Estimates of the Black Economy Based on Consumer Demand Approaches

Abstract

We propose a consumer demand system approach to estimating the size of the black economy where alternative hypotheses affecting the empirical results can be tested in a nested framework. This approach allows for the estimation of the under‐reporting of household income from various sources, dispensing with the need to use arbitrary criteria to classify households by their main source of income. It also avoids potential bias in black economy estimates arising from mistaking preference heterogeneity (substitution) as income effects. We illustrate these arguments by estimating the extent to which self‐employment income in the UK is under‐reported using parametric and nonparametric techniques.

Estimating the income reporting function for the self-employed

“…First, there is an implicit assumption of the Expenditure-Based Method that the Engel curve(s) employed in the estimation must be monotonic in income. In reference to Figure 1, if this critical assumption is violated, then a unique value of true income associated with a 4 Lyssiotou et al (2004) also allow for what they call "preference heterogeneity". They note that income from selfemployment may not be spent in the same way as income from other sources.…”

“…They assume that durable and nondurable goods are separable and base their demand system on nondurable goods only, namely: food, alcohol, fuel, clothing, personal goods/services, and leisure goods/services. Lyssiotou et al (2004) maintain the specification of the linear reporting function given in equation (1) above but avoid classifying households as either wage earners or self-employed. 4 The functional form for the Engel curve that is specified by Lyssiotou et al (2004) raises two concerns.…”

“…Lyssiotou et al (2004) maintain the specification of the linear reporting function given in equation (1) above but avoid classifying households as either wage earners or self-employed. 4 The functional form for the Engel curve that is specified by Lyssiotou et al (2004) raises two concerns. First, there is an implicit assumption of the Expenditure-Based Method that the Engel curve(s) employed in the estimation must be monotonic in income.…”

“…Previous studies have implemented the Expenditure-Based Method using highly parametric restrictions on: (1) an Engel curve (Pissarides and Weber 1989) or a system of Engel curves (Lyssiotou et al 2004);and (2) an income reporting function. These restrictions imply that households under-report their income by a constant fraction, independent of income.…”

“…One such approach, popularized by Pissarides and Weber (1989) and modified by Lyssiotou et al (2004), utilizes household income and expenditure data to estimate the degree of income under-reporting (i.e. the amount by which household income should be scaled upwards to obtain true, or actual, income as opposed to reported income).…”