Statistica in azienda

Statistici in azienda Evento satellite della

ENBIS-DEINDE 2011 Spring Conference

Efficiency frontier and Italian debate on federalism : looking for appropriate instrumental variables.

G. Büchi1 and R. Allais2

1 University of Turin, Dep. of Business Economics, Corso Unione Sovietica 218 bis – 10134 Turin, Italy2 University of Turin, Dep. of Statistics & Applied Mathematics, Corso Unione Sovietica 218 bis – 10134 Turin, Italy

Introduction

Conclusion

Result

References

Recent normative evolution on federalism in Italy, has indicated for the computation of standard costs of public firms (healthcare decision making units, local authorities etc) the same methodology which is used in the private sector in order to estimate, through a linear model obtained by ordinary least square techniques, expected income from the endowment of selected inputs of labour and capital. Statistically the residuals of this computation have an interpretation for taxation purposes.If the same procedure is carried out in the realm of public firms, statistically the residuals of this computation have an interpretation as efficiency measure as well the whole computation may be seen as an exercise of efficiency frontier which does not imply output measurement but only the depuration of (per capita) costs in order to single out a standard cost .In public health there are many data on performance, but often not linked to a summary measure that can ensure a benchmarking between regions and administrations. Our purpose is to build a synthetic efficiency index based on relationship between many variables of management and professional services that characterize public administrations in order to perform a system of benchmarking between regional health systems based on many of these indicators.Nevertheless a conceptual problem arises which is strictly linked to statistical issues. Whereas in the private sector there are no a priori reasons for expecting the endowment of selected inputs to be related to efficiency and income in the public sector this is definitely the case.Applying the same methodology as suggested by the regulations, there is therefore a problem of correlation between the predictors and the residuals of regression.To avoid this problem, we identify possible instrumental variable and resort to two stage least square method. Next, in order to identify the efficiency frontier, we use corrected ordinary least square methodology.

Possible solutions to endogeneity due to the correlation between the endowment of selected inputs and efficiency are to be found in the framework of the institutional behaviour of public firms which in many instances are involved in outsourcing of their institutional activities.Since empirical research has shown that the outsourcing behaviour is not related to efficiency, considering that outsourcing behaviour is obviously inversely related to endowment of selected inputs, we suggest that the weight of outsourcing may be appropriately used as an instrumental variable.

Coelli, T.J., Prasada Rao, D.S., O’Donnell, C.J., Battese, G.E., 2005. An introduction to efficiency and productivity analysis. SpringerDavidson, R., Mackinnon, J.G.,1993. Estimation and inference in econometrics. Oxford University Press.Hayashi, F., 2000. Econometrics. Princeton University Press.Peyrache, A., Coelli,T., 2008. Testing procedures for detection of linear dependencies in efficiency models. Working paper WPo2/2008, Centre for Efficiency and productivity analysis, University of QueenslandWooldridge, J.M., 2002. Econometric analysis of cross section and panel data, MIT Press

The database & the variables

The data, which describe the regional health system both from a technical-structural and economic standpoint, are mean values for the years 2005-2009 related to the whole population and are published by different sources (Agenas, Ministry of health, Istat, General Accounting Office) and elaborated ad hoc. On search of the efficiency index we have not considered the traditional measures of output of health and we relied only on economic considerations, assuming that regional spending is given one side by the efficiency in the use of factors and other by a set of a priori features of demand and supply of health services. Therefore we identify as response variable health expenditure per capita net mobility, while as possible explanatory variables we select:

Aiming to identify good predictors for the model, we decide not to resort to automatic methods, such as stepwise selection, which can lead to biased set of predictors, but to a “step by step” approach in which best predictors are those variables which are strongly correlated to the response, but not correlated with each other. Performing these steps, the selected predictors are:

The estimated model and the choice of IVWe therefore estimated efficiency frontier through corrected ordinary least square methodology (COLS).The validity of efficiency measurement methods relies upon the assumption that variables such as input quantities and output are independent of technical efficiency. An uncorrelation assumption is required for COLS estimators to be consistent.Among the variables representing the supply side, one of the factors we consider is the weight of units of national health service personnel on the population. Because the amount of this input could be correlated with efficiency, we have resorted to the two stage least square methodology identifying as possible instrumental variable (IV) the weight costs of the private sector on the total cost for local health ASL. This choice because IV is highly correlated with the endogenous variable (r = - 0,81) but not correlated with the response (r = 0,3) and the error term.

Best predictors Correlation with the response variable

Regional GDP per capita 0,612

Percentage of population aged 0-14 years -0,537

Percentage of population over 74 years 0,502

Weight of units of national health service personnel on the population

0,557

Public MRT 0,542

We obtained a linear model that significantly represent the health expenditure per capita net mobility (R = 0,604 F= 5,178, p = 0,017).COLS methodology attributes all deviations from the model to inefficiency.Calculating the opposite of estimated residuals and shifting the line towards the best performing region we obtain the efficiency frontier . Since the efficiency index is highly correlated (r = 0,81) with the result of regional health income statement per capita, this means that this result is the expression of efficiency in inputs use rather than endowment of the same or of demand.

Percentage of population aged 0-14 years and over 74 years represent demand, MRT and GDP per capita are capital expenditure proxies, weight of units of national health service personnel on the population represents labour.

Regions more distant from the efficiency frontier are less efficient. So we get an efficiency index that allows us to make a benchmarking between regions according to the health care costs saved (in figure below red bars identify those regions where health expenditure exceeds what would be justified by a priori characteristics of supply and demand).

Demand Variables

Percentuale nati vivi Percentuale popolazione di età 0-14 anni Percentuale popolazione di età 65-74 anni

Percentuale morti Percentuale popolazione di età 15-44 anniPercentuale popolazione di età superiore ai

74 anni

PIL regionale procapite Percentuale popolazione di età 45-64 anniPercentuale stranieri residenti

Percentuale immigrati irregolari

Supply Variables

Posti letto pubblici in Day Hospital (DH) procapite Ambulatori/laboratori procapite

Posti letto pubblici in Ricovero Ordinario (RO) procapite Altri tipi di strutture territoriali procapite

Posti letto pubblici a pagamento procapite Strutture semiresidenziali procapite

Posti letto accreditati in DH procapite Strutture residenziali procapite

Posti letto accreditati in RO procapite Strutture di guardia medica per 1.000.000 di abitanti

Posti letto complessivi procapite Personale del SSN rispetto alla popolazione

Apparecchiature tecnico-biomedicali di diagnosi e cura presenti nelle strutture di ricovero pubbliche e nelle case di

cura accreditate ed extraospedaliere. Indicatori per 1.000.000 di abitanti

Strutture pubbliche Strutture private

Acceleratore lineare (ALI) Acceleratore lineare(ALI)

Emodialisi (EMD) Emodialisi (EMD)

Gamma camera computerizzata (GCC) Gamma camera computerizzata (GCC)

Tomografo assiale computerizzato (TAC) Tomografo assiale computerizzato (TAC)

Tomografo a risonanza magnetica (TRM) Tomografo a risonanza magnetica (TRM)