Annex 3A Productivity Growth Decomposition

strategic sectors in the provision of incentive packages), and trade and investment promotion. • Consider that policy support has usually built and strengthened agglomeration economies and oftentimes has been associated with desired productivity and employment outcomes. Hence, carefully crafted interventions need to be aimed at accelerating urbanization as well as establishing and bolstering economic clusters. • Narrow the infrastructure gap by increasing public investment and adopting an appropriate public sector management system to facilitate job creation and productivity growth as well as accelerate much-needed structural change.

Annex 3A Productivity Growth Decomposition

Aggregate productivity (Φt) is defined as a weighted average of firm-level productivity (φit) in which firms’ market shares (Sit) are used as weights. Employment shares and value-added shares can also be used as alternative weights.

Φ ϕ ∑ =s t it it i

Following Olley and Pakes (1996), aggregate productivity is further decomposed into two components:

Φ ϕ= + t t ∑( )( ) ϕ ϕ it t – –s s it t

i

= ( ϕ ϕ cov + ,st it it ),

where ϕt is unweighted mean productivity and st is unweighted mean market share.

This technique does not follow firms over time, and the covariance term only captures the distribution of firm productivity and market shares in a given period t. To accommodate the contributions of incumbent, entering, and exiting firms, Melitz and Polanec (2015) extend the Olley-Pakes decomposition technique, which is dynamic OP decomposition with entry and exit.

To explain the technique, suppose SKt denotes aggregate market shares of survivors or incumbents (S), entrants (E), and exiters (X). That is,

SKt ∑ = s

it,

∈ i K

where K represents S, E , and X. To be precise with the definitions of firm types, an incumbent is a firm that has been in operation in periods t = 1 and t = 2. An entrant is a firm that has started operations in t = 2 but not in t = 1. By contrast, an exiter is a firm that was in operation in t = 1 but no longer in t = 2.

Now, aggregate productivity levels in periods t = 1 and t = 2 and growth over time can be expressed as follows:

Φ Φ S= +S X1 1 ( ) Φ ΦS X1 1 1 –Φ Φ S= +S E2 2 –(Φ Φ E S2 2 2 ) –∆ ∆ ∆ ( ) ( )Φ Φ Φ ϕ Φ Φ Φ Φ 2() () () () = = +cov +S +S2 1 s s E2 E2 S2 X1 S1 X1 – –1 3 4

where term (1) is changes in the unweighted mean productivity of incumbent firms. Term (2) is changes in the covariance term between productivity levels and market shares of incumbents. Term (3) captures the relative difference in the productivity levels of entrants and incumbents weighted by the market shares of entering firms in the second period. If entrants are relatively more productive (and have sizable market share), they positively contribute to growth in aggregate productivity. Term (4) compares the productivity levels of exiters and incumbents weighted by the market shares of exiting firms in the first period. If less productive firms leave (and previously had nonnegligible market shares), their market departure improves aggregate productivity.

The reference productivity levels vary across firm types, following from the timing assumptions on firm entry and exit. Entrants improve aggregate productivity if and only if they possess higher productivity levels than surviving firms in the period entry occurs (t = 2). The contribution of exiters to aggregate productivity growth is positive if and only if they have lower productivity than surviving firms in the period when exit takes place (t = 1).

Most techniques use the same reference productivity levels when comparing the contributions of one group of firms to contributions of another, which leads to measurement bias. The reference productivity levels in Griliches and Regev (1995) and Foster, Haltiwanger, and Krizan (2001) overestimate the contribution of entering firms to productivity growth and hence underestimate that of surviving and exiting firms. Through careful choice of appropriate references, the decomposition with entry and exit overcomes this measurement issue.