Divorce usually impacts both sides - but does that hold true for Brexit?

This gap in the conversation provides a great opportunity to try out a causal inference method from the CausalPy package, specifically, the synthetic control method (with the caveat that its implementation is still a wip, so the outputs should be taken with a grain of salt). Generally, this technique constructs a weighted combination of control units to mimic the characteristics of a treated unit, enabling us to estimate the causal effect of an intervention without a traditional control group.

For the analysis, I looked at the combined GDP of 20 eurozone countries from 2007 to 2023 as the outcome of interest. To construct the synthetic control group for counterfactual comparison, I used GDP data from selected OECD countries (non-EU, non-eurozone, non-UK) over the same period.

To my surprise, the results for the eurozone countries contrast pretty starkly with those for the UK (see the charts above). There doesn’t seem to be strong evidence of a significant negative impact from Brexit on eurozone GDP. Of course, this is just one facet of Brexit’s potential effects. There may be many other consequences - beyond what GDP metrics reveal - that apply to the eurozone as well. Still, it’s interesting to observe such a stark difference using the same type of data and methodology.

Maybe it reflects what we often see in personal relationships: divorce usually affects both sides, but the costs are only rarely distributed equally and/or in the same ways 🤔

P.S. If interested, the data from the OECD Data Explorer and the code for replicating this analysis are provided below.

# reticulate library for running Python in .Rmd file
library(reticulate)
# libraries for data manipulation and visualization
library(tidyverse)
library(DT)
 
# uploading the data from the OECD Data Explorer at https://data-explorer.oecd.org/
df <- readr::read_csv("oecd_data.csv")
 
# table view of two rows of the data
DT::datatable(
  df,
  class = 'cell-border stripe', 
  filter = 'top',
  extensions = 'Buttons',
  fillContainer = FALSE,
  rownames= FALSE,
  options = list(
    pageLength = 2, 
    autoWidth = TRUE,
    dom = 'Bfrtip',
    buttons = c('copy', 'csv', 'excel'),
    buttons = c('copy'), 
    scrollX = TRUE, 
    selection="multiple"
  )
)
 

Showing 20 of 3,968 rows and all 48 columns. View the full interactive table in the original post.

STRUCTURE	STRUCTURE_ID	STRUCTURE_NAME	ACTION	FREQ	Frequency of observation	ADJUSTMENT	Adjustment	REF_AREA	Reference area	SECTOR	Institutional sector	COUNTERPART_SECTOR	Counterpart institutional sector	TRANSACTION	Transaction	INSTR_ASSET	Financial instruments and non-financial assets	ACTIVITY	Economic activity	EXPENDITURE	Expenditure	UNIT_MEASURE	Unit of measure	PRICE_BASE	Price base	TRANSFORMATION	Transformation	TABLE_IDENTIFIER	Table identifier	TIME_PERIOD	Time period	OBS_VALUE	Observation value	REF_YEAR_PRICE	Price reference year	BASE_PER	Base period	CONF_STATUS	Confidentiality status	DECIMALS	Decimals	OBS_STATUS	Observation status	UNIT_MULT	Unit multiplier	CURRENCY	Currency
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	TUR	Türkiye	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2020-Q2		2128318.1						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2013-Q2		13306591.6						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2013-Q3		13451259.5						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	NOR	Norway	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2017-Q2		338596.8						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2007-Q3		11664361.8						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2007-Q4		11825294.7						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2008-Q1		12009899.7						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2008-Q2		12086395.2						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2008-Q3		12171946.9						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2008-Q4		12064306.4						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2012-Q4		13005144.7						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	LTU	Lithuania	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2020-Q2		109874.3						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2010-Q2		12127749.2						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2010-Q3		12227268						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2010-Q4		12395836.1						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2011-Q1		12618512.2						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2011-Q2		12729609.1						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2011-Q3		12820502.9						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2011-Q4		12797395.4						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar
DATAFLOW	OECD.SDD.NAD:DSD_NAMAIN1@DF_QNA_EXPENDITURE_USD(1.1)	Quarterly GDP and components - expenditure approach, US Dollars	I	Q	Quarterly	Y	Calendar and seasonally adjusted	EA20	Euro area (20 countries)	S1	Total economy	S1	Total economy	B1GQ	Gross domestic product	_Z	Not applicable	_Z	Not applicable	_Z	Not applicable	USD_PPP	US dollars, PPP converted	V	Current prices	LA	Annual levels	T0102	Table 0102 - GDP identity from the expenditure side	2012-Q1		12817163.5						False	Free (free for publication)	1	One	A	Normal value	6	Millions	USD	US dollar

# uploading libraries for data manipulation, visualization, and causal inference
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import arviz as az
import causalpy as cp
az.style.use("arviz-white")
 
# uploading the data from the OECD Data Explorer at https://data-explorer.oecd.org/
data = pd.read_csv('oecd_data.csv')
data.info()
data.head()
 
# keeping only relevant variables
data = data[[
    'Reference area',
    'TIME_PERIOD',
    'OBS_VALUE'
]]
 
# cleaning the quarter column
# function to calculate the last day of the quarter
def quarter_to_date(q):
    year, quarter = q.split('-')
    quarter_month_map = {
        'Q1': '03-31',
        'Q2': '06-30',
        'Q3': '09-30',
        'Q4': '12-31'
    }
    return f"{year}-{quarter_month_map[quarter]}"
 
data['TIME_PERIOD'] = data['TIME_PERIOD'].apply(quarter_to_date)
data['TIME_PERIOD'] = pd.to_datetime(data['TIME_PERIOD'], format='%Y-%m-%d')
 
# cleaning the country names
data['Reference area'] = data['Reference area'].str.replace('- ', '', regex=True).str.replace(' ', '_', regex=True).str.replace(r'[()]', '', regex=True)
 
# putting data on the trillion/billion (10^12) unit scale
data['OBS_VALUE'] = data['OBS_VALUE']/1000000
 
# getting data from long to wide format
melted_df = data.melt(id_vars=['Reference area', 'TIME_PERIOD'], var_name='Variable', value_name='Value')
pivoted_df = melted_df.pivot(index='TIME_PERIOD', columns='Reference area', values='Value')
pivoted_df.info()
 
# removing countries with missing values in the time series data
pivoted_df.drop(columns=['Saudi_Arabia', 'Russia'], inplace=True)
 
# removing row for date where we have data for only one country
pivoted_df = pivoted_df[pivoted_df.index != pd.to_datetime('2024-09-30')]
 
# identifying countries (that didn't left EU) GDP of which most strongly correlated with UK's GDP before actual Brexit (2020 January 31)
correlation_df = pivoted_df[pivoted_df.index <= pd.to_datetime("2020 January 31")].corr()
print(correlation_df[['United_Kingdom']].drop('United_Kingdom').sort_values(by='United_Kingdom', ascending=False))
 
 
 
# Analysis 1: The impact of Brexit on UK GDP
 
# target country of interest
target_country = 'United_Kingdom'
# control countries (top 15)
other_countries = [
    "United_States",
    "Costa_Rica",
    "Germany",
    "New_Zealand",
    "Sweden",
    "Austria",
    "Luxembourg",
    "Denmark",
    "Belgium",
    "Korea",
    "Canada",
    "Lithuania",
    "France",
    "India",
    "Estonia"
]
 
# formula
formula = target_country + " ~ " + "0 + " + " + ".join(other_countries)
print(formula)
 
# modeling data preparation
treatment_time = pd.to_datetime("2020 January 31")
modeling_data = pivoted_df.copy()
modeling_data = modeling_data[[target_country] + other_countries]
modeling_data.dropna(axis='rows', inplace=True, how='all')
 
# fitting the model
result = cp.SyntheticControl(
    modeling_data,
    treatment_time,
    formula=formula,
    model=cp.pymc_models.WeightedSumFitter(
        sample_kwargs={
        "random_seed": 2024, 
        "draws": 10000,
        "tune": 5000, 
        "target_accept": 0.99,
        "chains": 4 
      }
    )
)
 
# results summary
az.summary(result.idata, var_names=["~mu"])
 
# visualization of the posterior samples
az.plot_trace(result.idata, var_names="~mu", compact=False)
plt.show()
 
# visualization of the estimated causal effect
fig, ax = result.plot(plot_predictors=False)
for i in [0, 1, 2]:
    ax[i].set(ylabel="Trillion USD")
plt.show()
 
 
 
 
# Analysis 2: The impact of Brexit on the GDP of eurozone countries
 
# identifying countries (non-EU, non-eurozone, non-UK) GDP of which most strongly correlated with eurozone countries' GDP before actual Brexit (2020 January 31)
correlation_df = pivoted_df[pivoted_df.index <= pd.to_datetime("2020 January 31")].corr()
print(correlation_df[['Euro_area_20_countries']].drop('Euro_area_20_countries').sort_values(by='Euro_area_20_countries', ascending=False))
 
# target country of interest
target_country = 'Euro_area_20_countries'
# control countries (top 12)
other_countries = [
    "Costa_Rica",
    "New_Zealand",
    "United_States",
    "India",
    "Korea",
    "Colombia",
    "Canada",
    "Israel",
    "Iceland",
    "Switzerland",
    "Indonesia",
    "Australia"
]
 
# formula
formula = target_country + " ~ " + "0 + " + " + ".join(other_countries)
print(formula)
 
# modeling data preparation
treatment_time = pd.to_datetime("2020 January 31")
modeling_data = pivoted_df.copy()
modeling_data = modeling_data[[target_country] + other_countries]
modeling_data.dropna(axis='rows', inplace=True, how='all')
 
# fitting the model
result = cp.SyntheticControl(
    modeling_data,
    treatment_time,
    formula=formula,
    model=cp.pymc_models.WeightedSumFitter(
        sample_kwargs={
        "random_seed": 2024, 
        "draws": 10000,
        "tune": 5000, 
        "target_accept": 0.99,
        "chains": 4 
      }
    )
)
 
# results summary
az.summary(result.idata, var_names=["~mu"])
 
# visualization of the posterior samples
az.plot_trace(result.idata, var_names="~mu", compact=False)
plt.show()
 
# visualization of the estimated causal effect
fig, ax = result.plot(plot_predictors=False)
for i in [0, 1, 2]:
    ax[i].set(ylabel="Trillion USD")
plt.show()
 

Related notes

• Beyond prediction: Exploiting organizational events for causal inference in people analytics
• Modeling impact of the COVID-19 pandemic on people’s interest in work-life balance and well-being
• Did the Nobel Prize put causal inference on the public radar?
• The impact of the COVID pandemic on the popularity of people analytics
• What a European cigarette tax study taught me about employee listening

---

📄 Read the original post with full outputs on my blog.