Traded Intermediate Inputs, Aggregate Productivity Growth and Allocative Efficiency

France faces a decline of the aggregate productivity growth since a few decades. The IMF executive board has concluded in 2014 its consultation with France by pointing out the presence of significant rigidities that hinder economy's capacity to grow and create jobs. Since aggregate productivity growth is a sum of changes in within-firm productivity and changes in allocation of production factors (captured by the weights), market frictions reduce aggregate productivity growth. Indeed market frictions disturb resource allocation across firms and cause misallocation (Libert (2016), Fontagne and Santoni (2015)).

Decomposition of aggregate TFP growth
Figure 1: Contribution of allocative efficiency (AEst) and technical efficiency (Test) growths to the aggregate productivity growth (dlTFPst).
They are computed as simple averages of sector-level aggregates.

However in previous studies on misallocation, economists tend to care only about frictions on capital and labor markets. They totally missed the crucial role played by intermediate inputs in firm production process (Halpern, Koren and Szeidl (2015), Vandenbussche and Viegelahn (2016), Blaum, Lelarge, Peters (2015)). Intermediate inputs are goods used in the production process in order to produce other goods. They can be raw materials, energy or semi-finished goods. They represent more than 50% of total trade flows in 2000's and the majority of intermediate inputs used by firms are imported. How does reallocation of intermediate inputs contribute to aggregate productivity growth?

First, I use a theoretical framework to define misallocation. Firms face a CES demand and use a Cobb-Douglas technology to produce differentiated goods. I measure distortions facing by firms as the difference between marginal revenue product of inputs and the sectoral input price. If there are distortions, marginal revenue products of inputs are not equalized across firms. In this specific case, misallocation reduces aggregate productivity growth by allowing too many resources to some firms.

Then I decompose the aggregate productivity growth of incumbent firms to allocative efficiency and technical efficiency (Osotimehin, 2016). Allocative efficiency is a weighted average of changes in firm-level distortions. Technical efficiency is a weighted average of changes in within-firm productivities.

Decomposition of aggregate TFP growth
Figure 2: Contribution of reallocations of capital (AEkst), labor (AElst) and intermediate inputs (AEmst) to the aggregate allocative efficiency (AEst). They are computed as simple averages of sector-level aggregates.

Figure 1 shows that the better allocative efficiency accounts for around 60% of the aggregate TFP growth between 2002 and 2007. In figure 2, decreasing distortions on intermediate input market explain around 1/3 of the improving allocative efficiency. If firms only produce with capital and labor, allocative efficiency accounts for around 40% of aggregate TFP growth and 2/3 are explained by a higher allocative efficiency of capital.

Introducing traded intermediate inputs magnifies the contribution of allocative efficiency in aggregate productivity growth and considerably reduces measured misallocation on capital market.

References

Joaquim Blaum, Claire Lelarge and Michael Peters. "The Gains from Input Trade in Firm-based Models of Importing". NBER WP (2015)

Lionel Fontagné and Gianluca Santoni. "Firm Level Allocative Inefficiency: Evidence from France". Cepii WP (2015)

Laszlo Halpern, Miklos Koren and Adam Szeidl. "Imported Inputs and Productivity". American Economic Review (2015).

Thibault Libert. "Misallocation and Aggregate Productivity: Evidence from the French Manufacturing Sector". Unpublished

Sophie Osotimehin. "Aggregate Productivity and the Allocation of Resources over the Business Cycle". University of Virginia WP (2016)

Hylke Vandenbussche and Christian Viegelahn. "Input Reallocation within Firms". KU Leuven WP (2016)