10. The Gravity Model of Trade

Learning objectives

By the end of this chapter, you should be able to:

Explain the basic intuition of the gravity model of trade.
Identify why GDP and distance matter for bilateral trade flows.
Interpret the expected signs of common gravity variables.
Explain how trade costs affect bilateral trade.
Use a simple gravity-style equation to compare predicted trade across partners.
Connect gravity logic to regional trade agreements and TINA-style FTA simulations.

Why this chapter matters

Earlier chapters explained why countries trade using comparative advantage, factor endowments, and welfare analysis. The gravity model asks a different but very practical question:

Why does a country trade more with some partners than others?

The answer is usually not only comparative advantage. Trade also depends on the size of the partner economy, distance, transport costs, common borders, language, institutions, tariffs, and regional agreements.

For applied trade analysis, the gravity model is useful because it connects trade theory to observable country-pair data.

The basic idea

The gravity model is inspired by Newton’s law of gravity. In physics, the attraction between two objects increases with their mass and decreases with distance.

In trade economics, bilateral trade tends to increase with the economic size of the two countries and decrease with trade costs, especially distance.

A simple gravity-style expression is:

\[ Trade_{ij} = A \frac{GDP_i^{\alpha} GDP_j^{\beta}}{Distance_{ij}^{\gamma}} \]

where:

$Trade_{ij}$ is trade between country $i$ and country $j$,
$GDP_i$ is the economic size of country $i$,
$GDP_j$ is the economic size of country $j$,
$Distance_{ij}$ is distance between the countries,
$A$ is a scaling factor,
$\alpha$, $\beta$, and $\gamma$ are parameters.

The basic prediction is simple:

larger economies trade more,
closer economies trade more,
higher trade costs reduce trade.

Log-linear gravity equation

Empirical gravity models are often written in log form:

\[ \ln Trade_{ij} = \beta_0 + \beta_1 \ln GDP_i + \beta_2 \ln GDP_j - \beta_3 \ln Distance_{ij} + u_{ij} \]

The expected signs are:

Variable	Expected sign	Interpretation
Exporter GDP	Positive	Larger exporters can supply more goods.
Importer GDP	Positive	Larger importers demand more goods.
Distance	Negative	Greater distance raises transport and information costs.

This simple equation can be extended by adding trade-cost variables.

Trade-cost variables

Distance is only one proxy for trade costs. Many other factors affect bilateral trade.

Variable	Expected effect on trade	Reason
Common border	Positive	Transport and coordination costs are usually lower.
Common language	Positive	Information and contract costs are lower.
Historical or colonial links	Positive	Networks and institutions may already exist.
Common currency	Positive	Currency conversion and exchange-rate uncertainty are lower.
Better infrastructure	Positive	Goods move faster and more reliably.
Higher tariffs	Negative	Tariffs raise import prices.
Regional trade agreement	Usually positive for members	Preferential access lowers trade barriers.
Long border delays	Negative	Time costs reduce competitiveness, especially for perishable goods.

For agricultural trade, time and logistics are especially important. Fresh fruits, vegetables, fish, dairy products, and livestock products are more sensitive to delays than many durable manufactured goods.

Worked example: size versus distance

Suppose Oman is comparing two potential trading partners using a simplified gravity score:

\[ Gravity\ score = \frac{Partner\ GDP\ index}{Distance\ index} \]

This is not a full empirical model. It is only a teaching example.

Partner	Partner GDP index	Distance index	Gravity score
Partner A	500	1,000	0.50
Partner B	1,000	5,000	0.20

Partner B is economically larger, but it is much farther away. Partner A has the higher gravity score because distance reduces predicted trade.

Interpretation

The gravity model does not say countries only trade with nearby partners. It says that, other things equal, distance reduces trade. A very large distant economy can still be an important partner.

Gravity and regional trade agreements

Gravity models are often used to study regional trade agreements.

A simple empirical model may include an RTA dummy variable:

\[ RTA_{ij} = \begin{cases} 1 & \text{if countries } i \text{ and } j \text{ are in the same trade agreement} \\ 0 & \text{otherwise} \end{cases} \]

If the estimated coefficient on the RTA dummy is positive, members trade more with each other after controlling for GDP, distance, and other factors.

However, higher intra-bloc trade does not automatically mean the agreement is welfare-improving. As Chapter 8 explained, an RTA can create trade or divert trade.

Finding	Possible interpretation
Intra-RTA trade rises and trade with outsiders also rises	Likely trade creation or broader integration.
Intra-RTA trade rises but imports from efficient outsiders fall	Possible trade diversion.
No clear change	The agreement may be shallow, poorly implemented, or already anticipated by traders.

Gravity and trade facilitation

Gravity models are also used to study trade facilitation.

Trade facilitation means making it easier, faster, and cheaper for goods to cross borders. It includes customs procedures, port efficiency, documentation, inspection, digital systems, and transport infrastructure.

Border delays can reduce trade because they increase time costs. This is especially relevant for agricultural products that are perishable or time-sensitive.

Examples include:

fresh fruits and vegetables,
fish and seafood,
dairy products,
live animals,
chilled meat,
flowers and nursery products.

For these goods, trade costs are not only monetary. Time is also a trade cost.

Python application: simple gravity predictions

The following example uses artificial data to show how a gravity-style model works. The numbers are not real trade data. They are only for teaching.

Code

import pandas as pd
import numpy as np

partners = pd.DataFrame({
    "Partner": ["A", "B", "C", "D", "E"],
    "Partner_GDP_index": [500, 1000, 800, 300, 1500],
    "Distance_index": [1000, 5000, 2000, 800, 6000],
    "RTA": [1, 0, 1, 0, 0],
    "Common_language": [0, 0, 1, 0, 0]
})

partners["Simple_gravity_score"] = partners["Partner_GDP_index"] / partners["Distance_index"]
partners

Table 15.1

	Partner	Partner_GDP_index	Distance_index	RTA	Common_language	Simple_gravity_score
0	A	500	1000	1	0	0.500
1	B	1000	5000	0	0	0.200
2	C	800	2000	1	1	0.400
3	D	300	800	0	0	0.375
4	E	1500	6000	0	0	0.250

Now we can create a slightly richer gravity-style prediction. We use a simple log equation with assumed coefficients:

\[ \ln Trade = \beta_0 + \beta_1 \ln GDP - \beta_2 \ln Distance + \beta_3 RTA + \beta_4 Language \]

Code

beta_0 = 2.0
beta_gdp = 1.0
beta_distance = 0.8
beta_rta = 0.30
beta_language = 0.20

partners["Predicted_log_trade"] = (
    beta_0
    + beta_gdp * np.log(partners["Partner_GDP_index"])
    - beta_distance * np.log(partners["Distance_index"])
    + beta_rta * partners["RTA"]
    + beta_language * partners["Common_language"]
)

partners["Predicted_trade_index"] = np.exp(partners["Predicted_log_trade"])
partners[["Partner", "Predicted_log_trade", "Predicted_trade_index"]]

	Partner	Predicted_log_trade	Predicted_trade_index
0	A	2.988404	19.853968
1	B	2.094001	8.117325
2	C	3.103890	22.284464
3	D	2.356093	10.549654
4	E	2.353609	10.523476

Code

import matplotlib.pyplot as plt

plot_data = partners.sort_values("Predicted_trade_index", ascending=True)

ax = plot_data.plot(
    kind="barh",
    x="Partner",
    y="Predicted_trade_index",
    legend=False
)
ax.set_xlabel("Predicted trade index")
ax.set_ylabel("Partner")
ax.set_title("Simple gravity prediction")
plt.tight_layout()
plt.show()

Figure 15.1: Predicted trade index from a simple gravity-style model using artificial data.

Interpreting dummy variables

In a log-linear gravity model, dummy-variable coefficients are often interpreted as approximate percentage effects.

For example, if the RTA coefficient is:

\[ \beta_{RTA} = 0.30 \]

then the exact percentage effect is:

\[ 100 \times \left(e^{0.30} - 1\right) \approx 35\% \]

This means that, other things equal, members of the same RTA are predicted to trade about 35 percent more with each other.

Code

rta_coefficient = 0.30
rta_percent_effect = 100 * (np.exp(rta_coefficient) - 1)
print(f"RTA effect = {rta_percent_effect:.1f}%")

RTA effect = 35.0%

Be careful

A positive RTA coefficient does not automatically prove that the agreement caused all extra trade. Good empirical work must think about timing, country-pair characteristics, omitted variables, and whether the agreement was created between countries that already traded heavily.

Application to Oman

The gravity model is useful for thinking about Oman’s trade partners.

Oman may trade more with countries that are:

geographically close,
economically large,
connected through ports and logistics networks,
part of regional supply chains,
linked by trade agreements,
major importers of energy or petrochemical products,
important suppliers of food, machinery, vehicles, or intermediate goods.

For Oman, gravity logic helps explain why regional partners matter, but it also leaves room for distant large economies such as China, India, the European Union, and the United States.

Gravity model and the final project

In student FTA projects, gravity logic helps interpret simulation results.

When you analyze a possible FTA, ask:

Are the countries economically large enough to generate meaningful trade?
Are they close enough for transport costs to be manageable?
Are they already trading with each other?
Are there major tariffs or non-tariff barriers that the FTA can reduce?
Are the countries complementary in production and demand?
Is the simulated trade increase likely to be trade creation or trade diversion?

These questions connect the gravity model to Chapters 8, 12, and 13.

Key takeaway

The gravity model predicts that bilateral trade is larger when countries are economically large and smaller when trade costs are high. GDP, distance, language, borders, infrastructure, tariffs, and RTAs help explain trade patterns.

The model is simple, but it is powerful because it connects trade theory to observable data. It also gives students a practical way to interpret country-pair trade and FTA simulation results.

Review questions

What is the basic intuition of the gravity model of trade?
Why does GDP increase predicted trade?
Why does distance reduce predicted trade?
Give three examples of trade-cost variables.
Why can a nearby smaller economy trade more than a distant larger economy?
How can a gravity model be used to study RTAs?
Why does a positive RTA coefficient not automatically prove welfare gains?
Why are agricultural products sensitive to trade facilitation?
How does the gravity model help interpret TINA simulation results?
What are two gravity-based reasons Oman may trade strongly with nearby partners?

Practice problem

Suppose Oman is comparing two potential trade partners.

Partner	GDP index	Distance index
Partner X	900	3,000
Partner Y	400	800

Use the simple gravity score:

\[ Gravity\ score = \frac{GDP\ index}{Distance\ index} \]

Calculate the gravity score for each partner.
Which partner has the higher predicted trade potential according to this simple score?
Explain why the larger economy does not necessarily have the higher score.
Name two other variables that a fuller gravity model should include.
Explain how an FTA could change predicted trade between Oman and one of these partners.

--- title: "10. The Gravity Model of Trade" --- ## Learning objectives By the end of this chapter, you should be able to: 1. Explain the basic intuition of the gravity model of trade. 2. Identify why GDP and distance matter for bilateral trade flows. 3. Interpret the expected signs of common gravity variables. 4. Explain how trade costs affect bilateral trade. 5. Use a simple gravity-style equation to compare predicted trade across partners. 6. Connect gravity logic to regional trade agreements and TINA-style FTA simulations. ## Why this chapter matters Earlier chapters explained why countries trade using comparative advantage, factor endowments, and welfare analysis. The gravity model asks a different but very practical question: **Why does a country trade more with some partners than others?** The answer is usually not only comparative advantage. Trade also depends on the size of the partner economy, distance, transport costs, common borders, language, institutions, tariffs, and regional agreements. For applied trade analysis, the gravity model is useful because it connects trade theory to observable country-pair data. ## The basic idea The gravity model is inspired by Newton’s law of gravity. In physics, the attraction between two objects increases with their mass and decreases with distance. In trade economics, bilateral trade tends to increase with the economic size of the two countries and decrease with trade costs, especially distance. A simple gravity-style expression is: $$ Trade_{ij} = A \frac{GDP_i^{\alpha} GDP_j^{\beta}}{Distance_{ij}^{\gamma}} $$ where: - $Trade_{ij}$ is trade between country $i$ and country $j$, - $GDP_i$ is the economic size of country $i$, - $GDP_j$ is the economic size of country $j$, - $Distance_{ij}$ is distance between the countries, - $A$ is a scaling factor, - $\alpha$, $\beta$, and $\gamma$ are parameters. The basic prediction is simple: - larger economies trade more, - closer economies trade more, - higher trade costs reduce trade. ## Log-linear gravity equation Empirical gravity models are often written in log form: $$ \ln Trade_{ij} = \beta_0 + \beta_1 \ln GDP_i + \beta_2 \ln GDP_j - \beta_3 \ln Distance_{ij} + u_{ij} $$ The expected signs are: | Variable | Expected sign | Interpretation | |---|---:|---| | Exporter GDP | Positive | Larger exporters can supply more goods. | | Importer GDP | Positive | Larger importers demand more goods. | | Distance | Negative | Greater distance raises transport and information costs. | This simple equation can be extended by adding trade-cost variables. ## Trade-cost variables Distance is only one proxy for trade costs. Many other factors affect bilateral trade. | Variable | Expected effect on trade | Reason | |---|---:|---| | Common border | Positive | Transport and coordination costs are usually lower. | | Common language | Positive | Information and contract costs are lower. | | Historical or colonial links | Positive | Networks and institutions may already exist. | | Common currency | Positive | Currency conversion and exchange-rate uncertainty are lower. | | Better infrastructure | Positive | Goods move faster and more reliably. | | Higher tariffs | Negative | Tariffs raise import prices. | | Regional trade agreement | Usually positive for members | Preferential access lowers trade barriers. | | Long border delays | Negative | Time costs reduce competitiveness, especially for perishable goods. | For agricultural trade, time and logistics are especially important. Fresh fruits, vegetables, fish, dairy products, and livestock products are more sensitive to delays than many durable manufactured goods. ## Worked example: size versus distance Suppose Oman is comparing two potential trading partners using a simplified gravity score: $$ Gravity\ score = \frac{Partner\ GDP\ index}{Distance\ index} $$ This is not a full empirical model. It is only a teaching example. | Partner | Partner GDP index | Distance index | Gravity score | |---|---:|---:|---:| | Partner A | 500 | 1,000 | 0.50 | | Partner B | 1,000 | 5,000 | 0.20 | Partner B is economically larger, but it is much farther away. Partner A has the higher gravity score because distance reduces predicted trade. :::: {.callout-note} ## Interpretation The gravity model does not say countries only trade with nearby partners. It says that, other things equal, distance reduces trade. A very large distant economy can still be an important partner. :::: ## Gravity and regional trade agreements Gravity models are often used to study regional trade agreements. A simple empirical model may include an RTA dummy variable: $$ RTA_{ij} = \begin{cases} 1 & \text{if countries } i \text{ and } j \text{ are in the same trade agreement} \\ 0 & \text{otherwise} \end{cases} $$ If the estimated coefficient on the RTA dummy is positive, members trade more with each other after controlling for GDP, distance, and other factors. However, higher intra-bloc trade does not automatically mean the agreement is welfare-improving. As Chapter 8 explained, an RTA can create trade or divert trade. | Finding | Possible interpretation | |---|---| | Intra-RTA trade rises and trade with outsiders also rises | Likely trade creation or broader integration. | | Intra-RTA trade rises but imports from efficient outsiders fall | Possible trade diversion. | | No clear change | The agreement may be shallow, poorly implemented, or already anticipated by traders. | ## Gravity and trade facilitation Gravity models are also used to study trade facilitation. Trade facilitation means making it easier, faster, and cheaper for goods to cross borders. It includes customs procedures, port efficiency, documentation, inspection, digital systems, and transport infrastructure. Border delays can reduce trade because they increase time costs. This is especially relevant for agricultural products that are perishable or time-sensitive. Examples include: - fresh fruits and vegetables, - fish and seafood, - dairy products, - live animals, - chilled meat, - flowers and nursery products. For these goods, trade costs are not only monetary. Time is also a trade cost. ## Python application: simple gravity predictions The following example uses artificial data to show how a gravity-style model works. The numbers are not real trade data. They are only for teaching. ```{python} #| label: tbl-gravity-example #| echo: true import pandas as pd import numpy as np partners = pd.DataFrame({ "Partner": ["A", "B", "C", "D", "E"], "Partner_GDP_index": [500, 1000, 800, 300, 1500], "Distance_index": [1000, 5000, 2000, 800, 6000], "RTA": [1, 0, 1, 0, 0], "Common_language": [0, 0, 1, 0, 0] }) partners["Simple_gravity_score"] = partners["Partner_GDP_index"] / partners["Distance_index"] partners ``` Now we can create a slightly richer gravity-style prediction. We use a simple log equation with assumed coefficients: $$ \ln Trade = \beta_0 + \beta_1 \ln GDP - \beta_2 \ln Distance + \beta_3 RTA + \beta_4 Language $$ ```{python} #| label: calc-gravity-predictions #| echo: true beta_0 = 2.0 beta_gdp = 1.0 beta_distance = 0.8 beta_rta = 0.30 beta_language = 0.20 partners["Predicted_log_trade"] = ( beta_0 + beta_gdp * np.log(partners["Partner_GDP_index"]) - beta_distance * np.log(partners["Distance_index"]) + beta_rta * partners["RTA"] + beta_language * partners["Common_language"] ) partners["Predicted_trade_index"] = np.exp(partners["Predicted_log_trade"]) partners[["Partner", "Predicted_log_trade", "Predicted_trade_index"]] ``` ```{python} #| label: fig-gravity-predictions #| fig-cap: "Predicted trade index from a simple gravity-style model using artificial data." #| fig-width: 7 #| fig-height: 4 #| fig-format: svg #| echo: true import matplotlib.pyplot as plt plot_data = partners.sort_values("Predicted_trade_index", ascending=True) ax = plot_data.plot( kind="barh", x="Partner", y="Predicted_trade_index", legend=False ) ax.set_xlabel("Predicted trade index") ax.set_ylabel("Partner") ax.set_title("Simple gravity prediction") plt.tight_layout() plt.show() ``` ## Interpreting dummy variables In a log-linear gravity model, dummy-variable coefficients are often interpreted as approximate percentage effects. For example, if the RTA coefficient is: $$ \beta_{RTA} = 0.30 $$ then the exact percentage effect is: $$ 100 \times \left(e^{0.30} - 1\right) \approx 35\% $$ This means that, other things equal, members of the same RTA are predicted to trade about 35 percent more with each other. ```{python} #| label: calc-rta-effect #| echo: true rta_coefficient = 0.30 rta_percent_effect = 100 * (np.exp(rta_coefficient) - 1) print(f"RTA effect = {rta_percent_effect:.1f}%") ``` :::: {.callout-warning} ## Be careful A positive RTA coefficient does not automatically prove that the agreement caused all extra trade. Good empirical work must think about timing, country-pair characteristics, omitted variables, and whether the agreement was created between countries that already traded heavily. :::: ## Application to Oman The gravity model is useful for thinking about Oman’s trade partners. Oman may trade more with countries that are: - geographically close, - economically large, - connected through ports and logistics networks, - part of regional supply chains, - linked by trade agreements, - major importers of energy or petrochemical products, - important suppliers of food, machinery, vehicles, or intermediate goods. For Oman, gravity logic helps explain why regional partners matter, but it also leaves room for distant large economies such as China, India, the European Union, and the United States. ## Gravity model and the final project In student FTA projects, gravity logic helps interpret simulation results. When you analyze a possible FTA, ask: 1. Are the countries economically large enough to generate meaningful trade? 2. Are they close enough for transport costs to be manageable? 3. Are they already trading with each other? 4. Are there major tariffs or non-tariff barriers that the FTA can reduce? 5. Are the countries complementary in production and demand? 6. Is the simulated trade increase likely to be trade creation or trade diversion? These questions connect the gravity model to Chapters 8, 12, and 13. ## Key takeaway The gravity model predicts that bilateral trade is larger when countries are economically large and smaller when trade costs are high. GDP, distance, language, borders, infrastructure, tariffs, and RTAs help explain trade patterns. The model is simple, but it is powerful because it connects trade theory to observable data. It also gives students a practical way to interpret country-pair trade and FTA simulation results. ## Review questions 1. What is the basic intuition of the gravity model of trade? 2. Why does GDP increase predicted trade? 3. Why does distance reduce predicted trade? 4. Give three examples of trade-cost variables. 5. Why can a nearby smaller economy trade more than a distant larger economy? 6. How can a gravity model be used to study RTAs? 7. Why does a positive RTA coefficient not automatically prove welfare gains? 8. Why are agricultural products sensitive to trade facilitation? 9. How does the gravity model help interpret TINA simulation results? 10. What are two gravity-based reasons Oman may trade strongly with nearby partners? ## Practice problem Suppose Oman is comparing two potential trade partners. | Partner | GDP index | Distance index | |---|---:|---:| | Partner X | 900 | 3,000 | | Partner Y | 400 | 800 | Use the simple gravity score: $$ Gravity\ score = \frac{GDP\ index}{Distance\ index} $$ 1. Calculate the gravity score for each partner. 2. Which partner has the higher predicted trade potential according to this simple score? 3. Explain why the larger economy does not necessarily have the higher score. 4. Name two other variables that a fuller gravity model should include. 5. Explain how an FTA could change predicted trade between Oman and one of these partners.