consumption, investment and net exports: _GDP_ = _C_ + _I_ + ( _E − M_ ). The figures for _C_ and _I_ incorporate government consumption and investment. This definition of GDP corresponds to the format usually given in IMF country reports.

In our model the goods that are consumed (ignoring leisure), can be divided between _imports_ and non-imports ( _N_ ), where non-imports comprise _domestic_ and _untaxed_ . Total consumption in the model is thus given by _C_ = _N_ + _M_ . Using the definition of GDP we calculate the amount of non-imports consumed as _N_ = _GDP − I − E_ . Consumption of non-imports is equal to production of non-imports. Production of _domestic_ , the taxed non-imported good in the model, is calculated by dividing VAT revenue by the tax rate, giving the tax base: _D_ =<sup>_<u>R</u>_</sup> _tD_<sup>_<u>D</u>_.</sup> Consumer expenditure on the _untaxed_ good (equal to the value of production) is thus the residual of non-imports: _U_ = _N −_ (1 + _tD_ ) _× D_ .

Funds received by firms are spent on factors. Allocation of firm revenue between capital and labor is achieved using assumed labor-output ratios. The amount of formal factor usage is determined by dividing factor tax revenues by their tax rates. Informal factor usage is then the residual of total factor expenditure less formal factor expenditure.

The calibration process can be illustrated with data from Guinea-Bissau and the SAM of Table 2. The value of _investment_ , as a percentage of GDP at market prices, is available directly from the national accounts: _I_ = 18 _._ 9. The producer value of exports is derived by subtracting export tax revenue from the market value of exports: _E_ = 27 _._ 21 _−_ 2 _._ 61 = 24 _._ 6. The producer value of _domestic_ is determined by dividing tax revenue for domestic goods (0.74% of GDP) by the standard sales tax rate (15%): _D_ =<sup><u>0</u></sup> 0<sup>_<u>.</u>_</sup> _._<sup><u>74</u></sup> 15<sup>=4</sup><sup>_._93.Thevalueof</sup><sup>_untaxed_isthentheresidualof</sup> GDP less investment and the taxed value of _domestic_ and _exports_ , all expressed as a percentage of GDP: _U_ = 100 _−_ ( _D_ + 0 _._ 74) _−_ ( _E_ + 2 _._ 61) _− I_ = 48 _._ 20.

Total funds received by the firms in a sector is the sum of sales and investment. For example, firms producing exports receive _E_ + _IE_ = 24 _._ 60 + 5 _._ 99 = 30 _._ 59. It is assumed that production is competitive, so that all funds received by firms are paid out to factors. Capital and labor requirements for production are determined using the labor-output ratios. Thus, for example, with a labor-output ratio of 0.37 for exports, total capital used to produce exports is _KE_ = (1 _−_ 0 _._ 37) _×_ ( _E_ + _IE_ ) = 18 _._ 55. Since _untaxed_ uses only _informal capital_ and _informal labor_ , this procedure is all that is required to determine the allocation of capital and labor to _untaxed_ .

For _domestic_ and _exports_ , factor usage must be divided between formal and informal factors. The amounts of formal capital and labor are determined by dividing tax receipts by the legal tax rate. With a 39% corporations tax, total _formal capital_ is _K_<sup>_f_</sup> = 00 _.._ 3992<sup>=2</sup><sup>_._36.</sup> Applying a personal income tax rate of 10% implies total _formal labor_ of _L_<sup>_f_</sup> =<sup><u>0</u></sup><sup>_<u>.</u>_</sup> 0<sup><u>945</u></sup> _._ 1 = 9 _._ 45. These amounts are divided between _domestic_ and _exports_ in proportion to output. For example, _formal capital_ in _exports_ is _KE_<sup>_f_=</sup><sup>_Kf ×_</sup> _E_ + _<u>ED</u>_<sup>= 2</sup><sup>_._36</sup><sup>_×_</sup> 24 _._ <u>2460+4</u> _<u>.</u>_ <u>60</u> _._ 93<sup>= 1</sup><sup>_._97.Informal capital and labor</sup> are then the residuals of total capital and labor for each industry less formal capital and labor and the taxes paid on these factors. For example _informal capital_ used 11