Gravity with granularity

Holger Breinlich, Harald Fadinger, Volker Nocke, Nicolas Schutz 21 November 2020



International trade is of vital importance for modern economies, and governments around the world try to shape their countries' export and import patterns through numerous interventions. Economists have long thought to shape this political debate by analysing the effects of policy interventions such as free trade agreements or currency unions on trade flows. By far the most frequently used tool for doing so is the so-called gravity equation, which was first proposed by Dutch economist Jan Tinbergen over 50 years ago (Tinbergen 1962). In their most basic form, gravity equations predict that trade flows between countries are a function of the economic mass of the two trading partners (as measured by, for example, the trading partners’ GDPs) and bilateral frictions such as geographic distance or tariffs. Even in this simple form, gravity equations have substantial explanatory power, often explaining in excess of 70-80% of the variation in the trade flows between countries. This excellent predictive power allows economists to use gravity equations to evaluate the effects of policy interventions such as free trade agreements by comparing actual trade flows to those predicted by the gravity equation and attributing the difference to the policy intervention in question.

While gravity equations have proven to be an enormously useful tool for policy analysts, their theoretical foundations to date are at odds with an important fact about international trade: much of world trade is dominated by a small number of large firms. The classic example is the market for wide-bodied passenger aircraft, which comprises just two firms (Airbus and Boeing); but the markets of many other tradable goods such as cars, mobile phones, or television sets are also dominated by a handful of large producers. Given their size, it seems likely that such ‘granular’ firms enjoy substantial market power and have incentives to internalise the effects of their actions on aggregate market outcomes. Intuitively, how many aircraft Airbus or Boeing produce and sell in a given market will influence the price for such aircraft there, and Airbus and Boeing are likely aware of this impact. That is, in the language of economists, Airbus and Boeing will have a tendency to behave oligopolistically.

In recent research (Breinlich et al. 2020), we show that such oligopolistic behaviour complicates the estimation of gravity equations in important ways. In particular, firms that enjoy market power will use this power to charge higher prices for their products in a way which depends on the specific market in question. To continue with the previous example, if Airbus has a particularly high market share in a given South American economy, it will charge a high price for its products there. By contrast, in the US, where competition from Boeing will mean it has less market power, it will tend to charge a lower price. More generally, the higher its share in a given market, the higher the price it will charge.

This systematic connection between prices and market shares becomes problematic for the estimation of gravity equations because many of the policy interventions whose effects economists want to estimate also influence market shares and hence prices and the value of trade flows. For example, if a free trade agreement between countries A and B makes it easier for firms based in A to export to B, this means that the firms from A now enjoy higher market shares in B, inducing them to raise prices. But such higher prices will partially lower trade flows again, preventing trade flows from rising by as much as they would have without the price reaction. To the economist studying these data, it then looks as if the trade agreement didn’t reduce trade costs by as much as it really did, since firms from A partially use their newly found advantage to increase prices, rather than to maximise sales. More generally, gravity equations will yield incorrect estimates of any policy intervention or other factor influencing international trade and the market shares of exporting firms, if these exporting firms enjoy some degree of market power.

In our research, we propose a method to correct the resulting inaccuracies in gravity equation estimation. Intuitively, it is necessary to adjust trade flows for market power effects by subtracting a correction term that depends on the market share a firm or country has in the market in question. Once this correction has been carried out, researchers can again estimate gravity equations as usual.

We test the relevance of our proposed correction method by estimating standard gravity equations with and without correcting trade flows for market power and comparing coefficient estimates to gain a sense of the magnitude of the bias introduced by market power. We do this for a dataset of French and Chinese firm-level exports, as well as for product-level imports by the EU from around 50 EU and non-EU countries. Our results show that not correcting for market power can lead to substantial inaccuracies when estimating gravity equations. For example, when we estimate gravity equations using our sample of EU importing countries without correcting for market power, we find that membership in the euro area increases bilateral trade flows by around 48%. This euro trade bonus increases to 58% when we do correct for market power – a difference of over 20%. While in this case, our correction does not change the qualitative finding that the euro is good for trade, a bias of 20% is clearly of a relevant magnitude for policymakers trying to establish the effects of, say, a proposed free trade agreement. Given that our proposed correction method can be easily implemented with readily available data in many contexts, we hope that our research will help to further improve the accuracy of gravity-equation-based policy forecasts.


Breinlich, H, H Fadinger, V Nocke and N Schutz (2020), “Gravity with Granularity”, CEPR Discussion Paper 15374.

Tinbergen, J (1962), Shaping the World Economy: Suggestions for an International Economic Policy, Twentieth Century Fund, New-York.



Topics:  Industrial organisation International trade

Tags:  : gravity, granularity, Currency unions, free trade agreements, monopoly, market power

Professor of Economics, University of Surrey and CEPR Research Fellow

Professor of Economics, University of Mannheim and CEPR

Professor of Economics, University of Mannheim and CEPR Research Fellow

Professor of Economics, University of Mannheim and CEPR Research Fellow


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