Shadow Economy
One of the problems with the GDP indicator is its inability to account for the production of goods and services in the underground (shadow) economy. By this we mean not only illegal production of forbidden goods and services but also housework, helping friends, etc. — everything that is not observable for official statistics, but would have to be included in GDP if it were observable.
Clearly state two different approaches for estimating the size of the shadow economy of a country. Explain why your approaches may work to achieve this goal. Also explain why they might not work (the disadvantages).
The three approaches that are mostly used are the following.
1. Survey data; one can ask people how much they earn, or spend, or how busy they are with housekeeping etc. and compare it with the official statistics of income and consumption. Since people may take their unofficial activities into account when answering surveys, the comparison with the official statistics may to some extent reveal the unobserved part of the economy. The main disadvantage are common for surveys: the samples can be biased (it's unlikely that people who are rich and heavily engaged in tax evasion will take part), some people will refuse to respond, some of them will respond, but will not mention their unofficial earnings in fear that they can be investigated.
2. Using indirect (proxy) indicators of overall economic activity like electricity consumption, percentage of cash in the money supply, etc. This can work, because people inevitably leave 'fingerprints' when participate in the unofficial transactions, and they can be traces with this proxies. On the other hand, quantifying the shadow economy with these proxies is very difficult, so estimates can be way off.
3. Calculating GDP by definition, i.e., looking at the costs of production for the economy. It should work because even products sold illegally and unofficially are produced at the initial stages. The disadvantage of this approach is that we are missing most services.