María Arrazola

José De Hevia
email: jose.dehevia@urjc.es

JEL Code: E31 -Price Level|Inflation|Deflation < E3 -Prices, Business Fluctuations, and Cycles < E -Macroeconomics and Monetary

Keywords:

This paper proposes and estimates an inflation indicator for the European Monetary Union (EMU). This indicator is set up so that it is contemporarily not affected by the changes in price differentials among EMU countries. The results show that the Monetary Union Index of Consumer Prices (MUICP), which is the inflation measure that the European Central Bank (ECB) takes as a reference for monetary policy purposes, could be understating the value of the inflation in the euro zone. It is also concluded that regional peculiarities are fundamental in the evolution of prices in the different EMU countries.

Introduction

Since January 1999 a broad spectrum of European countries have a common currency: the euro. The European Monetary Union (EMU) is constituted by 12 countries (Belgium, Germany, Greece, Spain, France, Ireland, Italy, the Netherlands, Austria, Portugal, Finland and Luxembourg) each with its economic peculiarities but all of them with a common monetary policy conducted by the European Central Bank (ECB). The Treaty on European Union assigns the Eurosystem the primary objective of maintaining price stability in the euro area. The ECB has quantified this objective in terms of the Monetary Union Index of Consumer Prices (MUICP), which on a medium term should have an annual increase of below 2%.

In this context, with a common monetary policy focussing on price stability and with a very specific inflation objective, there has recently been a great interest in establishing good indicators of inflation in the euro area as alternatives to the MUICP. Efforts have mainly been devoted to the construction of reliable inflation indicators, and in particular to the setting up of what is usually known as core inflation indexes whose evolution is not distorted by transitory changes in the relative prices of goods that are unrelated to the medium-run objectives of central bankers (see, for example, [START_REF] Cristadoro | A Core Inflation Index for the Euro Area[END_REF], Bagliano et al., 2002and Vega and Wynne, 2003).

The aim of this work is to propose a simple indicator of inflation in the euro zone from a different perspective. The idea is that a good inflation indicator of a monetary region should not be affected by asymmetric shocks in prices in different union members nor by the idyosincratic effects of a common shock. A good euro zone inflation indicator should not be affected by changes in price differentials between countries. Taking this as a point of departure, a decomposition of the price variations in each country into two components is suggested, one common to all the countries and the other idiosyncratic.

The common component is the inflation indicator proposed in this work. Its advantage is that it is very simple to estimate and interpret.

In addition to this introduction the article contains three other sections. The second section describes the statistical framework in which the inflation indicator is defined.

The third section presents the empirical results. The paper ends with a section of conclusions.

A very simple framework for the analysis of inflation in the EMU

The approach to the problem of inflation measurement is purely statistical and very simple. In a monetary region like the euro zone, let us assume that the variations in prices of the goods in each country j at a moment t, denominated by ( ) ( ) ( )

=

. This suggests that a measurement of t * can be constructed, exploiting its independence of the observable components

d jit jt it = .

A proposal for the identification of the common component

We propose an identification strategy for the common component t * based on the information contained in jt : The orthogonality conditions are imposed in the first differences given the non stationary character usually presented by the variation rates of prices in the different countries (see, for example, Ribba, 2003, Marques el al., 2002, Freeman, 1998, Mishkin, 1984, and Schwert,1987).

t j j n jt * = = 1 where j j n = = 1 1 j n t T = = 1 2 1 2 , , .
Note that equation ( 2) gives (n-1)x(n-1) orthogonality conditions, (n-1)x(n-2) of them being redundant. So that (2) can be expressed as:

( ) [ ] Cov i n t T t t i t = = = * , , ..., , ,..., 1 0 2 3 1 2 (3)
The variations in t * are contemporarily independent of the variations in ( )

1t i t
which are a function of the price differentials in the different countries. It is in this sense that t * is independent of the price differentials between countries and constitutes the common component.

One advantage of this way of identifying t * is that its estimation becomes very simple.

The weights can be estimated by Least Squares from the following regression model: Once the common component has been identified it can be of interest to decompose the mean value of jt ( j ) into two components, the mean value of the common component and the mean value of the idiosyncratic component. From (1):

( ) ( ) ( ) = + + + + 1 2 1 2 3 1 3 1 t t
j j j n = + = * * * ,..., 1 (5)
It is also possible to analyse which part of the variance of jt comes from the common component and which part comes from the idiosyncratic one.

The empirical analysis

The data employed in the analysis come from the Eurostat database and cover the period between January 1999, the time at which the EMU was officially constituted, and August, 2004. Two possible price indicators were considered for each country: the Harmonized Index of Consumer Prices (HICP), and the component "All items excluding energy and unprocessed food" from the HICP (HICPEEUF), which is usually used as a core inflation indicator. To minimize the effect of seasonality we have used ( )

12 Ln HICPEEUF jt which show their I(1) character.

The HICP's of the EMU member countries are aggregated to set up an inflation indicator for the whole of the euro zone, the MUICP. In this indicator each country has a weight obtained from the share of each country's household final monetary consumption in the relevant total. The MUICP plays a key role in the design of the monetary policy of the euro area by the ECB, which has defined its objective of price stability as an annual increase in the MUICP of below 2% to be maintained over the medium term. Similarly to the MUICP, another aggregate inflation indicator for the euro area is obtained from the HICPEEUF of each country. The HICPEEUF of the euro zone is frequently used as an indicator of the core inflation in that monetary area.

Given the decisive role they play in the monitoring and control of EMU prices, it would seem to be relevant to analyse if the MUICP and the HICPEEUF of the euro zone inflations could constitute measures of the common component described in the previous section, which reflects the generalized rise in all the prices of goods denominated in euros. It is easy to verify that they could not. Table 1 presents, as an illustration, the correlation coefficients between the variations in ( )

12 Ln MUICP and the variations in some of the differentials between countries in

( )

12 Ln HICP jt . It also presents the correlation coefficients between the variations in ( )

12 Ln HICPEEUF of the euro area and the variations in some of the differentials between countries in

( )

12 Ln HICPEEUF jt . It can be seen that many of the correlations exceed 0.25 in absolute value, which suggests that neither the MUICP nor the HICPEEUF of the euro zone are independent of the price differentials between countries, so that any idiosyncratic shock in the prices of any country affects those indicators.

Table 2 shows the results of the estimation of equation ( 4), from which the weights of each country in the common component are obtained. The equation has been estimated

both with HICP and HICPEEUF data. For a large number of countries the weights were not statistically significant at usual significance levels, neither individually nor jointly 1 , so that restricted estimations of equation ( 4) are also presented. Also, as data starting from 1999 was being used, structural change tests were carried out in the weights in January 2001, when Greece was incorporated into the EMU. The results show that, either with the HICP data or with those of the HICPEEUF, the hypothesis of the absence of a structural change cannot be rejected 2 .

1 With the HICP data a Wald test was carried out of the hypothesis of joint significance of the weights of Belgium, Greece, Spain, France, Ireland, Luxembourg, Austria and Finland obtaining a p-value of 0.577.

For the HICPEEUF data a test was made for the weights of Greece, Spain, Luxembourg, Austria and Portugal obtaining a p-value of 0.165.

2 With the HICP data the p-value obtained was 0.621 and with the HICPEEUF data it was 0.587. 12 Ln HICP and in

( )

12 Ln HICPEEUF for each country in that part related to the common component and that related to the idiosyncratic component. The results are shown in Table 4 5 . It can again be seen that the idiosyncratic components have a great weight in the variance of the inflation measurements based on the HICP or on the HICPEEUF, exceeding 55% for all countries. For the euro area, the variations in the common component are only responsible for 42-43% of the variations in inflation measured with the MUICP or with the HICPEEUF, which is evidence on the limitations of these variables as measurements of the common component.

Conclusions

The aim of this work has been to propose a simple inflation indicator for the euro zone. the ECB takes as a reference for its monetary policy, could be understating the true rate of inflation in the euro zone. To be specific, for the period between 1999 and 2004, this undervaluation could be around 20%. The same happened with the HICPEEUF.

Another relevant conclusion is that the idiosyncratic components have a great weight in the usual inflation measurements used in each of the different countries in the euro zone, both in terms of the average and in terms of the variance. This suggests that, in spite of the unified monetary policy, regional peculiarities continue to be fundamental in the evolution of prices in the different EMU countries.

unrestricted and restricted equations. In this context, with a common monetary policy focussing on price stability and with a very specific inflation objective, there has recently been a great interest in establishing good indicators of inflation in the euro area as alternatives to the MUICP. Efforts have mainly been devoted to the construction of reliable inflation indicators, and in particular to the setting up of what is usually known as core inflation indexes whose evolution is not distorted by transitory changes in the relative prices of goods that are unrelated to the medium-run objectives of central bankers (see, for example, [START_REF] Quah | Measuring core inflation[END_REF][START_REF] Bjornland | Identifying domestic and imported core inflation[END_REF], Bagliano et al., 2002[START_REF] Bagliano | Measuring US core inflation: A common trends approach[END_REF], Vega and Wynne, 2003[START_REF] Marques | Evaluating core inflation indicators[END_REF][START_REF] Cristadoro | A core inflation indicator for the Euro Area[END_REF].

The aim of this work is to propose a simple indicator of inflation in the euro zone from a different perspective. The idea is that a good inflation indicator of a monetary region should not be affected by asymmetric shocks in prices in different union members nor should not be affected by changes in price differentials between countries. Taking this as a point of departure, a decomposition of the price variations in each country into two components is suggested, one common to all the countries and the other idiosyncratic.

The common component is the inflation indicator proposed in this work. Its advantage is that it is very simple to estimate and interpret.

In addition to this introduction the article contains three other sections. The second section describes the statistical framework in which the inflation indicator is defined.

The third section presents the empirical results. The paper ends with a section of conclusions.

A very simple framework for the analysis of inflation in the EMU

The approach to the problem of inflation measurement is purely statistical and very simple. In a monetary region like the euro zone, let us assume that the variations in prices of the goods in each country j at a moment t, denominated by

=

. This suggests that a measurement of t * can be constructed, exploiting its independence of the observable components

d jit jt it = .

A proposal for the identification of the common component

We propose an identification strategy for the common component The orthogonality conditions are imposed in the first differences given the non stationary character usually presented by the variation rates of prices in the different countries (see, for example, Charemza el al. 2005, Ribba, 2003[START_REF] Marques | Evaluating core inflation indicators[END_REF], Marques el al., 2002, Freeman, 1998, Mishkin, 1984, and Schwert,1987).

Note that equation ( 2) gives (n-1)x(n-1) orthogonality conditions, (n-1)x(n-2) of them being redundant. So that (2) can be expressed as:

( ) [ ] Cov i n t T t t i t = = = * , , ..., , ,..., 1 0 2 3 1 2 (3)
The variations in t * are contemporarily uncorrelated with the variations in ( )

1t i t
which are a function of the price differentials in the different countries. It is in this sense that t * is independent of the price differentials between countries and constitutes the common component.

One advantage of this way of identifying t * is that its estimation becomes very simple.

The weights can be estimated by Least Squares from the following regression model: Once the common component has been identified it can be of interest to decompose the mean value of jt ( j ) into two components, the mean value of the common component and the mean value of the idiosyncratic component. From (1):

F
j j j n = + = * * * ,..., 1 (5)
It is also possible to analyse which part of the variance of jt comes from the common component and which part comes from the idiosyncratic one. Taking equations ( 1) and ( 2

The empirical analysis

The data employed in the analysis come from the Eurostat database and cover the period between January 1999, the time at which the EMU was officially constituted, and Given the decisive role they play in the monitoring and control of EMU prices, it would seem to be relevant to analyse if the MUICP and the HICPEEUF of the euro zone inflations could constitute measures of the common component described in the previous section, which reflects the generalized rise in all the prices of goods denominated in euros. It is easy to verify that they could not. Table 1 presents, as an illustration, the correlation coefficients between the variations in ( )

12 Ln MUICP and the variations in some of the differentials between countries in

( )

12 Ln HICP jt . It also presents the correlation coefficients between the variations in ( )

12 Ln HICPEEUF of the euro area and the variations in some of the differentials between countries in

( )

12 Ln HICPEEUF jt . It can be seen that many of the correlations exceed 0.25 in absolute value and are statistically significant at the 5% level, which suggests that neither the MUICP nor the HICPEEUF of the euro zone are uncorrelated with the price differentials between countries, so that any idiosyncratic shock in the prices of any country affects those indicators.

Table 2 shows the results of the estimation of equation ( 4), from which the weights of each country in the common component are obtained. The equation has been estimated

both with HICP and HICPEEUF data. For a large number of countries the weights were not statistically significant at usual significance levels, neither individually nor jointly 1 , so that restricted estimations of equation ( 4) are also presented. Also, as data starting from 1999 was being used, structural change tests were carried out in the weights in January 2001, when Greece was incorporated into the EMU. The results show that,

1 With the HICP data a Wald test was carried out of the hypothesis of joint significance of the weights of Belgium, Greece, Spain, France, Ireland, Luxembourg, Austria and Finland obtaining a p-value of 0.577. For the HICPEEUF data a test was made for the weights of Greece, Spain, Luxembourg, Austria and Portugal obtaining a p-value of 0.165. It is also of interest to use the equation ( 6) to break down the variances of the variations in ( )

12 Ln HICP and in

( )

12 Ln HICPEEUF for each country in that part related to the common component and that related to the idiosyncratic component. The results are shown in Table 4 5 . It can again be seen that the idiosyncratic components have a great weight in the variance of the inflation measurements based on the HICP or on the HICPEEUF, exceeding 55% for all countries. For the euro area, the variations in the common component are only responsible for 42-43% of the variations in inflation measured with the MUICP or with the HICPEEUF, which is evidence on the limitations of these variables as measurements of the common component.

Conclusions

The aim of this work has been to propose a simple inflation indicator for the euro zone.

An inflation indicator was set up with changes contemporarily orthogonal to the variations in the inflation differentials between countries. In this sense, the inflation indicator constructed is not affected by the effects of asymmetric shocks in prices in the different countries. Its objective is to reflect the generalized rise in all the prices of goods denominated in euros.

The variations in the prices of the different countries can be broken down into two components: the common component, which is the inflation indicator proposed, and the (MUICP and HICPEEUF). It was concluded that the MUICP, which is the indicator that the ECB takes as a reference for its monetary policy, could be understating the true rate of inflation in the euro zone. To be specific, for the period between 1999 and 2004, this undervaluation could be around 20%. The same happened with the HICPEEUF.

Another relevant conclusion is that the idiosyncratic components have a great weight in the usual inflation measurements used in each of the different countries in the euro zone, both in terms of the average and in terms of the variance. This suggests that, in spite of the unified monetary policy, regional peculiarities continue to be fundamental in the evolution of prices in the different EMU countries.

  Figure3shows the evolution of

  An inflation indicator was set up with changes contemporarily orthogonal to the variations in the inflation differentials between countries. In this sense, the inflation indicator constructed is not affected by the effects of asymmetric shocks in prices in the different countries. Its objective is to reflect the generalized rise in all the prices of goods denominated in euros.The variations in the prices of the different countries can be broken down into two components: the common component, which is the inflation indicator proposed, and the idiosyncratic component. With data from the 12 EMU countries, both components were estimated and compared with two other current euro area inflation measurements (MUICP and HICPEEUF). It was concluded that the MUICP, which is the indicator that 5 Note that the estimated variances for the variations in the common component are the same in the

  effects of a common shock. A good euro zone inflation indicator

August, 2004 .

 2004 Two possible price indicators were considered for each country: the Harmonized Index of Consumer Prices (HICP), and the component "All items

  a negative contribution to the average of the idiosyncratic component, and that of Ireland with a positive contribution.

  With data from the 12 EMU countries, both components were estimated and compared with two other current euro area inflation measurements

  Figure 3

  , measures the generalized rise in all the prices of goods denominated in euros. The idiosyncratic component, denoted by jt ** , reflects the specific evolution of prices in each country, due for example to asymmetric shocks in the prices of one or several goods or to the idiosyncratic effects of a common shock. Thus:

				are assumed to be orthogonal,	t *	will also be orthogonal to
	d	jit	=	jt	it	=	jt **	it **	j i j i ,	=	,..., 1	n	. It is important to point out that
	d jit		jt	it
		jt	=	jt Ln P	=	jt Ln P		jt Ln P	1 , have two components, one common to all the
	countries in the monetary region and the other idiosyncratic. The common component,
	denoted by t
										jt	=		t	+	jt	j	=	n

*

=

, which is observable, only contains information on idiosyncratic movements of prices in the different countries. So, for instance, an autonomous shock in the prices of a country, j, would not be reflected in t * but they would in jt ** , which would cause a variation in d jit jt it

Table 1 Correlation coefficients between the variations in

 1

( )

12 Ln MUICP and in

( )

12 Ln HICPEEUF of

the euro area and the variations in some of the differentials between countries in

			( ) 12 Ln HICP j and in	( 12 Ln HICPEEUF j	)
		Differential with respect to		Differential with respect to
			Germany		Portugal
		MUICP	HICPEEUF of	MUICP HICPEEUF of
				the euro area		the euro area
	Germany		--	--		-0.60	-0.45
	Portugal		0.60	0.45		--	--
	The Netherlands		0.49	0.53		-0.12	0.14
	Italy Ireland Austria Greece Spain F o r	0.40 0.26 0.26 0.25 0.13	0.49 0.49 0.38 0.37 0.09		-0.28 -0.33 -0.41 -0.36 -0.53	-0.35 0.12 -0.04 -0.07 -0.38
	Finland France Belgium Luxembourg	0.17 0.05 -0.01 P -0.07 e	0.51 0.51 0.15 0.38		-0.47 -0.61 -0.41 -0.45	0.07 -0.04 -0.15 0.10
			e r
				R e v
				i e
					w

Note: MUICP: Monetary Union Index of Consumer Prices; HICPEEUF: All items excluding energy and unprocessed food from the Harmonized Index of Consumer Prices.

Table 3 Descomposition of the mean

 3

				Based on HICP	Based on HICPEEUF
		Mean ( 12 Ln HICP	)	Mean **	Mean 12 Ln HICPEEUF (	)	Mean **
	Germany		0.013		-0.012	0.009	-0.11
						(-92%)	(-122.2%)
	Portugal		0.031		0.006	0.032	0.012
						(19.4%)	(37,5%)
	The Netherlands		0.029		0.004	0.020	0.000
						(13.8%)	(0%)
	Italy		0.024		-0.001	0.022	0.002
						(-4.1%)	(9.1%)
	Ireland		0.038		0.013	0.038	0.018
						(34.2%)	(47.4%)
	Austria		0.016		-0.009	0.015	-0.005
						(-56.3%)	(-33.3%)
	Greece		0.031		0.006	0.030	0.010
						(19.4%)	(33.3%)
	Spain		0.030		0.005	0.028	0.008
						(16.6%)	(28.6%)
	Finland		0.018		-0.007	0.017	-0.003
						(-38.9%)	(-17,6%)
	France		0.017		-0.008	0.016	-0.004
						(-47.1%)	(-25%)
	Belgium		0.018		-0.007	0.016	-0.004
						(-38.9%)	(-25%)
	Luxembourg		0.024		-0.001	0.023	0.003
						(-4.2%)	(13%)
	Note: HICP: Harmonized Index of Consumer Prices. HICPEEUF: All items excluding
	energy and unprocessed food from the HICP. Numbers in parentheses are	12	** Ln HICP (	)	× 1 100	and
		**
	12	( Ln HICPEEUF	)	× 1 100	respectively.

** : Idiosyncratic component. Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Page 22 of 45 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	1. Introduction
	Since January 1999 a broad spectrum of European countries have a common currency:
	the euro. The European Monetary Union (EMU) is constituted by 12 countries
	(Belgium, Germany, Greece, Spain, France, Ireland, Italy, the Netherlands, Austria,
	Portugal, Finland and Luxembourg) each with its economic peculiarities but all of them
	with a common monetary policy conducted by the European Central Bank (ECB). The
	Treaty on European Union assigns the Eurosystem the primary objective of maintaining F price stability in the euro area. The ECB has quantified this objective in terms of the o r Monetary Union Index of Consumer Prices (MUICP), which on a medium term should
	P have an annual increase of below 2%.
	e
	e r
	R e v
	i e
	w

Table 1 Correlation coefficients between the variations in

 1

	( 12 Ln MUICP and in )

the euro area and the variations in some of the differentials between countries in

	( ) 12 Ln HICP j and in	( 12 Ln HICPEEUF j	)
	Differential with respect to		Differential with respect to
	Germany			Portugal
	MUICP	HICPEEUF of	MUICP HICPEEUF of
	Germany Portugal The Netherlands Italy Ireland Austria Greece Spain Finland F o r France Belgium P --0.60 * 0.49 * 0.40 * 0.26 * 0.26 * 0.25 * 0.13 0.17 0.05 -0.01 Luxembourg -0.07 e	the euro area --0.45 * 0.53 * 0.49 * 0.49 * 0.38 * 0.37 * 0.09 0.51 * 0.51 * 0.15 0.38 *		-0.60 * ---0.12 -0.2 * 8 -0.33 * -0.41 * -0.36 * -0.53 * -0.47 * -0.61 * -0.41 * -0.45 *	the euro area -0.45 * --0.14 -0.35 0.12 -0.04 -0.07 -0.38 * 0.07 -0.04 -0.15 0.10
	Note: MUICP: Monetary Union Index of Consumer Prices; HICPEEUF: All items excluding energy and unprocessed food from the Harmonized Index of e r
	Consumer Prices. (*) Significant at the 5% level. R e v
		i e
			w

Table 3 Descomposition of the mean

 3 : Augmented Dickey Fuller Unit Root Test PP: Phillips Perron Unit Root Test HICPEEUF: All items excluding energy and unprocessed food from the Harmonized Index of Consumer Prices. (*) Significant at the 5% level. .

					Based on HICP		Based on HICPEEUF
			Mean ( 12 Ln HICP	)	Mean **	Mean 12 Ln HICPEEUF (	)	Mean **
	Germany			0.013		-0.012		0.009	-0.11
							(-92%)			(-122.2%)
	Portugal			0.031		0.006		0.032	0.012
							(19.4%)			(37,5%)
	The Netherlands			0.029		0.004		0.020	0.000
							(13.8%)			(0%)
	Italy			0.024		-0.001		0.022	0.002
							(-4.1%)			(9.1%)
	Ireland			0.038		0.013		0.038	0.018
							(34.2%)			(47.4%)
	Austria			0.016		-0.009		0.015	-0.005
							(-56.3%)			(-33.3%)
	Greece			0.031		0.006		0.030	0.010
							(19.4%)			(33.3%)
	Spain			0.030		0.005		0.028	0.008
							(16.6%)			(28.6%)
	Finland			0.018		-0.007		0.017	-0.003
							(-38.9%)			(-17,6%)
	France			0.017		-0.008		0.016	-0.004
							(-47.1%)			(-25%)
	Belgium			0.018		-0.007		0.016	-0.004
							(-38.9%)			(-25%)
	Luxembourg			0.024		-0.001		0.023	0.003
							(-4.2%)			(13%)
	Note: HICP: Harmonized Index of Consumer Prices. HICPEEUF: All items excluding
	energy and unprocessed food from the HICP. ** : Idiosyncratic component.
									**
	Numbers	in	parentheses	are	12	( Ln HICP	)	× 1 100	and
		**
	12	( Ln HICPEEUF	)	× 1 100	respectively.

ADF

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

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

Ln MUICP and of the estimated common component of the HICP's, obtained both from the restricted and from the unrestricted estimations of equation (4). Likewise, Figure4presents the evolution of the

Note that the estimated variances for the variations in the common component are the same in the unrestricted and restricted equations.

ACKNOWLEDGEMENTS

We thank anonymous referee for useful comments on a previous draft of this paper. José de Hevia is grateful to Ministerio de Educación of Spain for financial support to carry out this research (project SEJ2006-06104).

Lag=3

Lag=12 ADF PP ADF Lag=3 Lag=12 ADF PP ADF

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

Appendix Table A.1

Unit Root Test ( )

Ln HICP = 12 excluding energy and unprocessed food" from the HICP (HICPEEUF), which is usually used as a core inflation indicator. To minimize the effect of seasonality we have used year-on-year variation rates, defined as:

Ln HICP Ln HICP Ln HICP ( )

12 Ln HICPEEUF jt which show their I(1) character.

The HICP's of the EMU member countries are aggregated to set up an inflation indicator for the whole of the euro zone, the MUICP. In this indicator each country has a weight obtained from the share of each country's household final monetary consumption in the relevant total. The MUICP plays a key role in the design of the monetary policy of the euro area by the ECB, which has defined its objective of price stability as an annual increase in the MUICP of below 2% to be maintained over the medium term. Similarly to the MUICP, another aggregate inflation indicator for the euro area is obtained from the HICPEEUF of each country. The HICPEEUF of the euro zone is frequently used as an indicator of the core inflation in that monetary area.

either with the HICP data or with those of the HICPEEUF, the hypothesis of the absence of a structural change cannot be rejected 2 .

Figure 3 shows the evolution of ( )

12 Ln MUICP and of the estimated common component of the HICP's, obtained both from the restricted and from the unrestricted estimations of equation ( 4). Likewise, Figure 4 presents the evolution of the ( )

12 Ln HICPEEUF of the euro zone together with its corresponding common components. In both cases it can be observed that there are no great differences between the common component calculated from the unrestricted and restricted models.

As can be seen, in both cases the common components are almost always above ( )

12 Ln MUICP and ( )

12 Ln HICPEEUF of the euro zone, which suggests that these measurements could be underestimating the inflation of the euro area. To be specific, the average of ( )

12 Ln MUICP for the period considered is 20% lower than that of the corresponding common components 3 and that of the ( )

12 Ln HICPEEUF of the euro zone is 15% lower 4 .

It is also useful to calculate for each country, from equation ( 5), the contribution of its corresponding idiosyncratic component to the average of ( )

12 Ln HICP and of ( )

12 Ln HICPEEUF , shown in Table 3. It should be highlighted the importance of the idiosyncratic components in usual inflation measures. Especially notable is the case of 2 With the HICP data the p-value obtained was 0.621 and with the HICPEEUF data it was 0.587. 3 The average of ( )

12 Ln MUICP is 0.020 and for both common components 0.025. 4 The average of ( )

12 Ln HICPEEUF of the euro-zone is 0.017 compared to 0.020 for both common components.


Keywords: Food-Away-From-Home, Quick-service, Maximum likelihood estimation, Semiparametric techniques Parametric vs. Semiparametric

Analysis

) disaggregated the Greek market into expenditure on restaurant meals, expenditure in coffee houses and expenditure on takeaway meals and canteens.

Introduction

Ireland has seen record levels of economic growth in recent times coupled with rising incomes and increased employment. These prosperous times have seen corresponding growth in the level of weekly household expenditure and labour force participation. As a result, food consumed away from home (FAFH) constitutes an increasingly important part of Irish food expenditure. 1 Between 1987 and 1999/2000 the proportion of total food expenditure allocated to FAFH increased from 14 per cent to 23 per cent. 2 In particular, the quick-service sector is recognised as the fastest growing component. The sector is somewhat diverse in that its components include the branded fast food chains, ethnic takeaways and traditional chip shop takeaways (Mintel, 2001). The sector has outperformed the wider eating out market in recent times in terms of growing market share at the expense of full service options such as hotel and restaurant meals.

The main objective of this paper is to analyse the factors determining expenditure on quick-service meals by Irish households. One feature of this study is that while previous studies on FAFH in Europe have examined the entire market [START_REF] Manrique | Working Women and Expenditures on Food-Away-From-Home in Spain[END_REF][START_REF] Mihalopoulos | Greek Household Consumption of Food-Away-From-Home: Microeconometric Approach[END_REF], little work has been done on disaggregating the market into its diverse sub-sectors. 3 A second objective is to compare some methodological alternatives which can be used in estimating models of household expenditure at the micro level. A F o r P e e r R e v i e w 2 discussion of both parametric and semiparametric alternatives to estimating limited dependent variable models of the kind proposed in this paper is also provided.

The paper is structured into the following sections. Section 2 describes the data and variables used in this study while Section 3 discusses the methodology.

Section 4 compares the performance of the various estimators considered and identifies the most appropriate one for use in this analysis. The results of the model are described in Section 5. The paper concludes with Section 6.

Data and Variables

The data used in this study are taken from the Irish Household Budget Surveys (HBS) of 1994/5 and 1999/2000, collected by the Central Statistics Office of Ireland (CSO) (CSO, 1997;[START_REF] Lazaridis | Household Consumption of Food-Away-From-Home in Greece[END_REF]. 4 In the HBS each household maintains a detailed diary of household expenditure over a two week period. Data on the socio-economic characteristics of household members are also collected. The survey covered a random sample of 7,877 and 7,644 households in both urban and rural areas throughout the state in 1994 and 1999 respectively. Only households whose size is readily identifiable from the HBS are included in this analysis. The records range from single adult households to households with up to four adults with and without children, resulting in a sample size of 7,305 households in 1994 and 7,171 households in 1999.

The dependent variable is household expenditure on quick service meals adjusted for household size using EU adult equivalence scales. 5 The HBS does not report price or quantity data and as a result price is assumed constant across 4 The 1994/5 HBS and the 1999/2000 HBS are hereafter referred to as 1994 and 1999.

5 EU adult equivalence scales give the first adult a weight of 1, each other adult 0.7, and each child under 14 years a weight of 0.5. 3 each cross-section. As quick-service meals are a relatively homogeneous product it is unlikely that there would be much variation in price. Quality differences are also uncontrolled for due to data limitations.

The theory of household production [START_REF] Becker | A Theory of the Allocation of Time[END_REF] underpins much of the literature on FAFH consumption. The household is seen as a consuming and a producing unit. The value of the household's time is therefore important as households with a higher opportunity cost of time can be expected to outsource household production such as meal preparation by purchasing time-saving products such as FAFH. In this study, the number of workers employed in the labour force is used as a proxy for household time constraints. 6 Furthermore, the ever expanding commuter belt around urban areas in Ireland and the increase in the length of the average commute to work places greater time pressures on individuals commuting long distances compared with those that do not. A variable representing whether or not the household is a 'commuter' household is therefore also incorporated into this analysis as a second proxy for the opportunity cost of time of the household.

Recent evidence of Irish households' food expenditure patterns has indicated that there are two competing factors influencing expenditure decisions: health knowledge and convenience [START_REF] Newman | Infrequency of Purchase and Double Hurdle Model of Irish Household Meat Expenditure[END_REF][START_REF] Yoo | A Robust Approach to Dealing with Zero Expenditures on Mobile Communications[END_REF]. In particular, recent media exposure to the health consequences of obesity and diabetes may affect the demand for quick-service foods. FAFH has been found to have lower nutritional quality than food prepared at home across international studies [START_REF] Binkley | The Relation between Dietary Change and Rising US Obesity[END_REF][START_REF] Burns | Foods Prepared Outside the Home: Association with Selected Nutrients and Body Mass Index in Adult Australians[END_REF][START_REF] Guthrie | Role of Food Prepared Away From Home in the American Diet, 1977-78 versus 1994-96: Changes and Consequences[END_REF]. In this analysis, the behaviour of 6 It can be hypothesized that the greater the proportion of household members in the labour force the less likely they will have time for food preparation in the home leading to a greater reliance on processed foods and other time-saving choices such as FAFH and quick-service meals. products associated with known health risks, are used to proxy the health awareness of households. Furthermore, it is hypothesised that education levels may have a bearing on the decision to participate in the FAFH market: better educated household managers could be expected to have greater awareness of the health consequences of eating certain types of foods.

Previous empirical research has identified how specific economic and demographic characteristics of the household influence demand for FAFH.

Household size, the presence of children, being resident in urban areas, age and income levels all have been found to be significant factors that should be considered in a study on FAFH expenditure. 7 In analysing food expenditure patterns of households on aggregate we are attempting to explain the expenditure decisions of the household manager, that is the individual primarily responsible for household activities including meal preparation. The HBS, however, does not indicate which household member this is. Following [START_REF] Stewart | The Demand for Food Away From Home: Full-Service or Quick-service?[END_REF], the household manager for single households is defined as the survey respondent while for married couples the household manager is defined as the person who works the fewest hours outside of the home. This approach, while straightforward for households of one adult or a married couple, becomes ambiguous for households of multiple unmarried adults. In these cases the household manager is always the survey respondent. 8 Where individual characteristics are used to explain expenditure on FAFH they refer to characteristics of the household manager defined in this way rather than the head of household as has been the 7 See for example, [START_REF] Byrne | Analysis of Quick-serve, Mid-scale and Up-scale Food Away From Home Expenditures[END_REF], [START_REF] Mccracken | Household Consumption of food-awayfrom-home: Total Expenditure and by Type of Facility[END_REF] and [START_REF] Stewart | The Demand for Food Away From Home: Full-Service or Quick-service?[END_REF] amongst others. 8 In the HBS the head of household is the oldest person in the household and given that the completion of the expenditure diary is in itself a task indicative of household management the choice of the head of household as the household manager can easily be justified.

F

Methodology

Cross-sectional data on household expenditure patterns are complicated by the existence of zero observations on expenditure, implying that the relationship between the independent variables and the expenditure variables may be more complex than assumed in conventional regression models. The standard tobit model [START_REF] Tobin | Estimation of Relationships for Limited Dependent Variables[END_REF] was originally developed to accommodate censoring in the dependent variable and was designed to overcome the bias associated with assuming a simple linear relationship between the dependent and independent variables in the presence of such censoring. The tobit model assumes that all zeros are attributable to standard corner solutions. Negative values of the dependent variable are assumed to exist but are considered to be unobservable and bunched at zero. By assuming that an unobservable latent framework generates the data the model incorporates this assumption into the modelling process. 9 The standard tobit model can be written as:

i i i u x y + = ' * ( ) 2 , 0 ~ N u i n i .., ,......... 1 = * i i y y = if 0 * > i y (1) 0 = i y otherwise 9
In the case of expenditure on food items, such as FAFH, we assume that the household's decision to purchase a food item depends on the utility they derive from the consumption of that item. It may be the case that the household dislikes the food item to such an extent that they attach a negative level of utility to it. In such a case, all we would observe in the expenditure data are zero values. As such, the tobit model, which takes account of censoring of this kind in the dependent variable, is appropriate in this case. is the observed level of expenditure by the ith household and y i * is an unobserved continuous latent variable assumed to determine the value of y i . The latent variable is only observed if it is greater than or equal to zero, however, it is allowed to take on negative values even though these values cannot be observed.

Standard estimators for these types of models are based on maximum likelihood estimation (MLE). MLE produces consistent estimates of the parameters of the tobit model under appropriate assumptions such as homoscedasticity and the normality of the error terms. The likelihood function of the tobit model can be written as [START_REF] Tobin | Estimation of Relationships for Limited Dependent Variables[END_REF]:

= = = 1 1 0 2 ' ' 1 ) , ( i i y i i y i x y x L (2)
where and refer to the standard normal cumulative distribution and density functions respectively. The consistency of MLE requires a complete and correct specification of a parametric family of the error distribution. If the model is misspecified, model assumptions must be relaxed, and estimators are needed which remain consistent under more general assumptions. Semiparametric estimators have been developed for this purpose.

Semiparametric estimators are hybrids of parametric and nonparametric approaches. They allow for a more general specification of the nuisance parameters, are more consistent than corresponding parametric models and are typically more precise than their nonparametric counterparts [START_REF] Powell | Estimation of Semiparametric Models[END_REF].

However, if the parametric model is correctly specified, they are in general less efficient than the corresponding maximum likelihood estimator [START_REF] Powell | Estimation of Semiparametric Models[END_REF].

Semiparametric estimators useful for cross-sectional type analyses include the [START_REF] Powell | Least Absolute Deviations Estimation for the Censored Regression Model[END_REF][START_REF] Powell | Symmetrically Trimmed Least Squares Estimation for Tobit Models[END_REF]. Both are considered in this paper.

The CLAD estimator was first proposed by [START_REF] Powell | Least Absolute Deviations Estimation for the Censored Regression Model[END_REF]. The CLAD model is a median estimator. To make the estimator robust to misspecification problems the sample is reduced eliminating data points and observations that fall outside the uncensored region from the sample (the recensoring step). Least absolute deviations is then applied to the remaining observations (the regression step). Bootstrapping is used to compute the residuals. The CLAD estimator is robust to heteroscedasticity and non-normality and provides consistent estimates in the presence of censored data. The estimator, however, may be less efficient than its parametric alternative depending on the extent to which outliers are a problem in the dataset. A number of studies have compared the CLAD approach to MLE with varying results. 10 Blisard et al. (2004) applied CLAD to analyse household expenditure on fruits and vegetables finding it to be more robust to outliers than least squares estimation. [START_REF] Chay | Semiparametric Censored Regression Models[END_REF], analysing the earnings gap between black and white households, found that semiparametric estimation produced much more precise estimates than MLE. In contrast, [START_REF] Berg | Cigarette Demand and Tax Policy for Race Groups in South Africa[END_REF] failed to reject a heteroscedasticity adjusted model estimated using MLE in favour of the CLAD approach in their application to cigarette demand in South Africa.

The SCLS estimator was also proposed by [START_REF] Powell | Symmetrically Trimmed Least Squares Estimation for Tobit Models[END_REF]. It is built on the CLAD estimator but uses symmetric trimming. By assuming that the true 10 A number of studies have also considered the Least Absolute Deviations approach, without censoring, as an alternative to the standard parametric models for dealing with censoring finding the former to be superior in most cases. See for example, [START_REF] Fullerton | Empirical Models for Secondary Market Debt Prices[END_REF], [START_REF] Yoo | A Robust Estimation of Hedonic Price Models: Least Absolute Deviations Estimation[END_REF] and Yoo et al. (2000). The coefficients can be estimated by least squares with observations falling outside the uncensored region purged, using the symmetrically trimmed data only to arrive at the SCLS estimator. 11 The motivation for using the symmetric trimming approach is that consistency will not be dependent on either homoscedasticity or the known distribution of the error terms [START_REF] Powell | Symmetrically Trimmed Least Squares Estimation for Tobit Models[END_REF]. [START_REF] Yoo | A Robust Approach to Dealing with Zero Expenditures on Mobile Communications[END_REF] found that SCLS significantly outperformed standard parametric alternatives in dealing with zero expenditures on mobile communications in South Korea. [START_REF] Chay | Semiparametric Censored Regression Models[END_REF] also used the SCLS estimation to analyse the black and white earnings gap however, they conclude that the CLAD estimator was superior due to its consistency under more general assumptions.

Model Comparison

INSERT TABLE 3 ABOUT HERE

The model of Irish households' quick-service expenditure is estimated using MLE, CLAD and SCLS estimation in econometrics software package STATA S/E Version 8. 12 Estimation of the tobit model using the 1994 data reveals that the semiparametric estimation performs poorly against MLE (Table 3). In particular, the results of the model are extremely different when estimated using SCLS compared with the other techniques. While the coefficients have mostly the same sign they diverge considerably in magnitude. For example the coefficient for income estimated using SCLS is 13.076, twice as large as the 11 For consistency, bootstrapping is also used to compute the residuals of the SCLS model. 12 The respective ado files were obtained at http://elsa.berkeley.edu/~kenchay. For consistency, the residuals of the tobit model estimated using MLE are computed using bootstrapping. [START_REF] Newey | Specification Tests for Distributional Assumptions in the Tobit Model[END_REF] proposed a version of the Hausman for testing between semiparametric and parametric alternatives of the censored tobit model. The null hypothesis for the test is that the parametric tobit model is consistent while the alternative is that it is inconsistent indicating the presence of misspecification problems such as heteroscedasticity or non-normality. The CLAD and SCLS estimators will be consistent under both the null and alternative hypotheses as they are robust to such misspecification errors. The test statistic is given by [START_REF] Newey | Specification Tests for Distributional Assumptions in the Tobit Model[END_REF]: The statistic is distributed 2 with degrees of freedom equal to the number of parameters. The results of this test comparing the parametric model to the semiparametric models in each year are presented in Table 4.

( ) ( ) ( ) [ ] ( ) ml sp ml sp ml sp V V H 1 ' = (3)

INSERT TABLE 4 ABOUT HERE

In all cases the tobit model estimated using MLE is strongly rejected in favour of the semiparametric alternatives. However, as our discussion above revealed, the semiparametric estimates are far inferior to the MLE estimates in efficiency terms, particularly in 1994. We are therefore faced with two options as to how we should proceed: on the one hand we could proceed with the semiparametric estimates accepting the loss in efficiency; or on the other hand we could attempt to adjust the tobit model so that MLE yields consistent estimates.

In this application, the extent of the efficiency loss in using the semiparametric approaches is so great that the analysis proceeds with the latter option.

The maximum likelihood estimates presented in Table 3, while more efficient than the semiparametric estimates are inconsistent as they are not robust to non-normality or heteroscedasticity. Further testing for these misspecification problems confirms our findings as both homoscedasticity and normality are rejected. 13 To correct for these problems multiplicative heteroscedasticity of the form given in Equation 4is assumed (where i z are the continuous variables of the model) and an inverse hyperbolic sine (IHS) transformation of the dependent variable (see Equation 5) is used to allow for non-normality (Burbidge et al., 1998). 14 The log likelihood for the adjusted model is given in Equation 6.

( )

' exp i i z =
(4) 13 The results of a Lagrange Multiplier test for heteroscedasticity, and [START_REF] Pagan | Diagnostic Tests for Models Based on Individual Data: A Survey[END_REF] moments based test for non-normality are presented in the Appendix. 14 See [START_REF] Newman | A Double-Hurdle Model of Irish Household Expenditure on Prepared Meals[END_REF] for an example of an application of the adjusted model.

i i i i y y y y T 1 2 1 2 2 sinh 1 log = + + = (5) ( ) + × = = = 1 2 1 2 2 1 0 2 1 ' ' 1 ) , ( i i y i i i i i y i i y x y x L (6)
Likelihood ratio tests imply that the adjusted tobit model is superior to the standard tobit model in modelling quick-service expenditure using Irish data (see Appendix). Adjusted for heteroscedasticity and non-normality the standard errors are dramatically lower than the unadjusted tobit and each of the semiparametric estimators for both of the datasets (Table 5).

Results

INSERT TABLE 5 ABOUT HERE

The results of the IHS heteroscedastic tobit model are presented in Table 5.

Income has a positive effect on quick-service expenditure but at a decreasing rate. This is in line with previous results: as households earn more income they purchase more leisure activities, including dining amenities [START_REF] Byrne | Analysis of Quick-serve, Mid-scale and Up-scale Food Away From Home Expenditures[END_REF][START_REF] Mccracken | Household Consumption of food-awayfrom-home: Total Expenditure and by Type of Facility[END_REF]. At higher income levels, households move away from quick service consumption potentially toward other full-service options.

Household size has a significantly positive effect on quick-service expenditure though at a decreasing rate. [START_REF] Lazaridis | Household Consumption of Food-Away-From-Home in Greece[END_REF] found that family size had a positive effect on expenditure on takeaway meals and attributed this to the fact that the more members in the household the greater the probability that at least one member will spend on FAFH. Mintel (2004) The age of the household manager has a negative and statistically significant effect on quick-service expenditure. The negative age effect is common to many studies on FAFH demand that have shown that older households display reduced levels of expenditures compared to younger households. [START_REF] Stewart | The Demand for Food Away From Home: Full-Service or Quick-service?[END_REF] found that older U.S. household managers are less likely to frequent quick-service outlets and have a preference for full-service options as they age.

Being a female has a significant and positive effect on quick-service expenditure in 1999. Interestingly this result is in line with that of Mintel (2004) who found that while overall the percentage of adults eating fast foods and takeaways have increased, women have shown a more positive shift than men. It is likely that increasing female labour force participation rates are influencing this result.

Being a married couple has a negative effect on quick-service expenditure.

This result supports the hypothesis that married couples would be more likely to eat food at home as against single couples due to economies of scale and possibly an added value associated with the family meal eating occasion. The results for single households are surprising as they indicate that being in such households has a negative effect on quick-service expenditure. This result is contrary to expectations given that the benefits of preparing one's meals diminish in smaller households. It is possible that an age effect is being observed here as single pensioners are one component of this category of households. In both sets of Households resident in urban areas have a significant and positive effect on quick-service expenditure. This can be explained by the fact that towns provide greater access to a variety of quick-service outlets compared with rural areas. [START_REF] Jekanowski | Convenience, Accessibility, and the Demand for Quick-service[END_REF] showed that increased outlet density of fast food restaurants enhanced the convenience associated with fast foods and thus increased the growth in fast food expenditure. They suggested that most of the growth in fast food consumption is due to an increasing supply of convenience.

Home ownership also has a negative effect on quick-service expenditure.

The act of owning a home can be considered indicative of a household investing time in household production, including meal preparation. Renters on the other hand, not having the same level of attachment to the home, and in all likelihood having more individualistic lifestyles, would be expected to favour quick-service as a convenience option. [START_REF] Manrique | Working Women and Expenditures on Food-Away-From-Home in Spain[END_REF] found a similar result for Spanish households.

As expected the number of workers is positively related to quick-service expenditure, consistent with the hypothesis that households with high time values will eat out rather than at home to save time. This result is consistent with household production theory as households with higher time constraints would be expected to sacrifice time from household production to engage in other activities [START_REF] Lazaridis | Household Consumption of Food-Away-From-Home in Greece[END_REF]. Similarly the coefficient on the commuter variable is positive and significant in both years. The positive relationship between commuters and The result for the health awareness variable highlights how there are two competing forces influencing demand for quick-service: the demand for convenience competes with the demand for a healthier lifestyle. This variable is negative and significant in both survey years indicating that households with high levels of health awareness are less likely to consume quick-service foods. In addition, in 1999, having higher levels of education has a significantly negative effect on quick-service expenditure. This could reflect, as hypothesised, that higher levels of education are consistent with greater levels of health awareness.

On the other hand, as found by [START_REF] Byrne | Analysis of Quick-serve, Mid-scale and Up-scale Food Away From Home Expenditures[END_REF], this result may reflect the fact that households with higher education levels may be more likely to consume FAFH at up-market facilities rather than at quick-service facilities. A similar result is found for the social class of the household manager with higher social classes spending less on quick-service.

The household appliances were included as they have been found to have significant effects on Irish expenditure on prepared meals [START_REF] Newman | A Double-Hurdle Model of Irish Household Expenditure on Prepared Meals[END_REF].

The results are as expected with freezer ownership, a proxy for close substitutes to FAFH expenditure such as prepared meals, having a negative effect on quickservice expenditure and microwave ownership, a proxy for convenience preferences in food preparation, having a positive effect. There is also some evidence of seasonality in the results supporting the inclusion of seasonal dummies.

Conclusion

The main objectives of this paper were to analyse the factors determining quick-service expenditure in Ireland and in so doing explore semiparametric alternatives to maximum likelihood estimation of tobit models. This study found that there was an efficiency/consistency trade-off when the semiparametric estimators were compared to the unadjusted tobit model. Despite the technical difficulties associated with estimating tobit models in the presence of heteroscedasticity and non-normality, the loss in efficiency suffered in the semiparametric approach was considered too great a sacrifice to make and so we proceeded with an adjusted model. While the findings of this study correspond with most others in terms of the outright rejection of the MLE approach (see for example [START_REF] Chay | Semiparametric Censored Regression Models[END_REF] and [START_REF] Yoo | A Robust Approach to Dealing with Zero Expenditures on Mobile Communications[END_REF]), in this case the semiparametric approaches were not considered efficient enough to be used as an alternative. This may be due to the larger dataset, more censoring and a greater number of outliers characteristic of the sample used in this study compared with others. Many of the results of the variables examined have the expected sign and most are significant. Household income, household size and urban residents have significant and positive influences on quick-service expenditure. Older families, single households and married couples and households with higher levels of education and health awareness experience reduced expenditure levels.

  to the purchase of goods such as alcohol and tobacco,

  is vector of explanatory variables corresponding to the ith household, y i

  deviation (CLAD) and symmetrically censored least squares (SCLS) estimators

  symmetrically distributed around the regression function and that the observed dependent variable will have an asymmetric distribution, symmetry can be restored by symmetrically censoring the dependent variable.

  usingMLE (5.1147). In addition, the estimated standard errors are much larger in the former resulting in what appears to be a very poorly specified model. This is due to the fact that SCLS estimation reduces the data to 1,744 observations through symmetric trimming, purging 5,561 observations in total. This suggests that the true distribution of the dependent variable is highly asymmetric and unlikely to be normal. CLAD estimation of the 1994 model performs slightly better with a sample of 2,381 after trimming, although standard errors are still larger than those produced using MLE.Similarly, in 1999 the sample for the CLAD (3,764) and SCLS (3,379) are greatly reduced by trimming when compared with the full sample of 7,171, clearly indicating the presence of a significant asymmetry in the distribution of the dependent variable. The SCLS performs poorly again with standard errors larger in most cases than in both the CLAD and MLE approaches. However, the CLAD estimates have shown some improvements. Standard errors are lower for CLAD estimation than MLE for many of the estimates.

  on the presence of children is insignificant throughout. One would have expected children to have a positive effect on quick-service expenditure given that advertising in the sector is heavily targeted at children. The results, however, do not bear this out.

  quick-service can be interpreted as a further demand for convenience products by commuters. With the ever expanding commuter belt in Ireland at present this will undoubtedly have a favourable impact on the quickservice industry into the future.

  found that households with

	four or more adults had the highest penetration for quick-service foods in Ireland,
	a result supportive of this finding. 15
	F o r
	P
	e
	e r
	R e v
	i e
	w
	12

Table 2 :

 2 Summary statistics Notes: ***significant at the 1% level, **significant at the 5% level, *significant at the 10 % level. Standard errors are given in parentheses.

		Mean (€)	Std. Deviation	Maximum(€)	% Zeros
	Dependent	1994	1999	1994	1999	1994	1999	1994	1999
	Quick Service	1.029	1.878	2.133	3.423	35.56	78.81	56%	50%
	Independent -Continuous
	Income (ln)	4.907	5.274	0.614	0.679	7.039	8.401
	Income2 (ln)	24.455 28.271 6.054	7.119 49.559 70.569
	Age	5.050	5.274	1.725	1.657	8	8
	Hhold	2.932	2.904	1.674	1.535	11	12
	Hhold2	11.398 10.789 12.222 10.676	121	144
	Workers	1.016	1.160	0.839	0.911	4	4
	Independent -Discrete
	Education	0.360	0.458
	Social1	0.217	0.242
	Social2	0.216	0.273
	Urban	0.553	0.649
	Children	0.390	0.376
	Female	0.464	0.449
	Single	0.241	0.281
	Married	0.406	0.370
	Homeowner	0.789	0.832
	Commuter	0.268	0.349
	Health	0.201	0.188
	Freezer	0.216	0.294
	Microwave	0.457	0.704
	Spring	0.238	0.195
	Summer	0.260	0.368
	Autumn	0.431	0.304

Table 4 :

 4 Hausman test of consistency of parametric tobit model

		Submitted Manuscript		Page 22 of 24
		1994		1999
		Test Statistic	P-value	Test Statistic	P-value
	MLE vs. SCLS	330.88	0.0000	178.93	0.0000
	MLE vs. CLAD	115.40	0.0000	170.31	0.0000

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

Table 5 :

 5 IHS heteroscedastic tobit results: 1994IHS heteroscedastic tobit results: , 1999 *** significant at 1% level, **significant at the 5% level, * significant at the 10% level. Standard errors are given in parentheses.

	Variable	1994	Heteroscedasticity	1999	Heteroscedasticity
		IHS Het Tobit	Terms	IHS Het Tobit	Terms
	Constant	-5.8034***	1.0623***	-8.7794***	1.2913***
		(0.8715)	(0.0754)	(1.0907)	(0.0925)
	Income	1.900***	-	2.7647***
		(0.3386)		(0.4034)
	Income 2	-0.1371***	-	-0.1997***
		(0.0332)		(0.0371)
	Age	-0.2072***		-0.2813***	-0.0174*
		(0.0145)		(0.0194)	(0.0099)
	Hhold	0.3667***	-0.3736***	0.6932***	-0.3287***
		(0.0623)	(0.0405)	(0.0833)	(0.0379)
	Hhold 2	-0.0336***	0.0311***	-0.0647***	0.0276***
		(0.0068)	(0.0053)	(0.0090)	(0.0049)
	Workers	0.1189***		0.0812***	0.0208
		(0.0183)		(0.0225)	(0.0153)
	Female	-0.0047		0.0719**
		(0.0272)		(0.0364)
	Education	-0.0489		-0.1348**
		(0.0306)		(0.0384)
	Single	-0.3983***		-0.4742***
		(0.0752)		(0.1000)
	Married	-0.3419***		-0.4334***
		(0.0343)		(0.0439)
	Social1	-0.1260**		-0.0842*
		(0.0383)		(0.0475)
	Social2	-0.0247		0.0046
		(0.0320)		(0.0394)
	Urban	0.2819***		0.4159***
		(0.0308)		(0.0360)
	Children	-0.0153		-0.0777
		(0.0441)		(0.0546)
	Homeowner	-0.1217**		-0.1555**
		(0.0384)		(0.0499)
	Commuter	0.0877**		0.1350***
		(0.0268)		(0.0352)
	Health	-0.2680***		-0.2055***
		(0.0468)		(0.0581)
	Freezer	-0.0398		-0.0760**
		(0.0296)		(0.0353)
	Microwave	0.0452		0.0884**
		(0.0277)		(0.0429)
	Spring	-0.0196		0.0294
		(0.0348)		(0.0570)
	Summer	0.0330		0.0703
		(0.0298)		(0.0526)
	Autumn	0.0633**		0.1237**
		(0.0290)		(0.0537)
	IHS Parameter	0.3812***		0.2830***
		(0.0244)		(0.0925)
	Log Likelihood	-3589.40		-4362.95
	Notes:

In contrast, it should be noted that[START_REF] Stewart | The Demand for Food Away From Home: Full-Service or Quick-service?[END_REF] found that larger households spend less on all segments of FAFH, supporting their hypothesis that such households benefit from economies of scale in food preparation at home.

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

Acknowledgements

The first author was funded for this research by a Walsh Fellowship from Ashtown Food Research Centre, Teagasc and this support is gratefully appreciated.

The authors would like to acknowledge feedback received at the 79 th Agricultural Economics Society Annual Conference in Nottingham in April 2005, in particular from Dr. Philip Lund and Dr. Geir Gustavsen.

The authors would also like to acknowledge the helpful comments of the editor and an anonymous referee.