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Using Engel Curves to Detect Underreporting of Income among the Self-employed

David McKenzie's picture
The self-employed often underreport income to tax authorities. Less is known about how trustworthy the income reported on household surveys is, but there is a concern that they may also underreport their income in surveys too – either because of concerns about it getting linked to official records, or because the easiest number for them to report is the one they tell the authorities. This raises obvious concerns about the measurement of items such as the poverty levels of the unemployed, the differential income gap between wage work and self-employment, and many other such uses.

In a paper recently published in the Review of Economics and Statistics, Hurst, Li and Pugsley (ungated version) propose using Engel curves to detect the level of underreporting of the self-employed. They assume that both wage workers and the self-employed correctly report expenditures, and then consider the log-linear Engel curve:
Log food consumption = a + b*Log income + d’X + e
Where X are controls for household composition, age, marital status, etc.

They assume the self-employed report a fraction of their income, and then augment the Engel curve by adding a term g*Self-Employed. The estimated fraction of income reported by the self-employed is then exp(-g/b).

Using U.S. data they observe that at each level of reported family income, the self-employed consume more food than wage workers do. g is estimated to be between 12 and 20%, i.e. for a given level of income, the self-employed are spending 12-20 percent more on food and on non-durables. From this and their estimates of b, they estimate that the self-employed are underreporting income by 25-30 percent in the Consumer Expenditure Survey and PSID. They note that this gap is enough to explain away most of the observed gap in earnings between wage work and self-employment that previous literature has attempted to explain by non-pecuniary benefits of self-employment (e.g. being one’s own boss, flexible time schedules, etc.).

Concerns
This is a simple and easy to apply procedure. But it assumes that the self-employed and wage workers should have the same consumption patterns. The authors discuss two concerns along these lines:
 
  • Differences due to hours worked: if the self-employed work longer hours, they may engage in less home production and therefore spend more. For example, they might eat out more or hire more child care. The authors deal with this by controlling for hours worked. This doesn’t make much difference.
  • Differences in savings patterns: if the self-employed have different risk profiles for income, or different temporal income patterns, they may differ in their need for precautionary saving and for life-cycle savings. They examine this by looking at differences by age profiles and by wealth quartiles, and don’t find much difference along either line. But these are weaker proxies for the variables one is concerned about.
Bottom Line
I was very skeptical of the idea behind the paper after reading the abstract and introduction – my feeling being that assuming the consumption-income relationships are the same for the self-employed and wage workers are the same seems problematic. I think there are two issues here. The first is the one that the authors attempt to deal with, which is the concern that being self-employed changes consumption preferences because of the hours and income risk of self-employment. However, there is a second concern which they don’t discuss, which is that the types of individuals who select into self-employment may inherently have different preferences from wage workers-  i.e. even if these same individuals did take up wage work, they may consume and save differently from the individuals who select into wage work. After all, we worry that the self-employed differ in many other respects from wage workers, including risk preferences, optimism, entrepreneurial attitude, and other personality features, and it seems plausible some of these also affect consumption.

Nevertheless, the idea is interesting, and might be particularly useful when looking at experiments on the self-employed – if we are worried for example that self-employed who go through business training over-report their incomes afterwards, comparing Engel curves for this group of self-employed to those who don’t go through training might be a useful check on whether treatment is leading to some change in reporting of income. The advantage here would be that you would just  be comparing self-employed with self-employed, and not assuming they have the same preferences as wage workers.
 

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