Determinants of Demand for HIV Testing. Part 8
As such, clinics base operating decisions by assessing the demand curve for their services. The implication of this assumption is that issues of endogeneity arising from estimating a demand curve without also controlling for factors affecting the supply curve for clinic services are irrelevant, since these firms essentially do not face a supply curve for their services.
Given our literature review and data constraints, we postulate a reduced form, linear in coefficients and variables equation to explain the demand for HIV testing, which we estimate using regression analysis techniques. The advantages of this approach are that it is both parsimonious and also allows the signs and significance of each individual coefficient estimate to test each of the hypotheses identified in our literature review.
The Probit Model
A crucial econometric issue is how to specify the dependent variable for our regression analysis, and consequently the regression technique to estimate our equation. We have two dependent variables, both of which express similar information, but in different ways. Our HIVDV variable is a binary indicator of whether or not a clinic offers HIV testing. We examine whether epidemiologic, clinic-specific and socio-economic factors influence the demand for testing by estimating a standard Probit model (Greene, 2000).
One other technical note about the probit model deserves mentioning. Because the model is estimated via maximum likelihood (an inherently non-linear procedure), the coefficient estimates in the probit model cannot be directly interpreted as marginal effects, as is the case in other regression procedures such as ordinary least squares (OLS). However, the probit model does facilitate the construction of marginal effects, which are directly dependent on these coefficient estimates. As such, when interpreting the results of the probit model, we give primary emphasis to interpreting the signs, magnitudes and significance of the marginal effects, as opposed to the coefficient estimates.
The signs and significance of our marginal effects (and their underlying parameter estimates) can be used to test Hypotheses 1 – 3. For example, if the marginal effects for our HIV/AIDS variables are significantly different from zero, then we would reject Hypothesis 1 (in its null form). Moreover, the magnitudes of these marginal effects (if significant) allow us to gain additional information about how epidemiological conditions impact whether clinics perform HIV tests. Similar analysis of the clinic-specific and socio-economic marginal effects can be used to test Hypotheses 2 and 3, respectively.
The Tobit Model
The HIV variable takes this a step further by identifying the number of tests provided, and zero otherwise. Thus, HIV is essentially a variable that is either censored or truncated (on the left side of the distribution) at zero. The crucial issue is how to interpret the values of HIV at the censoring or truncation point. One approach is to assume that the zero values are determined simultaneously with the positive values. Our HIV variable is actually a count variable. This implies that the distribution is censored, and can be estimated with a standard Tobit model (Greene 2000).
As with the probit model, the Tobit model is estimated by defining and subsequently maximizing the (cumulative) log likelihood function for a censored (at HIV = 0) normal distribution. When testing Hypotheses 1 – 3, this also forces us to calculate and interpret marginal effects, as opposed to simply interpreting the model’s coefficient estimates.