The Health of Elderly Persons

Abstract

This chapter uses data from India’s National Sample Survey (NSS), relating to respondents’ health outcomes between January and June 2014, to quantify a particular form of gender inequality: inequality in self-rated health (SRH) outcomes between men and women aged 60 years or over. In so doing, it makes five contributions to the existing literature. The first is in terms of analytical technique: this study contains a more detailed and nuanced exposition of the regression results than in previous studies. Second, it controls for environmental factors—such as poor drainage, absence of toilets or lack of ventilation in the kitchen—which might adversely impact on health and, in particular, affect the health of women more than that of men. Third, it takes account of interaction effects by which the effect of a variable on an elderly person’s SRH differed according to whether the person was male or female. Lastly, it examines whether SRH is correlated with objective health outcomes. In particular, this study answers two central questions. Did men and women, considered collectively, have significantly different likelihoods of “poor” SRH between the different regions/income classes/social groups/education levels? Did men and women, considered separately, have significantly different likelihoods of a “poor” SRH within a region/income class/social group/education level?

Appendix

5.1.1 Ordered Logit Models

Suppose there are N persons (indexed i = 1…N). Let the values taken by the variable Y _i represent the health status of these persons such that: Y _i  = 1 if the person was in “excellent/very good health”; Y _i  = 2 if the person was in “fairly good health”; and Y _i  = 3 if the person was in “poor health”. Since these outcomes are inherently ordered—in the sense that the outcome associated with a higher value of Y _i is less desirable than that associated with a lower value—the appropriate method of estimation is that of ordered logit .

The idea behind this model (Borooah 2002) is that the health of a person may be represented by the value of the latent variable, H _i , with higher values of H _i representing poorer health. One may consider this latent variable to be a linear function of K health-determining factors whose values for individual i are: X _ik , k =1…K. Consequently,

$$H_{i} = \sum\limits_{k = 1}^{K} {X_{ik} \beta_{k} } + \varepsilon_{i} = Z_{i} + \varepsilon_{i}$$

(5.1)

where β _k is the coefficient associated with the k^th variable and $Z_{i} = \sum\limits_{k} {X_{ik} \beta_{k} }$. An increase in the value of the k^th factor will cause the health of a person to improve if $\beta_{k} < 0$ and to deteriorate if $\beta_{k} > 0$.

Since the values of H _i are, in principle and in practice, unobservable, Eq. (5.1) represents a latent regression which, as it stands, cannot be estimated. However, what is observable is a person’s health status (in this study: good; fairly good; poor) and the categorisation of persons in the sample in terms of health status is implicitly based on the values of the latent variable H _i in conjunction with “threshold values”, $\delta_{1}$ and $\delta_{2}$ ($\delta_{1} < \delta_{2}$) such that:

$$\begin{gathered} Y_{i} = 1,\quad {\text{if}}\quad H_{i} \le \delta _{1} \hfill \\ Y_{i} = 2,\quad {\text{if}}\quad \delta _{1} < H_{i} \le \delta _{2} \hfill \\ Y_{i} = 3,\quad {\text{if}}\quad H_{i} > \delta _{2} \hfill \\ \end{gathered}$$

(5.2)

The $\delta_{1} , \, \delta_{ 2}$ of Eq. (5.2) are unknown parameters to be estimated along with the $\beta_{k}$ of Eq. (5.1).

A person’s classification in terms of his/her health status depends upon whether the value of H _i crosses a threshold and the probabilities of a person being in a particular health status are:

$$\begin{aligned} & \Pr (Y_{i} = 1) = \Pr (\varepsilon_{i} \le \delta_{1} - Z_{i} ) \\ & \Pr (Y_{i} = 2) = \Pr (\delta_{1} - Z_{i} \le \varepsilon_{i} < \delta_{2} - Z_{i} ) \\ & \Pr (Y_{i} = 3) = \Pr (\varepsilon_{i} \ge \delta_{2} - Z_{i} ) \\ \end{aligned}$$

(5.3)

If it is assumed that the error term ε _i , in Eq. (5.1) follows a logistic distribution, then Eqs. (5.1) and (5.2) collectively constitute an ordered logit model²² and the estimates from this model permit, through Eq. (5.3), the various probabilities to be computed for every person in the sample, conditional upon the values of the health-determining factors for each person.

Table 5.7 shows the estimates from the ordered logit model (that is, Eqs. (5.1) and (5.2)). These estimates are then used in Eq. (5.3) to compute the probabilities shown in Tables 5.1 and 5.2. Table 5.8 shows the quantile estimates which underpin the results of Table 5.4.

Table 5.7 Ordered logit estimates for the SRH of elderly persons equation

Table 5.8 Quantile regression estimates for the out-patient expenditure by elderly persons equation