The name is absent

y_it^j = β0+ β_wlw_i^j_t +β_blb_it^j + β_kk_it^j +β_ee_it^j + β_mm_i^j_t +ω_it^j +ε_it^j

where yit is the log of gross output (proxied by sales)²⁴ , kit is the log of the plant's
capital stock, lwit is the log of hours worked by skilled workers (white), lbit is the log of
hours worked by unskilled workers (blue), and mit and eit denote log-levels of materials,
and energy (which includes consumption of fuel and electricity). The error term has two
unobserved components, ωit ,the transmitted productivity components and εit,, the
random noise component. The difference between the two is that ωit is a state variable,
known by the firm when deciding the amount of input to employ in production²⁵, while
εit is independent with respect to input choices. The correlation between the error
component and inputs leads to the well known simultaneity problem firstly highlighted
by Marschak and Andrews (1944). Estimations that ignore this correlation yield biased
results. This is the case for OLS that, most commonly, overestimate the labour
coefficient and underestimates the capital coefficient.

To overcome this problem we use the Levinshon and Petrin (2003) methodology²⁶. This
approach builds on the work of Olley and Pakes (1996) that proposed the use of
investments as proxy to control for the correlation between the unobserved productivity
shock and capital (assuming that labour and materials are freely available inputs). The
Olley-Pakes procedure can be applied only to plants reporting non-zero investments and
this criteria would require a significant truncation of our sample²⁷. For this reason, as
suggested by Levinshon and Petrin, we use intermediate input demand as proxy. In
particular, we use raw material inputs²⁸ that become a valid proxy when their demand
function is monotonic in firm’s productivity for all levels of capital. Appendix A reports
the details of the Levinshon-Petrin estimation procedure, its implementation and a
description of the variables used in estimations.

²⁴ We did also estimated the value added production function, assuming weak separability on materials.
The TFP estimations did not differ substantially.

²⁵ But not by the econometrician.

²⁶ If the productivity is assumed to be plant specific and time invariant, the simultaneity problem can also
be solved including in the regression firm specific effects (fixed-effect panel estimations). However this
estimator does not fully exploit the cross-sectional variation which, especially in our case, with a short
panel, is a relevant dimension.

²⁷ In the case of the ICS of India, new investments are reported only for 1999 and 2001 and even in those
case there is a high frequency of zero observations.

²⁸ Alternatively also electricity consumption, possibly in physical quantities, can be a good proxy but we
have only data on cost of energy. For a more detailed discussion on the choice of proxies see Appendix A.

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