The name is absent

Appendix A

Production Function Estimations with Levinshon-Petrin Correction

The main benefit of using the Levinshon and Petrin methodology instead of Olley and
Pakes is essentially data driven. The use of the investment proxy to control for
unobservables so to overcome the endogeneity of labour and inputs in production function
estimations (Marschak and Andrews,1944, Griliches and Mairesse, 1998) is valid only
when firms report non-zero investments and this would imply a severe truncation of our
sample.

The idea suggested by Levinsohn and Petrin (2003), is to use, instead of investments,
intermediate inputs to control for producer unobservables. In details, we start from a
Cobb-Douglas production function (as equation (7)),

y_it^j = β₀+ β_wlw_it^j +β_blb_it^j +β_kk_it^j +β_ee_it^j + β_mm_it^j +ω_it^j +ε_it^j

where yit is the log of gross output (proxied by sales) for firm i in year t lwit is the log of
white (skilled) labor input, lbit is the log of the blue (unskilled) labor input, and eit and mit
denote log-levels of materials, and energy (which includes consumption of fuel and
electricity).

Here, we consider that the demand for intermediate inputs mit depends on capital, kit , and
on the productivity component ωit , that are both firm’s state variables.

mit= mit(ki , ωit)

Inverting this function⁴⁶, we have that ωit=ωit(kit ,mit), so the unobservable productivity
term becomes a function of observed inputs.

Then, following Olley and Pakes (1996), the final identification restriction relies on the
fact that productivity is governed by a first-order Markov process:

ωit =E[ωit | ωit-1 ] + ξit

where ξit is an innovation in productivity uncorrelated with kit .

Substituting for ωit in the production function, we have that

y_it = +β_wlw_it +β_blb_it +β_ee_it +φ_it(k_it,m_it)+ε_it

where φ_it(k_it,m_it)=β₀ +β_kk_it +β_mm_it +ω_it(k_it,m_it).

⁴⁶ Levinshon and Petrin, 2003 show that under mild assumptions, the input demand function is
monotonically increasing in ωit

35

<<   34   35   36   37   38   39   40   >>

More intriguing information