Gender Differences in the Incidence of Depression and Anxiety: Econometric Evidence from the USA

Abstract

Using data from the Collaborative Psychiatric Epidemiology Surveys (CPES) for the United States for the period 2001–2003, this paper addresses a vexed question relating to inter-gender differences in depression rates, namely how much of the observed difference in depression rates between men and women may be explained by differences between them in their exposure, and how much may be explained by differences between them in their response, to depression-inducing factors. The contribution of this paper is to propose a method for disentangling these two influences and to apply it to US data. The central conclusion of the paper was differences between men and women in rates of depression and anxiety were largely to be explained by differences in their responses to depression-inducing factors: the percentage contribution of inter-gender response differences to explaining the overall difference in inter-gender probabilities of being depressed was 93 percent for “sad, empty type depression”; 92 percent for “very discouraged” type depression; and 69 percent for “loss of interest” type depression.

Technical Appendix: The Decomposition of Probabilities

More formally, there are N people (indexed, i = 1…N) of whom N _M are men and N _W are women: k = M (men), W (women.). Define the variable Y _i such that Y _i  = 1, if the person has had a condition (depression, anxiety), Y _i  = 0, otherwise. Then, under a logit model, the likelihood of a man or woman having had the condition is:

$$ \Pr (Y_{i} = 1) = {\frac{{\exp ({\mathbf{X}}_{{\mathbf{i}}}^{k} {\varvec{\upbeta}}^{k} )}}{{1 + \exp ({\mathbf{X}}_{{\mathbf{i}}}^{k} {\varvec{\upbeta}}^{k} )}}} = F({\mathbf{X}}_{{\mathbf{i}}}^{k} {\varvec{\hat{\upbeta }}}^{k} ), \quad k = M,W $$

(1)

where $\mathbf{X}^{k}_{i} = \left\{ {X_{ij} ,\,j = 1 \ldots J} \right\}$ represents the vector of observations, for person i of group k, on J variables which determine the likelihood of the person having that condition, and ${\varvec{\hat{\upbeta }}}^{k} = \left\{ {\beta^{k}_{j} ,\,j = 1 \ldots J} \right\}$ is the associated vector of coefficient estimates for persons from group k.

The average probability of a man or woman having had the condition is:

$$ \bar{Y}^{k} = \bar{P}(\mathbf{X}^{k}_{i} ,{\varvec{\hat{\upbeta }}}^{k} ) = N_{k}^{ - 1} \sum\limits_{i = 1}^{{N_{k} }} {F(\mathbf{X}^{k}_{i} ,{\varvec{\hat{\upbeta }}}^{k} )} \quad k = M,W $$

(2)

So that:

$$ \bar{Y}^{W} - \bar{Y}^{M} = \left[ {\bar{P}\left( {\mathbf{X}^{M}_{i} ,{\varvec{\hat{\upbeta }}}^{W} } \right) - \bar{P}\left( {\mathbf{X}^{M}_{i} ,{\varvec{\hat{\upbeta }}}^{M} } \right)} \right] + \left[ {\bar{P}\left( {\mathbf{X}^{W}_{i} ,{\varvec{\hat{\upbeta }}}^{W} } \right) - \bar{P}\left( {\mathbf{X}^{M}_{i} ,{\varvec{\hat{\upbeta }}}^{W} } \right)} \right] $$

(3)

Alternatively:

$$ \bar{Y}^{W} - \bar{Y}^{M} = \left[ {\bar{P}\left( {\mathbf{X}^{W}_{i} ,{\varvec{\hat{\upbeta }}}^{W} } \right) - \bar{P}\left( {\mathbf{X}^{W}_{i} ,{\varvec{\hat{\upbeta }}}^{M} } \right)} \right] + \left[ {\bar{P}\left( {\mathbf{X}^{W}_{i} ,{\varvec{\hat{\upbeta }}}^{M} } \right) - \bar{P}\left( {\mathbf{X}^{M}_{i} ,{\varvec{\hat{\upbeta }}}^{M} } \right)} \right]. $$

(4)

The first term in square brackets, in Eqs. 3 and 4, represents the “response effect”: it is the difference in average rates (of having had a condition) between women and men resulting from inter-gender differences in responses (as exemplified by differences in the coefficient vectors) to a given vector of attribute values.¹⁶ The second term in square brackets in Eqs. 3 and 4 represents the “attributes effect”: it is the difference in average rates (of having had a condition) between women and men resulting from inter-gender differences in attributes, when these attributes are evaluated using a common coefficient vector.

So for example, in Eq. 3, the difference in sample means is decomposed by asking what the average rates for men would have been, had they been treated as women; in Eq. 4, it is decomposed by asking what the average rate for women would have been, had they been treated as men. In other words, the common coefficient vector used in computing the attribute effect is, for Eq. 3, the female vector and, for Eq. 4, the male vector.