in the form of lower prices, revenue-based measures using industry price deflators will not capture the improvements in productivity.<sup>3</sup> Recent work by Garcia-Marin and Voigtlnder (2019) on Chile suggests that this could be the reason why empirical studies have not been able to find evidence of firms improving productivity after they begin exporting. They compare revenue-based measures of productivity that are typically used with marginal costs and find that while firms do not become more productive, as measured by revenue productivity, they do become more efficient as measured by marginal costs, post entry into export markets.<sup>4</sup> This finding on Chile has highlighted the need to correct for biases that arise from revenue-based measures of productivity (that use industry rather than firm prices) to understand the relationship between exports and productivity. The data set I use in this paper contains information on firm prices and allows me to recover measures of physical productivity that account for variation in prices across firms.<sup>5</sup> In this paper, I ask, do firms become more productive after they enter export markets? And if so, what are the mechanisms through which firms improve productivity? I examine the role of two possible mechanisms - imports of intermediate inputs and investment in R & D.

A large number of firms are two-way traders i.e., they export final goods while also importing intermediate inputs. An Indian manufacturing firm that exports its products is five times more likely than not to also be an importer of intermediate inputs. If firms import intermediate inputs from abroad to improve productivity and reduce marginal costs of production, when imports are not accounted for, differences in measured productivity could possibly be reflecting these differences in the use of imported intermediate inputs across firms. This export-import complementarity, where access to export markets allows firms to pay the fixed costs of importing intermediate inputs and thus improve productivity has largely been ignored in the export-productivity literature. The export-technology complementarity has been emphasized in theoretical models such as Melitz and Costantini (2007) where access to larger markets allows firms to pay the fixed cost of R & D. I examine the relative contributions of these two channels to productivity improvements of export starters.

I use CMIE Prowess, a panel data set of manufacturing firms from India. I first recover the parameters of the production function by explicitly including imported intermediate inputs and investment in R & D within the production function of the firm while also taking into account heterogeneity in firm prices. I use proxy methods as suggested by Ackerberg et al. (2006) to

> 3Foster et al. (2008) use data on physical quantities of a few homogeneous industries in the United States and find a negative correlation between price and efficiency. More productive firms charge lower prices and there is wider variation across firms in physical productivity as compared to revenue productivity.

> 4Smeets and Warzynski (2013) estimate value added production functions using firm price deflators and find that these yield higher trade premia in Danish firms as compared to revenue based measures.

> 5While most empirical work ignores price variation, there are a few exceptions. They control for unobserved prices by modeling demand under the assumptions of single product monopolistically competitive firms. Aside from the fact that they usually assume that firms produce only a single product, monopolistic competition implies a optimal price where prices are a constant markup over marginal costs where the markup ratio is determined by the elasticity of demand in the industry and is assumed to be the same for all firms in the industry. I observe in the data that a large proportion of the firms are multiproduct firms. The advantage of directly observing product level revenue and price data is that I can directly control for price heterogeneity without making these assumptions.

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