Sector Switching: An Unexplored Dimension of Firm Dynamics in Developing Countries

The production technology in this paper is therefore defined separately for each sub-
sector using a stochastic production frontier which expresses output as a function of
inputs, technical inefficiencies capturing the degree to which firms produce below the
optimal level of production and a random error component (Pitt and Lee, 1981).

yt = f ( xt ; β ) ev^- uⁱ

i =1,2, ,nj; t=1,2,...T

where y_i^t represents the output of the i th firm in a particular sub-sector in time period
t , x_i^t the vector of inputs into the production process, β the vector of parameters of the
production function, and v_i^t statistical noise and other random external events
influencing the production process.¹² The technical efficiency of the ith firm relative to
the stochastic frontier for its group is given by the ratio of observed output to the
corresponding stochastic frontier output:

As such, u_i are the firm specific inefficiency effects for a particular sector, and we
assume v_i^v and u_i are independent. If u_i = 0 , the firm is efficient and operates on the
group specific production frontier. If u_i > 0 , there are inefficiencies and the firm
operates beneath the best-practice frontier for the sub-sector.

The stochastic production function for each sub-sector can be estimated by specifying
an appropriate functional form for each model. We use a translog production function
which incorporates controls for exogenous fixed time effects ω^v , for example, due to
technological change or policy changes which affect all firms equally.

K1KL

lnyt = ^{α +} ∑^βk ln^xtk ⁺-∑∑^βkl ln^xtk ln^xtι ^{+ ω + v}t ^-U                  (3)

k=12 k=1 l=1

12 t                                                 2

¹² v_ij is assumed to be iid N (0,σ_vj

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