Non‐ and semi‐parametric estimation of age and time heterogeneity in repeated cross‐sections: an application to self‐reported morbidity and general practitioner utilization1

Patterns of self‐reported morbidity and general practitioner (GP) utilization exhibit complex age, sex and time heterogeneity. Underlying patterns are often obscured by data which are overly ‘rough’ because of noise associated with adjacent year fluctuations. In this paper we describe methods to obtain smoothed estimates of age, time and birth‐cohort effects using data from the General Household Survey (GHS), covering the period 1984–1995/6 inclusive. The methods outlined offer powerful analytic tools to research complex profiles or trends, particularly over age or time. The relationships of the morbidity and GP utilization measures with age, sex and survey year characteristics are estimated non‐parametrically using roughness penalized least squares (RPLS). A semi‐parametric extension of this model is used to estimate the effect of the morbidity variables on GP utilization. Tests are employed for various forms of age and time heterogeneity including birth‐cohort effects. Linear age specifications are rejected for all variables and evidence is found of time heterogeneity in one of the morbidity measures—limiting long‐standing illness (LS)—and GP utilization. The advantages of employing non‐ and semi‐parametric estimations in the presence of complex relationships such as those observed for age and time profiles are discussed. Adoption of these techniques by applied econometricians working in health economics is encouraged. Copyright © 1999 John Wiley & Sons, Ltd.