Abstract
This chapter examines the use of symbolic regression to tackle a real world problem taken from economics: the estimation of the size a country’s ’shadow’ economy. For the purposes of this chapter this is defined as a country’s total monetary economic activity after subtracting the official Gross Domestic Product. A wide variety of methodologies are now used to estimate this. Some have been criticized for an excessive reliance on subjective predictive variables. Others use predictive data that are not available for many developing countries. This chapter explores the feasibility of developing a general-purpose regression formula using objective development indicators. The dependent variables were 260 shadow economy measurements for various countries from the period 1990- 2006. Using 16 independent variables, seven basis functions, and a depth of one grammar level a search space of 1013 was created. This chapter focuses on the power conferred by an abstract expression grammar allowing the specification of a universal goal formula with grammar depth control, and the customization of the scoring process that defines the champion formula that ’survives’ the evolutionary process. Initial searching based purely on R-Squared failed to produce plausible shadow economy estimates. Later searches employed a customized scoring methodology. This produced a good fit based on four variables: GDP, energy consumption squared, this size of the urban population, and the square of this figure. The same formula produced plausible estimates for an out of sample set of 510 countries for the years 2003-2005 and 2007. Though shadow economy prediction will be controversial for some time to come, this methodology may be the most powerful estimation formula currently available for purposes that require verifiable data and a single global formula.
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Truscott, P.D., Korns, M.F. (2011). Detecting Shadow Economy Sizes with Symbolic Regression. In: Riolo, R., Vladislavleva, E., Moore, J. (eds) Genetic Programming Theory and Practice IX. Genetic and Evolutionary Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1770-5_11
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