(This essay was published in Hong Kong Economic Journal on 13 March 2013)


In February I wrote two articles about how to draw a poverty line, that have raised some attention among my colleagues at universities in Hong Kong. I compared two poverty lines – one based on household size (Poverty Line A) and the other based on age (Poverty Line B) – and concluded that Poverty Line A was decidedly inferior to Poverty Line B in identifying poor households. Bear in mind that households below the poverty line constitute about 20-25% of families in Hong Kong based on the 2011 Census of Population figures.


A number of my colleagues expressed uncertainty about dismissing Poverty Line A as I have suggested. Their worry is that household expenditures are higher in households with more members. Since the scale of consumption must vary positively with household size, it puzzles them that it is possible to ignore household size when drawing a poverty line.


Differences Between Poverty Lines A and B


To refresh readers’ memory Poverty Line A defines those households whose monthly incomes are below 50% of the median income of households with the same household size. This is the definition used in a number of OECD countries and by the Hong Kong Council of Social Services and Oxfam in their studies of the poverty line. According to this definition, I found 22% of the households were below Poverty Line A based on the 2011 Census data.


However, my alternative definition – Poverty Line B – was shown to be a better indicator of poverty. Poverty Line B defines those households whose monthly incomes are below 50% of the median income of households of the same age cohort. I found about 24% of the households below Poverty Line-B.


The differences between these two poverty lines are not trivial. Although 400,740 households are classified as being below both Poverty Lines A and B, however, 150,800 households classified as below Poverty Line B are not so classified using Poverty Line A, and vice versa 109,220 households classified as below Poverty Line A are not so classified under Poverty Line B. In particular, they identify different segments of the population that are poor.


Poverty Line A finds poor households are more concentrated among elderly households, while Poverty Line B finds them more concentrated among small sized households. Poverty Line B also finds that the poor are almost equally represented in all age groups as one would expect, which is in sharp contrast to the concentration of elderly under the Poverty Line A definition.


If Poverty Line B were to be adopted as the standard for distinguishing which households are poor, then can we safely ignore the effects on those households that are larger in size? My colleagues have pointed out that larger households have higher incomes. They therefore also spend more. Should we not seek to correct for differences in the scale of spending due to household size if we are going to make meaningful income comparisons across different households?


To answer this question one has to consider a number of complex theoretical and empirical issues.


From Inequality of Expenditures to Inequality of Incomes


For many people including my colleagues, the real concern about the inequality of household income is the inequality of household consumption. This concern relates to the distribution of household welfare in the population and it is motivated by an interest in enhancing the consumption of poor households. Income supplementation, consumption vouchers (food, health, rent, transport, etc.), subsidies-in-kind are all designed to enhance consumption levels.


The interest in consumption leads naturally to a comparison of consumption levels across households of different sizes. Clearly larger households spend more on consumption. Differences in age may also lead to differences in spending on consumption. Furthermore, larger households enjoy economies of scale in consumption; for example, members may share in the use of certain consumption items. In the past, these concerns motivated economists to search for consumption equivalence scales among households of different sizes and compositions.


These exercises were interesting but the findings were often politically contentious and policy makers seldom adopted them. It was also costly to collect survey information on household expenditures so these surveys were conducted far less frequently than the relatively inexpensive household income surveys. So for reasons of convenience policy makers adopted household income as a substitute for household expenditure. The implicit assumption is that income and expenditure had to be highly correlated, so income would therefore provide a good approximation.


The adoption of household income as a measure had one important consequence. The search for consumption equivalence scales became irrelevant and was abandoned. There was then no meaningful basis for comparing households of different sizes and compositions. But many still felt it was inappropriate to compare household income without taking into account the size and composition variations.


A simplifying ad hoc solution was subsequently devised to compare household income only among households of the same size. This implicitly acknowledged that there was no meaningful basis for conducting income comparisons across the whole population. Variations in household composition other than size were ignored for simplicity. A different Poverty Line A had to be found for each household size.


Income of course can only be observed among household members who work in the labor force. The young go to school and the elderly are retired so both do not work. Among prime age adults a considerable proportion chooses voluntarily to stay at home and not go to work; and a small proportion are unable to find work and are unemployed.


Many married women choose to stay at home when they have young children, especially those with less schooling because their forgone earnings from not working are usually less than those of women with more schooling. There are of course also differences in women’s preference for work relative to raising children at home. Women who stay at home do not contribute to household income, but they make an important non-market economic contribution. Such an economic contribution should be part of a household’s total economic resources, but it is not recorded as such. Measured market income is therefore flawed and understates true household income.


On the other hand, measured household income also overstates the inequality of household income distribution. While many married women from lower income households are unlikely to be working in the labor force and receiving earnings, higher income households are more likely to hire domestic helpers as a partial substitute for working mothers’ time in household work. Expenditures on domestic helpers are arguably a net deduction from household income. As a consequence, incomes of these households are overstated, which leads to overstating the inequality of household income distribution.


We should note there is an important conceptual difference between income and expenditure. Income is what household members receive for working in the labor force. What is not spent is saved. It is well known that savings vary systematically by the age of the household. Young households tend to have low levels of income and do not save a lot in order to maintain their desired levels of consumption. They begin to save a growing proportion of their income as they age and as their incomes grow in order to support themselves in old age when they retire.


Age and Household Income Inequality


How much households save over their adult life depend on how much they expect their children to contribute to their old age support. And this in turn depends on how much the government provides for old age support through social schemes. The more generous the government provision for old age support, the less will be the amount contributed by children. Moreover, generous government support schemes discourage parents from having more children and investing in their children as their value to parents is lowered.


As a general observation, households belonging to the same age cohort would have similar savings behavior because they are at the same stage of their lifecycle. They share the same beliefs about their life expectancies and face similar economic and other conditions specific to their times. Household size and composition tend to be more similar for households of the same age cohort at the same life cycle stage. In other words, comparing household income differences at the same age is more likely to mirror differences in household expenditures because there is less variation in savings differences among them.


Any remaining variations in household income within the same age cohort would then reflect differences in productivity among households, planned life cycle events, and chance factors.


Measured household income, on the other hand, is predominantly labor income. The distribution of household income reflects primarily the distribution of the sum of individual labor earnings of members in the household. Differences in individual earnings are due primarily to variations in human capital. Economic research has shown three factors account for variations in human capital: early childhood learning, schooling, and work experience.


Variations in work experience are usually small among members in the same age cohort, although those with more schooling usually have fewer years of work experience. For example, a 40-year old person with university education is likely to have only 18 years of experience, but a similarly aged person who is a secondary school graduate is likely to have 22 years of experience. However, those with more schooling are more productive because they have a larger stock of human capital. They have higher earnings compared with others in same age cohort. If we compare households belonging to different age cohorts then even those with the same years of schooling would have different years of work experience. Older cohorts would then have more years of work experience and therefore a higher stock of human capital. Their higher incomes, however, are a result of comparing households at different stages of their life cycle.


Another source of difference in household income among those in the same age cohort is due to variations in life cycle choices. These include marriage, fertility, timing and number of children, and so on. These life cycle choices are made together with labor market choices. As mentioned, a decision by a married woman to withdraw from the labor force to stay at home to care for children would lower observed household income. This income is therefore an outcome of the life cycle and labor market choices of the household. But when a woman withdraws from the labor market to take care of young children at home and household income drops, should we then consider this household to have descended towards poverty?


I would not think so because the choice to withdraw from the labor market is made by the household voluntarily. And I think it is silly to imply that households would voluntarily choose to become poorer. Rather, I believe, the household has made a sophisticated consumption and investment decision to sacrifice market income in order to have a child and invest the mother’s time in raising the child. Any poverty line is too crude a measure to capture these intricacies because it approximates spending with income and ignores intricate savings and investment decisions.


In summary, what are the advantages of Poverty Line B (based on age cohort) over Poverty Line A (based on household size)?


First, savings patterns change over the household life cycle but tend to be more similar among households in the same age cohort. Making income comparisons across age cohorts suffers from the distorting effects of savings on measured incomes. But these distortions are minimized when we make income comparisons within the same age cohort.


Second, among individuals in the same age cohort, those with more schooling are more productive because they have a larger stock of human capital.

Their higher earnings compared with their peers are not distorted by comparing households at different stages of their life cycle.


Third, the intricate ways in which household size and household income are related makes it meaningless to interpret their correlations. This is especially so in households where mothers drop out of the labor force after having young children and return when the children grow up. Comparing households in the same age cohort where the age of the children are more likely to be similar is not perfect, but it will be less distorting than comparing households across age cohorts.


Poverty Line should Not be Anchored on Household Size


To examine the relevance of age cohort and household size in accounting for variations in household income, I perform several linear regressions of log household income against age, household size, and a set of variables that proxy for human capital to capture the market productivity of household members. Table 1 shows that when log household income is regressed against age variables and household size variables separately and without entering the human capital variables only a small amount of variation in household income is accounted for. Specifically age variables alone in equation (1) explain 16.0% of the variation in log household income as measured by R2, a commonly used measure of explanatory power of the regression equation. Household size variables alone in equation (2) explain only 14.4%.


Note that entering the human capital variables into the regression equations increases the explanatory power significantly. In equation (4) the age and human capital variables account for 46.1% of the variation in log household income. In equation (5) the household size and human capital variables account for 54.1% of the variation. More importantly the estimated effects of the age variables are unchanged even after all the human capital variables are included as additional explanatory variables, which means age and human capital variables are not correlated with each other. However the effects of the household size variables are significantly affected after the human capital variables are entered as additional explanatory variables. This confirms what we have been proposing all along. Household size is an endogenous dependent variable that is an outcome on many work and family formation decisions that are correlated with human capital variables. The latter also determine household income. Anchoring the poverty line on household size is therefore meaningless and not interpretable.


In equations (3) and (6) both age and household size variables are entered as explanatory variables together. The estimated effects of the age and household size variables on log household income are significantly different from the estimated effects in equations (1-2) and (4-5). The instability of these estimated effects show that the household size variables are correlated with age and human capital variables in multiple and complex ways, which makes household size an unreliable anchor for determining the poverty line.


Equation (7) is the same regression as equation (4) except we have forced all the effects of the age and human capital variable on log household income in equation (7) to be identical to equation (4). This forces the household size variables to only account for those variations in household income that is not accounted from in equation (4).  Including household size variables increases the explanatory power from 46.1% to 52.1%; a mere 6%. Ignoring household size considerations loses very little information in helping us identify who are the poor households.


We now know that using household income to measure income inequality and define poverty has many flaws. On balance Poverty Line B is preferable to Poverty Line A for one basic reason. Comparing individuals and households of the same age cohort is far more likely to be meaningful because we are comparing households with their peers who are at the same stage of their life cycle, have grown up in the same era, and have the same vintage of schooling. Age is the better choice for anchoring the poverty line.


Table 1: Regression of Log Household Income by Age, Human Capital and Household Size Variables and Explained Percentage of Variation


  Human Capital Variables Omitted Human Capital Variables Included
  (1) (2) (3) (4) (5) (6) (7)
Intercept 9.190 8.569 8.911 7.839 8.169 7.296 7.181
Age 0.052   0.019 0.053   0.040 0.053
Age2  -0.001   -0.0004 -0.001   0.0004 -0.001
Household Size   0.672 0.542   0.523 0.507 0.283
Household Size2   -0.063 -0.047   -0.038 -0.037 -0.015
R2: The Explained Percentage of Variance of Log Household Income 16.0% 14.4% 26.2% 46.1% 54.1% 54.8% 52.1%


Note:   (1) All estimated effects are statistically significant at the 99% level.

(2) The human capital variables include schooling, gender of household head, marital status, birth place, duration in Hong Kong, occupation, and industry.

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