Health Expenditure and Income in the United States

This paper investigates the long-run economic relationship between health care expenditure and income in the US at a State level. Using a panel of 49 US States followed over the period 1980-2004, we study the non-stationarity and cointegration between health spending and income, ultimately measuring income elasticity of health care. The tests we adopt allow us to explicitly control for cross-section dependence and unobserved heterogeneity. Specifically, in our regression equations we assume that the error is the sum of a multifactor structure and a spatial autoregressive process, which capture global shocks and local spill overs in health expenditure. Our results suggest that health care is a necessity rather than a luxury, with an elasticity much smaller than that estimated in other US studies. Further, we observe a significant spatial spill over, though with a smaller intensity than that detected in other studies on spatial concentration of US health spending. Our broad perspective of cross section dependence as well as the methods used to capture it give new insights on the debate over the relationship between health spending and income.


Introduction
Despite years of concern and attempts at cost containment, aggregate health care expenditure in the US, and other western countries, has increased substantially. This has heated the discussion on the underlying reasons for the rise in health expenditure, as well as the alternative policy solutions to control such spending growth. Since the seminal papers by Kleiman (1974) and Newhouse (1977), much emphasis has been given to the role of income in determining health care expenditure. The debate is still open on whether health care is a luxury or a necessity good, namely, if income elasticity of expenditure is above or below unity (Parkin et al., 1987;Gerdtham et al., 1992;Hitris and Posnett, 1992;Hansen and King, 1996;Blomqvist and Carter, 1997; Di Matteo and Di Matteo, 1998, Freeman, 2003. The controversy over the nature of health care has been exacerbated by the policy implications of the empirical results. If one recognizes that health care is a necessity will often support the idea of greater public involvement in health care. Conversely, advocates of health care being a luxury, would argue it is a commodity much like any other and best left to market forces alone (Culyer, 1988). Empirical evidence varies according to the statistical units considered in the investigation (Manning et al., 1987;Blomqvist and Carter, 1997;Getzen, 2000). As the focus shifts from …ne disaggregations of the population (e.g.: individuals, provinces, regions) to larger groups of actors (e.g., States, Countries), we observe a higher estimated income elasticity of health care. Put di¤erently, associations observed between macro-factors do not seem to re ‡ect associations that exist at the individual level. As pointed out by Getzen (2000), one reason might be that individual budget constraints in health spending are largely removed through insurance …nancing, while at aggregate level the resources allocated on health care are constrained by the budget rather than being in ‡uenced by health status. Another explanation is that cross-country data are characterised by strong heterogeneity that, if not properly incorporated in econometric models, could lead to the estimation of income elasticities greater than one (Hansen and King, 1996). Limiting the analysis to one country with multiple jurisdictions might reduce this problem.
When looking at the link between spending and income, one important issue is whether the stationarity assumption holds for both time series variables. It is well known that the violation of this assumption leads to spurious statistical results under the OLS (Engle and Granger, 1987). Indeed, if the two series are both integrated, the absolute value of their correlation coe¢ cient will be nonzero, whether or not an economic relationship between them exists. Nonstationarity in the two series introduces the issue of determining whether there is a long-run equilibrium between health expenditure and income. If both time series variables are integrated and there exists a linear combination of these variables that is itself stationary, we can conclude that the two variables are cointegrated. In this case, the stationary linear combination represents the cointegrating or long-run relationship, which can be speci…ed in levels with short-run dynamics modelled via an error correction process. It follows that integration and cointegration between spending and income represent fundamental properties when specifying and interpreting a model for health expenditure.
A large number of studies investigate the non-stationarity in health expenditure and income and their long-run relationship in a panel data framework (Mc-Coskey and Selden, 1998;Roberts, 1999 Wang andRettenmaier, 2006, Chou, 2007). Most empirical work has been focusing on OECD countries, while less attention has been paid to the US case, at a State level. Cross country analysis on the OECD area provide empirical evidence that is often contradictory. For example, Gerdtham and Lothgren (2000), using country-by-country and panel unit root tests, reach the conclusion that in OECD countries health care expenditure and GDP are non-stationary and cointegrated. Similar results, employing more advanced econometric techniques, are reported in Dreger and Meiers (2005). On the contrary, McCoskey and Selden (1998) reject the null of non-stationarity for health care expenditures and GDP, though they observe that results change when a time trend is included in the augmented Dickey-Fuller equation. Jewell et al. (2003) and Carrion-i-Silvestre (2005) conclude that health expenditure and GDP are stationary around one or two breaks. In general, major concern is expressed by several authors on how to deal with heterogeneity and cross section dependence, characteristics that are very likely to be present in health panel data, when testing for unit roots and cointegration (McCoskey and Selden, 1998;Roberts, 1999).
The empirical evidence on US is scant. Freeman (2003) …nds that health care expenditure and income at State level in the US in the period 1966-1998 are non-stationary and cointegrated, ultimately observing that health care is a necessity good. More recently, Wang and Rettenmaier (2006), allowing for structural breaks in unit root tests, support the evidence that spending and income in US States are non-stationary, though not cointegrated. Further, they …nd an income elasticity below 1 for 16 States, and above 1 for the remaining 32 States.
In this paper we aim at giving new insights on the debate over the long-run economic relationship between health care expenditure and income, focusing on the US case. Using a panel of 49 US States followed over the period 1980-2004, we study the non-stationarity and cointegration properties of health spending and income. Our ultimate goal is to provide an estimate of income elasticity of health care which is more accurate than that o¤ered by the current literature. To this end, we apply newly developed econometric techniques for panel data that explicitly control for cross-section dependence as well as unobserved heterogeneity. Following recent contributions to the literature on panel unit roots, cross section dependence is incorporated in econometric models through an approximate multifactor structure (Pesaran, 2006;Bai and Ng, 2004). Speci…cally, in our regression equations we assume that the error term is a linear combination of few common time-speci…c e¤ects with heterogeneous loadings plus a spatial process. Hence, we examine the extent to which spending is driven by income, unobservable common shocks and spatial spill overs, determining the speed of adjustment of health expenditure to deviations from the long-run equilibrium relation.
Though the issue of cross section dependence in this strand of health economics has been tackled by other authors, our broader perspective of cross section dependence as well as the methods used to capture it give new insights on the debate on the long-run relationship between health spending and income.
In the following, we …rst discuss the issue of contemporaneous correlation in health expenditure and its econometric representation. We then turn to a preliminary descriptive analysis of cross section dependence for health and income. Hence, we compute a set of panel unit root tests to investigate the possible non-stationarity of temporal patterns of these variables. We perform a cointegration analysis, focusing on the long-run relationship between health spending and income, assessing whether expenditure on health care is a necessity or a luxury good. Finally, we measure the amount of spatial correlation in the data due the possible presence of spill over e¤ects.
The plan of the paper is as follows. In Section 2 we discuss the issue of cross section dependence in health expenditure. In Section 3 we introduce the econometric methods used in the empirical study. Section 4 describes the data and provides a preliminary exploratory analysis. Section 5 goes through the empirical econometric evidences, giving economic content to the …ndings. Finally, Section 6 ends with some concluding remarks.

Cross section dependence in health expenditure
An important characteristic of health expenditure is the presence of cross section dependence in the data. The assumption of zero correlation on the shocks a¤ecting individual population units 1 in a given cross section is very strong and is not likely to hold in empirical studies of health expenditure. We can recognize two sources of interdependence among statistical units. The …rst arises when agents react in a similar manner to external forces and unanticipated events such as technological advances, health shocks, the implementation of new health policies and sociological structural changes (Andrews, 2003). Correlation arises because the responses to such common external forces or perturbations is similar though not identical across individuals. For example, innovations in diagnostic tools and therapies such as a new vaccine might render treatable health conditions for which past options consisted only of minimal treatments. Epidemics or diseases whose incidence suddenly raises regionally or worldwide might generate a risk adverse behaviour that translates in the accumulation of drugs and increase of pharmaceutical expenditure. The sexual behaviour of a generation may also exacerbate the spread of certain epidemics, thus, impacting on health services use. The implementation of new health policies, such as campaigns through the media on highway regulations may reduce avoidable accidents, ultimately impacting on costs of the health system. These shocks are often unobservable to the econometrician and perturb the health system as a whole, simultaneously a¤ecting the behaviour of agents (e.g., recipients, providers, etc.), ultimately impacting on health costs. An important feature of these shocks is that they induce a correlation between pairs of statistical units that does not depend on how close they are in the geographical space. Accordingly, we will refer to this type of correlation as long-range or global interdependence. We …nally note that some of the unexpected events that a¤ect health spending directly might also impact indirectly by hitting the fundamentals of health expenditure, such as disposable income.
An alternative source of interdependence, namely spatial correlation, is related to location and distance among units, with respect to the geographical, economic or social space in which they are embedded (Anselin, 2001). Neighbouring US States may share common general population characteristics or underlying socio-economic features that have an e¤ect on the consumption of health care resources. For example, environmental stressors such as air pollution could be linked to regional rather than simply local trends, in ‡uencing prevalence and need across a wide area, eventually a¤ecting health spending (Moscone et al., 2007). States from the Southwest region, such as Arizona and Texas, are likely to face high rates of illegal immigration, which may directly or indirectly in ‡uence their health costs. Spatial correlation might also be generated by cross State borders movements of health services bene…ciaries (Centers for Medicare & Medicaid Services, 2007). Indeed, it is plausible that individuals move to regions whose revenues and expenditure pattern best match their preferences (Tiebout, 1956;Baicker, 2005). Other reasons of why we should expect spatial dependence in health spending have been suggested by a recent strand of literature in public economics and health economics, which focuses on strategic interaction among jurisdictions in deciding resources allocation (Brueckner, From the above discussion it emerges that reactions to external events as well as spatial spill overs are likely to induce a structure of correlation in health expenditure data. The distinction between global interdependence and local correlation arising from spatial spill overs is that the latter concerns only …nite subsets of statistical units that do not spread widely as sample size increases. When data contain cross section dependence, conventional estimators such as ordinary least squares are ine¢ cient, and the estimated standard errors are biased (Andrews, 2003). Phillips and Sul (2003) proved that when cross section dependence occurs but is not incorporated in the panel regression, the pooled ordinary least squares (OLS) estimator provides little gain in precision compared with single OLS equation. Further, least squares may be biased if regressors are correlated with the source of interdependence. Ignoring contemporaneous correlation has also serious drawbacks on commonly used panel unit root tests.
Indeed, stationary tests that assume independence might have substantial size distortions when this assumption does not hold (Phillips and Sul, 2003;Maddala and Wu, 1999).
Few works on health expenditure explicitly account for cross section dependence when studying its long-run economic relationships. Jewell et al. (2003) control for contemporaneous correlation by introducing time-speci…c e¤ects in the econometric speci…cation. However, the inclusion of time-varying e¤ects implies that the common shocks have identical in ‡uences on each unit, an assumption that might be quite restrictive in empirical analysis. In fact, it is reasonable to expect the e¤ect of global shocks to vary considerably across individuals, also depending on the characteristics of the population units. To allow for more general error cross section dependence, other studies build the empirical distribution of unit root test statistics by bootstrap techniques (Freeman, 2003; Carrion-i-Silvestre, 2005; Wang and Rettenmaier, 2006; Chou, 2007). However, the bootstrap procedure is subject to size distortions in …nite samples, particularly in cases where N is small relative to T , as in the study of health expenditure in the OECD countries (Maddala and Wu, 1999). Also, a recent Monte Carlo study in Smith et al. (2004) indicates that the bootstrap statistic tends to be undersized when N and T are the same order of magnitude.
In the following we review a number of methods that allow us to study the long-run relationship of health care expenditure in the US, taking into account possible cross section correlation arising from unobservable common shocks and local interdependence.

The econometric model
The econometric framework of our analysis is the following simple linear heterogeneous panel h it = i + i y it + u it ; i = 1; :::N ; t = 1; :::T; (1) where h it and y it indicate, respectively, the logarithm of real per-capita health expenditure and the logarithm of real per-capita disposable income in the i th State at time t, i is a State-speci…c intercept, and u it is the error term. In this paper we suggest to incorporate in equation (1) cross section dependence arising from global shocks by assuming that the errors have the following multifactor structure in which f t is the m 1 vector of unobserved common e¤ects and it is a State-speci…c error. The coe¢ cients ij ; for i = 1; :::; N and j = 1; :::; m, are called factor loadings, and represent the sensitivities of statistical units, here the US States, to movements in the factors f t . Hence, according to this speci…cation, each State can respond, with a di¤erent intensity, to unanticipated events, or perturbations, such as new medical technologies and health shocks.
We incorporate cross section dependence arising from spatial spill overs by assuming that it follows a spatial autoregressive process (Cli¤ and Ord, 1981) where is a scalar parameter, and is the so-called spatial lag of it (Anselin, 1988). w ij is the generic (i; j)th element of a N N nonnegative matrix, W, known as spatial weights matrix, which provides information on the neighborhood linkages among States. In our empirical study we de…ne neighbourliness via a contiguity criterion, and assign w ij = 1 when States i and j share a common border or vertex, and w ij = 0 otherwise. Hence, in model (3) the error term, it , associated to the i th State at a point in time t depends on the average of errors in its adjacent States at time t.
In model (1), we allow y it to be correlated with the unobserved e¤ects f t , and assume that where i is a m 1 vector of factor loadings, and v it is an error term assumed to be distributed independently of the common factors f t and of " it . Therefore, common factors can impact on health expenditure not only directly via the factor structure (2), but also indirectly by hitting income via equation (4).
To sum up, model (1)-(4) represents the relationship between health spending and income, taking into account the sources of cross section dependence described in Section 2, namely global shocks and spatial spill overs.
Our estimation and testing strategy is based on the Common Correlated Effects (CCE) approach advanced by Pesaran (2006). According to this method, the unobservable e¤ects f t can be well approximated by the cross section averages of the dependent and explanatory variables. As a way of illustrating this result, rewrite equations (1)-(4) more compactly as and consider the simple cross section average of (5) with Assume that Rank C = m, we can rewrite (6) as Under the condition that the spatial weights matrix, W, has bounded absolute row and column sums, it is possible to show that (Pesaran and Tosetti, 2007) t q:m: ! 0; as N ! 1: It follows that the cross section averages, z t , can be used to approximate the common factors. Hence, the slope parameters i can be consistently estimated applying standard panel techniques to the following equation where z t = h t ; y t 0 . Once the slope parameters have been estimated, since z t is consistent for f t , the spatial coe¢ cient in (3) can be obtained by applying the maximum likelihood method (Anselin, 1988) to residualsê it from equation (8). Estimation of income elasticity (average, and State by State) is provided in Section 5.2, while the estimation of the spatial parameter is considered in Section 5.5. Pesaran (2006) suggests the following CCE estimator for the i th slope coef-…cient^ with M = I T H H 0 H 1 H 0 , and H = ; Z with = (1; ::::; 1) 0 and Z being the T 2 matrix of observations on z t , t = 1; :::; T . Further, he proposes the following two estimators for the mean of the slope coe¢ cientŝ The …rst, known as CCE Mean Group estimator, is a simple average of the individual CCE estimators in (9). The second is the CCE Pooled estimator, which gains e¢ ciency from pooling observations. Their variances is provided in Pesaran (2006). Monte Carlo studies in Pesaran (2006) and in Pesaran and Tosetti (2007) have shown that these estimators perform well in small samples as small as N=20 and T=10. We stress that one important advantage of this approach is that it does not require to know the number of factors m. Further, it allows common factors and the idiosyncratic component, it , to be serially correlated, and it yields consistent estimators regardless of the factors being stationary or non-stationary, as long as it is stationary and m is a …nite …xed number (Kapetanios at al., 2006).
Before concluding, we note that model (1)-(4) is able to capture some discontinuities in the relationship between spending and income by the means of the factor structure. However, we remark that it does not allow for the presence of structural breaks in the slope coe¢ cients, i . In principle, we do recognize the potential role of structural breaks in the relation between health expenditure and income. However, we believe that this would be marginal in our empirical application given the relatively short time span considered (see Section 4).
In the following section, we explain how the CCE approach can be adopted when testing for unit roots, controlling for cross section dependence. Again, the idea is to use cross section averages of health expenditure and disposable income as proxies for the unobserved common factors, in the context of a Dickey Fuller regression.

Testing for unit roots
Consider the p th order augmented Dickey Fuller regression where q it is either the logarithm of real per-capita health spending, the logarithm of real disposable income, or regression residuals from equation (1). u it are errors that we assume to have a single factor structure, where the idiosyncratic component follows a spatial autoregressive process as in (3). When testing for unit roots, the null hypothesis is against the alternative that (Breitung and Pesaran, 2007) where N 1 is such that N 1 =N is nonzero and tends to a …xed constant as N goes to in…nity. Following the same rational as in Section 3.1, we consider the following Dickey Fuller (CADF) regression augmented with the cross section averages q t 1 and q t j , for j = 0; :::; p where z t = ( q t 1 ; q t ; q t 1 ; :::; q t p ) 0 . Pesaran (2007) proposes to test (13) against (14) by computing the simple average of the t-ratios of the OLS estimates of b i in equation (15), namely, wheret i is the OLS t-ratio of b i . The critical values for the CIP S tests are given in Tables 2(a)-2(c) in Pesaran (2007). We remark that the CIPS unit roots test requires that the errors u it in (12) have a single factor structure. However, controlling for only one global shock might not be enough to capture the whole, long-range, contemporaneous correlation present in the data. In our empirical investigation we provide some statistics of cross section dependence after having controlled for such common factor to see whether signi…cant correlation is left in the residuals.

Cross section dependence tests
We now brie ‡y review some statistics of cross section dependence that we use in our empirical work. A statistic which captures the overall amount of cross section dependence in the data, at a descriptive level, is the following average pairwise correlation coe¢ cient where ij is given by and q it is either the logarithm of real per-capita health spending or the logarithm of real disposable income, expressed in …rst di¤erences, or regression residuals from equations (1), and (12). We also consider two diagnostic tests for cross section dependence, based on the above pairwise correlation coe¢ cients. The CD P test, recently advanced by Pesaran (2004), is and the CD LM test based on the Lagrange Multiplier statistic (Frees, 1995) is Under the null hypothesis of no cross section dependence, the CD P tends to a N (0; 1) for N and T going to in…nity in any order, and the CD LM tends to a N (0; 1) with T ! 1 and then N ! 1. We note that, while the CD P is based on the pair-wise correlation coe¢ cients, the CD LM uses their squares. In practice, the CD P test might give misleading results when the cross correlations cover negative as well as positive values. Though the CD LM does not su¤er from this problem, we note that it is likely to exhibit some size distortions for N large and T small (Frees, 1995). These statistics measure the average amount of dependency between all pairs of units. They assign equal weights to all pairwise correlations regardless the geographical position of the US States. In other words, in these statistics the correlation between California and Maine has the same importance as the correlation between California and its adjacent States such as Oregon. Accordingly, the above CD statistics do not consider the distance decay e¤ect that underlies spatial interaction theory, and should be interpreted as measures of long-range or global dependency.
In our empirical study we also test for spatial correlation, after having controlled for long-range dependence represented by the common factors structure. In particular, we compute the following Moran's I test statistic 2 (Kelejian and Prucha, 2001) where s 2 t = 1 N P N i=1 ê it ê :t 2 , and w ij , i; j = 1; :::; N , are the spatial weights, andê it , for i = 1; :::; N , are the estimated regression residuals in (8) or in (15). The Moran's I is asymptotically normally distributed 3 as N goes to in…nity, for …xed T . Spatial statistics such as the Moran's I di¤er from the CD statistics (17)- (19) since they exploit information on the spatial ordering of data, giving more importance to States that are close to each other. As such, the Moran's I should be interpreted as a measure of local cross section dependence. In the computation of (20), again we use contiguity as measure of distance among States, and assign a non-zero link only to pairs of States that share a common border or vertex.

Data description
Our investigation uses annual data on the US States plus the District of Columbia, from 1980 to 2004. Given their unusual socio-economic characteristics we excluded Alaska and Hawaii from our analysis, leaving us with 49 units. We gathered data on personal health care expenditure at State level from the Centers of Medicaid and Medicare Services 4 . This aggregate, which represents the total amount spent to treat individuals, includes private funds, mainly private insurance and out-of-pockets payments, and public resources, for the majority composed by Medicare and public assistance (Medicaid) 5 . On aggregate, in the US, private funds represent the largest …gure of total expenditure, though we observe that they have been decreasing over time, from 58 per cent in the 1980 to roughly 54 per cent as a proportion of total expenditure. We note that personal health care expenditure is measured by the States of the provider without distinguishing between local and cross-border bene…ciaries of services.
We obtained data on disposable income and the State population from the Bureau of Economic Analysis 6 . Finally, as there is no US State level consumer price index (CPI), we constructed State level general price index, based on the CPI of the cities/areas 7 , which are available from the Bureau of Labor Statistics 8 . We used this index to de ‡ate health expenditure and income.
We begin our empirical investigation with a preliminary analysis on the spatial distribution and concentration of health expenditure and income across the 49 US States. In Table 2 we show the statistics (17)- (19) for the …rst di¤erences of the logarithm of per-capita health expenditure and per-capita income. Results suggest the existence of cross section correlation among States of pervasive nature, which should be taken into consideration when studying income elasticity. At this stage we have not tested for spatial correlation in the data, something that we will do after controlling for long-range dependence arising from the common factor structure (see Section 5). However, in Table 3 we show the average correlation coe¢ cients within and between the 8 Bureau of Economic Analysis (BEA) regions 9 , which provides a subdivision of US states in larger units that are similar in terms of historical development, population characteristics, and economy. This should capture at descriptive level spatial concentrations of our variables across the territory. Looking at the values in the diagonal of Table 3, compared with the o¤-diagonal elements, we observe that for many regions the within region correlation is larger than the between region correlation. Such di¤erence is more marked for income than for spending. For example, the States of the Mideast region are more correlated on average among themselves than with the States of South West, both for spending and income. The di¤erence is more marked for income. This might suggest the presence of geographical concentration both in health expenditure and income, though with a more important role in the latter. We will explore these issues later in the paper.
5 Empirical evidences 5.1 Non-stationarity of health expenditure and income Table 4 reports the CIPS statistics for the logarithm of real per-capita health expenditure and real per-capita disposable income for the 49 US States over the years from 1980 to 2004 for the lag orders p = 0; 1; 2; 3. The inclusion of lags allow us to control for possible serial correlation in the data.
Health expenditure is non-stationary when including an intercept, as well as when adding an intercept and a linear trend in the CADF regression. The nonstationary nature of health care expenditure may be explained by the increase of disposable income, as well as changes in medical technology and treatment. As for income, the unit root hypothesis is rejected when an intercept only is included, while it cannot be rejected in the intercept and trend case, for any choice of p. Given the trended nature of our variables, these results lead us to conclude that health expenditure and disposable income are non-stationary. This empirical evidence is consistent with research on US data at a State level by Freeman (2003) and other works on national-level OECD data by Blomqvist and Carter (1997) and Gerdtham and Lothgren (2000).
In Table 5 we compute the cross section dependence statistics (17)-(19) on residuals from the CADF regressions, before and after having controlled for the common factor. Speci…cally, in panel (A) we base the CD statistics on residualŝ ij q i;t j , while in panel (B) we use residuals that have been defactored, namelyê it = q it â i b i q i;t 1 ĉ i t p X j=1d ij q i;t j ĝ 0 i z t where z t = ( q t 1 ; q t ; q t 1 ; :::; q t p ) 0 , (see equation (15)). As we move from panel (A) to panel (B) all CD statistics report a sizeable reduction in the degree of cross section dependence, with the average pairwise correlation coe¢ cient going from roughly 55 per cent for health spending (40 per cent for disposable income) to zero. It follows that the inclusion of cross section averages in the ADF regressions, as in (15), seems to capture well the cross section dependence present in the data. This may suggest that the CIPS panel unit root test can e¤ectively deal with correlation across section. Panel (B) in Table 5 also reports the Moran's I test statistic onê it , to check whether there exists any residual spatial correlation after having controlled for the common factor. Results show a signi…cant value for the Moran's I for disposable income and not for health care expenditure. This is in line with our preliminary exploratory statistics that suggested the presence of geographical concentration both in health expenditure and income, though more pronounced in the latter.

The income elasticity of health expenditure
We now turn our attention to the relationship between health expenditure and disposable income. Table 6 reports the estimated income elasticity for each of the 49 States. It clearly emerges a wide variation in how health expenditure responds to income across territory. Though elasticity is above unity for six States, it is significantly larger than 1, indicating that health care is a luxury good, only for four States, namely Washington, Wisconsin, South Carolina and Florida. The majority of the States presents an income elasticity lower than one, con…rming that health care is, overall, a necessity good. We note that three States, namely, Maine, North Dakota, and District of Columbia, display negative signi…cant co-e¢ cients, while several other States show statistically insigni…cant coe¢ cients. One reason behind these results might be that there exist unobserved cross border movements of recipients that alter the relationship between health spending and income at State level. This problem is more pronounced when estimating a State by State elasticity than when considering the average relation, since averaging is likely to cancel out the estimation error due to movements. Finally, we note that estimating coe¢ cients States by States reduces the degrees of freedom, implying wider con…dence intervals.
Our results di¤er from those in Wang and Rettenmeir (2006), who obtain an income elasticity between 0 and 1 in 16 States, and larger than 1 in 32 States. However, we note that when estimating elasticity, they do not allow for contemporaneous correlation 10 , which might lead to erroneous conclusions. We further observe that they do not report the t-statistics and associated p-values for their estimates of income elasticity. Table 7 reports results from the …xed e¤ects (FE) estimation (column I), the CCE Mean Group (column II), and the CCE Pooled estimator (column III). From column I the coe¢ cient on income is roughly 0.90. However, such estimator, ignoring the sizeable amount of cross section dependence in spending, is likely to be seriously biased. Our FE coe¢ cient, though close to 1, is smaller than that obtained by Freeman (2003), which is roughly 1.30. We note that Freeman's study di¤ers from ours in a number of characteristics that might explain (in part) the di¤erences in the FE estimation. First, Freeman's analysis covers the time period from 1966 to 1998, which is di¤erent from ours. Further, in his study health care spending is missing in some years, and has been estimated via geometric interpolation, thus adding uncertainty on his results. Finally, while we use the State level CPI index as de ‡ator of expenditure and income, Freeman adopts the national CPI.
When controlling for cross section dependence, the coe¢ cient on income is signi…cantly lower, 0.45 in the CCE Mean Group and 0.36 for the CCE Pooled estimator. Overall, our results show that growth in income boosts health expenditure. However, health expenditure rises less than proportionally, thus, supporting the hypothesis that health care is a necessity good. This is in line with Freeman (2003), who, by using a dynamic OLS approach, obtains an elasticity of 0.82. The relatively low income elasticity we obtain supports the idea that, while the ability to pay is a determinant of health care spending, the exis-tence of publicly …nanced programmes such as Medicare and Medicaid weakens the link between disposable income and the standard of care. Table 7 also reports the cross section dependence statistics (17)-(19) on residuals from the CCE regression, before and after having controlled for common factors. We observe the sizeable reduction of contemporaneous correlation when passing from panel (A) to panel (B). In panel (B), the average pairwise correlation coe¢ cient and the CD P test statistic indicate that there is no significant long-range cross section dependence left in the residuals, once controlled for common factors. On the contrary, the CD LM points to the existence of signi…cant cross section dependence in the residuals. One reason behind such di¤erence might be that CD LM is detecting some spatial correlation present in the data, an hypothesis that is supported by the signi…cant value obtained for the Moran's I test. This issue will be explored in Section 5.5.
We conclude this section by checking how robust our estimated income elasticity is when controlling for other non-income determinants of health expenditure that have been identi…ed by the literature (Karatzas, 2000; Hansen and King, 1996;Hitiris and Posnett, 1992). We have estimated by CCE Mean Group and by …xed e¤ects four di¤erent speci…cations that include the following variables: percentage of people over 65 years old, numer of phisicians per 100,000 population, numer of beds per 100,000 population 11 , and the share of public …nanced total health spending 12 . Table 8 shows that the CCE Mean Group estimation of income elasticity is robust to the introduction of other regressors, falling in the range 0.36-0.43. The FE estimator still remains close to one. We also report a not signi…cant e¤ect of people over 65 on health spending, and a negative relationship between proportion of public spending and total health expenditure. This latter result might indicate the importance of fostering public expenditure in reducing total health expenditure.

Cointegration analysis
The possibility of cointegration between health expenditure and disposable income is explored using a two-stages procedure, along the lines suggested by Pesaran et al. (2006), Chang (2005), and Bai and Kao (2006). In a …rst step we estimate the CCE Mean Group (CCE Pooled) estimator^ and compute the residualsû it = h it ^ y it ^ i ; while in the second stage we run the CIPS panel unit root tests to assess whetherû it is stationary. If results lead to a rejection of a unit root inû it , we can conclude that health spending and income are cointegrated. One advantage of this procedure is that we take into account contemporaneous correlation in both steps, rather than only in one step as in 1 1 These data have been gathered from the Statistical Abstract of the United States. 1 2 This variable has been computed as the ratio of Medicare and Medicaid spending over total health expenditure. Note that Medicare and Medicaid expenditures account for roughly 90% of public health spending. Wang and Rettenmeir (2006). As a comparator, we also implement this twostages procedure using the …xed e¤ects estimator in the …rst step, which ignores cross section dependence.
As shown in Table 9, when using the FE estimator, we reject the unit root hypothesis in the residuals, for p = 0; 1. The use of the CCE Mean Group or Pooled estimators in the …rst step shows that residuals are stationary for p = 0; 1; 2, leading to a strongest evidence in favour of the existence of a long-run relationship between health spending and income. On the basis of these results we can conclude that health spending and income are cointegrated, hence, that the rise in health expenditure is sustained by movements in disposable income.
This conclusion conforms well to the of work of Freeman (2003), who, by using …rst generation panel unit root tests on OLS residuals, …nds evidence of cointegration between expenditure and income. We note however that his procedure neglects the possibility that observations are correlated. Finally, our conclusions diverge from those in Wang and Rettenmeir (2006), who report weak evidence on the existence of cointegration in a State by State analysis. Their analysis is based on Maddala and Wu (1999) test applied to the residuals from an OLS regression where one structural break is permitted. To allow for dependent observations they compute the empirical distribution of their unit root tests via the bootstrap method. However, the approach used to compute the residuals does not allow for cross section dependence. Further, we remark that the properties of the bootstrap method applied to Maddala and Wu test have not yet been explored for the case of N larger than T , as in the study by Wang and Rettenmeir (2006).

Error correction model
Having established the existence of a cointegration relationship, we now turn to the estimation of the following error correction model where in the parenthesis we have the previous period's cointegrating relation. Again we estimated the above model using 49 US States followed over 25 years. The coe¢ cient i measures the speed of adjustment of health care spending to a deviation from the long-run equilibrium relation between expenditure and disposable income. We …rst estimate (21) by …xed e¤ects and then by CCE method, where factors are approximated by h t ; h t 1 ; y t ; and h t 1 ^ y t 1 , where^ is the estimated income elasticity with either the …xed e¤ects, the CCE Mean Group or the CCE Pooled estimator. Table 10 reports the results. For all estimators the coe¢ cient of the error correction term has the expected, negative, sign. However, the …xed e¤ects estimator reveals a speed of adjustment of -0.05, much lower than that assessed by the CCE, respectively -0.31 and -0.20 for the MG and Pooled estimators. The extremely low speed of adjustment of the …xed e¤ects estimator might re ‡ect some distortions due to the fact that it ignores cross the section dependence present in the data.

Estimating spatial correlation
We now focus on the estimation of the spatial coe¢ cient in model (3). We aim at measuring the amount of spatial correlation due to unobserved spill overs, after adjusting for cross section dependence due to common factors. We consider where the common factors have been approximated by z t , the cross section averages of h it and y it , and estimatê e it = ê it + " it : The above model has been estimated by maximum likelihood (Anselin, 1988).
We obtain a signi…cant spatial coe¢ cient^ of 0.30, with a standard error of 0.035, yielding a z-value of 8.571. This result supports the existence of some unobservable risk factors geographically concentrated that a¤ect health spending, or the presence of cross State borders movements of health services bene…ciaries (Tiebout, 1956). This also conforms well with the empirical …ndings in Baicker (2005), who has found that individual State's medical spending has a signi…cant and positive spill over e¤ect on the spending of its neighbours. However, her study shows that each dollar of State spending causes spending in neighboring States to increase by almost 90 cents, a value which is much higher than that found in our analysis. Our smaller spatial coe¢ cient might be explained by the fact that data have been purged by the e¤ect of common shocks.

Concluding remarks
In this paper, using a panel of 49 US States followed over 25 years, we have investigated the non-stationarity and cointegration properties of health care expenditure and personal disposable income. We aimed at contributing to the existing debate on whether health care is a luxury or a necessity good. Recent work in this …eld has recognized that cross section dependence is an important feature of health care spending. However, we argue that correlation across sections has not yet been dealt with in a satisfactory manner. Hence, in this paper we discuss the possible sources of interdependence, namely, the existence of unobservable global shocks, and the presence of spill over e¤ects. We then review the recently advanced CCE approach to study the non-stationarity and cointegration of health spending and income, assuming that cross section dependence is generated by a common factor structure and a spatial process.
Our panel unit root tests suggest that both variables are integrated and that they exhibit a long-run relation. The increase of disposable income and changes in technology and treatment are the likely explanation for the rising of health care expenditures. Further, we estimate an income elasticity below unity, suggesting that health is a necessity good. This evidence is supported by the estimate of both average and State by State elasticities. We remark that our estimated average elasticity is much lower than that detected in other studies at US State level. The relatively low coe¢ cient for disposable income we obtain supports the hypothesis that, while the ability to pay is a determinant of health care spending, the existence of publicly …nanced programmes such as Medicare and Medicaid weakens the link between income and the standard of care. In our empirical analysis, we have also estimated the amount of spatial correlation in the data, after having controlled for common factors. Results indicate the presence of a signi…cant spatial spill over, though smaller than that identi…ed in other studies.
In conclusion, our analysis points out the existence of global and local forms of cross section dependence in health spending and income, that, if not taken into account in the study of health expenditure, are likely to provide policy makers with misleading results. It would be interesting to use this approach to analyse health spending for the OECD countries, to see if the same conclusions hold in the case of a group of heterogenous, cross sectionally dependent countries.  Notes: , CD P ,CD LM are computed as in (17), (18) and (19), respectively.  Table 2).  (A): The CD statistics are computed onû it = q it â i b i q i;t 1 ĉ i t for CADF(0) and on ij q i;t j for CADF(p), with p=1,2,3.
(B): The CD statistics are computed onê it = q it â i b i q i;t 1 ĉ i t ĝ 0 i z t for CADF (0) and ij q i;t j ĝ 0 i z t for CADF(p), with p=1,2,3, where z t = ( q t 1 ; q t ; q t 1 ; :::; q t p ) 0 , q it being h it or y it We report M oran = I E(I) std(I) , where I is given by (20). Notes: The individual coe¢ cients have been computed according to formula (9), and their variance as in (??). The superscript " " means that the coe¢ cient is signi…cant at 5% level. Notes: (+) : time dummies were included. The superscript " " indicates that the coe¢ cient is signi…cant at the 5% level.
(A): The CD statistics are computed onû it = h it ^ i ^ y it , (B): The CD statistics are computed onê it = h it ^ i ^ y it ĝ 0 i z t where z t = h t ; y t 0 : For the Moran statistic see the notes to Table 5.  : time dummies were included. The superscript " " indicates that the coe¢ cient is signi…cant at the 5% level.  Table 7. Critical value for the intercept only case -2.11. The superscript " " indicates that the test is signi…cant a the 5% level. Notes: the superscript "*" indicates that the coe¢ cient is signi…cant at the 5% level. . For the Moran statistic see the notes to Table 5.