Péter Elek

A light-tailed conditionally heteroscedastic model with applications to river flows

A conditionally heteroscedastic model, different from the more commonly used autoregressive moving average-generalized autoregressive conditionally heteroscedastic (ARMA-GARCH) processes, is established and analysed here. The time-dependent variance of innovations passing through an ARMA filter is conditioned on the lagged values of the generated process, rather than on the lagged innovations, and is defined to be asymptotically proportional to those past values. Designed this way, the model incorporates certain feedback from the modelled process, the innovation is no longer of GARCH type, and all moments of the modelled process are finite provided the same is true for the generating noise. The article gives the condition of stationarity, and proves consistency and asymptotic normality of the Gaussian quasi-maximum likelihood estimator of the variance parameters, even though the estimated parameters of the linear filter contain an error. Copyright 2007 The Authors Journal compilation 2007 Blackwell Publishing Ltd.

Forecasting and simulating mortality tables

In this paper we suggest solutions to the actuaries, facing the problem of estimating future mortality tables, especially in cases where there is a lack of relevant data and where the tendencies are not easy to estimate directly. We propose the utilization of external sources of information in the form of other, published mortality tables and use formal statistical tests to decide among these possible candidates. The procedure can also be applied for checking e.g. the goodness of mortality selection factors. We suggest the use of parametric families in modelling; for example the simple 2-parameter Azbel model. We conclude the paper by a simulation study which allows for the quantification of the possible risks related to unforeseen changes in the mortality tables in the future. To calibrate the variances of these models, initial estimates are needed, which we get by the Lee-Carter method.

Tail behaviour and extremes of two-state Markov-switching autoregressive models

We examine the tail behaviour and extremal cluster characteristics of two-state Markov-switching autoregressive models where the first regime behaves like a random walk, the second regime is a stationary autoregression, and the generating noise is light-tailed. Under additional technical conditions we prove that the stationary solution has asymptotically exponential tail and the extremal index is smaller than one. The extremal index and the limiting cluster size distribution of the process are calculated explicitly for some noise distributions, and simulated for others. The practical relevance of the results is illustrated by examining extremal properties of a regime-switching autoregressive process with Gamma-distributed noise, already applied successfully in river flow modeling. The limiting aggregate excess distribution is shown to possess Weibull-like tail in this special case.

Implication of external price referencing and parallel trade on pharmaceutical expenditure: indirect evidence from lower-income European countries

External price referencing (EPR) is applied more and more frequently worldwide by payers to control pharmaceutical prices. Together with the parallel trade of pharmaceuticals, EPR may result in lower pharmaceutical prices in higher-income countries and higher prices in lower-income countries, which implies that pharmaceutical expenditure grows more rapidly in the latter than in the former group. Our objective was to assess this hypothesis. We used hierarchical linear models on country-level panel data to show that-after controlling for compounding factors such as GDP, the proportion of the old-age population or life expectancy-the annual growth rate of pharmaceutical expenditure was 2.1% points larger in the lower- than in the higher-income members of the European Union between 2000 and 2008. This difference in trends became non-significant (0.6% points) after the onset of the global economic crisis. There was no significant difference between lower- and higher-income countries in the growth rate of non-pharmaceutical health expenditure in either period. Our results indirectly support the presence of price convergence of pharmaceuticals among European countries, and EPR and parallel trade may provide a reasonable explanation to the observed trend difference of pharmaceutical expenditure in the two groups of countries between 2000 and 2008. This higher growth rate of pharmaceutical expenditure put extra burden on public health care budgets in lower-income countries and resulted in disproportionately more cost-containment measures compared to higher-income countries after 2008. It remains to be seen whether the disappearance of the difference in trend growth rates due to special health policy interventions in countries with economic difficulties is temporary or permanent.

Effects of Geographical Accessibility on the Use of Outpatient Care Services: Quasi-Experimental Evidence from Panel Count Data

In 2010-2012, new outpatient service locations were established in Hungarian micro-regions, which had lacked such capacities before. We exploit this quasi-experiment to estimate the effect of geographical accessibility on outpatient case numbers using both individual-level and semi-aggregate panel data. We find a 24-27 per cent increase of case numbers as a result of the establishments. Our specialty-by-specialty estimates imply that a 1-min reduction of travel time to the nearest outpatient unit increases case numbers for example by 0.9 per cent in internal care and 3.1 per cent in rheumatology. The size of the new outpatient capacities has a separate effect, raising the possibility of the presence of supplier-induced demand. By combining a fixed-effects logit and a fixed-effects truncated Poisson estimator, we decompose the effects into increases in the probability of ever visiting a doctor on the one hand and an increase of the frequency of visits on the other hand. We find that new visits were dominant in the vast majority of specialties, whereas both margins were important for example in rheumatology. Finally, we demonstrate the usefulness of the fixed-effects truncated Poisson estimator in modelling count data by examining its robustness by simulations.

How does retirement affect healthcare expenditures? Evidence from a change in the retirement age: Retirement and health care expenditures

Using individual-level administrative panel data from Hungary, we estimate causal effects of retirement on outpatient and inpatient care expenditures and pharmaceutical expenditures. Our identification strategy is based on an increase in the official early retirement age of women, using that the majority of women retire upon reaching that age. According to our descriptive results, people who are working before the early retirement age have substantially lower healthcare expenditures than nonworkers, but the expenditure gap declines after retirement. Our causal estimates from a two-part (hurdle) model show that the shares of women with positive outpatient care, inpatient care, and pharmaceutical expenditures, respectively, decrease by 3.0, 1.4, and 1.3 percentage points in the short run due to retirement. These results are driven by the relatively healthy, by those who spent some time on sick leave and by the less educated. The effect of retirement on the size of positive healthcare expenditures is generally not significant.

Policy objective of generic medicines from the investment perspective: The case of clopidogrel

The objective of generic drug policies in most countries is defined from a disinvestment perspective: reduction in expenditures without compromising health outcomes. However, in countries with restricted access of patients to original patented drugs, the objective of generic drug policies can also be defined from an investment perspective: health gain by improved patient access without need for additional health budget. This study examines the investment aspect of generic medicines by analyzing clopidogrel utilization in European countries between 2004 and 2014 using multilevel panel data models. We find that clopidogrel consumption was strongly affected by affordability constraints before the generic entry around 2009, but this effect decayed by 2014. After controlling for other variables, utilization had a substantially larger trend increase in lower-income European countries than in the higher-income ones. Generic entry increased clopidogrel consumption only in lower- and average-income countries but not in the highest-income ones. An earlier generic entry was associated with a larger effect. The case of clopidogrel indicates that the entrance of generics may increase patient access to effective medicines, most notably in lower-income countries, thereby reducing inequalities between European patients. Policymakers should also consider this investment aspect of generic medicines when designing pharmaceutical policies.