National Institute of Economic and Social Research WP8: Methodological Issues in Development Scenarios for Health Expenditures for EU Ehsan Khoman and Martin Weale

Introduction Share of public health spending in GDP and in total expenditure has increased significantly in the EU since the 1960s. This trend is likely to continue over the coming decades. Health care projections are far more uncertain than pension expenditure projections since there are no rules for estimating future demand and supply of health care. The projections are based on a no policy change scenario and on existing legislation. Thus, a certain level of caution must be exercised the further the projections go into the future.

Data and Methodology A balanced panel dataset covering 26 countries was used. The data was separated into two sub-group of countries, (i) old EU15 and (ii) EU anticipated member states and Turkey. The panel has 24 yearly time periods ( ) for the EU15, but only 8 yearly time periods for the EU11 ( ). We attempt to model health care expenditure against a number of variables using the dataset provided by Christiansen et. al (2006) in work package 6. Also we have included a ‘mortality’ variable to account for the recent arguments made that the increase of health costs at higher ages may not be a function of age per se, but rather of individual proximity to death.

Data and Methodology The dependent variable used in this paper is the natural logarithm of total health care expenditure per capita (THEPC) measured in US nominal prices and adjusted for both PPP and inflation. The explanatory variables can be grouped into three categories: (i) economics variables, (ii) institutional variables and (iii) technology variables. We had hoped to include tobacco consumption as well but the data did not seem to be reliable. Female labour force participation rates were left out of the analysis as discussed later. The projections are in general made on the basis of no policy change, in that they reflect only existing legislation and not possible future policy changes.

The Model – Panel Unit Root and Co-integration Tests Along with the ADF test (1979) and the Im, Pesaran and Shin test (2003) four other unit root tests were performed. Only UNEMP was rejected for the existence of a unit root. Following Breitung (2005) we next consider how many co- integrating vectors there may be present in our model. His test statistics for co-integrating spaces of up to rank 6 against alternatives of lower rank – we focus on THEPC, GDPPC, MORTALITY, LE65F, LE65M, AGE65-74, AGE75+ and PUHES. Our finding suggests that there is at most one co-integrating vector linking the variables in levels.

The Model – Arellano-Bond (1991) estimation The model is constructed using the Arellano and Bond (1991) estimation technique which allows for the use of lags of the dependent and explanatory variables to model health care. Consider: (1) In order to get a consistent estimator of we first difference the equation above to eliminate the heterogeneous effects (2) So Arellano and Bond (1991) derive a GMM estimator for and the other explanatory variables using lagged levels of the dependent variable and the predetermined variables.

The Model – Least-squares restriction From the Arellano-Bond method we therefore have a regression equation. This is defined as the unrestricted model. By applying least-squares estimation we use this unrestricted equation to estimate a restricted model by removing the insignificant coefficients. It is assumed that there is a parameter vector defined as the unrestricted set of variables which satisfies the constraint,. It is also observed that the parameters are distributed without bias around the true data with known variance matrix,. Our problem is to find a vector to satisfy the account constraint,.

The Model – Least-squares restriction The least-squares problem is that of minimising (3) subject to the constraint (4) The least-squares solution is given by (5) The estimator is just a linear combination of the unrestricted parameters. The mean of the estimator can be shown to be (6) Balancing of the data also leads to a reduction in the data variance which can be demonstrated by evaluating the variance matrix of the balanced data (7)

Long-Run Elasticity Restrictions on the model VariableUnrestricted Base Restrictions CAPGP GLOBALHO CASEHO COPAYGP COPAYHO FREEGP FREEHO BEDS MORTALITY VariableUnrestricted Base Restrictions GDPPC AGE0_ AGE65_ AGE75_ AVELE UNEMP ALCCON PUHES SALARYGP We place restrictions on UNEMP(-1), PUHES(-1), GLOBALHO, COPAYGP, COPAYGP(-1), BEDS, BEDS(-1).

Long-Run Elasticities including and excluding FLFPR VariableUnrestricted Models GDPPC AGE0_ AGE65_ AGE75_ FLFPR AVELE UNEMP ALCCON PUHES SALARYGP VariableUnrestricted Models CAPGP GLOBALHO CASEHO COPAYGP COPAYHO FREEGP FREEHO BEDS MORTALITY