In sickness and in health: The association between health and household income

By Steve Martin
Income Statistics Division, Statistics Canada

Release date: July 24, 2018

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Abstract

This study examines the association between self-reported health and spouse-pair labour-market income using data from the Longitudinal and International Study of Adults. To explore the channels through which health associates with individual labour-market income, the association between health and spouse-pair income is further broken down into the association between health and the probability of working, hours worked, and hourly wage, both for an individual’s health and their spouse’s health.

Keywords: Health, household income, human capital, Longitudinal and International Study of Adults.

1. Introduction

Poor health is costly for society. Addressing both the acute effects of poor health in the short-term, and the more detrimental effects of poor health in the long-term, requires the use of scarce resources and highly skilled labour.Note 1 Beyond this direct cost, however, human capital theory stipulates that an individual’s health is positively correlated with their functioning as an economic unit—a healthy individual can both supply more labour and supply higher quality labour through increased productivity. Bad health outcomes are then costly for society, not only because of the direct costs associated with treating poor health, but also because of the indirect costs stemming from changes in individuals’ labour supply.Note 2

In addition to having a potentially large impact on the societal allocation of resources, poor health can have a significant impact on a household’s economic well-being if it results in reduced household income. This can lead to financial hardships, compounding lower income with increased medical or other associated expenses. There can also be intra-household spillovers from poor health resulting in a change in the labour-market activity of other working-age members of the household that further influence household income. For example, if an individual becomes chronically ill and drops out of the labour force, their spouse may work fewer hours to help care for them, which would in turn further reduce household income.

This study uses data from the Longitudinal and International Study of Adults (LISA) to analyze the association between health and household income. In order to focus on the labour-market outcomes associated with poor health and the intra-household spillovers that can come from poor health outcomes, the study restricts attention to spouse-pairs and considers the association between individual health and spouse-pair labour-market income—the sum of labour-market income for both members of a couple—rather than total household income. While there are non-labour market channels through which health can affect household income (e.g., by affecting discount rates), spouse-pair income is nonetheless a major component of household income for couples. In contrast to much of the existing literature that examines the association between health and a particular labour-market outcome for an individual, examining spouse-pair income allows the study to focus on the association between broader household income and health, and the labour-market channels through which this association propagates.

Using data on both self-reported general health and self-report mental health, as well as self-reported labour-market outcomes and linked tax records, the association between spouse-pair labour-market income and health is further decomposed into an employment effect reflecting the association between health and the probability of employment, an hours worked effect reflecting the association between health and the number of hours worked, and a wage effect reflecting the association between health and hourly wages. This is done for both for an individual’s health and their spouse’s health in order to examine intra-household spillovers from changes in health that correlate with spousal labour-market outcomes.

There is a large literature that examines the impact of self-reported health on particular labour-market outcomes, such as number of hours worked or hourly wages, with recent analyses exploiting panel datasets (e.g., Contoyannis and Rice, 2001; Cai, 2009; Han et al., 2009; Jäckle and Himmler, 2010).Note 3 Most of these studies use large socio-economic panel surveys (e.g., German Socio-Economic Panel, British Household Panel Survey) to examine the relationship between a measure of self-reported health and some labour-market outcome. While these analyses offer insights into the association between health and particular labour-market outcomes, they are silent on the size of intra-household spillovers from health, and how an individual’s health in turn relates to household income. Older studies find that men’s health can have an impact on the labour supply of female spouses (Chirikos, 1993).

Furthermore, very little research uses Canadian data, with no analyses using the LISA. The closest studies using Canadian datasets are those by Jeon (2014) and Jeon and Pohl (2016), who examine the impact of cancer diagnosis on both employment and household income using a panel dataset, and particularly Uppal (2009), who evaluates the assocation between self-reported health (both physical and mental) and hours worked for an individual.Note 4

In terms of results for this study, there is a strong negative association between both general and mental health and spouse-pair labour-market income, for both men and women. Spouse-pair income is particularly sensitive to mental health for men and general health for women. Poor mental health for men is associated with a $19,000 lower spouse-pair income, relative to those who do not have poor mental health. For women, having poor general health is associated with having a $28,000 lower spouse-pair income, relative to those who do not have poor general health. While the association between men’s mental health and spouse-pair income is almost entirely explained by the association between mental health and individual labour-market income for men, there are significant intra-household spillovers associated with women’s general health that are reflected in their spouse’s labour-market income. Put differently, the study finds a statistical association between women’s general health and their male spouse’s labour supply that does not operate in the other direction (i.e., when it is the male partner that has poor health). It should be underscored that this result is not demonstrated to be causal; poor health for women does not necessarily cause their male partners to reduce their labour supply. However, it suggests that women with poor general health may face an additional disadvantage, as their spouses tend to have diminished labour supply. 

Decomposing these associations, men who have poor mental health earn less in the labour market because they are less likely to work, relative to those who do not have poor mental health. Of those who do work, men with poor mental health receive smaller hourly wages. Women with poor general health earn less because they are less likely to work, with those who do work spending fewer hours per week at work. In addition, women with poor general health have spouses with signficantly lower hourly wages. These channels of association accumulate to make spouse-pair income particularily sensitive to women’s health.

2. Data

The data used for this study come from the second wave of the Longitudinal and International Study of Adults (LISA), conducted in 2014. The LISA is a biennial Canadian household survey that follows the same individuals over time, asking a variety of socio-economic questions. It targets individuals living in the ten provinces as of 2012, and is administered to all members of the household that are 15 years of age and older. The full description of the target population for the LISA can be found in Statistics Canada (2015).

For the purpose of this study, the LISA collects information on self-reported general and mental health for all respondents. Both general and mental health are measured using a five point scale—poor, fair, good, very good, and excellent. The LISA also asks the Kessler K10 set of questions on mental distress (Kessler et al., 2002), which can be used as an alternate measure of mental health.Note 5 For labour-market outcomes, the LISA collects self-reported information on employment, average hours worked per week, and hourly wages, as well as a variety of other socio-economic variables such as age, education, and household composition. To avoid issues associated with absenteeism at work stemming from poor health, whether an individual worked in the week of the interview or not is used to measure employment.

Table 1
Summary statistics
Table summary
This table displays the results of Summary statistics. The information is grouped by Labour-market variables (appearing as row headers), Men and Women, calculated using dollars, hours and percent units of measure (appearing as column headers).
Labour-market variables Men Women
dollars
Spouse-pair income 104,800 103,800
Individual income 67,600 36,500
Hourly wage 31.8 25.3
   hours
Hours worked per week 45.1 37.5
   percent
Employment rate 86.5 75.9
Self-reported general health
Good/very good/excellent 93.1 93.9
Fair/poor 6.9 6.1
Self-reported mental health
Good/very good/excellent 95.9 95.6
Fair/poor 4.1 4.4
Kessler K10
Below 20 93.0 90.4
Above 20 7.0 9.6
N. Obs. 2,820 2,814

The LISA also links with administrative tax data, which gives a measure of annual before-tax labour-market income at the individual level. Spouse-pair labour-market income is simply the sum of both member’s before tax labour-market income.Note 6 In this study, income refers to before-tax income from the previous tax year, whereas employment, hours worked, and wages are measured in the week of the interview. Interviews occur near the start of the calendar year, so there is minimal lag between measuring annual income from tax data and the other labour-market variables.

In order to focus on the labour-market implications of poor health and capture any intra-household spillovers from an individual’s health, attention is restricted to spouse-pairs where both members are between 18 and 64 years of age, not enrolled in an education program, and not self-employed. The result is a sample of 5,634 spouse pairs. Table 1 provides basic summary statistics. The vast majority of spouse-pairs are of the opposite sex, so that any association between spousal health and an individual’s labour-market outcomes can be broadly interpreted as coming from a member of the opposite sex.

Before presenting the model used to analyze the data, it is useful to examine the association between health and spouse-pair income graphically. Charts 1 and 2 show how spouse-pair labour-market income relates to both general and mental health for men and women, respectively. For men, having either poor general health or poor mental health is associated with a roughly $30,000 drop in spouse-pair income compared to those with good to excellent health. Most of this drop is accounted for by a reduction in individual labour-market income, with only a small decrease in spousal labour-market income.

Compared to men, women’s general health has a stronger association with spouse-pair income—poor health is associated with a $37,000 drop in spouse-pair income relative to those that have good to excellent health (Chart 2). Only half of this association, however, is related to lower individual labour-market income for women. The other half comes from lower spousal labour-market income, suggesting that there may be important intra-household spillovers from women’s health that are reflected in poorer spousal labour-market outcomes.

Compared to men, women’s mental health is not as strongly associated with spouse-pair income—having poor mental health is associated with a $22,000 lower spouse-pair income, compared to $29,000 less for men. As was the case for men, most of this association is accounted for by reduced individual labour-market income, with spousal income being only slightly lower.

Data table for Chart 1

Data table for Chart 1
Chart 1
Labour market income and general health, men
Table summary
This table displays the results of Labour market income and general health Spouse-pair income, Individual income and Spousal income, calculated using dollars units of measure (appearing as column headers).
Spouse-pair income Individual income Spousal income
dollars
General health: Good/Very good/Excellent 107,000 69,400 37,600
General health: Poor/Fair 75,800 44,000 31,800
Mental health: Good/Very good/Excellent 106,000 68,500 37,500
Mental health: Poor/Fair 77,500 47,100 30,400

Data table for Chart 2

Data table for Chart 2
Chart 2
Labour market income and general health, women
Table summary
This table displays the results of Labour market income and general health Spouse-pair income, Individual income and Spousal income, calculated using dollars units of measure (appearing as column headers).
Spouse-pair income Individual income Spousal income
dollars
General health: Good/Very good/Excellent 106,000 37,700 68,400
General health: Poor/Fair 68,900 19,100 49,800
Mental health: Good/Very good/Excellent 104,700 37,200 67,600
Mental health: Poor/Fair 82,500 22,400 60,100

3. Empirical model

In order to understand the channels through which health associates with spouse-pair income, the study examines how health—both for an individual and their spouse—associates with an individual’s labour-market income. A change in an individual’s labour-market income resulting from a change in health (either individual or spousal health) can be decomposed into three separate effects; see the Appendix for details.

  1. i) The employment effect that results from a change in the probability of employment from a change in health.
  2. ii) The hours worked effect that results from a change in the average number of hours worked from a change in health, conditional on working.
  3. iii) The wage effect that results from a change in the hourly wage from a change in health, conditional on working.

To estimate the association between health and household income, and operationalize the income decomposition presented above, a series of linear regression models are estimated, for both men and women, of the form

y i =α+βhealt h i o +γhealt h i s + X i θ+ u i . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaa aaaaaaa8qacaWG5bWdamaaBaaaleaapeGaamyAaaWdaeqaaOWdbiab g2da9iabeg7aHjabgUcaRiabek7aIjabgwSixlaadIgacaWGLbGaam yyaiaadYgacaWG0bGaamiAa8aadaqhaaWcbaWdbiaadMgaa8aabaWd biaad+gaaaGccqGHRaWkcqaHZoWzcqGHflY1caWGObGaamyzaiaadg gacaWGSbGaamiDaiaadIgapaWaa0baaSqaa8qacaWGPbaapaqaa8qa caWGZbaaaOGaey4kaSIaamiwa8aadaWgaaWcbaWdbiaadMgaa8aabe aak8qacqaH4oqCcqGHRaWkcaWG1bWdamaaBaaaleaapeGaamyAaaWd aeqaaOWdbiaac6caaaa@5F78@

Here yi is a labour-market outcome for individual i, healt h i o MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaa aaaaaaa8qacaWGObGaamyzaiaadggacaWGSbGaamiDaiaadIgapaWa a0baaSqaa8qacaWGPbaapaqaa8qacaWGVbaaaaaa@4013@  is an individual’s own self-reported health status, healt h i s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaa aaaaaaa8qacaWGObGaamyzaiaadggacaWGSbGaamiDaiaadIgapaWa a0baaSqaa8qacaWGPbaapaqaa8qacaWGZbaaaaaa@4017@  is an individual’s spouse’s self-reported health status, and Xi is a vector of observable covariates. Covariates include five equal-sized bins for age (for individuals and spouses); dummies for education—no post-secondary, post-secondary below the bachelors level, post-secondary at the bachelors level or above (for individuals and spouses); dummies for age of children (0-5, 6-17, 18-24); province dummies and a dummy for if the household is in a rural area; and a dummy for being born in Canada (for individuals and spouses).Note 7 These correspond closely to the controls found in existing research — e.g., Cai (2009), Uppal (2009), and Jäckle and Himmler (2010).  

When the dependent variable yi equals labour-market income, the regression coefficient β gives the association between an individual’s health and their income, and γ gives the association between spousal health and an individual’s income. Setting yi equal to a dummy indicating employment, the number of hours worked, and the hourly wage in turn gives the employment effect, hours worked effect, and wage effect discussed above, both with respect to own health, β, and spousal health, γ.Note 8 As the vast majority of spouse-pair couples in the data are of the opposite sex, the spousal coefficient γ can broadly be interpreted as coming from a member of the opposite sex.

4. Results

Table 2 presents the model results for men. The left-most column shows the association between general health and mental health—both for an individual and their spouse—and spouse-pair labour-market income, analogous to chart 1. Looking at the first two rows, poor general health is associated with having $12,000 less in spouse-pair income relative to those with good to excellent general health, whereas poor mental health is associated with having $19,000 less in spouse-pair income relative to those with good to excellent mental health.

Moving from left to right across the table, the association between men’s health and spouse-pair income is almost entirely explained by the association between men’s health and individual income (second column). For general health, this association is driven primarily by a strong negative association between health and the probability of working (third column)—men with poor general health are 20 percentage points less likely to be employed compared to men with good to excellent general health. For men who are employed, there is little association between either the number of hours worked (fourth column) or the hourly wage (fifth column) and general health.

For mental health, a lower probability of working (third column) and a lower hourly wage (fifth column) contribute to the negative association with income. Men with poor mental health are 10 percentage points less likely to be employed, and those who are employed make $3 less per hour on average. This may explain why the association between labour-market income and mental health is so much larger than the association between labour-market income and general health. Poor mental health not only makes it less likely that an individual will work, but those that do work are less productive in the labour market.

Table 2
Association between health and income, men
Table summary
This table displays the results of Association between health and income Spouse-pair income, Individual income, Employment, Hours worked and Hourly wage, calculated using dollars, percentage points and hours units of measure (appearing as column headers).
Spouse-pair income Individual income Employment Hours worked Hourly wage
dollars percentage points hours dollars
Individual health
Self-reported general health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -11,800Note * -13,800Note * -19.7Note * 0.5 1.1
Self-reported mental health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -18,900Note * -15,100Note * -10.3Note * -2.8 -2.7Note *
Spousal health
Self-reported general health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -28,200Note * -13,000Note * -1.8 0.0 -4.9Note *
Self-reported mental health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -10,600Note * -2,300 1.3 -0.5 -1.3
N. Obs. 2,820 2,336

Examining the last two rows of the table, a spouse with poor general health is associated with a $28,000 lower spouse-pair income, well over double the size of the association between men’s own general health and spouse-pair income. Moving from left to right across the columns of the table, about half of this association is explained by smaller labour-market income for men (second column)—poor spousal health is associated with their male partner’s labour-market income being $13,000 lower.  This smaller labour-market income in turn comes primarily from a $5 lower average hourly wage for men (fifth column), suggesting that there are large intra-household spillovers associated with women’s health that are negatively reflected in their male partner’s labour-market productivity. In contrast, while spousal mental health is negatively associated with spouse-pair income (an $11,000 reduction in spouse-pair income), there are no significant intra-household spillovers from spousal mental health that are seen in men’s labour-market income.

Analogous to table 2, table 3 gives the model results for women. As the vast majority of spouse-pairs are of the opposite sex, the first column in table 3 is nearly identical to the first column in table 2. Working across the first two rows, women’s poor general health has a strong, negative association with spouse-pair income—having poor general health is associated with $28,000 less in spouse-pair income. Consistent with table 2, about half of this association is accounted for by the association between individual income and general health (second column). This is in turn is driven by both a lower probability of working and fewer hours worked. Relative to those with good to excellent general health, women having poor health are 22 percentage points less likely to be employed (third column) and those who are employed work 3 hours less per week on average (fourth column).

Table 3
Association between health and income, women
Table summary
This table displays the results of Association between health and income Spouse-pair income, Individual income, Employment, Hours worked and Hourly wage, calculated using dollars, percentage points and hours units of measure (appearing as column headers).
Spouse-pair income Individual income Employment Hours worked Hourly wage
dollars percentage points hours dollars
Individual health
Self-reported general health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -27,800Note * -14,800Note * -22.1Note * -3.1Note * -1.3
Self-reported mental health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -10,500Note * -8,100Note * -13.5Note * 0.3 -1.0
Spousal health
Self-reported general health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -11,900Note * 2,500 -0.8 -1.7 -0.1
Self-reported mental health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -19,000Note * -3,600 -2.5 -1.0 -2.1
N. Obs. 2,814 2,074

As for mental health, women having poor mental health is associated with an $11,000 lower spouse-pair income, with this association almost entirely explained by the association between mental health and individual income (second column). This lower individual income is in turn explained primarily by a lower probably of working—women with poor mental health are 14 percentage points less likely to work than those reporting good to excellent mental health (third column). 

Moving to the last two rows of the table, spousal health—especially spousal mental health—is strongly associated with spouse-pair income. Consistent with table 1, however, there is very little association between women’s labour-market income and spousal health. The contribution of men’s health to spouse-pair income is almost entirely explained by the association between men’s health and men’s labour-market income.

Tables 4 and 5 are analogous to tables 3 and 4, except that the previous measure of mental health is now replaced by the Kessler K10 measure of psychological distress. The regression coefficients for general health, both for an individual and their spouse, are virtually unchanged across the columns of both tables. The coefficients for mental health are smaller in both tables, particularly for women’s mental health, although the main qualitative insights from tables 2 and 3 remain unchanged.

Table 4
Association between health and income, men
Table summary
This table displays the results of Association between health and income Spouse-pair income, Individual income, Employment, Hours worked and Hourly wage, calculated using dollars, percentage points and hours units of measure (appearing as column headers).
Spouse-pair income Individual income Employment Hours worked Hourly wage
dollars percentage points hours dollars
Individual health
Self-reported general health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -13,500Note * -14,100Note * -19.3Note * 0.2 0.9
Self-reported mental health
K10 below 20 (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
K10 above 20 -14,600Note * -16,300Note * -13.5Note * -1.1 -2.6Note *
Spousal health
Self-reported general health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -29,600Note * -13,300Note * -0.9 -0.2 -5.8Note *
Self-reported mental health
K10 below 20 (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
K10 above 20 -3,500 -1,700 -3.5 0.4 1.9
N. Obs. 2,820 2,336

5. Conclusions

This study examines the association between self-reported general and mental health and spouse-pair labour-market income for couples using data from the LISA. Focusing on labour-market income rather than total income allows the analysis to examine the labour-market channels through which health associates with income, while focusing on spouse-pairs allows the analysis to examine intra-household spillovers in labour-market outcomes from poor self-reported health. This offers a novel perspective on the association between health and household income using a previously unexploited dataset, assessing both the channels through which health associates with income and extent to which intra-household spillovers in labour-market activity from health are reflected in household income.

The results show that spouse-pair income is strongly associated with both men’s and women’s self-reported health. For men, the association between mental health and income is particularly strong, whereas for women it is the association between general health and income that is stronger. While the association between men’s health and spouse-pair income is almost entirely explained by the association between men’s health and individual income, for women about half of the association between general health and spouse-pair income is explained by lower income for their male partners. This latter finding suggests that there may be important intra-household spillovers from women’s health that are associated with their partner’s labour supply.

While the LISA is a panel dataset, the analysis is entirely cross-sectional in nature as the panel is still short. However, the longitudinal aspect of the LISA offers interesting opportunities for future research, as future waves of the survey will allow for the estimation of fixed-effects models that control for time-invariant individual heterogeneity. This is practically relevant when using self-reported health data, as this offers a means to control for individual-specific reference points when reporting health, as well as historical health that can be correlated with both current health and current labour-market outcomes.

Table 5
Association between health and income, women
Table summary
This table displays the results of Association between health and income Spouse-pair income, Individual income, Employment, Hours worked and Hourly wage, calculated using dollars, percentage points and hours units of measure (appearing as column headers).
Spouse-pair income Individual income Employment Hours worked Hourly wage
dollars percentage points hours dollars
Individual health
Self-reported general health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -28,300Note * -15,300Note * -22.9Note * -3.0Note * -1.8
Self-reported mental health
K10 below 20 (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
K10 above 20 -6,400 -4,200Note * -6.8Note * -0.4 1.1
Spousal health
Self-reported general health
Good/very good/excellent (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
Fair/poor -12,900Note * 1,700 -1.8 -2.0 -0.1
Self-reported mental health
K10 below 20 (ref.) Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable Note ...: not applicable
K10 above 20 -17,700Note * -1,200 -0.2 1.0 -2.6Note *
N. Obs. 2,814 2,074

Appendix

This appendix shows the details of the income decomposition used in section 3. To fix notation, let w denote the hourly wage rate, l the number of hours worked, and e an indicator of employment. Conditional on a vector of covariates x and health, denoted by h, expected labour-market income is
E( wle|h,x )=P( e=1|h,x )E( wl|h,x,e=1 ). MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaa aaaaaaa8qacaWGfbWaaeWaa8aabaWdbiaadEhacaWGSbGaamyzaiaa bYhacaWGObGaaiilaiaadIhaaiaawIcacaGLPaaacqGH9aqpcaWGqb WaaeWaa8aabaWdbiaadwgacqGH9aqpcaaIXaGaaeiFaiaadIgacaGG SaGaamiEaaGaayjkaiaawMcaaiaadweadaqadaWdaeaapeGaam4Dai aadYgacaqG8bGaamiAaiaacYcacaWG4bGaaiilaiaadwgacqGH9aqp caaIXaaacaGLOaGaayzkaaGaaiOlaaaa@56E0@

In order to lighten notation, in what follows the conditioning vector x is omitted; all expectations should be interpreted as conditional on x. From the above expression, it follows that a change in health status from h to h' is given by

E( wle| h )E( wle|h )            =[ P( e=1| h )P( e=1|h ) ]E( wl|h,e=1 )           +[ E( wl| h ,e=1 )E( wl|h,e=1 ) ]P( e=1| h ) . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabe aaqaaaaaaaaaWdbiaadweadaqadaWdaeaapeGaam4DaiaadYgacaWG LbGaaeiFaiqadIgapaGbauaaa8qacaGLOaGaayzkaaGaeyOeI0Iaam yramaabmaapaqaa8qacaWG3bGaamiBaiaadwgacaqG8bGaamiAaaGa ayjkaiaawMcaaaqaaiabg2da9maadmaapaqaa8qacaWGqbWaaeWaa8 aabaWdbiaadwgacqGH9aqpcaaIXaGaaeiFaiqadIgapaGbauaaa8qa caGLOaGaayzkaaGaeyOeI0Iaamiuamaabmaapaqaa8qacaWGLbGaey ypa0JaaGymaiaabYhacaWGObaacaGLOaGaayzkaaaacaGLBbGaayzx aaGaamyramaabmaapaqaa8qacaWG3bGaamiBaiaabYhacaWGObGaai ilaiaadwgacqGH9aqpcaaIXaaacaGLOaGaayzkaaaabaGaey4kaSYa amWaa8aabaWdbiaadweadaqadaWdaeaapeGaam4DaiaadYgacaqG8b GabmiAa8aagaqba8qacaGGSaGaamyzaiabg2da9iaaigdaaiaawIca caGLPaaacqGHsislcaWGfbWaaeWaa8aabaWdbiaadEhacaWGSbGaae iFaiaadIgacaGGSaGaamyzaiabg2da9iaaigdaaiaawIcacaGLPaaa aiaawUfacaGLDbaacaWGqbWaaeWaa8aabaWdbiaadwgacqGH9aqpca aIXaGaaeiFaiqadIgapaGbauaaa8qacaGLOaGaayzkaaaaaaa@824E@

Since E( wl|h,e=1 )=E( w|h,e=1 )E( l|h,e=1 )+cov( w,l|h,e=1 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaa aaaaaaa8qacaWGfbWaaeWaa8aabaWdbiaadEhacaWGSbGaaeiFaiaa dIgacaGGSaGaamyzaiabg2da9iaaigdaaiaawIcacaGLPaaacqGH9a qpcaWGfbWaaeWaa8aabaWdbiaadEhacaqG8bGaamiAaiaacYcacaWG LbGaeyypa0JaaGymaaGaayjkaiaawMcaaiaadweadaqadaWdaeaape GaamiBaiaabYhacaWGObGaaiilaiaadwgacqGH9aqpcaaIXaaacaGL OaGaayzkaaGaey4kaSIaam4yaiaad+gacaWG2bWaaeWaa8aabaWdbi aadEhacaGGSaGaamiBaiaabYhacaWGObGaaiilaiaadwgacqGH9aqp caaIXaaacaGLOaGaayzkaaaaaa@6182@ , after some manipulation this expression can be written as

E ( w l e | h ) E ( w l e | h )            = [ P ( e = 1 | h ) P ( e = 1 | h ) ] e m p l o y m e n t   e f f e c t E ( w l | h , e = 1 ) > 0            + [E(l|h,e=1)E(l|h,e=1)] hours worked effect E(w|h,e=1)P(e=1|h) >0            + [E(w|h,e=1)E(w|h,e=1)] wage effect E(l|h,e=1)P(e=1|h) >0            + [cov(w,l|h,e=1)cov(w,l|h,e=1)]P(e=1|h) residual effect . MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabe aaqaaaaaaaaaWdbiaadweapaGaaiika8qacaWG3bGaamiBaiaadwga paGaaiiFa8qacaWGObGaeyOmGi6daiaacMcapeGaeyOeI0Iaamyra8 aacaGGOaWdbiaadEhacaWGSbGaamyza8aacaGG8bWdbiaadIgapaGa aiykaaqaa8qacqGH9aqpdaagaaqaa8aacaGGBbWdbiaadcfapaGaai ika8qacaWGLbGaeyypa0JaaGyma8aacaGG8bWdbiaadIgacqGHYaIO paGaaiyka8qacqGHsislcaWGqbWdaiaacIcapeGaamyzaiabg2da9i aaigdapaGaaiiFa8qacaWGObWdaiaacMcacaGGDbaal8qabaGaamyz aiaad2gacaWGWbGaamiBaiaad+gacaWG5bGaamyBaiaadwgacaWGUb GaamiDaiaacckacaWGLbGaamOzaiaadAgacaWGLbGaam4yaiaadsha aOGaayjo+dWaaGbaaeaacaWGfbWdaiaacIcapeGaam4DaiaadYgapa GaaiiFa8qacaWGObGaaiilaiaadwgacqGH9aqpcaaIXaWdaiaacMca aSWdbeaacqGH+aGpcaaIWaaakiaawIJ=aaWdaeaapeGaey4kaSYaaG baaeaapaGaai4wa8qacaWGfbWdaiaacIcapeGaamiBa8aacaGG8bWd biaadIgacqGHYaIOcaGGSaGaamyzaiabg2da9iaaigdapaGaaiyka8 qacqGHsislcaWGfbWdaiaacIcapeGaamiBa8aacaGG8bWdbiaadIga caGGSaGaamyzaiabg2da9iaaigdapaGaaiykaiaac2faaSWdbeaaca WGObGaam4BaiaadwhacaWGYbGaam4CaiaacckacaWG3bGaam4Baiaa dkhacaWGRbGaamyzaiaadsgacaGGGcGaamyzaiaadAgacaWGMbGaam yzaiaadogacaWG0baakiaawIJ=amaayaaabaGaamyra8aacaGGOaWd biaadEhapaGaaiiFa8qacaWGObGaaiilaiaadwgacqGH9aqpcaaIXa WdaiaacMcapeGaamiua8aacaGGOaWdbiaadwgacqGH9aqpcaaIXaWd aiaacYhapeGaamiAaiabgkdiI+aacaGGPaaal8qabaGaeyOpa4JaaG imaaGccaGL44paaeaacqGHRaWkpaWaaGbaaeaacaGGBbWdbiaadwea paGaaiika8qacaWG3bWdaiaacYhapeGaamiAaiabgkdiIkaacYcaca WGLbGaeyypa0JaaGyma8aacaGGPaWdbiabgkHiTiaadweapaGaaiik a8qacaWG3bWdaiaacYhapeGaamiAaiaacYcacaWGLbGaeyypa0JaaG yma8aacaGGPaGaaiyxaaWcbaWdbiaabEhacaqGHbGaae4zaiaabwga caqGGcGaaeyzaiaabAgacaqGMbGaaeyzaiaabogacaqG0baak8aaca GL44padaagaaqaa8qacaWGfbWdaiaacIcapeGaamiBa8aacaGG8bWd biaadIgacqGHYaIOcaGGSaGaamyzaiabg2da9iaaigdapaGaaiyka8 qacaWGqbWdaiaacIcapeGaamyzaiabg2da9iaaigdapaGaaiiFa8qa caWGObGaeyOmGi6daiaacMcaaSqaa8qacqGH+aGpcaaIWaaak8aaca GL44paaeaapeGaey4kaSYdamaayaaabaGaai4wa8qacaWGJbGaam4B aiaadAhapaGaaiika8qacaWG3bGaaiilaiaadYgapaGaaiiFa8qaca WGObGaeyOmGiQaaiilaiaadwgacqGH9aqpcaaIXaWdaiaacMcapeGa eyOeI0Iaam4yaiaad+gacaWG2bWdaiaacIcapeGaam4DaiaacYcaca WGSbWdaiaacYhapeGaamiAaiaacYcacaWGLbGaeyypa0JaaGyma8aa caGGPaGaaiyxa8qacaWGqbWdaiaacIcapeGaamyzaiabg2da9iaaig dapaGaaiiFa8qacaWGObGaeyOmGi6daiaacMcaaSqaa8qacaqGYbGa aeyzaiaabohacaqGPbGaaeizaiaabwhacaqGHbGaaeiBaiaabckaca qGLbGaaeOzaiaabAgacaqGLbGaae4yaiaabshaaOWdaiaawIJ=aiaa c6caaaaa@2E06@

Under the assumption that cov(w,l|h,e=1) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaa aaaaaaa8qacaWGJbGaam4BaiaadAhacaGGOaGaam4DaiaacYcacaWG SbGaaiiFaiaadIgacaGGSaGaamyzaiabg2da9iaaigdacaGGPaaaaa@4447@  is constant the residual effect disappears, so that

E( wle| h )E( wle|h )           = [ P( e=1| h )P( e=1|h ) ] employment effect E( wl|h,e=1 ) >0           + [ E( l| h ,e=1 )E( l|h,e=1 ) ] hours worked effect E( w|h,e=1 )P( e=1| h ) >0           + [ E( w| h ,e=1 )E( w|h,e=1 ) ] wage effect E( l| h ,e=1 )P( e=1| h ) >0 . MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbcvPDwzYbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0x e9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKk Fr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabe aaqaaaaaaaaaWdbiaadweadaqadaWdaeaapeGaam4DaiaadYgacaWG LbGaaeiFaiqadIgapaGbauaaa8qacaGLOaGaayzkaaGaeyOeI0Iaam yramaabmaapaqaa8qacaWG3bGaamiBaiaadwgacaqG8bGaamiAaaGa ayjkaiaawMcaaaqaaiabg2da9maayaaabaWaamWaa8aabaWdbiaadc fadaqadaWdaeaapeGaamyzaiabg2da9iaaigdacaqG8bGabmiAa8aa gaqbaaWdbiaawIcacaGLPaaacqGHsislcaWGqbWaaeWaa8aabaWdbi aadwgacqGH9aqpcaaIXaGaaeiFaiaadIgaaiaawIcacaGLPaaaaiaa wUfacaGLDbaaaSqaaiaabwgacaqGTbGaaeiCaiaabYgacaqGVbGaae yEaiaab2gacaqGLbGaaeOBaiaabshacaqGGcGaaeyzaiaabAgacaqG MbGaaeyzaiaabogacaqG0baakiaawIJ=amaayaaabaGaamyramaabm aapaqaa8qacaWG3bGaamiBaiaabYhacaWGObGaaiilaiaadwgacqGH 9aqpcaaIXaaacaGLOaGaayzkaaaaleaacqGH+aGpcaaIWaaakiaawI J=aaqaaiabgUcaRmaayaaabaWaamWaa8aabaWdbiaadweadaqadaWd aeaapeGaamiBaiaabYhaceWGObWdayaafaWdbiaacYcacaWGLbGaey ypa0JaaGymaaGaayjkaiaawMcaaiabgkHiTiaadweadaqadaWdaeaa peGaamiBaiaabYhacaWGObGaaiilaiaadwgacqGH9aqpcaaIXaaaca GLOaGaayzkaaaacaGLBbGaayzxaaaaleaacaqGObGaae4Baiaabwha caqGYbGaae4CaiaabckacaqG3bGaae4BaiaabkhacaqGRbGaaeyzai aabsgacaqGGcGaaeyzaiaabAgacaqGMbGaaeyzaiaabogacaqG0baa kiaawIJ=amaayaaabaGaamyramaabmaapaqaa8qacaWG3bGaaeiFai aadIgacaGGSaGaamyzaiabg2da9iaaigdaaiaawIcacaGLPaaacaWG qbWaaeWaa8aabaWdbiaadwgacqGH9aqpcaaIXaGaaeiFaiqadIgapa Gbauaaa8qacaGLOaGaayzkaaaaleaacqGH+aGpcaaIWaaakiaawIJ= aaqaaiabgUcaRmaayaaabaWaamWaa8aabaWdbiaadweadaqadaWdae aapeGaam4DaiaabYhaceWGObWdayaafaWdbiaacYcacaWGLbGaeyyp a0JaaGymaaGaayjkaiaawMcaaiabgkHiTiaadweadaqadaWdaeaape Gaam4DaiaabYhacaWGObGaaiilaiaadwgacqGH9aqpcaaIXaaacaGL OaGaayzkaaaacaGLBbGaayzxaaaaleaacaqG3bGaaeyyaiaabEgaca qGLbGaaeiOaiaabwgacaqGMbGaaeOzaiaabwgacaqGJbGaaeiDaaGc caGL44padaagaaqaaiaadweadaqadaWdaeaapeGaamiBaiaabYhace WGObWdayaafaWdbiaacYcacaWGLbGaeyypa0JaaGymaaGaayjkaiaa wMcaaiaadcfadaqadaWdaeaapeGaamyzaiabg2da9iaaigdacaqG8b GabmiAa8aagaqbaaWdbiaawIcacaGLPaaaaSqaaiabg6da+iaaicda aOGaayjo+daaaaa@EC5B@

This constant covariance assumption is standard for system equation models; see Greene (2011, Chapter 10) for details. Importantly, this assumption does not imply that wages and hours of work are uncorrelated; rather, the correlation does not change with health status after controlling for key demographic variables. If this assumption does not hold, then the residual covariance term does not disappear. While the decomposition used in section 3 is still valid in this case, it is no longer an exact decomposition.

Under the usual assumptions of the linear regression model, the employment effect, the hours worked effect, and the wage effect can be estimated respectively by regressing an employment indicator, hours worked, and hourly wage on health status (and a vector of covariates).

References

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Jeon, S.-H., and Pohl, R. V. (2016). Health and Work in the Family: Evidence from Spouses’ Cancer Diagnoses. Analytical Studies Branch Research Paper Series, Statistics Canada.

Kessler, R. C., Andrews, G., Colpe, L. J., and Hiripi, E. (2002). Short screening scales to monitor population prevalences and trends in non-specific psychological distress. Psychological Medicine, 32(6), 959-976.

Lundberg, O., and Manderbacka, K. (1996). Assessing reliability of a measure of self-rated health. Scandinavian Journal of Social Medicine, 24(3), 218-224.

Public Health Agency of Canada. (2014). Economic Burden of Illness in Canada, 2005-2008.

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