A New Public Sector Comparison Tool: Empirical Evaluation in the Healthcare Sector


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1 A New Public Sector Comparison Tool: Empirical Evaluation in the Healthcare Sector Miguel Gouveia 1 CLSBE, Universidade Católica Portuguesa Pedro Raposo CLSBE, Universidade Católica Portuguesa June, 2012 ABSTRACT Public sector comparators (PSC) offer official estimates of how much a project would cost if it were carried out by the government, versus production by public sector entities. Comparisons may suggest a benefit of a public private partnership (PPP), due to competitive bidding by potential private partners, which leads to various economic advantages. However, most PSCs require complex processes and offer little transparency; this study instead proposes a general approach that provides an external benchmark for the PSC, using public data, and illustrates the approach in the healthcare sector. Estimates of the PSC of two hospitals built using PPP in Portugal, compared against the official PSC values, reveal that the official construction PSCs were close to the upper limits of the prediction confidence intervals but the operations PSC were very different, whether well above the upper limit or close to the lower limit. The bidding process for one project produced a winning bid substantially below the PSC, so competition partially mitigated the upper bias in the PSC estimate. Keywords: PPP, Public sector comparator, Cost function JEL codes: D24, H43, L32, L33 1. INTRODUCTION There are multiple reasons to use public private partnerships (PPP), ranging from the benevolent belief that PPP are more efficient than traditional procurement or direct public sector production to a more cynical view that PPP shelter governments and politicians from accountability, because they can rely on off budget financing or provide rents to powerful interest groups. Regardless of their impetus though, it is necessary to gauge the potential efficiency advantage of PPP by comparing the costs to society when governments carry out projects in a traditional way versus developing an otherwise similar project using PPP. This public sector comparator (PSC) is a key parameter of the 1 Corresponding author. Miguel Gouveia; tel: ; fax: E mail addresses: ucp.pt (P.S. Raposo), ucp.pt (Miguel Gouveia).
2 PPP process that defines whether there is any economic advantage in forming a partnership, according to its comparison against the outcomes of a competitive bidding process. In practice the PSC also serves as a parameter in the bidding process, such that it establishes a ceiling for private firms bids. A low PSC puts more pressure on firms to minimize costs; a high PSC makes a project more attractive to potential private partners. In turn, the official PSC values are often the subject of controversy and accusations that they have been generated by black box processes that are too complex and insufficiently transparent. It would be useful to have clear terms of comparison to clarify the official values of the PSC. This study aims to provide an external view of the PSC, using public data to obtain magnitude estimates. We add to existing literature by presenting an initial empirical analysis of the value of the PSC used in two actual PPP projects. Specifically, we gather data from the Portuguese National Health Service (NHS). Portugal has extensive experience using PPP for roads, water management, energy production, and distribution, dating back to the 1970s (OPPP, 2011). Furthermore, Portugal exhibits the greatest use of PPP among European countries, as measured by the ratio of expenditures on PPP to gross domestic product or overall government budget (Moreno, 2010). Such projects more recently have extended into health care settings, including the construction and, in some cases, operation of hospitals integrated with the NHS. We concentrate on the first two PPP hospital projects, in Braga and Cascais, and provide estimates of their PSC using publicly available data, then contrast our estimates with the official values for PSCs. Because we are dealing with both construction and operation costs, the analysis relies on two distinct sets of data. The first, small data set covers construction costs and basic characteristics of hospitals built by the government using traditional procurement. The second data set instead includes outputs and operating costs for almost all hospitals in the NHS. We thus can estimate construction and operation cost functions that summarize and quantify public sector cost structures. We use data about the hospitals characteristics, the output of clinical services defined in the PPP contracts, and the estimated cost functions to generate our PSC estimates. Our results show that the official PSCs for construction costs in both cases are close to the upper limit of our prediction confidence intervals. The PSC for operations differ though: In Braga, they were well above the upper limit of our prediction, whereas in Cascais, they were close to the lower limit. The bidding process in Braga led to a winning bid that was substantially below the PSC, proving that competition at least partially addressed the upward bias in PSC estimates. In Cascais, press reports indicate the hospital s financial difficulties. Perhaps the PSC was too low, and the even lower bid that won the contest now is suffering from a winner s curse. 2. PUBLIC SECTOR COMPARATOR A PSC is usually an aggregate of many partial estimates. For example, in engineering projects, these estimates might combine unit costs, developed through past experience, to estimate separate costs for a multitude of the components that go into complex structures. Input requirement lists can be long; the relevant market prices may not be obvious; and even the appropriate amounts for some inputs may be unclear, ranging 2
3 from specialized labor to energy and raw materials. Similar problems arise for complex services, such as the provision of healthcare. The public sector costs may not be explicit, such as when a project involves the use of scarce land already in the public domain or relies on earmarked funds from public sector capital budgets. Overall then, arriving at a PSC estimate is a long, complex, and non transparent process. In such a setting, government officials could easily introduce biases into an estimate, pushing it above or below the accurate value. For example, government officials might prefer a PSC that is too high, because they want to favor private sector interests or ensure that a PPP project that is less socially desirable but politically convenient moves ahead, particularly if it can be done off budget. These cases offer examples of strategic misrepresentation (Flyvbjerg, 2008). On the other side, a PSC might be too low because the official hopes to extract larger surpluses from private partners. However, this latter example is usually not a great cause for concern, because nothing prevents governments from using bidding processes that set a ceiling on private sector bids below the PSC. 2 Instead, it appears optimal to design a bidding process in which a strategically chosen ceiling maximizes the gains from using PPPs. Thus an optimal ceiling choice should be a function of the PSC, as well as government s beliefs about the distribution of efficiency levels in the private sector. Given these temptations for governments to manipulate the PSC, combined with the margin for unintended error or bias, we see value in deriving a methodology that can provide reasonable estimates of the PSC at low costs, using publicly available information. The best solution might be to use historical data and econometrics to obtain a statistically based estimate, rather than relying on costly procedures and expert opinions. A similar philosophical approach to problem solving is suggested by Meehl (1954) and Tversky and Kahneman (1974). Beyond the hypothetical political reasons for biases, we also acknowledge that mistakes can occur naturally; public officials make mistakes because to err is human. Kahneman and Tversky (1979) note the planning fallacy, which states that people are prone to error, and committees of people can produce estimates that are very far from reality. Flyvbjerg (2008) explains the dangers of relying solely on engineering expertise to generate project forecasts and documents a series of errors to avoid in public projects mistakes that are not due to poor data or models but instead take the form of systematic biases, such as the optimism bias, and do not tend to disappear with experience. 3. METHODOLOGY use hedonic regressions to model the costs of infrastructure and estimates of the hospital cost functions. Thus we can calculate the expected costs of the new clinical services in hospitals, classified according to operational characteristics (i.e., number of inpatient stays, outpatient visits, outpatient services, day surgeries, emergency care). Hedonic models do not replace traditional cost methods, because they use little 2 In some situations, such as when governments or key decision makers change, new authorities might not feel a sense of ownership of the PPP project, or they may not work to their political advantage. In these cases, officials could try to shut down the process expediently by imposing an artificially low PSC. 3
4 information. However, they support a synthesis of modeled and quantified historical data and are convenient for carrying out predictions, as we attempt to do. methodology thus reflects the hospitals characteristics, defined in the PPP contract. We first estimate the model econometrically using historical data about costs and characteristics. Then, we predict the mean and build a confidence interval for the PSC, to predict the cost to the government to build and operate the two focal hospital projects. These projects each comprise two components: hospital construction and hospital operation over a period of time. In parallel with the official PSC, which were published separately, we present separate estimates for each component. 4. DATA We searched for historical data on public hospitals and collected information on costs, project characteristics, and multiple size measures. For clinical services, we used data related to the operational costs of two types of National Health Service (NHS) hospitals: administrative sector institutions (SPA) and government owned corporations (EPE). Our data also reveal the main production lines: inpatient admissions, outpatient visits, outpatient services, day surgeries, and emergency care. Finally, we gathered data about the average complexity of hospital care, measured by a case mixed index. Data on infrastructure costs are very scarce. Ideally we would prefer to have information about many cases of constructing and equipping new hospitals, each with clear, unique characteristics (e.g., construction area, total number of beds, number of intensive care beds, number of operating rooms, existence of transplant units). In practice though the available data were well below our expectations. Specifically, we obtained data about 10 hospitals, and the available measures common across all hospitals were the built area (m 2 ) and number of beds, as we detail in Tables 1 and 2. Table 1: Relevant dates, beds, and built area Hospital Bid Opening Date Date of delivery / Number of Inauguration Beds Fernando da Fonseca Hospital 24 Jul May ,948 Built up Area (m 2) Hospital N ª Sr ª da Graça  Tomar 09 Feb Aug ,202 Pedro Hispano Hospital Apr Apr ,279 Matosinhos Hospital Santo Andre  Leiria 03 Jun Apr Hospital S. Teotonio  Viseu 23 Oct Jul ,697 Hospital Santa Maria da Feira 11 Sep Jan ,405 Hospital Barvalento Algarve 11 Aug Apr ,005 Hospital Centre Cova da Beira 03 Sep Dec ,342 Vale do Sousa Hospital 07 Jan Aug ,743 Rainha Santa Isabel Hospital  Torres Vedras 18 Apr Sep ,493 4
5 Table 2: Costs of construction, building supply (medical equipment, IT and others), and other ( ). Hospital Wining bid Total additional TOTAL WORK Equipment Costs Other Costs TOTAL COST HOSPITAL Fernando da Fonseca 27,985,760 28,712,786 56,698,546 27,082,097 7,593,111 91,373,754 Hospital Hospital N ª Sr ª da Graça  23,379,089 7,995,586 31,374,675 13,134, ,993,560 Tomar Pedro Hispano Hospital  20,878,463 31,305,856 52,184,319 15,759,209 4,898,870 72,842,398 Matosinhos Hospital Santo Andre  19,377,081 26,999,700 46,376,781 19,092,681 3,514,463 68,983,925 Leiria Hospital S. Teotonio  Viseu 35,916,527 8,471,624 44,388,151 17,941,257 3,560,358 65,889,766 Hospital Santa Maria da 29,527,599 6,716,868 36,244,467 5,495,304 3,226,452 44,966,223 Feira Hospital Barvalento Algarve 22,255,577 4,046,785 26,302,362 19,340,360 2,471,975 48,114,697 Hospital Centre Cova da 24,792,889 6,183,159 30,976,048 16,677,238 2,452,952 50,106,238 Beira Vale do Sousa Hospital 36,565,003 6,617,562 43,182,565 27,858,761 2,707,040 73,748,366 Rainha Santa Isabel Hospital  Torres Vedras 16,500,231 4,975,009 21,475,240 13,224,807 1,281,691 35,981,738 Systematic information was available regarding the operating costs of public facilities and key production measures. For each public hospital, ACSS annually discloses the operating costs and volumes of inpatient admissions, day surgeries, outpatient visits, outpatient services, and emergencies. Thus, we obtained operating cost data for the period related to 58 hospitals or hospital centers, which we followed for an average of 7.8 years. 3 We detail these data in Tables 3 and 4. Table 3: Descriptive statistics: Hospital activity Variable Observations Mean Standard Deviation Log (Total Cost) EPE Log (Inpatient Episodes) Log (Day Surgeries) Log (Emergencies) Log (Outpatient Visits) Log (Outpatient Services) Log (Case Mix) Table 4: Hospital activity by year Year Means Log (Total Cost) EPE Log (Inpatient Episodes) Log (Day Surgeries) Log (Emergencies) Log (Outpatient Visits) Log (Outpatient Services) Log (Case Mix) See the Appendix for the list of hospitals
6 Although the data about the operating costs of NHS hospitals offer some precision to the estimates, we lacked comparable access to information about various PPP contracts. To estimate reference values that could serve as PSCs, we used information related to two specific cases of new hospitals in Cascais and Braga. 5. ECONOMETRIC ESTIMATES OF INFRASTRUCTURE COSTS Using the data from Tables 1 and 2, we estimate regressions and develop Figures 1 and 2. Figure 1 shows the relationship between the number of beds and construction costs; Figure 2 depicts the relation between equipment costs and the hospital s built area. Figure 1: Costs of construction and number of beds lthough the number of observations in Figure 1 is relatively small, the regression offers a good fit to the data. 4 In contrast, in Figure 2 we find an "outlier" an extreme, misaligned observation. At Feira Hospital, equipment costs are well below the statistical norm. Therefore, we excluded Feira Hospital from the sample used to run the regression to predict equipment costs. By doing so, we can effectively predict equipment costs using the construction area of the hospital, better than with the number of beds. Thus, we use the area regression to predict equipment costs. 4 See the Appendix for the results of all regressions. 6
7 Equipment Costs PORTIMÃO BEIRA T.NOVAS TOMAR FEIRA V.SOUSA LEIRIA MATOSINHOS AMSINT VISEU Area (1,000 sq meters) Figure 2: Cost of equipment and hospital area. built a statistically significant model to explain "other costs" according to the built area of the hospital, which then enabled us to estimate a statistically significant regression to explain the total costs per built area. However, we also needed to correct the predicted cost values by the consumer price index (CPI) for the health sector. In Figure 3 we present these values for several recent years, such that the data values collected from the PSC for hospitals in Braga and Cascais indicate 2005 and 2006 prices. For comparability, we corrected them by factors of and 1.378, respectively Figure 3: Consumer price index for the health sector. 6. RESULTS 6.1. Estimating the Cost of Infrastructure 7
8 We predict the costs of new hospitals in Braga and Cascais as if they were built by the public sector. To compare these predictions with the PSC actually used, we tested two estimation methods. All regressions reported here were carried out in logarithmic form, which not only ensures appropriate functional specifications but also helps minimize heteroskedasticity problems. Method 1 relies on a single, univariate regression, 5 in which the total cost of construction and equipment reflects the built area of the hospital. High collinearity prevents us from using the variables area and number of beds simultaneously in the regression; we therefore choose built area, because it is the best variable in terms of goodness of fit. Method 2 instead uses three partial models. A first submodel explains the cost of the building using the number of beds (the best specification found). A second submodel explains the cost of equipment by built area, and the third submodel explains other costs (e.g., overruns, extra charges), again as a function of the built area. This method provides the final costs as the sum of the predictions of each submodel. As an aggregation of forecasts of different regressions, Method 2 does not support the construction of the confidence interval using standard techniques. In this case, the problem must be solved using bootstrapping predictions, which build a distribution of estimates from the construction of multiple samples, taken with replacement from the original sample available. Furthermore, Method 2 offers slightly better fit with the historical data compared with Method 1 (lower mean squared error of prediction). However, for completeness, we provide the results from both methods. Specifically, we generated forecasts and a confidence interval (95%), then multiplied all values by the CPI Health to generate the estimates in Table 5. Table 5: Infrastructure cost estimates for hospitals in Cascais and Braga ( million) Prediction Mean Estimate 95% Confidence Interval Lower Limit Upper Limit Official PSC Method 1 (model Cascais (P 2005) area in m 2) Braga (P 2006) Method 2 (partial models with bootstrap) Cascais (P 2005) Braga (P 2006) The estimated costs suggest that the values of the public comparators are greater than the average estimates we derived using historical construction data (even after adjusting by CPI Health). In Method 1, the PSC fall within the 95% confidence interval, whereas with Method 2, they are above the upper limit. Of course, these estimates use limited data, depend on CPI Health, and do not account for the teaching hospital status of Braga all of which could justify higher infrastructure costs. 5 See the Appendix for the detailed results. 8
9 6.2. Estimating the Cost of Clinical Services There are many available functional forms for econometric estimates of the relationship between costs and outputs. One of the best known and most commonly used is the translog, which takes the following form for our study context:! ln! =! +!!!"!! + 0.5!!"!"!!!"!! + h! h +!!!!!!!!!!!! h!!!!!!!!!, where C refers to total costs; Y is the output vector measured by inpatient admissions, outpatient visits, outpatient services, emergency episodes, day surgeries, and case mixed index; and H and T are dummy variables for hospitals and years, respectively. We provide the statistically significant results from this regression in Table 7; the independent variables offer good predictive power. Table 7: Estimates of the regression of the logarithm of total operating costs Log (Total Cost) Coefficient Robust Std. Deviation t P> t Indicator EPE Year Year Year Year Year Year Year Log (Episodes) Log (Amb Surgery.) Log (ER) Log (Consultations) Log (Hosp. Day) Log (Case Mix) Log (Epis.) * Log (Case Mix) Log (Hosp. Day) Log (Epis.) * Log (Consultations) Log (surgical) * Log (ref.) Log (Hosp. Day) * Log (Consultations) Constant Notes: This regression used 458 observations, with 58 groups. The overall R square is
10 Cascais, Clinical Services Using the preceding regression estimates, we compared the model prediction for the hospital in Cascais with its PSC. The PPP in Cascais entailed operating the old hospital for two years, then moving into the new hospital and operating it for eight years. We generated two predictions for these operating costs. First, we used the cost function for an average public hospital. Second, we turned to the cost function estimated for the former hospital in Cascais, or an historical Cascais fixed effect, which generates higher than average costs. The results, in Table 8, reveal that the official PSC for the public hospital were below the average prediction and near the lower limit of the forecasting interval. These estimates thus indicate greater cost pressures on clinical services than we found for the infrastructure. Table 8: Cascais Comparison Against Average Hospital Estimated Average Lower Limit Upper Limit PSC First 2 years Last 8 years Present Value for 10 years Against Cascais in the past Estimated Average Lower Limit Upper Limit PSC First 2 years Last 8 years Present Value for 10 years Clinical Services The PPP in Braga required operating the old hospital for one year, moving into the new hospital, and operating there for nine years. Using the same methodology we applied to the Cascais Hospital, we compared the predictions of the cost of PSC against the average of all hospitals and the former Braga Hospital costs (Table 9). The comparison revealed values well above the upper limits of our prediction, in contrast with the situation in Cascais. However, as we noted previously, these estimates fail to take into account that Braga s new hospital is a teaching hospital. Table 9: Braga Comparator Against Average Hospital Estimated Average Lower Limit Upper Limit PSC First year Last 9 years Present Value for 10 years Against Braga in the past Estimated Average Lower Limit Upper Limit PSC First year Last 9 years Present Value for 10 years
11 6.3. General Discussion Table 10 contains the overall results of the estimates for two scenarios: one in which the costs are given by the lower estimates (both construction and operation) and another in which the costs are given by the higher estimates. Table 10: Overall results of estimates for Braga and Cascais Prediction Interval 95% Confidence ( million) Estimated Average Lower Limit Upper Limit PSC High Cascais Infrast Cascais Services Total Cascais * * Braga Infrast Braga Services Total Braga * * Low Cascais Infrast Cascais Services Total Cascais * * Braga Infrast Braga Services Total Braga * * * Asymptotic approximate values. We find that the official PSCs for construction costs in both cases were close to the upper limit of our prediction confidence intervals but that the PSCs for operations were very different: In Braga the PSC for clinical services was well above the upper limit of our prediction. In Cascais the same PSC was closer to the lower limit of our prediction. Because the operational costs of the clinical services are much larger than the infrastructural costs, they dominate the final results. Therefore we find that the overall PSC for Braga is well above the upper limit of our estimates, whereas for Cascais, the overall PSC is within the prediction confidence interval, and near its lower limit. 7. CONCLUSIONS The results show that the PSC for infrastructures ranged above the average of the estimates based on historical data. The PSCs for clinical services seem substantially different though. In the case of the new hospital in Braga, the official PSC value is clearly above average, and even above the upper limit of the forecast range. In the case of Cascais, the PSC value is below average and close to the lower limit of the forecast range. As it turns out, the bidding process in Braga led to a winning bid substantially below the PSC, proving that competition at least partially reduced the upward bias in the PSC estimate. This is good news, because competition in this case seems to have worked. 11
12 The case of Cascais is also interesting. The firm that won the Cascais bid apparently is suffering losses, and the press has reported that it is even trying to sell its concern and extricate itself from the PPP contract (Santos, 2011). The low PSC initially defined, by comparison with our estimates, makes these results not entirely surprising. REFERENCES Flyvbjerg B. (2008), Curbing optimism bias and strategic misrepresentation in planning: Reference class forecasting in practice. European Planning Studies, Vol. 16, No. 1, Kahneman, D & Tversky, A (1979). Prospect theory: an analysis of decision under risk. Econometrica, Vol. 47, No. 2, Meehl, P E (1954). Clinical versus statistical prediction: A theoretical analysis and a review of the evidence. Minneapolis, MN: University of Minnesota Press. Moreno, C (2010). Como o Estado gasta o nosso dinheiro. Caderno, Lisboa. OPPP (2011). Relatorio das PPP em Portugal. Observatory on public private partnerships (OPPP), Lisbon, Portugal. Santos, A (2011). Hospital de Cascais é um sarilho. Expresso. July 9. Tversky, A, & Kahneman, D (1974). Judgments under uncertainty: Heuristics and biases. Science, Vol. 185,
13 STATISTICAL APPENDIX This appendix reports the technical details about the methodology used. Table A0. Data Base Hospital CEdif CEquip OutCus Custos Camas Area Ano AMADORASINTRA Nª SRª DA GRAÇA  TOMAR PEDRO HISPANO  MATOSINHOS SANTO ANFRÉ  LEIRIA S. TEOTÓNIO  VISEU SANTA MARIA DA FEIRA BARLAVENTO ALGARVIO PORTIMÃO HOSPITALAR COVA DA BEIRA VALE DO SOUSA (INCLUI A PSIQUIATRIA) RAINHA SANTA ISABEL TORRES NOVAS Cascais Braga Costs in Millions. Table A.1. Regression of the Cost of Construction reg LCEdif LCAM Source SS df MS Number of obs = F( 1, 8) = Model Prob > F = Residual Rsquared = Adj Rsquared = Total Root MSE = LCEdif Coef. Std. Err. t P> t [95% Conf. Interval] LCamas Constante Note that the time variable did not prove statistically significant in any of the regressions presented in this appendix. Forecasts for the logarithms of the costs of the hull and Braga Threshold Limit forecast Hospital Inf Sup Hospital Forecast Limit Inf Limit Sup IC 95% IC 95% Cascais Braga Note: STAT command used was "predictnl LCEdhat = predict (), ci (lled uled)" Table A.2. Regression of the equipment costs (excluding H Feira) reg LCEquip LArea if CEquip>5.5 Source SS df MS Number of obs = F( 1, 7) = 6.41 Model Prob > F = Residual Rsquared = Adj Rsquared = Total Root MSE = LCEquip Coef. Std. Err. t P> t [95% Conf. Interval] LArea Constante Forecasts for the logarithms of the costs of the equipment in Cascais and Braga Hospital Forecast Limit Inf Limit Sup IC 95% IC 95% Cascais Braga
14 Table A.3. Regression of Other Costs reg LCOu LArea Source SS df MS Number of obs = F( 1, 8) = Model Prob > F = Residual Rsquared = Adj Rsquared = Total Root MSE = LCOu Coef. Std. Err. t P> t [95% Conf. Interval] LArea Constante Forecasts for Other Costs of logarithms in Cascais and Braga Hospital Previsão Limite Inf Limite Sup IC 95% IC 95% Cascais Braga Table A.4. Regression of Total Costs reg LCustos LArea Source SS df MS Number of obs = F( 1, 8) = Model Prob > F = Residual Rsquared = Adj Rsquared = Total Root MSE = LCustos Coef. Std. Err. t P> t [95% Conf. Interval] LArea _cons Forecasts for the logarithms of the total costs in Cascais and Braga Hospital Previsão Limite Inf Limite Sup IC 95% IC 95% Cascais 4, , , Braga 4, , , Note: The exponential average of the residuals is , so there was no need to use a correction in the forecast, because the estimator is "smeared." The list of hospitals whose data were used to estimate operating costs appears in Table A.5. Table A.5. Hospitals and medical centers EPE hospitals in
15 1 CH Alto Ave 2 CH Alto Minho 3 CH Baixo Alentejo 4 CH Coimbra 5 CH Cova Beira 6 CH do Barlavento Algarvio 7 CH do Porto 8 CH Lisboa Norte 9 CH Lx Central 10 CH Lx Ocidental 11 CH Médio Ave 12 CH Médio Tejo 13 CH Nordeste 14 CH Setúbal 15 CH Tâmega e Sousa 16 CH Trás os Montes e Alto Douro 17 CH VN Gaia / Espinho 18 H de Nossa Senhora do Rosário,  Barreiro 19 H do Espírito Santo  Évora 20 H Garcia de Orta,  Almada 21 H Infante D. Pedro,  Aveiro 22 H S. Sebastião,  Vila da Feira 23 H S. Teotónio,  Viseu 24 H Santa Maria Maior,  Barcelos 25 H Santo André,  Leiria 26 H São João  Porto 27 HD da Figueira da Foz, 28 HD de Santarém, 29 IPOFG  CRO de Coimbra, 30 IPOFG  CRO de Lisboa, 31 IPOFG  CRO do Porto, 32 ULS de Matosinhos, 33 ULS Norte Alentejano Outros Hospitais  SPA 1 CH da Póvoa do Varzim/Vila do Conde 2 CH das Caldas da Rainha 3 CH de Cascais 4 CH de Torres Vedras 5 H Amato Lusitano  Castelo Branco 6 H Curry Cabral  Lisboa 7 H da Universidade de Coimbra 8 H Distrital de Águeda 9 H Distrital de Faro 10 H Distrital de São João da Madeira 11 H Reynaldo dos Santos  Vila Franca de Xira 12 H São Marcos  Braga 13 H Sousa Martins Guarda 14 H Bernardino Lopes de Oliveira  Alcobaça 15 H Cândido de Figueiredo  Tondela 16 H Distrital de Pombal 17 H do Litoral Alentejano  Santiago do Cacém 18 H do Montijo 19 H Dr Francisco Zagalo  Ovar 20 H José Luciano de Castro  Anadia 21 H Nossa Senhora da Assunção  Seia 15
16 22 H Nossa Senhora da Conceição  Valongo 23 H São Miguel  Oliveira de Azeméis 24 H São Pedro Gonçalves Telmo  Peniche 25 H Visconde de Salreu  Estarreja Table A.6. Estimation of the translog cost function, global xi: xtreg lcustot epe i.ano lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia2 lepi_cons lcons_cir lcons_hdia, fe robust Fixedeffects (within) regression Number of obs = 458 Group variable: id Number of groups = 58 Rsq: within = Obs per group: min = 5 between = avg = 7.9 overall = max = 8 F(19,57) = corr(u_i, Xb) = Prob > F = (Std. Err. adjusted for 58 clusters in id) Robust lcustot Coef. Std. Err. t P> t [95% Conf. Interval] epe _Iano_ _Iano_ _Iano_ _Iano_ _Iano_ _Iano_ _Iano_ lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia lepi_cons lcons_cir lcons_hdia _cons The next two tables contain the STATA code used to produce estimates of the hospital operating costs. Note that on average, SPA hospitals are 57% of the sample, and SPC hospitals make up the remaining 43%. Table A.7. Procedures for comparing the expected costs with the PSC  Cascais 1. Without fixed effects a) 8 years xi: xtreg lcustot epe i.ano lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia2 lepi_cons lcons_cir lcons_hdia, fe robust adjust epe=0.57 _Iano_2001=0 _Iano_2002=0 _Iano_2003=0 _Iano_2004=0 _Iano_2005=0 _Iano_2006=0 _Iano_2007=1 lepisodios= lciramb= lurgencias= lconsultas= lhdia= licm_drgs= lepi_icmdrgs= lhdia2= lepi_cons= lcons_cir= lcons_hdia= , ci level(95) b) 2 years 16
17 xi: xtreg lcustot epe i.ano lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia2 lepi_cons lcons_cir lcons_hdia, fe robust adjust epe=0.57 _Iano_2001=0 _Iano_2002=0 _Iano_2003=0 _Iano_2004=0 _Iano_2005=0 _Iano_2006=0 _Iano_2007=1 lepisodios= lciramb= lurgencias= lconsultas= lhdia= licm_drgs= lepi_icmdrgs= lhdia2= lepi_cons= lcons_cir= lcons_hdia= , ci level(95) 2. With fixed effects a) 8 years xi: reg lcustot epe i.ano lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia2 lepi_cons lcons_cir lcons_hdia i.id, robust adjust epe=0.57 _Iano_2001=0 _Iano_2002=0 _Iano_2003=0 _Iano_2004=0 _Iano_2005=0 _Iano_2006=0 _Iano_2007=1 lepisodios= lciramb= lurgencias= lconsultas= lhdia= licm_drgs= lepi_icmdrgs= lhdia2= lepi_cons= lcons_cir= lcons_hdia= if id==12, ci level(95) b)2 years xi: reg lcustot epe i.ano lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia2 lepi_cons lcons_cir lcons_hdia i.id, robust adjust epe=0.57 _Iano_2001=0 _Iano_2002=0 _Iano_2003=0 _Iano_2004=0 _Iano_2005=0 _Iano_2006=0 _Iano_2007=1 lepisodios= lciramb= lurgencias= lconsultas= lhdia= licm_drgs= lepi_icmdrgs= lhdia2= lepi_cons= lcons_cir= lcons_hdia= if id==12, ci level(95) Table A.7. Procedures for comparing the expected costs with the PSC  Braga 1. Without fixed effects a) 9 years xi: xtreg lcustot epe i.ano lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia2 lepi_cons lcons_cir lcons_hdia, fe robust adjust epe=0.57 _Iano_2001=0 _Iano_2002=0 _Iano_2003=0 _Iano_2004=0 _Iano_2005=0 _Iano_2006=0 _Iano_2007=1 lepisodios= lciramb= lurgencias= lconsultas= lhdia= licm_drgs= lepi_icmdrgs= lhdia2= lepi_cons= lcons_cir= lcons_hdia= , ci level(95) b) 1 year xi: xtreg lcustot epe i.ano lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia2 lepi_cons lcons_cir lcons_hdia, fe robust adjust epe=0.57 _Iano_2001=0 _Iano_2002=0 _Iano_2003=0 _Iano_2004=0 _Iano_2005=0 _Iano_2006=0 _Iano_2007=1 lepisodios= lciramb= lurgencias= lconsultas= lhdia= licm_drgs= lepi_icmdrgs= lhdia2= lepi_cons= lcons_cir= lcons_hdia= , ci level(95) 2. With fixed effects a)9 years xi: reg lcustot epe i.ano lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia2 lepi_cons lcons_cir lcons_hdia i.id, robust adjust epe=0.57 _Iano_2001=0 _Iano_2002=0 _Iano_2003=0 _Iano_2004=0 _Iano_2005=0 _Iano_2006=0 _Iano_2007=1 lepisodios= lciramb= lurgencias= lconsultas= lhdia= licm_drgs= lepi_icmdrgs= lhdia2= lepi_cons= lcons_cir= lcons_hdia= if id==8, ci level(95) b)1 year xi: reg lcustot epe i.ano lepisodios lciramb lurgencias lconsultas lhdia licm_drgs lepi_icmdrgs lhdia2 lepi_cons lcons_cir lcons_hdia i.id, robust adjust epe=0.57 _Iano_2001=0 _Iano_2002=0 _Iano_2003=0 _Iano_2004=0 _Iano_2005=0 _Iano_2006=0 _Iano_2007=1 lepisodios= lciramb= lurgencias= lconsultas= lhdia= licm_drgs= lepi_icmdrgs= lhdia2= lepi_cons= lcons_cir= lcons_hdia= if id==8, ci level(95) 17
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