the ST-MTAR unit root test found to provide the most conclusive results of the alternative tests considered.

  u it are zero mean I(0) error processes. A further testing equation, denoted as Model D, is provided in subsequent analysis by[START_REF] Vougas | Unit roots and (deterministic) smooth transitions II[END_REF]:

( 2004 )

 2004 has extended the ST unit root tests given by Models A, B and C ¡ s α , s α(β) , s αβ ¢ to allow for asymmetric adjustment about the non-linear trend specified by the fitted smooth transition. To do this, Sollis employs threshold autoregression with a Heaviside indicator function (I t ) defined as below:

  ),[START_REF] Cook | The convergence of regional house prices in the UK[END_REF] or[START_REF] Dickey | Distribution of the estimators for autoregressive time series with a unit root[END_REF] respectively for Models A, B and C. The resulting test F and t statistics are denoted as F α and ts α for Model A, F α(β) and ts α(β) for Model B and F αβ and ts αβ for Model C. However, while this TAR-based extension to permit asymmetry is to be welcomed, it is suggested here that an MTAR-based indicator function can be employed also to derive a range of alternative asymmetric ST tests. As stated above, this extension has obvious appeal given the power advantage of MTAR tests relative to TAR tests in the context of unit root and cointegration analysis noted previously in the literature (see[START_REF] Enders | Unit root tests and asymmetric adjustment with an example using the term structure of interest rates[END_REF][START_REF] Enders | Cointegration and threshold adjustment[END_REF]. Under MTAR adjustment, the relevant indicator function is then defined as:

  ) for F * αβ and ts * αβ . All of the smooth transition tests are therefore based upon Model C given the noted trending nature of the series, with the degree of augmentation determined as for the τ τ and τ gls τ tests. Before considering the results for the smooth transition unit root tests, Figure Two presents the UK house price series along with the fitted smooth transition. It can be seen that the smooth transition process closely fits the recessionary and recovery periods observed in the 1990s. In

Figure 1 : 16 Page

 116 Figure 1: Aggregate house prices in the UK, 1973-2005.

Figure 2 :

 2 Figure 2: Aggregate house prices in the UK and fitted logistic smooth transition function.

  or the individually most significant parameter. Following earlier notation, the resulting F and

	t statistics are denoted as F * α and ts * α for Model A, F * α(β) and ts * α(β) for Model B, F * αβ and ts * αβ for
	Model C and F * β and ts * β for Model D. 2
	3 Critical values and empirical power analyses
	3.1 Finite-sample critical values of the ST-MTAR test

To generate critical values for the newly proposed ST-MTAR tests, the following data generation process (DGP) is employed:

  To examine the empirical powers of the ST, ST-TAR and ST-MTAR unit root tests, Monte Carlo simulation experimentation is undertaken. The experimental design employed is based upon Sollis

	F o r
	P
	e
	e r
	R e v
	Table One about here i e
	3.2 Empirical power analyses	w

  maximum lag length given by int [12 (T/100)] 0.25 . Justification of this upper bound is provided by[START_REF] Hayashi | Econometrics[END_REF]. The resulting calculated test statistics are reported in TableOne. Comparison of the reported values to the appropriate critical values as provided by, inter alia, Fuller (1996) and Elliott et al.

	F o r
	P
	e
	e r
	R e v
	i e
	w
	The two tests applied are the augmented Dickey-Fuller (1979) (ADF) test and the higher powered
	GLS-based Dickey-Fuller test of Elliott et al. (1996). These resulting unit root test statistics are
	denoted as τ τ and τ gls τ respectively. From inspection of Figure One it can be seen that UK house
	prices display strong trending behaviour. As a result of this, an intercept and linear trend are
	included as deterministic terms when employing the τ τ and τ gls τ tests. The degree of augmentation

of the tests is determined via the Akaike Information Criterion following initial consideration of a

3

The series are mixed-adjusted observations on all properties drawn from the Nationwide Building Society.

Table Four ,

 Four the calculated s αβ , F αβ , ts αβ , F * αβ and ts * αβ test statistics are provided. Considering the original LNV s αβ

Table One :

 One Critical values for the ST-MTAR unit root test

	T		t s * α	F * α	ts * α(β)	F * α(β)	ts * αβ	F * αβ	ts * β	F * β
	50	10%	-3.587	8.620	-4.075 11.553	-4.302 13.037	-3.465	7.948
		5%	-3.901 10.063	-4.387 13.197	-4.630 14.937	-3.808	9.434
		1%	-4.538 13.269	-5.062 16.792	-5.338 19.008	-4.436 12.924
	100 10%	-3.562	8.335	-3.966 10.754	-4.162 12.091	-3.417	7.713
		5%	-3.858	9.653	-4.250 12.177	-4.468 13.663	-3.754	9.029
	1% 250 10% 5% 1%	-4.475 12.917 -3.486 8.077 -3.788 9.329 F o r -4.871 15.400 -3.894 10.315 -4.174 11.524 -4.328 12.018 -4.713 14.180 P	-5.098 16.994 -4.116 11.670 -4.383 13.057 -4.935 16.154	-4.387 12.223 -3.364 7.416 8.699 -3.675 -4.224 11.323
	500 10% 5% 1%	-3.474 -3.751 -4.309 11.611 7.935 9.022	-3.875 10.138 e -4.158 11.541 -4.684 14.176 e r R e -4.065 11.400 -4.353 12.721 -4.892 15.507 v	-3.341 -3.628 -4.208 11.111 7.282 8.450
							i e
							w

Table Two :

 Two Empirical powers in the presence of a stationary ST-TAR process

					s α		ts α		F α		ts * α		F * α
	ρ 1	ρ 2	α 2 γ	10%	5%	10%	5%	10%	5%	10%	5%	10%	5%
	-0.1 -0.3 2 0.5 0.427 0.266 0.371 0.222 0.425 0.269 0.309 0.187 0.412 0.256
	-0.1 -0.9 2 0.5 0.726 0.589 0.752 0.620 0.747 0.615 0.669 0.531 0.753 0.615
	-0.3 -0.1 2 0.5 0.424 0.265 0.387 0.248 0.420 0.267 0.319 0.195 0.417 0.261
	-0.9 -0.1 2 0.5 0.705 0.527 0.746 0.627 0.741 0.578 0.658 0.511 0.736 0.586
	-0.1 -0.3 5 0.5 0.418 0.245 0.358 0.214 0.415 0.251 0.307 0.177 0.400 0.248
	-0.1 -0.9 5 0.5 0.721 0.565 0.751 0.628 0.747 0.601 0.665 0.521 0.748 0.608 -0.3 -0.1 5 0.5 0.410 0.245 0.373 0.236 0.404 0.252 0.312 0.194 0.409 0.255 -0.9 -0.1 5 0.5 0.695 0.522 0.748 0.621 0.729 0.569 0.650 0.516 0.729 0.575 -0.1 -0.3 10 0.5 0.397 0.246 0.342 0.215 0.392 0.247 0.302 0.178 0.382 0.247 F o r -0.1 -0.9 10 0.5 0.702 0.522 0.730 0.608 0.725 0.567 0.611 0.492 0.710 0.568 -0.3 -0.1 10 0.5 0.375 0.225 0.348 0.203 0.377 0.226 0.298 0.180 0.384 0.238 P -0.9 -0.1 10 0.5 0.687 0.526 0.746 0.627 0.724 0.576 0.632 0.493 0.712 0.576 -0.1 -0.3 2 e 5 0.419 0.248 0.357 0.222 0.414 0.256 0.303 0.178 0.399 0.247 -0.1 -0.9 2 5 0.704 0.554 0.724 0.598 0.732 0.588 0.639 0.509 0.728 0.588 5 0.404 0.233 0.369 0.227 0.403 0.238 0.313 0.187 0.407 0.247 e r -0.3 -0.1 2 -0.9 -0.1 2 5 0.693 0.549 0.749 0.625 0.732 0.590 0.665 0.508 0.731 0.583 -0.1 -0.3 5 5 0.375 0.223 0.336 0.198 0.374 0.230 0.285 0.171 0.369 0.226 -0.1 -0.9 5 5 0.677 0.495 0.725 0.581 0.714 0.539 0.597 0.469 0.686 0.540 -0.3 -0.1 5 R e v 5 0.350 0.203 0.321 0.179 0.351 0.204 0.280 0.165 0.361 0.216 -0.9 -0.1 5 5 0.660 0.491 0.738 0.597 0.698 0.547 0.618 0.465 0.686 0.540 -0.1 -0.3 10 i e 5 0.307 0.175 0.286 0.171 0.309 0.177 0.259 0.153 0.315 0.181 -0.1 -0.9 10 5 0.623 0.453 0.710 0.575 0.667 0.517 0.597 0.467 0.667 0.515 w
	-0.3 -0.1 10	5 0.309 0.178 0.282 0.163 0.309 0.186 0.237 0.140 0.311 0.182
	-0.9 -0.1 10	5 0.615 0.456 0.703 0.563 0.661 0.504 0.595 0.456 0.650 0.514
	Notes: The tabulated figures represent empirical power of the alternative smooth transition unit
	root tests under a ST-TAR data generation process.

Table Three :

 Three Empirical powers in the presence of a stationary ST-MTAR process * The tabulated figures represent empirical power of the alternative smooth transition unit root tests under a ST-MTAR data generation process.

				s α		ts α		F α		ts * α		F * α
	ρ 1	ρ 2	α 2 γ	10%	5%	10%	5%	10%	5%	10%	5%	10%	5%
	-0.1 -0.3 2 0.5 0.534 0.340 0.465 0.295 0.532 0.345 0.621 0.464 0.643 0.447
	-0.1 -0.9 2 0.5 0.997 0.986 0.995 0.969 0.999 0.989 1.000 1.000 1.000 1.000
	-0.3 -0.1 2 0.5 0.541 0.350 0.492 0.324 0.545 0.361 0.626 0.465 0.646 0.457
	-0.9 -0.1 2 0.5 0.998 0.983 0.994 0.978 0.999 0.990 1.000 1.000 1.000 1.000
	-0.1 -0.3 5 0.5 0.526 0.329 0.453 0.279 0.523 0.334 0.614 0.460 0.635 0.442
	-0.1 -0.9 5 0.5 0.996 0.987 0.995 0.971 0.999 0.991 1.000 1.000 1.000 1.000 -0.3 -0.1 5 0.5 0.527 0.340 0.463 0.302 0.528 0.344 0.620 0.451 0.638 0.454 -0.9 -0.1 5 0.5 0.999 0.986 0.996 0.982 1.000 0.992 1.000 1.000 1.000 1.000 -0.1 -0.3 10 0.5 0.504 0.328 0.440 0.287 0.500 0.335 0.594 0.446 0.617 0.444 -0.1 -0.9 10 0.5 0.995 0.984 0.994 0.981 0.997 0.988 1.000 1.000 1.000 1.000 -0.3 -0.1 10 0.5 0.502 0.316 0.455 0.293 0.502 0.322 0.597 0.454 0.615 0.441 -0.9 -0.1 10 0.5 0.997 0.988 0.995 0.983 0.999 0.993 1.000 1.000 1.000 1.000 -0.1 -0.3 2 5 0.519 0.327 0.445 0.277 0.517 0.342 0.596 0.422 0.609 0.422 -0.1 -0.9 2 5 0.995 0.979 0.991 0.974 0.997 0.984 1.000 1.000 1.000 1.000 -0.3 -0.1 2 5 0.525 0.332 0.466 0.313 0.533 0.337 0.590 0.436 0.627 0.442 -0.9 -0.1 2 5 0.997 0.987 0.996 0.982 1.000 0.993 1.000 1.000 1.000 1.000 -0.1 -0.3 5 5 0.477 0.302 0.409 0.263 0.469 0.299 0.580 0.416 0.585 0.405 -0.1 -0.9 5 5 0.994 0.981 0.994 0.979 0.996 0.988 1.000 1.000 1.000 1.000 -0.3 -0.1 5 5 0.470 0.283 0.421 0.258 0.474 0.290 0.573 0.421 0.586 0.404 -0.9 -0.1 5 5 0.996 0.982 0.993 0.979 0.999 0.991 1.000 1.000 1.000 1.000 -0.1 -0.3 10 5 0.430 0.248 0.381 0.232 0.432 0.256 0.604 0.429 0.575 0.379 -0.1 -0.9 10 5 0.993 0.976 0.992 0.971 0.997 0.984 1.000 1.000 1.000 1.000 -0.3 -0.1 10 5 0.425 0.255 0.374 0.239 0.424 0.261 0.572 0.411 0.566 0.378 -0.9 -0.1 10 5 0.997 0.984 0.993 0.980 0.998 0.991 1.000 1.000 1.000 1.000 o r P e e r R e v i e Notes: F w

Table Four :

 Four Linear and smooth transition unit root tests for UK house prices The tabulated figures represent empirical output resulting from the application of linear and smooth transition unit root test statistics for UK aggregate house price data. All smooth transition unit root tests are performed using the Model C testing specification. A single, double or triple asterisk denotes rejection at the 10%, 5% or 1% levels of significance respectively.

	Test	Calculated test statistic	AIC	(ρ 1 , ρ 2 )
	ADF	τ τ : -2.207
	GLS-DF	τ gls τ : -1.737
	LNV	s αβ : -5.184 * *	-8.175	-
	ST-TAR	F α,β : 13.328 * ts α,β : -4.223 * *	-8.159	-0.150, -0.156
	ST-MTAR	F * α,β : 15.304 * * ts * α,β : -5.401 * * *	-8.187	-0.186, -0.094
	Notes:

15 Page 15 of 17 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

In the interest of brevity calculation of the smooth transition unit root tests is only outlined here. Further details can be obtained from reference to LNV and[START_REF] Vougas | Unit roots and (deterministic) smooth transitions II[END_REF].

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

[START_REF] Vougas | Unit roots and (deterministic) smooth transitions II[END_REF] provides a detailed discussion of alternative approaches to the NLS estimation required for smooth transition unit root tests, with close attention paid to the impact of differing optimisation algorithms upon resulting critical values. In this paper, critical values for the ST-MTAR tests are generated using the superior NLP R °constrained optimiser of the GAUSS subroutine FANPAC R °. This optimiser combines the Broyden, Fletcher, Goldfarb and Shanno (BFGS) algorithms utilised by LNV, with the Newton-Raphson algorithm. This superior optimiser is utilised for all of the tests employed. Also, an initial grid search is employed for both τ and γ, thereby fully endogenising structural change. 6 Page 6 of 17 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript