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A count‐amount model with endogenous recording of observations

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  • B. M. S. Van Praag
  • E. M. Vermeulen

Abstract

This paper discusses some of the problems which are encountered if an event Ỹ is only recorded if its value satisfies a recording criterion A. It follows that we get an incorrect idea of the frequency of the events and of its true distribution. In order to solve these problems, an econometric model has been constructed by means of which consistent estimation of the true parameters is possible. The model is estimated on consumer purchases, where the number of purchases is assumed to be NEGBIN‐distributed and the purchase amounts obey a lognormal distribution. Purchases are only recorded if their value exceeds Dfl. 10. It is shown that ignoring the recording condition will result in biased estimates and invalid predictions. Apart from this, the model is, among others, relevant for insurance problems, marketing surveys and criminological and epidemiological phenomena.

Suggested Citation

  • B. M. S. Van Praag & E. M. Vermeulen, 1993. "A count‐amount model with endogenous recording of observations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 383-395, October.
    • Handle: RePEc:wly:japmet:v:8:y:1993:i:4:p:383-395
    DOI: 10.1002/jae.3950080406
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    References listed on IDEAS

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    4. Lee, Lung-Fei, 1983. "Generalized Econometric Models with Selectivity," Econometrica, Econometric Society, vol. 51(2), pages 507-512, March.
    5. Morrison, Donald G & Schmittlein, David C, 1988. "Generalizing the NBD Model for Customer Purchases: What Are the Implications and Is It Worth the Effort? Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(2), pages 165-166, April.
    6. Alessie, Rob & Gradus, Raymond H J M & Melenberg, Bertrand, 1990. "The Problem of Not Observing Small Expenditures in a Consumer Expenditure Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 151-166, April-Jun.
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    8. Morrison, Donald G & Schmittlein, David C, 1988. "Generalizing the NBD Model for Customer Purchases: What Are the Implications and Is It Worth the Effort?," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(2), pages 145-159, April.
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