# **Section III: Variation in bias by income**

It is possible that these differences in weekly versus monthly data are not a terrible problem. If the underestimation of the frequency of illness and the use of health services were orthogonal to variables that researchers are interested in using to explain these phenomena, then the overall explanatory power of models using monthly data would be lower than with weekly and there would be bias in the scale of all coefficients uniformly – all effects would be about half of their real effect. Relative impacts of different variables would still be recoverable. However, in this section, we use the observational data to show that this recall effect is related to an important determinant of health care demand – household income. In this case, mismeasurement of the dependent variable biases gradients like the income elasticity of doctor visits, and therefore, affects our understanding of how illnesses are reported and how individuals seek treatment.

Specifically, we can decompose the income elasticity of expenditures on health, commonly believed to be quite high, into three parts – the probability of being ill, the probability of seeking treatment conditional on being ill, and the price of services sought. We present four figures that explore each of these components in turn. We then turn to a further aspect of health reporting. It is possible that many of the episodes not reported in the monthly recall surveys are ―minor‖ with few impacts on households, and small expenditures. We therefore also look at the effect of the recall period on labor impacts of sickness, again across poor and non-poor households.

Figure 2 shows the number of family members who reported at least one acute illness in any one month when asked on a weekly versus a monthly basis as a function of the family‘s log per capita expenditure.<sup>11</sup> In this and other figures, the vertical line represents the income range beyond which the data is very sparse and therefore, less reliable. There is an obvious difference between the recall periods; the outcome variables measured with weekly recall are always significantly larger than those measured with monthly recall. The slope of the weekly recall curve is very steep, and for the highest income values, approaches the monthly recall curve. While more than two episodes of illness are forgotten per month by the poorest, the wealthiest forget less than half an episode per month on average. When measured using monthly data, the difference between the rich and the poor is slightly less than one acute episode per family per month. The apparent recall effect

> 11 Chronic illnesses are excluded here because the survey methodology guarantees that the chronically ill are recorded as sick (with a chronic illness) once diagnosed regardless of the recall period used. To create monthly measures of reported doctor‘s visits and total expenditures from weekly data, we can just sum the visits and expenditures.  Creating a monthly measure of health events is somewhat more difficult.  For example, an event with duration greater than a week would be reported in multiple surveys in the weekly recall group but only in one survey in the monthly recall group, leading us to overestimate the total number of health events per month using the weekly data.  As a result, we also variously use the total duration of health events in a month or condition on having at least one health event in a given month to ensure that the results on recall and morbidity are not driven by potential ―double-counting‖.

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