2.4 Gravity model of international trade

Gravity Model of International Trade

The gravity model predicts how much two countries will trade with each other based on two main factors: their economic sizes and the distance between them. It's one of the most empirically successful models in all of economics, and understanding it gives you a framework for analyzing why certain trade relationships are massive (like U.S.-Canada) while others are surprisingly small.

Principles of the Gravity Trade Model

The gravity model draws directly from Newton's law of universal gravitation. Just as two objects attract each other based on their masses and the distance between them, two countries trade more when their economies are larger and less when they're farther apart.

The core assumptions are straightforward:

• Larger economies trade more with each other. The U.S. and Canada, the two largest economies in North America, are each other's biggest trading partners. More GDP means more production capacity and more consumer demand.
• Greater distance reduces trade. The U.S. trades far more with neighboring Canada than with Australia, even though both are English-speaking, high-income countries. Distance acts as a drag on trade.
• Other factors shift trade up or down. Shared language (U.S. and U.K.), shared borders (U.S. and Mexico), and trade agreements (USMCA, formerly NAFTA) all tend to boost trade beyond what size and distance alone would predict.

Determinants of Bilateral Trade Flows

Economic size is the strongest predictor. Measured by GDP (or sometimes GNP), it captures both a country's ability to produce exports and its demand for imports. The U.S.-Japan trade relationship is enormous precisely because both economies are huge.

Geographical distance serves as a proxy for several costs at once: shipping expenses, transit time, communication barriers, and general unfamiliarity. U.S.-Brazil trade, for example, is smaller than you might expect given Brazil's large economy, partly because of the distance involved.

Beyond these two core variables, several other factors matter:

• Common language and cultural ties lower transaction costs. The U.S. and Australia trade more easily because of shared language and legal traditions.
• Shared borders (contiguity) make overland transport cheap and supply chains easier to coordinate, as with U.S.-Canada trade.
• Trade agreements and economic unions reduce tariffs and regulatory barriers. EU member states trade dramatically more with each other than with comparable non-member countries.
• Historical and colonial relationships create lasting trade links through established business networks and institutional familiarity, as between the U.K. and India.

Interpretation of Gravity Model Results

The gravity model is typically estimated as a log-linear regression:

$\ln(Trade_{ij}) = \beta_0 + \beta_1 \ln(GDP_i) + \beta_2 \ln(GDP_j) + \beta_3 \ln(Distance_{ij}) + \epsilon_{ij}$

Where:

• $Trade_{ij}$ = bilateral trade flows between countries $i$ and $j$
• $GDP_i$ and $GDP_j$ = economic sizes of countries $i$ and $j$
• $Distance_{ij}$ = geographical distance between countries $i$ and $j$
• $\epsilon_{ij}$ = error term capturing everything the model doesn't measure

Because the equation is in logs, the coefficients are elasticities. Here's how to read them:

• $\beta_1$ and $\beta_2$ should be positive. A $\beta_1$ of 0.9 means a 1% increase in country $i$'s GDP is associated with roughly a 0.9% increase in bilateral trade.
• $\beta_3$ should be negative. A typical estimate is around -1.0, meaning a 1% increase in distance is associated with about a 1% decrease in trade.

The log-log form is what makes this interpretation clean. If you see the equation and remember "coefficients = elasticities," you can interpret any gravity model output.

Applications and Limitations in Trade Analysis

Common applications:

• Evaluating trade agreements. Researchers compare actual trade flows after NAFTA/USMCA to what the gravity model predicts without the agreement, isolating the agreement's effect.
• Identifying "missing trade." If two countries trade much less than the model predicts, that gap points to hidden barriers worth investigating (political tensions, regulatory mismatches, etc.).
• Assessing trade policy impacts. The model can estimate how much a new tariff or sanction would reduce trade between specific partners.

Key limitations to know:

• Omitted variable bias. The basic model leaves out factors like political stability, infrastructure quality, and exchange rate volatility. Adding control variables helps but never fully solves this.
• Endogeneity. GDP and trade influence each other. Countries that trade more tend to grow faster, which means GDP isn't purely an independent variable. This makes causal interpretation tricky.
• No product-level detail. The model treats all trade as one aggregate flow. It can't tell you whether two countries are trading oil, semiconductors, or agricultural goods, and the determinants may differ across product types.
• Distance is a rough proxy. Physical distance doesn't capture modern realities like digital trade, air freight, or the fact that shipping costs vary enormously by route and product.

Despite these limitations, the gravity model remains the workhorse of empirical trade research. It consistently explains a large share of variation in bilateral trade flows, and its predictions hold up across time periods, country pairs, and levels of development.