Papeles de trabajo

It is assumed that planti’s time tvalue-added,yit, is determined by Cobb-Douglas tech- nology defined in logarithms as:

yit=βllit+βkkit+ωit+εit, (4.8)

where lit and kit, denote the plant i’s time t levels of labor and capital, respectively.9 The plant’s productivity,ωit, is a plant- and time-specific productivity measure. The error term,

εit, is considered a measurement error. It is assumed the capital, kit, is a state variable that is updated through investment over time, but is not variable within time periodt. Labor and materials are assumed to be freely variable within the time period.

A plant’s value-added is defined as deflated gross revenues minus the deflated cost of materials and services. The use of a value-added production function, instead of revenue deflated by the an industry-level price index, is used in the analysis for several reasons. First, the next section involves the use of simulations that require the dynamic update of inputs across years. The use of materials in the estimation of a deflated revenue production function would require the update of plant-level materials usage. However, the updating of plant- level materials based on an estimated first-order condition in the simulation of heterogeneous plants produces unreasonable results. The use of value-added extends beyond technical con- straints. A large section of the Chilean manufacturing sector is involved in the conversion

9

I do not distinguish between skilled and unskilled labor for expositional simplicity. Labor is divided into skilled and unskilled variables in the results presented later in the paper.

of the country’s natural resources into manufactured products. Accordingly, growth in the manufacturing sector’s value-added is the more likely welfare-enhancing target than growth in deflated revenue, which may occur solely through the increased depletion of the country’s natural resources. However, despite these differences, value-added and revenues remain highly correlated in the data.10

The estimation of the production function follows Levinsohn and Petrin (2003) which is motivated by the estimation strategy of Olley and Pakes (1996) to use intermediate inputs as a proxy in the identification of ωit. Levinsohn and Petrin (henceforth LP) note that the use of materials, mit, will be increasing in productivity for a givenkit.11 Thus, the demand for materials, mit = mit(ωit, kit), is a monotonic function in ωit. Given this monotonicity, the materials demand equation can be inverted to obtainωit =ωit(mit, kit). The production function (4.8) can now be rewritten as:

yit=βllit+βkkit+φit(mit, kit) +εit, (4.9)

where

φit(mit, kit) =βkkit+ωit(mit, kit). (4.10)

I assume that each plant’s capital stock evolves according to

Kit=Kit−1(1−δ) +Iit, (4.11)

whereδ is a time- and plant-invariant depreciation rate andIit is planti’s investment in time periodt. A final identification restriction is required in the estimation process. Following LP I assume that productivity follows a first-order Markov process:

ωit=E[ωit|ωit−1] +ξit, (4.12)

10_{The correlation coefficient is .90 in the industries examined.} 11

where ξit is an unanticipated productivity shock that is uncorrelated with kit. Given the nature of the evolution of capital in (4.12), investment becomes active as capital immediately. Thus, if investment in time t is made with knowledge of ωit, then ξit would influence the investment decision. I avert this issue by following LP’s timing, which assumes that the time

tinvestment decision is made with only knowledge of ωit−1.

The equation used for the first stage of estimation is created by substituting in a third- order polynomial approximation inkit and mit:

yit=βllit+ 3 X j1=0 3−j1 X j2=0 γj1j2k j1 itm j2 it +εit. (4.13)

This first stage identifies the coefficient on labor, ˆβl, but does not identify the coefficients on capital and labor. To identify these remaining coefficients some additional steps are required. The second stage of estimation is based upon the Generalized Method of Moments (GMM) estimator. The moment condition stems from the timing assumption that assumes that capital does not respond to unexpected innovations in productivity:

E(ξit+εit|kit) =E(ξit|kit) = 0. (4.14)

The second moment condition identifies βm under the premise that materials use in the

previous time period is uncorrelated with the innovation to productivity in the current period:

E(ξit+εit|mit−1) =E(ξit|mit−1) = 0. (4.15)

To implement the estimation process, ˆφit is computed as the predicted level of output exclud- ing the influence of labor:

ˆ φit=yit−βˆllit− 3 X j1=0 3−j1 X j2=0 γj1j2k j1 itm j2 it. (4.16)

Using this computed value of ˆφit, an estimate of ˆωit for potential values ofβk∗ can be created

as

ˆ

ωit= ˆφit−βk∗ (4.17)

Likewise, an estimated prediction of the expectation of productivity can be created as

E[ωit|ωit−1] =α0+α1ωit−1+α2ωit2−1+α3ωit3−1+εit. (4.18) Utilizing the constructed values above alongside ˆβland the potential value forβk∗, the residual of the production function, which enters the moment conditions, is calculated as

ˆ

ξit+ ˆεit=yit−βˆllit−βk∗kit−(E[ωitˆ|ωit−1]), (4.19)

which is inserted into a GMM criterion function to obtain estimates on the coefficients on capital and labor. The GMM criterion function yielding these estimates is

min(β∗ m,β∗k) X j∈Zt ( X t ( ˆξit+ ˆεit)Zjt2 ) , (4.20)

whereZt≡(mt−1, kt) . The estimation of the production function allows the predicted level of productivity to be created. This plant- and time-specific productivity level, ˆωit, is created as

ˆ

ωit=yit−βˆllit−βˆkkit. (4.21)

The previous estimation of the production function allows the plant- and time-specific measure of productivity to be utilized in investment and export decision making processes of each plant. The estimates of the above coefficients and a comparison of productivity between exporters

and non-exporters are presented in the next section. Further, the productivity measure

stemming from this estimation allows a plant- and time-specific measure of productivity to be created, which can be employed in the examination of plant-level investment and exports. However, additional estimations are required to address the influence of a plant’s export intensity on its investment in capital.