A Two-Level Top-Down Decomposition of Aggregate Productivity Growth: The Role of Infrastructure

Using a Bennet-type symmetric method, the discrete-time counterpart of our continuous-time decomposition in Eq. (3) can be written as:

We also use a Bennet-type symmetric method to get the discrete-time counterparts of all continuous-time decomposition included in this chapter. Notice that the above productivity decomposition looks like a Törnqvist productivity index. It is worth mentioning that we do not need to introduce in the above decomposition the conventional covariance (or second order) term that appears, for instance, in Baily etal. (1992) and Diewert (2015). The covariance-type terms disappear from the productivity decomposition because the Bennet method is symmetric (Balk 2016a). Diewert (2015) proposed a simplified decomposition with only three terms as in (3) by assigning second- and third-order terms to corresponding first-order terms in a symmetric, even handed manner. He points out in footnote #14 that this assignment scheme is similar to that applied by Bennet (1920).

In our empirical application, we cannot compute K _n for each industry because we do not have the industry volumes for the capital input, just the economy-wide capital level. To address this issue, we will assume that the temporal evolution of K _n is the same in all industries or that \( {\dot{K}}_n=\dot{K},\forall n=1,..,N \).

As θ _n is a combination of a direct effect through the frontier and an indirect effect through the efficiency term, a portion of the within-industry productivity gains captured by WE is caused by a better reallocation of resources between firms, and hence the WE term cannot be completely interpreted as a term capturing pure (e.g., technological) productivity improvements. The pure productivity within effect can be computed and decomposed using (13) but ignoring the inefficiency term (i.e., using γ_n instead of θ _n).

The output share of each industry also depends on capital and labor and the time trend. Therefore, they also generate interindustry reallocation effects.

Notice that we have ignored in (18) the subscript for country to simply the notation.

Notice that this capital variable has been computed using both private and public investments at country level. Therefore, K is likely correlated with our Z variables.

In general, we were not able to find a significant effect for human capital as standard input in previous version of this paper. For this reason, we only include this variable as an inefficiency determinant.