4 Gravity Theory
4.1 Introduction
Gravity models explain bilateral trade using economic size and trade costs. In the Post-Soviet replication, bilateral trade is measured by \(flow\), economic mass by \(gdp\_o\) and \(gdp\_d\), distance by \(distw\), and institutional alignment by \(wto\_joint\), \(EU\_joint\), and \(EAEU\_joint\).
The model begins with an intuitive analogy, but modern gravity research requires fixed effects, multilateral resistance, and estimators that handle heteroskedasticity.
4.2 Newtonian intuition
The gravity analogy comes from physics: larger bodies attract more strongly, and distance weakens attraction. In trade, larger economies tend to trade more, while distance and other trade frictions reduce trade.
A basic gravity relationship can be written as:
\[ X_{ij} = G Y_i^{\beta_1} Y_j^{\beta_2} D_{ij}^{\beta_3} \]
where \(X_{ij}\) is trade from exporter \(i\) to importer \(j\), \(Y_i\) and \(Y_j\) measure economic size, and \(D_{ij}\) measures distance or trade costs.
This equation is useful for intuition, but it is not yet a complete empirical model.
4.3 Economic mass
Economic mass captures the idea that larger economies trade more. Exporter GDP, \(gdp\_o\), measures production capacity. Importer GDP, \(gdp\_d\), measures market size and absorption capacity.
In the Post-Soviet replication, both GDP variables are central in baseline OLS and PPML specifications. In fixed-effects and structural models, GDP may be absorbed by exporter, importer, exporter-year, or importer-year fixed effects.
4.4 Bilateral trade costs
Trade costs include more than distance. The replication uses:
| Variable | Trade-cost interpretation |
|---|---|
| \(distw\) | Weighted distance between exporter and importer |
| \(contig\) | Shared land border |
| \(comlang\_off\) | Common official language |
| \(wto\_joint\) | Shared WTO membership |
| \(EU\_joint\) | Shared EU membership |
| \(EAEU\_joint\) | Shared EAEU membership |
Some variables measure geography. Others measure institutional alignment. All are interpreted conditionally on the model.
4.5 Log-linear gravity
The teaching baseline is the log-linear gravity model:
\[ \begin{aligned} \log X_{ijt} &= \beta_0 + \beta_1 \log GDP_{it} + \beta_2 \log GDP_{jt} \\ &\quad + \beta_3 \log Dist_{ij} + \gamma Z_{ijt} + \varepsilon_{ijt} \end{aligned} \]
Here, \(Z_{ijt}\) includes variables such as \(comlang\_off\), \(contig\), \(wto\_joint\), \(EU\_joint\), and \(EAEU\_joint\).
OLS remains useful for teaching because coefficients are easy to interpret and the model reveals the core gravity logic. It is not sufficient on its own because log-linear models exclude zero trade flows and may be biased under heteroskedasticity.
4.6 Structural gravity
Structural gravity connects the empirical model to general equilibrium trade theory. A simplified structural form is:
\[ \begin{aligned} X_{ij} &= \frac{Y_i E_j}{Y} \left( \frac{\tau_{ij}}{\Pi_i P_j} \right)^{1-\sigma} \end{aligned} \]
where \(Y_i\) is exporter output, \(E_j\) is importer expenditure, \(\tau_{ij}\) is bilateral trade cost, and \(\Pi_i\) and \(P_j\) are outward and inward multilateral resistance terms.
The important lesson is that bilateral trade depends not only on the direct cost between \(i\) and \(j\), but also on how difficult it is for each country to trade with all other partners.
4.7 Multilateral resistance
Multilateral resistance means that trade between two countries depends on their alternatives. A country pair may trade a lot not only because they are close to each other, but because other trading options are costly.
Ignoring multilateral resistance can bias distance and policy coefficients. Modern gravity models therefore use fixed effects to absorb unobserved exporter, importer, and country-year conditions.
4.8 Why fixed effects matter
Fixed effects control for unobserved heterogeneity.
| Fixed effect | What it absorbs |
|---|---|
| Exporter fixed effects | Time-invariant exporter characteristics |
| Importer fixed effects | Time-invariant importer characteristics |
| Pair fixed effects | Time-invariant bilateral characteristics |
| Exporter-year fixed effects | Time-varying exporter conditions and outward resistance |
| Importer-year fixed effects | Time-varying importer conditions and inward resistance |
In the Post-Soviet replication, fixed effects change institutional interpretation. For example, \(wto\_joint\) is specification-sensitive, while \(EU\_joint\) remains positive across models.
4.9 Why PPML matters
PPML estimates a multiplicative gravity model in levels:
\[ \begin{aligned} E[X_{ijt} \mid Z_{ijt}] &= \exp\left( \beta_0 + \beta_1 \log Dist_{ij} + \gamma Z_{ijt} \right) \end{aligned} \]
PPML matters because it can include zero trade flows when they are present and is robust to common forms of heteroskedasticity. Even when a teaching dataset has no zero flows, PPML is useful because it estimates the model in levels rather than logged trade.
4.10 What students should take forward
Gravity intuition is simple: large economies trade more, and trade costs reduce trade. Applied gravity research is more demanding: students must choose variables carefully, understand fixed effects, handle zeros transparently, and interpret institutional coefficients across specifications.
The rest of the course turns this logic into a reproducible Python replication and then into a publication-style regional gravity paper.