International Trade and Macroeconomic Dynamics with Heterogeneous Firms*

A haircut costs three times as much in Zurich as in Lisbon, even after you convert currencies. That's not a rounding error; it's a persistent, systematic fact about the world. Standard economic models said it shouldn't last. The argument went that trade would equalize prices over time. However, the gap between Zurich and Lisbon doesn't close. It stays. For decades, international macroeconomics lacked a convincing explanation for why. That's the problem Fabio Ghironi and Marc Melitz set out to solve. The standard models they inherited had a structural blind spot. They treated the pattern of trade as given—determining which goods get traded and which don't—and focused on long-run comparisons rather than the short-to-medium-run dynamics that actually show up in data. The textbook version of the Harrod-Balassa-Samuelson effect, the observation that richer, more productive countries tend to have higher price levels, required you to assume from the start that some goods are traded while others simply aren't. In that setup, only sector-specific productivity shocks move the real exchange rate, which is the ratio of price levels across countries. A general productivity boost would do nothing. That's a tough prediction to defend when you look at the data. Micro evidence made the problem worse. Only twenty-one percent of U.S. manufacturing plants export. About thirteen percent of plants switch export status in any given year. Between 1987 and 1992, thirty-eight percent of U.S. export growth came from firms entering export markets for the first time, not from existing exporters shipping more. The traded versus nontraded divide isn't fixed; it moves. And the models weren't built to track that movement. So, Ghironi and Melitz built a model that could. The architecture is a two-country, stochastic general equilibrium model with heterogeneous firms, meaning firms differ in productivity, and that difference determines everything. Each firm draws its productivity when it enters the domestic market, paying a sunk entry cost upfront. Most firms survive and serve the home market. Only the more productive ones can also afford to export because exporting requires paying both a fixed cost, which is an ongoing overhead regardless of how much you ship, and a per-unit iceberg cost, meaning a fraction of every unit shipped effectively melts away in transit, absorbed by transport and logistics. The productivity cutoff for exporting is the model's central selection mechanism. Below the cutoff, you stay home. Above it, you go global. The calibration is grounded in U.S. data. The model runs at quarterly frequency, with a firm exit rate of two-point-five percent per quarter and an elasticity of substitution across varieties set to three-point-eight. The steady-state iceberg cost is one-point-three, and in equilibrium, exporters are on average fifty-eight-point-two percent more productive than non-exporters. The share of firms that export, which is twenty-one percent, matches the micro evidence directly. These aren't free parameters chosen to make the model look good; they're anchored to observable facts about how firms actually behave. Now here's the payoff. In this setup, the traded versus nontraded distinction isn't assumed; it emerges. All goods are in principle tradable, but some end up nontraded in equilibrium because the firms producing them can't clear the productivity bar for exporting. When aggregate conditions change, such as a productivity shock or a shift in entry costs, the bar moves, and so does the composition of what gets traded. That endogeneity is what drives the model's most important result. To understand the real exchange rate dynamics, it helps to know how Ghironi and Melitz decompose the price index. The welfare-based aggregate price index equals the number of varieties raised to a power determined by the elasticity of substitution, multiplied by the average nominal price. That means variety and average prices can move in opposite directions, and a consumer price index-based real exchange rate can tell a completely different story than a welfare-based one. When a country gets a productivity boost, three channels drive the real exchange rate. First, the cost of effective labor at home appreciates, pushing up the relative price of goods produced there. Second, the export productivity cutoff shifts—more productive firms now export—changing average import prices. Third, the number of domestic varieties rises relative to foreign ones, and consumers shift spending toward those more abundant domestic goods. All three channels push in the same direction: the real exchange rate, measured using average prices, appreciates. Critically, this happens with fully flexible prices—no price stickiness and no nominal frictions. Persistent deviations from purchasing power parity emerge purely from firm entry, exit, and the changing mix of consumed varieties. The model generates a first-order autocorrelation in the real exchange rate of about zero-point-eight-nine. That's substantial persistence—roughly in line with what we observe in the data—arising not from assumed rigidities but from the slow buildup of the firm population. The impulse response analysis makes the mechanism concrete. Hit the model with a permanent one percent increase in home productivity. On impact, demand rises for all home varieties and the productivity cutoff for exporting shifts. However, entry is sluggish—firms paid a sunk cost to enter, and new entrants take time to start producing. So, the number of producing firms rises gradually, like a capital stock accumulating. In the short run, the real exchange rate actually depreciates slightly. Then, as entry builds up over time, home labor demand rises and the appreciation begins. Less than half of the long-run appreciation materializes within five years. The Harrod-Balassa-Samuelson effect is real, but it arrives slowly. A deregulation shock, which is a permanent one percent fall in entry costs, follows similar logic with one key difference. There's no short-run excess labor supply, so appreciation begins immediately and is amplified. Home consumption initially falls to finance the wave of new entrants, temporarily reducing import demand and crowding out some foreign exporters. Again, less than half of the long-run appreciation appears within five years. For transitory shocks, the persistence is striking. With a productivity process where roughly eighty-four percent of an initial shock remains after ten years, the real exchange rate is still far from steady state five years after the shock hits. That persistence emerges endogenously—the model doesn't need to assume it. Allowing international bond trading changes the quantitative dynamics without altering the qualitative story. With bond markets open, home households can borrow to front-load entry: more firms enter earlier, the home country runs a current account deficit and accumulates foreign debt, and foreign households lend to share in the productivity gains. A small quadratic bond-adjustment cost is enough to pin down a unique steady state. The path of consumption is qualitatively similar to the financial autarky case, but entry is earlier, and net foreign assets temporarily move away from zero. On the business cycle scorecard, the model captures the patterns that matter most and misses some magnitudes. The ratio of consumption volatility to output volatility in the model is about zero-point-five-nine, roughly ten percent higher than the Backus-Kehoe-Kydland benchmark. The model underpredicts output volatility and generates a real exchange rate that is less variable than in the data. However, it successfully reproduces the qualitative autocorrelation functions for output, consumption, investment in new firms, and the stock of firms. For a model built to explain price level differences and exchange rate persistence rather than volatility per se, that's a meaningful result. The trade policy results add one more layer. A symmetric worldwide reduction in iceberg trade costs or fixed export costs substantially increases the number of exporters, lowers the productivity cutoff for exporting, and raises overall variety. The welfare gains are larger for iceberg cost reductions than for equivalent cuts in fixed export costs, and much of the trade increase comes from the extensive margin, meaning more firms exporting, rather than existing exporters simply shipping more. The broader point holds across all of these exercises. Firm-level heterogeneity is not a microeconomic refinement that you add after building the macro model. It changes the macro predictions themselves. It generates persistent real exchange rate dynamics in a world of flexible prices. It produces a Harrod-Balassa-Samuelson effect without assuming a nontraded sector. It creates new channels through which productivity shocks and trade cost reductions propagate across countries. The next time you hear that a haircut costs three times as much in Zurich as in Lisbon—and that the gap persists—this is the model that explains why. This lecture was created by ennepō. Go to https://ennepo.ai to Discover, Create and Follow the latest research in your field. Read when you can. Listen when you want to.