where the subscripts i and t represent the i-th firm and the t-th year of observation,
respectively; Y represents real gross output; x1 represents the logarithm of
intermediate inputs, m ; x2 represents the logarithm of capital stock, k ; x3 represents
the logarithm of total employment, e ; x4 represents a time trend to take account of
technical progress, t ; Dl is a set of dummy variables indicating export status,
including EXPnever , EXPentry , EXPexit , EXPboth 26 ; REGn and INDp are region and
industry dummies variables respectively; and the composite error term has three
elements with ηi affecting all observations for the cross-section firm i; tt affects all
firms for time period t; and eit affects only firm i during period t.27 Note here we
divide firms into 5 different sub-groups based on exporting status: those that always
exported, those that never exported, those that entered into exporting, those that exited,
and lastly, those that started and then stopped exporting more than once.
To allow for potential endogeneity of factor inputs and exporting, Equation (5) is
estimated using the Generalised Method of Moments (GMM) systems approach
available in STATA 9 (Arellano and Bond, 1998). This is sufficiently flexible to
allow for both endogenous regressors (through the use of appropriate instruments
involving lagged values - in both levels and first differences - of the potentially
endogenous variables in the model) and a first-order autoregressive error term.
Thirdly, the standard Heckman two-stage (or control function) approach is a widely
used approach to dealing with self-selection bias, which is closely linked to the IV
approach. This approach begins with a first-stage use of a probit (or logit) estimator to
26 Note, Dι is a constant that defines each sub-group (the baseline group are those that always exported,
i.e. EXPalways ). However, for the last three sub-groups (ι=2, 3, 4) firm i switches into the sub-group at
time t, and therefore we denote this by Dιit. The latter variable enters contemporaneously and with a
lead and lagged term, to consider whether firms experience ‘export-by-learning’ effects with time lags.
27 Note, if eit is serially correlated such that eit = ρeit-1 + uit then uit is uncorrelated with any other part of
the model, and ∣ρ∣<1 ensures the model converges to a long-run equilibrium (i.e. the variables in the
model are cointegrated).
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