Research

Do product and customer margins interact in shaping firm size? Using the universe of firm-to-firm transactions in Chile, we show that they are interconnected. The largest growth episodes combine new buyers with new products, and within suppliers a 10\% increase in buyers is associated with a 5.6\% increase in product scope, much of it among products sold to incumbent buyers. We develop a model of multiproduct firms embedded in a production network in which the two margins are jointly determined through two channels: amortization, as a firm-level product-adoption cost is spread over more buyer relationships, and matching, as a broader buyer base gives each product more opportunities to find a profitable buyer. The model allows us to separate the two channels and assess their relative importance. Using only firm-level moments, amortization can explain up to about 40\% of the co-movement, while adding within-link moments shifts most of the explanation toward matching. The model reproduces the buyer--product relationship and implies spillovers across margins. Frictions affecting buyer acquisition also shape firms' product scope, and those affecting product adoption also shape their buyer networks. For the firm-size distribution, the two margins are not symmetric: the buyer margin alone reproduces about 88\% of the dispersion in firm sales, compared with 66\% for the product margin, with product scope amplifying differences generated through the buyer network.

We investigate the role of trade credit (TC) and input-output (I-O) linkages in allocating liquidity and propagating shocks across a network of firms. We use two natural experiments and supervisory, transaction-level data on the universe of firms in Chile to identify demand and financial shocks to firms, and estimate how these shocks propagate differently through the supply chain depending on the use of trade credit. Guided by a general model of trade credit, we decompose these estimated effects into two channels: a trade credit channel and an input-output channel. Our preliminary results indicate that while trade credit does not propagate demand shocks, it propagates financial shocks upstream, suggesting that trade credit serves to reallocate liquidity in the input-output network. However, because trade contracts are sticky, firms respond to financial shocks not by borrowing more or less from a given supplier, but rather by substituting inputs across suppliers who offer different trade credit terms. These results suggest that, due to frictions to adjusting trade credit contracts, financial shocks temporarily alter the structure of the input-output network.