Constrained least squares estimation of payment lag distributions in the United States' Medical Assistance Program

The financial effectiveness of the United States' Medical Assistance Program (Medicaid) depends on sound financial management at all political levels. States receive payments from the Federal Government based on the number, kinds and payment rates of services provided to eligible patients. Because payments can lag services by a considerable time and because claims may be denied, adjusted or reprocessed, the state cannot easily predict its total payments for services recently delivered. As a matter of fact, some claims linger as long as 24 months in the system. This paper presents a procedure to estimate the percentages of payments due in the months following the service delivery month. The procedure relies on the most recent 24 months of services and payments. Service months from the recent past generate fewer monthly payments than those more distant and can have large, unknown outstanding balances. Through a transformation of the available data, our procedure takes into account the dwindling amounts of data available. The procedure, optimal in the sense of constrained least squares, results in estimates of the percentages paid as a function of time elapsed since service. A dynamic programming procedure stabilizes tail area percentages and a hold-out sample provides evidence of good fit. Real-world data illustrate the process.