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

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Azienda Ospedaliera Nazionale“SS. Antonio e Biagio e Cesare Arrigo”Working Paper of Public Healthnr. 3/2012To solve model (2), Koenker (2004) has considered a class of penalized estimators toestimate several quantiles simultaneously, which can be stated as:qnmi(3) min k ( yij i x'ij ( k)) k( , )k 1 j1 i1 i1n| |iwhere ρ τ (u) = u (τ – I (u ≤ 0)) is the quantile loss function and ω j is a relative weightgiven to the jth quantile. The last one controls the influence of the quantiles on theestimation of individual effects (α i ). When the penalty is bigger than zero (λ > 0)penalized fixed effects are estimated, while λ = 0 means that no penalty is applied, so asimple fixed-effects estimator is obtained.Due to the recent developments in this field, a few papers have used this method inapplied econometrics. Some examples are: Koenker (2004), Abrevaya and Dahl (2005),Pianto et al. (2005) and Lamarche (2005). However, this method has a huge potential,with many attractive features, so we believe that the number of publications using thisapproach will increase exponentially in the next few years.4. Application and ResultsJust to compare the main results from quantile regression for panel data (QR for PD), wehave run a conventional analysis of the panel data (PD). The model used in the last onewas by feasible generalized least squares (GLS), with a heteroscedastic error structureand no cross-sectional correlation. Data sets like the one analyzed in this paper (data fromcountries) generally do not have constant variance for each individual. As the estimatesfrom QR for PD have shown, in the case of this sample, the quantile coefficients areasymmetric throughout the conditional distribution of response variable. All the estimatesfrom the panel data are statistically significant at the 1% level and bigger than othersfrom quantile regression for panel data.13
Azienda Ospedaliera Nazionale“SS. Antonio e Biagio e Cesare Arrigo”Working Paper of Public Healthnr. 3/2012The main specification of the model sets the log of cadaveric organ donation as afunction of a dummy for presumed consent, log of: number of deaths from celebrovasculardisease; number of deaths from traffic accident; GDP per capita; the percentageof population that has the Internet access, a dummy for catholic countries and a dummyfor common law. The same model is used including the log of total health expenditureper capita and excluding GDP per capita. We do not put health expenditure and GDP intothe same model because they are highly collinear. Tables 2 and 3 report the main results.Table 2: The effect of presumed consent law on cadaveric organ donation:Estimates from panel data and quantile regression for panel dataDependent variable: Log cadaveric organdonation PD 25 th 50 th 75 thPresumed Consent 0.4039 0.2230 0.2440 0.2150(0.000) (0.000) (0.000) (0.000)Log Brain 0.1417 -0.0030 0.0590 0.0390(0.003) (0.479) (0.160) (0.262)Log Traffic 0.3078 0.2350 0.2170 0.2390(0.000) (0.000) (0.000) (0.000)Log GDP per capita 0.9546 0.8180 0.7420 0.6420(0.000) (0.000) (0.000) (0.000)Log Internet access 0.1156 0.0680 -0.0116 0.0200(0.004) (0.009) (0.196) (0.033)Catholic Country 0.1722 0.1550 0.0480 0.0240(0.001) (0.000) (0.054) (0.235)Common Law 0.1281 0.0700 0.1230 0.1230(0.001) (0.001) (0.000) (0.000)Constant -8.9367 -6.6620 -5.7550 -4,706(0.000) (0.000) (0.000) (0.000)Note: Coefficients in bold and p-values in parentheses.The estimates from quintile regression for panel data show a positive effect of presumedconsent on cadaveric organ donation, even controlling for other determinants of theresponse variable. The same qualitative predictions are verified with differentspecifications 16 , which can be viewed as a measure of robustness of the model. Allcoefficients are statically significant at the 1% level. The magnitude of the coefficients16 The other specifications set the vector of covariates as: i) presumed consent (PC), celebro-vasculardisease (brain) and traffic accident (traffic); ii) same as (i), plus GDP per capita; iii) same as (i), plus healthexpenditure; iv) same as (i), plus catholic and common law dummies; v) same as (iv), plus internet dummy;vi) PC, catholic and common law dummies; and vii) PC. The estimates from these models are availableupon request.14
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