The Economic Model

In document Three essays in health economics (Page 145-154)

Insurance Type Differences in Medical Productivity

4.1 The Economic Model

A health production model introduced by Michael Grossman (1972) facilitates a comparison of insurance type disease treatment effects. The model assumes that medical care and non-medical care services act as inputs into the production of health. Medical care inputs include drugs, hospital stays, Dr. office visits, and other medical care services. All of the medical care inputs are available in the MEPS. Non-medical care health inputs include diet, exercise, and proper adherence to medical care protocol. Non-medical care health inputs are largely unavailable in the MEPS and are therefore controlled using demographic characteristics, such as the income and education of the patient. Technological advancements in the

production of health are identified in this model as time effects. The following list specifies notation:

• m = (m1, ..., mK) is a 1xK vector of medical care service quantities

• Mr = f (m1, ..., mK) is a treatment. Treatments are discrete indicators that are one for a specific set of non-zero medical care service quantities and zero for any other set of medical care service quantities

• Z = (z1, ..., zJ) represent the J types of non-medical care health inputs and time effects

• Θ = (θ1, ..., θR−1), β = (β1, ..., βR), γ = (γ1, ..., γJ) are parameter vectors to be estimated in the demand and health production models

• ˆΘ = (ˆθ1, ..., ˆθR−1), ˆβ = ( ˆβ1, ..., ˆβR), ˆγ = (ˆγ1, ..., ˆγJ) are the estimated values for the parameter vectors in the demand and health production models

• H = H(h1(M1, Z, t, Θ1), · · · , hD(MD, Z, t, ΘD)) a production function relating inputs to disease treatments d = 1, · · · , D

Health production is modelled as if medical providers produce health subject to available technologies, prices of services, and constraints imposed by the insurance firm. We assume that medical providers act as perfect agents of the patient, and thus act subject to the constraints imposed on them by the patient’s income in addition to the institutional features of the insurance firm.

The formal analysis involves a series of modelling stages. The first stage models the demand for medical care services. The demand for medical care services is performed separately for patients of different insurance types. Medical care service demand is modelled as an input demand into the production of health. Input de-mands depend on prices of medical care, patient characteristics and insurance type.

The second stage models the production of health. Health depends on medical care treatments and demographic characteristics. The results from the first two stages are combined and used to determine the expected health outcomes conditioned on the service demands for the different insurance types. The insurance types are com-pared with respect to the treatments chosen and the outcomes that occur as a result of those treatments.

4.1.1 Medical Care Input Demand

Medical care service bundles are organized into treatments. Treatments are defined by the set of non-zero medical care service expenditures used to treat a specific disease. Treatments are discrete items that are exhaustive and mutually exclusive.

All patients defined as having a specific disease are assigned to a single treatment.

The array of available treatments is disease specific and available to each insurance type. As an example, depression has several treatments that include office visits alone and office visits with prescribed drugs.

Treatment demand is modelled as a discrete choice by the insurance firm. An insurance firm chooses to treat a patient with treatment r if treatment r is better for the firm than all of the available treatments s 6= r. The probability that an insurance firm chooses a specific treatment depends on the characteristics of the individual and the prices faced by the insurance firm. The functional relationship is given below:

P r(M = Mr) = Λ((θ0r+ θ0zrZ) − (θ0s+ θzs0 Z) > (s− r)) ∀s 6= r (4.1)

If s ∀s are independent and distributed Weibull then Λ can be estimated using a standard multi-nomial logit. The resultant probability that a specific

treat-ment is chosen is estimated from this model and calculated as:

P r(M = Mr) = ˆΛr(·) = exp(ˆθ0r+ ˆθ0zrZ)

1 +PR−1s=1 exp(ˆθ0s+ ˆθzs0 Z) (4.2) The probability of choosing each treatment Mr r = 1, ..., R is determined for each insurance type l = 1, ..., L such that the technological protocol of the insurance type is defined as ˆΛl = ( ˆΛl1, · · · , ˆΛlR). The differences in technological protocol across insurance types are determined by taking the difference in these probabilities.

4.1.2 Health Production

The relationship between health outcomes and medical care service inputs is deter-mined by estimating a health production function. Health is modelled as a latent variable, hi, that depends on the observed treatments, Mi = (M11i, · · · , MLRi), and

In the health equation above, the relationship between health output and the medical care service inputs is linear and dependent on the parameters γ = (γ1, ..., γJ), β = (β1, ..., βLR). The vector of inputs used in determining health production depends on the disease type considered. To allow for the possibility that treatment type quality varies by insurance type, insurance is interacted with treatment type. This type of interaction allows for the possibility of inferior physicians treating Medicaid patients, or inferior hospital services provided to the Uninsured.

Many of the observed health outcomes are health indicators. For instance, the observed outcome may be an indicator of whether an adverse health state oc-curred during the period, or whether mental health improved. The observed health

indicators, I, are modelled as being directly related to the latent health variable.

The relationship between latent health and the health indicator may either be in-creasing or dein-creasing in health. To fix ideas consider indicators that are dein-creasing in health. If the indicator variable takes on only two values, such as whether health deteriorated, then the indicator function is defined as follows:

• if h< h then I=1

• if h>= h then I=0

This binomial function describes the relationship between latent health and health outcomes. The relationship between the medical care service inputs and health outcomes is determined by replacing the right-hand side of equation 3 with hin the above equation. The relationship between medical care services and health outcomes is estimated by modelling the probability of observing the health outcome that depends on latent health. The probability that a health outcome occurs de-pends on treatments, patient characteristics, and the total expenditure spent on treatment.

The effect of total medical care spending on health depends on the type of condition considered. Medical spending is interacted with age for progressive chronic conditions such as arthritis and hypertension. This interaction implicitly models medical care treatment as an effort to delay the inevitable consequences of persistent chronic conditions. For other types of conditions, such as depression, the association of the disease with age is not straightforward. For these conditions the effects of treatment enter independent of age. The effect of no treatment is determined by considering the effects of trivial medical care spending on the worst treatment for all diseases.2

In the binomial case, the probability that an observed health outcome occurs

2Trivial spending is defined as one dollar for depression and less than twenty dollars for

hyper-for an indicator function that decreases in health is defined using the following

If υ = (h − ) is distributed standard normal then Φ(·) is the cumulative normal distribution function, and this relationship can be estimated with a probit using standard techniques.

4.1.3 Health Outcome Differences Across Insurance Types

Observed differences in health outcomes between the insurance types can be sep-arated into demographic, protocol and quality effects. Quality effects are defined as the outcome differences between the insurance types for the same treatments.

Protocol effects are defined as the probability difference of observationally equiva-lent individuals receiving different treatments for the same condition. Demographic effects are the health outcome differences between the insurance samples that are explained by differences in the sample treated.

Both treatment quality and protocol differences across observationally equiv-alent individuals have several theoretical explanations. Physician quality may be heterogeneous. Physicians may expend more effort for some patients as compared to others. The drugs prescribed for a treatment considered in our analysis may have adverse interaction effects with unobserved drugs prescribed for other conditions.

Patients may not be warned to avoid certain food types or behaviors, or they may not adhere to warnings when given.3 Unobserved individual characteristics such as smoking status, weight, or unobserved co-morbidities may also affect treatment.

Drugs may interact with health conditions not considered in the analysis. These unobserved differences in individual heterogeneity may affect either the treatment quality or protocol, or both.

3For instance, grapefruits commonly interact adversely with many drugs.

In order to explain the outcome differences between insurance types the results are decomposed using an extension of the Oaxaca-Blinder decomposition.

Fairlie (2003) describes the technique for limited dependent variable models. The difference in probability of observing a health outcome is decomposed into quality, demographic and protocol components for two insurance samples l and k. The total difference between the samples is defined by the following equation:


The above equation defines the total difference in the probability of observing a the health outcome between insurance types l and k with sample sizes Nl and Nk, respectively. In order to decompose the overall differences into components, one must specify which group is the comparison group, l, and the compared group, k.4 Private insurance is considered the comparison group in each analysis. The component effects are determined by setting the predicted outcome difference equal to the linear sum of the quality component, the demographic component, and the protocol component. This equation is defined as following:

Φl(·) − Φk(·) = ( 1

Equation 6 introduces some notation. Xl are the observed demographic and treatment characteristics for individual i with insurance type l. ˆXk is the vector of predicted treatments for an individual with characteristics Xk if they were to have

4The decomposition is sensitive to the comparison group chosen.

insurance type l as determined by Equation 2.

The first term on the right hand side is the quality component. The quality component is identified by holding the demographics and treatment protocols con-stant across groups and comparing the changes in quality effects. This difference is performed by assigning the quality effects of insurance type l to the sample of insurance type k and comparing the predicted outcomes to the predicted outcomes of insurance type k’s own quality effects. The second term on the right-hand side is the demographic component. The demographic component is identified by holding the quality and protocol effects constant and comparing the predicted outcome dif-ferences that occur as a result of different sample compositions. The third term on the right-hand side is the protocol component. The protocol component is identified by holding the demographic and quality types constant and comparing the outcomes of the observed protocols for insurance type k with the outcomes from the predicted protocols of the insurance type k sample if they were to have received the protocol of an insurance type l individual.

4.2 Data

The data requirements necessary to estimate the differences in disease treatment outcomes across insurance types are demanding. The data must include detailed information on medical care insurance, medical care services and enough detailed health information to construct disease treatments and evaluate their outcomes. The data employed to estimate this relationship is the 1996-2003 Medical Expenditure Panel Surveys (MEPS). The MEPS reports demographic, health and medical care expenditure information for approximately 30,000 individuals per year.5 The MEPS has a complicated data structure that links individuals from a nationally

represen-5Specifically, the sample sizes are 1996: 22,601; 1997: 34,551; 1998: 24,072; 1999: 24,618; 2000:

25,096; 2001: 33,556; 2002: 39,165; 2003: 34,215

tative household survey to medical ”events” that are defined by the survey. The MEPS defines events as one of eight possible interactions of a patient with a medical care provider. The nature of the event depends on the service provider and includes a hospital stay, a home health month, a filled prescription, a dental care visit, and a physician visit. The reported expenditures associated with each event includes and distinguishes between all payments made by and in behalf of the individual or household member for services defined by the event type. Chapter 2 provides a full description of these event types. The participants are interviewed five times over a 2.5 year period in order to report every medical event that occurs within a two-year window. The resultant panel reports all expenditures made beginning on January 1 of the first interview year and ending on December 31 of the following year for everyone in the survey. All other time dependent information on the survey depends on the date of the interview round.

The medical care insurance information includes whether the individual is covered by private insurance, Medicaid, Medicare, veteran’s insurance, other public insurance, or remains uninsured. The survey also provides further detail related to the type of private insurance held by the individual. This information includes an identifier for the policyholder and plan characteristics such as whether the insurance was provided through the job, supplemental insurance information, and the out-of-pocket insurance premiums paid by the family. The survey identifies all insurance plans, both private and public, that cover the individual.

The MEPS reports several categories of health indicators for every individ-ual in the sample. The indicators include both objective and subjective measures of health. All years of the survey include the objective three-digit International Classification of Disease version 9 (ICD-9) code indicator for everyone in the survey.

These codes are obtained by professional coders interpreting descriptions of ailments made by the survey participants. Individuals may be associated with multiple ICD-9

codes. Some conditions are associated with additional health information including the date at which the individual first contracted the condition, whether the individ-ual is still receiving treatment for the condition, and a subjective measure of how the condition affects the individual’s overall health. All surveys also include yes/no indi-cators for whether the individual has limitations in daily activities. Included among these indicators are whether the individual has difficulty lifting 10 pounds, difficulty walking up 10 stairs, and difficulty grasping with their fingers. Early surveys include height and weight bio-metric information for children. This information is omitted in later surveys which instead reports the body mass index for both children and adults. Finally, all surveys include subjective measures (integer ratings from 1-5) of overall and mental health.

In addition to the medical care insurance, medical care expenditure and health information provided by the MEPS, the MEPS also reports detailed labor supply and demographic information for each individual. This information includes geographic region, educational attainment, marital status, age, sex, race, ethnicity, and total income.

In document Three essays in health economics (Page 145-154)