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Determinants of health-system efficiency: evidence from OECD countries

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Abstract

This paper analyzes the most important determinants of healthcare efficiency across OECD countries. As previously documented in the literature, we first provide evidence of significant differences in the cross-country level of efficiency in healthcare provision. We then investigate how improvements in efficiency can be achieved by considering alternative efficiency indices (parametric and non-parametric) and a novel dataset with information on the characteristics of healthcare systems across OECD countries. Our empirical findings suggest a positive correlation between policies such as increasing the regulation of prices billed by providers and reducing the degree of gate keeping and the efficiency of national healthcare systems.

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Notes

  1. Note that the literature on efficiency measurement in health production is enormous at the hospital level (e.g. Athanassopoulos et al. 1999; Dismuke and Sena 1999; Hofmarcher et al. 2002). Hollingsworth et al. (1999) and Hollingsworth (2003) provide an overview.

  2. In any case, we still consider that our results should be interpreted with caution as emphasized in Spinks and Hollingsworth (2009).

  3. Note that this latter finding is somehow in contrast with previous literature. For instance, gatekeeping has been traditionally associated with lower utilization (Bolin et al. 2009), lower costs (Gerdtham et al. 1998) and higher efficiency (Bhat 2005).

  4. Moreover, the efficiency measures used in the literature may refer to different levels of the healthcare system. Generally, a distinction is made between those papers that measure gains in health status for each type of illness across the various sub-sectors of the healthcare system (hospitals, chemist’s, etc.) or the healthcare system as a whole (see Häkkinen and Joumard 2007, for a discussion of the advantages and drawbacks of these three approaches).

  5. More detailed information on the definition of the indicators and their construction can be found in Paris et al. (2010) and OECD (2010).

  6. For the sake of brevity we do not report the alternative SFA rankings but they are available upon request.

  7. See Table 9. Additional information about the results using the alternative SFA efficiency index is available upon request.

  8. Moreover, unreported Hausman tests clearly indicate that the fixed effects specification is more appropriate than the alternative random effects specification within the panel SFA approach.

  9. Despite there is no consensus in the literature about the appropriateness of Tobit-type approaches in this setting due to the inexistence of a “latent efficiency”, Fried et al. (1999) and Rosko (1999) are examples of previous efficiency studies considering Tobit-based estimators. Note also that, if there are no censored observations, the Tobit approach is equivalent to the least squares approach; hence, given that the number of censored countries is very low in our sample, we expect the Tobit results to be similar to the least squares results.

  10. Considering the random priors in Ley and Steel (2009), the prior inclusion probability for a given variable follows a Beta distribution so that it does not necessarily coincide for all the variables and a meaningful (and common) threshold is therefore not available.

  11. Due to its single-case nature and as a result of masking, the employed deletion diagnostic can fail in the presence of multiple unusual countries jointly influencing the results.

  12. Paris et al. (2010) provides detailed information on all the twenty indicators.

  13. Moreno-Torres et al. (2010) analyze the effects of 16 regulatory policies in Catalonia between 1995 and 2006, classifying the policies in five groups: (i) those aimed at reducing the margins of drug distributors and retailers; (ii) those based on lists of drugs excluded from receiving public funding; (iii) those in which the public authorities unilaterally impose a reduction on drug manufacturers’ maximum selling prices; (iv) those based on reference prices, i.e. when there are several drugs with the same characteristics and end-use and Footnote 13 continued a reference price is set on the basis of the cheapest drug in the group, which will be the maximum amount that the public health system may reimburse for any drug in the group; (v) regulations whose purpose is to economically generic drugs. Given these five types of policies, the results in the paper indicate that, on one hand, 12 of the 16 regulations were not effective in reducing spending on drugs; and, on the other, of the four regulations that were effective in the short term; none had significant effects in the medium/long term. Sood et al. (2009) obtain the same result using different data and methodology.

  14. Note that this finding provides support for the theoretical “excessive specialization” channel proposed by Brekke et al. (2007). However, it is in contrast with previous empirical literature, which has typically found that higher degrees of gate keeping are associated with lower utilization (Bolin et al. 2009), lower costs (Gerdtham et al. 1998) and higher efficiency (Bhat 2005).

  15. The efficient country will be the one with the higher life expectancy given certain inputs. This may arise because life expectancy is higher for the same given level of expenditure, or because for the same life expectancy, there is a lower level of expenditure or of other inputs.

  16. Note that dummy variables are also included for each year, reducing the potential correlation between each country’s error terms. This is a vital prerequisite for the consistency of the estimates.

  17. In fact, the OECD (2010) also performs very similar panel regressions to that considered in this paper. However, it does not calculate SFA efficiency indices in the proper sense of the term; it rather uses estimated residuals as proxies of efficiency.

  18. Even if the posterior inclusion probability is lower than the prior inclusion probability for a given variable, it might be the case that this particular variable is important to decision-makers under some circumstances. Therefore, although useful for presentation purposes, the mechanical application of a threshold, or a simple comparison between the prior and the posterior, should often be avoided.

  19. While the ratio of posterior mean to posterior standard deviation is not distributed according to the usual t-distribution, having a ratio around two in absolute value indicates an approximate 95 % Bayesian coverage region that excludes zero (see Sala-i-Martin et al. 2004).

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Acknowledgments

The authors would like to thank Beatriz González López-Valcárcel, Guillem López-Casasnovas, Eloísa Ortega, Bazoumana Ouattara, Anna Tur Prats, Laura Vallejo-Torres and Dominika Wranik for useful comments and discussions. They also thank two anonymous referees and Pedro Barros (The Editor) for helpful suggestions. The opinions and analyses in this paper are the responsibility of the authors and are not necessarily shared by the Banco de España or the Eurosystem.

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Correspondence to Enrique Moral-Benito.

Appendices

Appendix 1: Estimation of efficiency indices

Two main alternative approaches have been considered in the literature for estimating efficiency indices: data envelopment analysis (DEA) and stochastic frontier analysis (SFA). DEA is deterministic and non-parametric, i.e. as it is non-parametric it need not assume any functional form for the production frontier; however, as it is deterministic, any deviation between the actual production and the frontier is classified as inefficiency without any possibility of randomness. Conversely, SFA is parametric and stochastic. That is to say, using SFA it is necessary to assume a specific functional form for the production frontier, but at the same time we can include a source of randomness in production. The literature that compares both approaches is very extensive but relatively inconclusive regarding the preferred alternative (see, for example, Gong and Sickles 1992; Bjurek et al. 1990; Hjalmarsson et al. 1996). Moreover, efficiency estimates crucially depend on the methodology used. For instance, using data compiled by the World Health Organization (WHO 2000), Hollingsworth and Wildman (2003) estimate DEA indices of healthcare efficiency for 191 countries while Greene (2004) estimates SFA indices, and the results are significantly different. Also in the sphere of healthcare efficiency, Chirikos and Sear (2000) and Hollingsworth and Wildman (2003) confirmed that the efficiency rankings resulting from both approaches applied to the same data usually differ considerably, hence the importance of their comparison and the relevance of presenting the results in accordance with both alternatives (e.g. Hollingsworth 2003, p. 209).

(a) Efficiency measures based on non-parametric techniques (DEA)

As earlier mentioned, DEA relates output (measured by life expectancy or DALE) to inputs (healthcare expenditures and the socioeconomic/lifestyle characteristics of the population, essentially). More specifically, DEA analysis conducted by the OECD (2010) for a group of 29 countries is based on defining a frontier of production of life expectancy (a measure of the health system’s output) using a series of resources such as per capita healthcare expenditure, the level of per capita income and the level of educational attainment of the population, and the lifestyle characteristics of each country (i.e. the inputs the national health system disposes of to “produce” life expectancy). Taking the production frontier estimated through non-parametric techniques, the country will be efficient if it stands on this frontier, i.e. if it cannot produce more output without using more inputs.Footnote 15 Accordingly, the efficient countries will have the highest efficiency index and the other countries will have efficiency levels that are always below this maximum and calculated on the basis of their distance from the production frontier on which the most efficient country stands (Farrell 1957). Details on the estimation of production frontiers by means of DEA can be found in Chap. 6 of Coelli et al. (2005).

For the sake of comparability with earlier literature we consider the same DEA index estimated by the OECD (2010). However, we also replicated the estimation of this index substituting life expectancy by disability-adjusted life expectancy (DALE) and mortality amenable to healthcare as outputs in the production function. The Spearman rank correlation between the resulting efficiency indices is 0.99 and 0.96, respectively. Moreover, since we fail to reject the null that these correlations are equal to one at the 1 % level in both cases, we do not present the results corresponding to the DEA index using DALE and amenable mortality as outputs because they are basically equivalent.

(b) Efficiency measures based on stochastic frontier analysis (SFA)

As previously indicated, data envelopment analysis is based on the non-parametric estimation of the production frontier using linear programming methods. Alternatively, we now present the basics of the SFA approach and estimate efficiency indicators for national healthcare systems based on this stochastic technique. Under this methodology the output frontier is estimated assuming a specific functional form and distinguishing between two components in the error term, one due to inefficiency (always zero or positive) and another due to randomness. The inefficiency term captures unobservable characteristics which systematically make production to lie below its potential level (this term is zero for the efficient unit which lies in the frontier).

The stochastic frontier model can be estimated from panel or cross-section approaches. In particular, the panel approach adopted in this paper assumes that inefficiency is invariant over the sample period and do not require any distributional assumption to separate noise from inefficiency in the error term (Schmidt and Sickles 1984). In contrast, the SFA alternative based on cross-section data requires additional assumptions on the distribution of the noise and inefficiencies across countries in order to ensure identification.

We first present our preferred SFA alternative based on a panel approach. We depart from the following parametric production function:

$$\begin{aligned} Y_{it} = \alpha +X_{it}^{{\prime }}\beta +v_{it} -u_{i}, \end{aligned}$$
(2)

where \(Y_{it}\) represents life expectancy as an output of the healthcare system in country \(i\) in year \(t\). This output arises from inputs included in the vector \(X_{it}\) and which include socio-economic factors such as the level of educational attainment, per capita income and pollution, lifestyle characteristics such as fruit and alcohol consumption and, lastly, each country’s healthcare expenditure.Footnote 16 Namely, the inputs considered in our estimates are the same as those used by the OECD (2010) in the estimation of the DEA index set out in the previous section.Footnote 17 Finally, \(v_{it}\) represents sources of random change in the model and \(u_{i} \ge 0\) is a non-negative random variable that represents the specific inefficiency of each country. For estimation purposes, we define the country-specific effect as \(\alpha _{i} = \alpha u_{i}\)Schmidt and Sickles (1984) propose estimating the resulting equation using a fixed-effects estimator due to the possible correlation between the inefficiency and the inputs. In this framework, the country with the biggest estimated fixed effects is considered the most efficient country and that which therefore defines the production frontier \((\tilde{\alpha }=\max (\hat{{\alpha }}_i ))\). To calculate the inefficiencies of each country relative to the benchmark, ensuring in turn that they are all positive, we estimate \(\tilde{u}_i =\tilde{\alpha }-\hat{{\alpha }}\).

We can thus define the stochastic efficiency, or technical efficiency (TE), index as follows:

$$\begin{aligned} TE_{i} =\frac{E(Y_{it} |\tilde{u}_{i} ,X_{it})}{E(Y_{it} |\tilde{u}_{i} =0,X_{it})}. \end{aligned}$$
(3)

Note that other panel SFA approaches are available in the literature, Coelli et al. (2005) is an excellent reference for the different methods for estimating efficiency indices based on panel SFA approaches. For this panel approach we cannot replicate our estimates using alternative health status indicators instead of life expectancy because data on DALE and mortality amenable to healthcare are not available for the full period 1997–2009.

Turning to the approach based on cross-sectional data for the year 2007, we estimate a stochastic production function model following (Aigner et al. 1977):

$$\begin{aligned} Y_{i} =X^{\prime }_{i} \beta +v_{i}^{c} -u_{i}^{c}, \end{aligned}$$
(4)

where output (\(Y_{i}\)) and inputs (\(X_{i}\)) are defined as in Eq. (2). The term \(u_{i}^{c}\) is a non-negative random variable associated with technical inefficiency, and \(v_{i}^{c}\) is a symmetric random error which accounts for statistical noise. In this framework, the most common output-oriented measure of technical efficiency is given by

$$\begin{aligned} TE_{i}^{c} =\hbox {exp}\left( -u_{i}^{c}\right) \end{aligned}$$
(5)

which takes a value between zero and one. In order to estimate the unknown parameters and thus the efficiency measure we need to complete the model with certain distributional assumptions in addition to homoskedasticity and lack of correlation between the error components. A common alternative suggested by Aigner et al. (1977) is to assume normality of the noise term together with half-normality of the inefficiency term and then proceed to estimate the model by maximum likelihood. Despite we consider this half-normality assumption as baseline when estimating the SFA index based on cross-sectional data, we also experimented with alternative distributional assumptions for the inefficiency term such as exponential or truncated normal, and the differences in the resulting efficiency indices were negligible.

Appendix 2: Bayesian model averaging (BMA)

In this appendix we present the basics of the BMA methodology. A more detailed discussion is available for instance in Hoeting et al. (1999) and Moral-Benito (2011). The BMA approach considered in this paper estimates by OLS (or Tobit) all the models resulting from the possible combinations (subsets) of the 20 explanatory variables we have, that is, \(2^{20}=1,048,576\) different models. We refer to each of these models as \(M_{i}\), with \(i=1,\ldots ,2^{20}\). Following Raftery (1995) we can estimate the posterior probability of each model:

$$\begin{aligned} P(M_{i} |y)=\frac{P(M_{i})N^{{-k_{i}}/2}SSE_{i}^{{-N}/2} }{\sum _{j=1}^{2^{20}} {P(M_{j})N^{{-k_{j} }/2}SSE_{j}^{{-N}/2}}}, \end{aligned}$$
(6)

where \(P(M_{i})\) is the prior probability of each model set by the researcher, \(N\) is the number of observations, \(k_{i}\) is the number of parameters to be estimated in model \(i\) and \(SSE_{i}\) is the sum of the squared errors of model \(i\). Furthermore, \(P(M_{i} \vert y)\) is the posterior probability of model \(i\), i.e. a type of measure of goodness of fit from a Bayesian standpoint (note that \(y\) refers to the data, i.e. we have the prior probability \(P(M_{i})\), before seeing the data, and the posterior probability \(P(M_{i} \vert y)\), after seeing the data).

Once we have the posterior probability of each model, we can calculate the posterior inclusion probability (PIP) of each variable, i.e. the probability that the coefficient accompanying the variable is other than zero. This probability will be given by the sum of the probabilities of all the models in which the variable in question is included. Specifically, the probability of variable \(h\) being included in the model is:

$$\begin{aligned} PIP_{h} =P(\theta _{h} \ne 0|y)=\sum \limits _{\theta _{h} \ne 0} {P(M_{i} |y)}. \end{aligned}$$
(7)

Those variables with higher posterior inclusion probabilities (PIP) will be those that most contribute to explaining the variation of the efficiency index and can, therefore, be considered as robust determinants of the level of efficiency. Specifically, we can consider as robust those variables whose PIP is greater than 0.5. This is so because we will assume a priori that each model is equally probable a priori (\(P(M_{i}) = 1/2^{20} \forall i)\), meaning that the prior inclusion probability is 0.5 for all the variables. As a result, the variables with \(\hbox {PIP}>0.5\) will be considered robustFootnote 18 because the data favour their inclusion in the model or, otherwise expressed, they are those which most contribute to explaining the variation of the dependent variable.

BMA also provides information about the effect of a particular regressor on the dependent variable. In particular we also compute the posterior mean of the coefficient distribution which is given by a weighted average of the model-specific coefficient estimates across all the models using \(P(M_{i} \vert y)\) as weights. Additionally, we compute the posterior variance (and standard deviation) of our estimates which incorporates not only the weighted average of the estimated variances of the individual models but also the weighted variance in estimates of the \(\theta \)’s across different models.

Finally, the ratio of posterior mean to posterior standard deviation gives us another measure of robustness (in addition of the posterior inclusion probability—PIP) of a particular indicator on explaining the variation in efficiency scores. In particular, this ratio can be interpreted as a pseudo-t statistic which indicates whether the BMA coefficient estimate is significantly different from zero.Footnote 19 Interested readers can consult Raftery (1995) and Hoeting et al. (1999) for more details on the statistical foundations of BMA, and Moral-Benito (2011) for an overview of recent applications of BMA in economics.

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de Cos, P.H., Moral-Benito, E. Determinants of health-system efficiency: evidence from OECD countries. Int J Health Care Finance Econ 14, 69–93 (2014). https://doi.org/10.1007/s10754-013-9140-7

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