Working Paper of Public Health Volume 2012 - Azienda Ospedaliera ...

More documents

Recommendations

Info

Azienda Ospedaliera Nazionale“SS. Antonio e Biagio e Cesare Arrigo”Working Paper of Public Healthnr. 16/2012Moreover, the classical assumption of free disposability does no longer hold for all outputs,but only for the good ones, which can be reduced without costs. In notation, where 0 1and P(x) is the production possibility set, we denote weak disposability in (y,b)( x,y,b) P(x) ( x, y,b) P(x)(2)whereas free disposability in y( x,y,b) P(x) ( x,y, b) P(x), ( x,y,b) P(x)(3)Then, weak disposability implies that good and bad outputs can be proportionatelycontracted, but only good outputs can be freely reduced without costs.The directional output distance function (DODF) gives the maximum feasible proportionalcontraction in bad outputs and expansion in good outputs. The DODF is defined on P(X),which takes on a value equal to 0 for efficient firms (which contribute to frontieridentification) and increases with inefficiency. Formally, the directional output distancefunction is defined as follows:D( x,y,b;g , g ) max{ : ( y,b) ( g, g) P(x)}(4)ybybwhere g g y, g) is the directional vector and P(x) is the production possibility set(bestimated via the DEA by solving, for each firm (i.e., hospital in the paper), the followinglinear problem after defining a particular directional vector g = (y,-b):( x , y , b ; y,b) max D W000s.t.x(1 ) y00(1 ) b0 Xz Yz Bzz 0, 0Where, given K as the number of hospitals, X is the NxK matrix of inputs; Y is the MxKmatrix of good outputs, and J is the JxK matrix of bad outputsIn practice, the directional output distance function re-scales the observed output vector (y,b)on the frontier following the direction of g, which is (y,-b) in our case.Applying the DODF, production technology is represented in a way which immediatelyderives from reality, without transformations, and every constraint in the estimation of P(x)could be formulated in linear form; hence, DEA framework is immediately applicable. In ourwork, all the linear programs are written and solved using R software.In the next subsection, the adopted data and relative descriptive statistics are proposed.(5)7
Azienda Ospedaliera Nazionale“SS. Antonio e Biagio e Cesare Arrigo”Working Paper of Public Healthnr. 16/20122.2 DataTable 1 presents the variables adopted in the first stage. Health production is the good output,whereas financial loss is the bad output. This work proposes the following inputs: hospitalbeds (i.e. day, day surgery, and ordinary) and hospital workers (i.e. administrative andsupport staff, nurses and technicians, physicians, general healthcare personnel andspecialists). Outputs are expressed in thousands of Euros, whereas inputs are proposed insingle units.Data about both technical inputs and financial outputs are collected in the database of theItalian national healthcare system (http://www.salute.gov.it) and they refer to public Italianhospitals in 2007. 4 This work considers only autonomous hospitals (which are known in Italyas AOs); thus not including all the medical centers linked to the Local Health Authorities(which are known in Italy as ASLs or AUSLs). Data about financial outputs are extractedfrom the hospitals’ financial statements. The financial loss refers to the hospital result (i.e.code Z9999), assuming the value 0 if there is no loss or if there is a positive result. In theItalian system, the health production considers the reimbursements of medical treatmentsfrom Local Health Authorities (i.e. code A0060), both from the region of the hospital inquestion and from another region (i.e. patients’ positive mobility). Some observations havebeen dropped from the dataset since there is no health production. These atypicalobservations concerns regions in the South of Italy: Calabria (2 hospitals), Sardinia (1hospital) and Sicily (7 hospitals).Table 1Inputs and outputs, Italian public hospitals (2007)Variables Obs. Mean Std. Dev. Min. Max.Good output Health Production 94 124617.70 106818.50 2 371700Bad output Financial loss 94 12458.37 27203.08 0 154534Day Hospital Beds 94 75.51 46.47 4 282Day Surgery Beds 94 19.48 21.89 0 88Ordinary Hospital 94 695.00 360.77 61 1680BedsAdministrative and 94 424.50 264.35 14 1288Inputs support staffNurses and94 1228.19 680.18 141 2842techniciansPhysicians 94 447.80 250.33 49 1285General healthcare 94 282.27 210.50 12 1085Specialist healthcare 94 41.34 33.11 3 160Source: Italian National Healthcare System8
Page 2 and 3:
La serie di Working Paper of Public
Page 4 and 5:
Azienda Ospedaliera Nazionale“SS.
Page 6 and 7:
Page 8 and 9:
Page 10 and 11:
Page 12 and 13:
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
Azienda Ospedaliera NazionaleSS. An
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 92 and 93:
Page 94 and 95:
Page 96 and 97:
Page 98 and 99:
Page 100 and 101:
Page 102 and 103:
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
Page 110 and 111:
Page 112 and 113:
Page 114 and 115:
Page 116 and 117:
Page 118 and 119:
Page 120 and 121:
Page 122 and 123:
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
Page 130 and 131:
Page 132 and 133: Azienda Ospedaliera Nazionale“SS.
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
Page 238 and 239:
Page 240 and 241:
Page 242 and 243:
Page 244 and 245:
Page 246 and 247:
Page 248 and 249:
Page 250 and 251:
show all

Working Paper of Public Health Volume 2012 - Azienda Ospedaliera ...

Create successful ePaper yourself

Delete template?

Save as template?