10  Bonus Vetus

10.1 Purpose

This chapter explains Bonus Vetus gravity models and prepares students to implement BVU and BVW for the Post-Soviet replication. Bonus Vetus methods approximate multilateral resistance adjustments when a researcher wants a trade-cost interpretation without estimating a fully structural high-dimensional model.

10.2 Method overview

Method	Meaning	Weighting
BVU	Bonus Vetus Unweighted	Country means enter symmetrically
BVW	Bonus Vetus Weighted	Country means are weighted by trade or economic shares

The Post-Soviet case uses the same trade and institutional variables as earlier chapters: flow, gdp_o, gdp_d, distw, comlang_off, contig, wto_joint, EU_joint, EAEU_joint, and year.

10.3 Theory

The Bonus Vetus idea starts from the fact that bilateral trade costs affect trade not only directly but also through multilateral resistance. A naive log-linear model estimates the direct association between bilateral variables and trade, but it does not fully account for the way each country relates to all other partners.

Bonus Vetus transformations approximate the general-equilibrium resistance terms by transforming bilateral trade-cost variables before estimation. This is useful when the goal is to estimate trade-cost effects while retaining an interpretable OLS-style model.

10.4 Derivation

Start with a log-linear trade-cost component:

\[ \begin{aligned} \log \tau_{ij} &= \theta_1 \log(distw_{ij}) + \theta_2 comlang\_off_{ij} + \theta_3 contig_{ij} \\ &\quad + \theta_4 wto\_joint_{ijt} + \theta_5 EU\_joint_{ijt} + \theta_6 EAEU\_joint_{ijt} \end{aligned} \]

For a bilateral variable \(x_{ij}\), the unweighted Bonus Vetus transformation can be written as:

\[ \begin{aligned} x^{BVU}_{ij} &= x_{ij} - \bar{x}_{i \cdot} - \bar{x}_{\cdot j} + \bar{x} \end{aligned} \]

where \(\bar{x}_{i \cdot}\) is the exporter mean, \(\bar{x}_{\cdot j}\) is the importer mean, and \(\bar{x}\) is the overall mean.

The weighted version replaces simple means with share-weighted means:

\[ \begin{aligned} x^{BVW}_{ij} &= x_{ij} - \sum_k s_k x_{ik} - \sum_m s_m x_{mj} \\ &\quad + \sum_k \sum_m s_k s_m x_{km} \end{aligned} \]

where the weights \(s_k\) and \(s_m\) can be based on economic size or trade shares, depending on the replication design.

10.5 Why Bonus Vetus exists

Bonus Vetus exists because researchers often need a practical bridge between simple OLS gravity and fully structural gravity. It provides a way to approximate multilateral resistance adjustments while keeping a transparent regression workflow.

10.6 Advantages

• More structural than naive pooled OLS.
• Easier to understand than fully saturated exporter-year and importer-year fixed effects.
• Can be implemented with transformed variables.
• Useful for comparing R gravity package workflows with Python code.

10.7 Limitations

• It is an approximation, not a substitute for all structural gravity designs.
• Weighted versions require defensible weights.
• Implementation details must match the original replication workflow.
• It does not automatically solve zero-flow or heteroskedasticity problems.

10.8 BVU equation

A BVU model for the Post-Soviet case can be written as:

\[ \begin{aligned} \log(flow_{ijt}) &= \beta_0 + \beta_1 \log(gdp\_o_{it}) + \beta_2 \log(gdp\_d_{jt}) \\ &\quad + \lambda_1 \log(distw)^{BVU}_{ij} + \lambda_2 comlang\_off^{BVU}_{ij} + \lambda_3 contig^{BVU}_{ij} \\ &\quad + \lambda_4 wto\_joint^{BVU}_{ijt} + \lambda_5 EU\_joint^{BVU}_{ijt} + \lambda_6 EAEU\_joint^{BVU}_{ijt} \\ &\quad + \delta_t + \varepsilon_{ijt} \end{aligned} \]

10.9 BVW equation

The BVW model uses weighted transformed variables:

\[ \begin{aligned} \log(flow_{ijt}) &= \beta_0 + \beta_1 \log(gdp\_o_{it}) + \beta_2 \log(gdp\_d_{jt}) \\ &\quad + \lambda_1 \log(distw)^{BVW}_{ij} + \lambda_2 comlang\_off^{BVW}_{ij} + \lambda_3 contig^{BVW}_{ij} \\ &\quad + \lambda_4 wto\_joint^{BVW}_{ijt} + \lambda_5 EU\_joint^{BVW}_{ijt} + \lambda_6 EAEU\_joint^{BVW}_{ijt} \\ &\quad + \delta_t + \varepsilon_{ijt} \end{aligned} \]

10.10 R implementation

If the original replication uses the R gravity package, the workflow may call Bonus Vetus routines directly. Students should match the function arguments to the manuscript’s specification.

library(dplyr)
library(gravity)

df <- read.csv("data/gravity_clean.csv")

bv_df <- df %>%
  filter(flow > 0) %>%
  mutate(
    log_flow = log(flow),
    log_gdp_o = log(gdp_o),
    log_gdp_d = log(gdp_d),
    log_distw = log(distw)
  )

# Package-style workflow, if used in the original replication:
# bvu_model <- bvu(
#   dependent_variable = "flow",
#   distance = "distw",
#   additional_regressors = c("comlang_off", "contig", "wto_joint", "EU_joint", "EAEU_joint"),
#   code_origin = "iso3_o",
#   code_destination = "iso3_d",
#   data = bv_df
# )

When direct package calls are not flexible enough, compute transformed variables explicitly and estimate with feols.

double_demean <- function(x, exporter, importer) {
  x - ave(x, exporter) - ave(x, importer) + mean(x, na.rm = TRUE)
}

bv_df$log_distw_bvu <- double_demean(bv_df$log_distw, bv_df$iso3_o, bv_df$iso3_d)
bv_df$contig_bvu <- double_demean(bv_df$contig, bv_df$iso3_o, bv_df$iso3_d)

# Estimate after constructing all required BVU variables.

10.11 Python implementation: BVU

The Python implementation makes the transformation explicit.

import numpy as np
import pandas as pd
import statsmodels.formula.api as smf

df = pd.read_csv("data/gravity_clean.csv")

bv_df = df.loc[df["flow"] > 0].copy()
bv_df["log_flow"] = np.log(bv_df["flow"])
bv_df["log_gdp_o"] = np.log(bv_df["gdp_o"])
bv_df["log_gdp_d"] = np.log(bv_df["gdp_d"])
bv_df["log_distw"] = np.log(bv_df["distw"])

def bvu_transform(data, variable, exporter="iso3_o", importer="iso3_d"):
    overall = data[variable].mean()
    exporter_mean = data.groupby(exporter)[variable].transform("mean")
    importer_mean = data.groupby(importer)[variable].transform("mean")
    return data[variable] - exporter_mean - importer_mean + overall

for variable in [
    "log_distw",
    "comlang_off",
    "contig",
    "wto_joint",
    "EU_joint",
    "EAEU_joint",
]:
    bv_df[f"{variable}_bvu"] = bvu_transform(bv_df, variable)

bvu_formula = (
    "log_flow ~ log_gdp_o + log_gdp_d + "
    "log_distw_bvu + comlang_off_bvu + contig_bvu + "
    "wto_joint_bvu + EU_joint_bvu + EAEU_joint_bvu + C(year)"
)

bvu_py = smf.ols(bvu_formula, data=bv_df).fit(cov_type="HC1")

10.12 Python implementation: BVW

BVW requires weights. A transparent teaching choice is to use destination GDP shares within year, but students must match the weights used in the Post-Soviet replication if the manuscript specifies them.

def weighted_mean_by_group(data, variable, group, weight):
    weighted_sum = (data[variable] * data[weight]).groupby(data[group]).transform("sum")
    weight_sum = data[weight].groupby(data[group]).transform("sum")
    return weighted_sum / weight_sum

def bvw_transform(
    data,
    variable,
    exporter="iso3_o",
    importer="iso3_d",
    weight="gdp_d",
):
    exporter_wmean = weighted_mean_by_group(data, variable, exporter, weight)
    importer_wmean = weighted_mean_by_group(data, variable, importer, weight)
    overall_wmean = (data[variable] * data[weight]).sum() / data[weight].sum()
    return data[variable] - exporter_wmean - importer_wmean + overall_wmean

for variable in [
    "log_distw",
    "comlang_off",
    "contig",
    "wto_joint",
    "EU_joint",
    "EAEU_joint",
]:
    bv_df[f"{variable}_bvw"] = bvw_transform(bv_df, variable, weight="gdp_d")

bvw_formula = (
    "log_flow ~ log_gdp_o + log_gdp_d + "
    "log_distw_bvw + comlang_off_bvw + contig_bvw + "
    "wto_joint_bvw + EU_joint_bvw + EAEU_joint_bvw + C(year)"
)

bvw_py = smf.ols(bvw_formula, data=bv_df).fit(cov_type="HC1")

10.13 Interpretation

BVU and BVW coefficients should be interpreted as associations between transformed trade-cost variables and log trade. They are not identical to pooled OLS coefficients because the variables have been adjusted to approximate multilateral resistance.

For institutional variables:

\[ 100 \times \left(\exp(\lambda) - 1\right) \]

converts a transformed dummy coefficient into an approximate percent difference. The interpretation must state that the coefficient is based on the Bonus Vetus transformation.

10.14 Replication checks

Students should record:

• exact weights used in BVW;
• whether weights vary by year;
• whether transformations are computed by year or over the full panel;
• whether R and Python transformations produce the same columns;
• whether the estimation sample matches the OLS sample.

10.15 Research output

Prepare BVU and BVW table shells, including a note that no results should be interpreted until the transformations match the Post-Soviet replication design.