_'_ Combining the first derivate of consumption, 1 = ( 1 + _q_ ) _f_ ( _k_ ) , with income in efficiency units and in its steady state form from (16) yields the golden rule capital stock in (18)<sup>10</sup> . The decentralized optimum ( _k_<sup>∗</sup> ) can now be compared with the (dynamically) efficient capital stock per effective worker ( _kGR_ ) : In case Brazil’s capital stock lies far away from its optimal level, then the efficient use of natural resource revenues would be to invest them and not transfer any part for consumption. Alternatively, if Brazil’s capital stock is close to its optimal level, then just a smaller fraction of the oil revenue should be invested, and it would be more optimal to consumption the rest. In the latter case, the optimal share that should be consumed depends endogenously on the choice of distribution mechanism the government chooses – since they all affect private capital accumulation which, in turn, changes both the optimal decentralized capital stock and the optimal golden rule capital stock.

**<u>Table 2. Calibration of the Model</u>**

|_Parameter_|_Value_|_Interpretation of steady state parameters_|
|---|---|---|
|_α_|0.1867|The capital share in output|
|_τ_|0.4450|The pension replacement rate|
|_g_|1.8626|The steady state growth rate of productivity|
|_q_|0.0700|The share of oil revenue in GDP (varies across scenarios)|
|_λ_|0.6088|The length of the retirement period|
|_n_|0.4726|The population growth rate|
|_β_|0.2785|The discount rate, yielding a saving rate of 20.91 percent for the aggregate economy|
|_δ_|1|The rate of capital depreciation|
|_κ_|1|The weight on workers in oil revenue transfers|

Sources and notes: Time periods of the model are assumed to be 25 years. In order to calibrate for life expectancy, the length of the model’s first period is normalized at unity, while the length of the second period equals 61 percent (estimated as the share of total life spent in retirement: average retirement age equals 57.83 (Queiroz and Figoli, 2010); average entry-age into the labor force is 13.3 (Leme & Málaga, 2001)]; life expectancy equals 69.3 (average life expectancy at birth over the period 1998–2088; UN Population Division **,** the 2008 Revision). The contribution rate to the social PAYG pension system is calibrated to 31 percent (11 percent from workers and 20 percent from employers (Queiroz and Figoli, 2010). The average replacement rate, weighted by the share of the population receiving pension benefits at various rates, for pensions is estimated to be 45 percent. The replacement rate to public servants is assumed to be 95 percent, since older public servants participated in a plan of virtually 100 percent replacement rate, while younger generations receive slightly less. The replacement rate for nonpublic-servants is estimated residually based on pension payment data for the two groups. The weighted average is constructed based on the share of the population is each group; the effective weighted average is found to equal 45 percent (data from DATAPREV, SUB, Plano Tabular da DIIE, and Ministerio da fazenda).

1 10 The expression stated in dynamic terms: _kGRt_ = (α( 1 + _qt_ ) / [( 1 + _nt_ )( 1 + _gt_ )]α ~~)~~ 1 −α .

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