The name is absent

The estimation of the coefficient on the labour inputs and energy are obtained substituting
a third order polynomial approximation in kit and mit to φit and then using OLS. From
this first stage of the estimation routine we obtain β_w, ∣.'^,^b, β_e and
^φit = ^yit ^{- β}w^lwit ^{- β}b^lbit ^{- β}e^eit ∙

In the second stage, for any candidate value⁴⁷ of β_k* and β_m* it is possible to compute ω^_it
using ^ωit = ^φit ^{- β}k kit ^{- β}m ^mit

Subsequently, from the regression

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^ω it = ^γ0 ^{+ γ}1^ωt-1 ^{+ γ} 2^ωt-1 ^{+ γ} 3^ω_t-1 ^{+ η}it

we obtain a consistent (non parametric) approximation of E[ω_it | ωit_-1 ], E[ω_it ∣ω_it-ɪ] that
is used to compute the sample residual for the production function (as a function of βk*
and βm*)

^ε it (^βk^{, β}m ) ^{+ ξ}it = yit ^{- β}w^bwit ^{- β}b^lbit ^{- β}e^eit ^{- β}k ^kit ^{- β}m ^mit ^- E

To identify both βk and βm separately we need two moment conditions∙ The first will be
(as in Olley and Pakes) that the capital does not respond to shocks to this period’s
innovation in productivity ξit, providing the population moment:

E[ξit + εit | kit]=0

The second condition, needed to identify βm , uses the fact that last period’s material
choices should be uncorrelated with the innovation in productivity in this period∙

E[ξit + εit | mit-1]=0

Finally, with Z_it=( k_it ,m_it-1 ), β_m and βk are obtained minimizing the GMM criterion
function,

Q(β*) = min ∑ ∑ (ξit + εit )Zit

With respect to inference, given the fact that this is a multi stage estimation procedure, the
covariance matrix of the final parameters must account for variance and covariance of
every estimator that enters the routine∙ This problem is solved by bootstrapping standard
errors∙

⁴⁷ good starting values might be the OLS estimates from the production function∙

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