Multi Product Firms, Import Competition, and the Evolution of Firm-product Technical Efficiencies

We study how increased import competition affects the evolution of firm-product technical efficiencies in the small open economy of Belgium. We observe quarterly firm-product data at the 8-digit level on quantities sold and firm-level labor, capital, and intermediate inputs from 1997 to 2007, a period marked by stark declines in tariffs applied to Chinese goods. Using Diewert (1973) and Lau (1976) we show how to estimate firm-product quarterly technical efficiencies using a multi-product production (MPP) function that avoids using single-product (SP) production func- tion approximations to it. We find that a 0.01 increase in the import share leads to a 1.05% gain in technical efficiency. This elasticity translates into gains from com- petition over the sample period exceeding 1.2 billion euros, which is over 2.5% of the average annual value of manufacturing output in Belgium. Firms appear to be less technically efficient at producing goods the further they get from their ”core” good and firms respond to competition by focusing more on their core products. Instrumenting import share - while not important for the signs of the coefficients - is very important for the magnitudes as the effect of competition increases tenfold when one moves from OLS to IV. We close by testing the SP approximation to MPP and reject in eight of twelve industries.