Question:
You are given the full text of a scientific research paper.

    Summarize the **research methods** used in the study in a way that is informative for policy audiences. Your response should:
    - Describe the overall study design, data sources, tools, and models used
    - Avoid unnecessary technical details or equations
    - Use accessible but precise language

    Write a short paragraph suitable for the “Scientific Research Study Methods” section of a policy brief.

    Scientific Research Paper:
    Nature Climate Change | Volume 13 | July 2023 | 679–684
679
nature climate change
https://doi.org/10.1038/s41558-023-01710-8
Article
Global benefits of the international diffusion
of carbon pricing policies
Manuel Linsenmeier
  1,2
, Adil Mohommad
  3 & Gregor Schwerhoff
  3
Carbon pricing policies are essential for mitigating climate change, but the
global benefits of leadership and the international diffusion of these policies
are not well understood. Here we provide robust and statistically significant
evidence showing that the adoption of carbon pricing in one country can
explain the subsequent adoption of carbon pricing in other countries. For a
neighbouring country, diffusion increases the probability of policy adoption
on average by several percentage points. Translating these empirical
estimates with Monte Carlo simulations into global reductions in emissions
through policy diffusion suggests that for many countries, decreases in
emissions as a result of diffusion could be larger than domestic emission
reductions. These results support the adoption of stringent climate
policies, especially in countries in which climate change mitigation
might be considered as not very important because of relatively low levels
of domestic emissions.
Despite the need for more stringent climate policies to achieve the Paris
climate targets, many countries seem reluctant to ratchet up their miti-
gation efforts. This might be partly because the costs of mitigation are
incurred domestically and immediately, whereas most of its benefits will
be reaped globally and in the future. In addition, more ambitious climate
action might be hindered by concerns about the limited effectiveness
of nations’ domestic efforts to reduce greenhouse gas (GHG) emissions
if other countries do not do make similar changes. This consideration
is especially pertinent in relatively small countries. Indeed, in 2021 the
smallest 90% of emitters contributed only about 20% of global GHG
emissions. Such a narrow perspective, however, neglects the fact that
international leadership in climate change mitigation can yield sub-
stantial benefits beyond domestic emission reductions1,2. For exam-
ple, stringent climate policies at home can support the international
diffusion of technological innovations that reduce mitigation costs in
other countries3,4. Furthermore, domestic climate policies can show
the political feasibility and certain benefits of carbon pricing5, and they
can create incentives related to trade6 and diplomacy7 that can nudge
other countries to adopt the same or similar policies. This latter process
whereby adoption of a policy in one country increases the probability
of adoption in other countries is usually referred to as policy diffusion8.
Results from qualitative studies provide ample evidence for climate
policy diffusion. For example, evidence has been described for strong
mutual influences among the world’s first adopters of carbon pricing
policies in Scandinavia in the 1980s (ref. 9). According to one study10,
the subsequent adoption of carbon pricing by other countries can
be at least partially explained by the emulation of earlier policies and
learning from previous experiences. International diffusion has also
been actively promoted by early adopters themselves and through
multilateral initiatives such as the World Bank’s Partnership for Market
Readiness (PMR)11. Furthermore, several case studies of carbon pric-
ing policies report empirical evidence for international diffusion—for
example, for California12, Kazakhstan13 and China14—and the influence
of multilateral initiatives has been acknowledged for carbon pricing
policies in Latin America15. Earlier work also examined the diffusion of
support for carbon pricing at the subnational level and between firms
or organizations16,17. Several quantitative studies also provide evidence
in support of an international diffusion of climate policies6,18–22.
In this study, we empirically examine the international diffusion of
climate policies from 1988 to 2021 and quantify its global benefits. The
analysis focuses on carbon pricing policies, which can be considered
the most salient and possibly the most stringent policies for climate
change mitigation. We first construct a global dataset of carbon pric-
ing policies, countries’ characteristics and linkages between countries
related to geography, trade and international organizations. We then
estimate Cox proportional hazard models that include spatial lags
Received: 3 November 2022
Accepted: 22 May 2023
Published online: 3 July 2023
 Check for updates
1Climate School, Columbia University, New York, NY, USA. 2Department of Geography and Environment, London School of Economics and Political
Science, London, UK. 3Research Department, International Monetary Fund, Washington, DC, USA.
 e-mail: mpl2157@columbia.edu

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Mexico were followed by other pricing policies in the same region. For
Latin America, the role of international organizations has been empha-
sized15. In Asia, early carbon pricing policies in Japan were followed by
pricing policies in China and South Korea.
Motivated by these findings, we next conduct an econometric
analysis to more systematically identify whether the adoption of car-
bon pricing in one country affected the probability of its subsequent
adoption elsewhere. To do so, we estimate a Cox proportional hazard
model (equation (1) in Methods) with several country characteristics
as explanatory variables. We use Lasso regressions and a detailed
examination of multicollinearity for the selection of variables (Methods
and Supplementary Tables 4–6). On the basis of a statistical test
using Schoenfeld residuals23 we cannot reject the null hypothesis
of proportional hazards for models with the preferred five or more
control variables. To model international diffusion, we also include
a spatial lag of prior carbon pricing adoption in other countries. For
this variable, we use several alternative metrics of the proximity of
countries (Methods). We find the best model fits for a metric that
combines the gross domestic product (GDP) of countries with the
geographical distances between them in the spirit of gravity models
of international trade, and for a metric based on joint membership in
international organizations (Supplementary Table 7). We then multiply
of policy adoption (Methods). The spatial lags are constructed using
alternative metrics of the proximity of countries. Possible concerns
about causality are addressed with a series of robustness tests and a
placebo test. In the last part, we use our empirical estimates to calculate
the expected emission reductions due to policy diffusion using Monte
Carlo simulations. We consider these indirect reductions in emissions
as a proxy for the international leverage of a country’s domestic climate
policy and examine its variation across countries. We also use these
simulations to quantify the global coverage of carbon pricing policies
that can be expected because of policy diffusion.
Results
We first examine our dataset of carbon pricing policies from 1988 to 2021
to identify possible patterns of policy diffusion. Visual inspection of the
relative timing of policy adoption shows that carbon pricing was often
introduced successively by geographically close countries (Fig. 1a).
In Europe, for example, the earliest carbon pricing policy in Finland
was followed by similar policies in Scandinavian countries, the Baltics
and other parts of Europe. Qualitative work on the role of diffusion in
this context highlighted the importance of the pioneering adoption in
Finland, which was soon “emulated by its Nordic neighbors”9. Similarly,
in the Americas, relatively early carbon pricing policies in Canada and
1990
1995
2000
2005
2010
2015
2020
Year
0
5%
10%
15%
20%
Share of countries with a carbon pricing policy
Tax
ETS
2015
2005
2015
2013
2011
1991
2019
2012
2015
2013
2012
2008
2018
2017
2017
2014
2019
1990
a
b
c
...
AFG
PAK
TJK
TKM
UZB
IRN
KGZ
NPL
AZE
BTN
ARE
QAT
BGD
KWT
MDV
OMN
IND
ARM
BHR
IRQ
SYR
MMR
SAU
YEM
JOR
LBN
LKA
TUR
ISR
ERI
THA
DJI
EGY
SOM
SDN
CYP
LBY
ETH
GRC
CHN
MYS
IDN
CAF
COD
UGA
SSD
KEN
–100
–60
–40
–20
0
20
40
60
–50
0
50
Longitude (degrees)
Year of adoption
Latitude (degrees)
100
150
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
2010
2012
2014
2016
2018
2020
2022
Fig. 1 | Adoption of carbon pricing policies over time and around the world.
a, Map showing the adoption of the first carbon pricing policy for every country.
Hashes indicate countries in which the first policy was a subnational policy. See
Supplementary Fig. 2 for a more detailed map of Europe (blue box). b, Adoption
of carbon taxes and ETSs over time. c, Proximity of countries on the basis of
physical distance, GDP and joint membership in international organizations.
Arrows indicate the three strongest influences on every country; position in chart
approximates average distances. Countries are indicated by ISO three-letter
country codes. See Supplementary Fig. 3 for the complete version of c. Base map
adapted from World Bank Official Boundaries under a Creative Commons licence
CC BY 4.0.

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these two metrics to create a hybrid metric for the empirical analysis
and simulations. Furthermore, in our main specification we focus on
the first policy in every country and we consider all members of the
European Union (EU) emissions trading system (ETS) without a prior
carbon tax together as one country that adopted its first carbon pricing
policy in 2005 (Methods and Supplementary Fig. 2).
Our empirical analysis yields robust statistical evidence for an
international diffusion of carbon pricing policies (Table 1, column
1). The magnitude of the estimated coefficient of policy diffusion is
substantial. For example, according to our main estimates (Table 1,
column 1), prior adoption of carbon pricing by Canada increases the
probability of adoption in the USA by a factor of about 1.78, or by 78%
(95% confidence interval (CI) of 35–134%). In Germany, prior adoption
by France increases the probability by 20% (10–31%), whereas in China,
prior adoption by Japan increases it by 25% (12–39%). For comparison,
in the USA, prior adoption by China increases the probability of adop-
tion by 8.5% and in Germany, prior adoption by Japan by about 1.9%.
In our main specification, we consider carbon taxes and ETSs as
two alternative designs of the same policy. This is informed by previous
findings that there are no systematic differences between countries
that chose either of the two designs24. Furthermore, we consider it
likely that in many cases the decision to adopt carbon pricing was made
before the choice of instrument design, as in the case of the EU ETS9.
Consistent with this idea, we find stronger evidence for policy diffusion
if we consider ETSs and taxes as the same policy than if we distinguish
between them (Table 1). In additional analysis, we find suggestive
evidence that carbon pricing policies with a higher stringency (higher
economy-wide average carbon prices, taking into account sectoral
prices and emissions) exert a stronger influence on subsequent adop-
tion elsewhere (Supplementary Table 8, column 5).
We conduct several robustness checks (Methods). This includes
three ways of treating members of the EU ETS (Supplementary Fig. 2
and Supplementary Table 8, columns 1–3), dropping subnational
policies (Supplementary Table 8, column 4), adding control variables
(Supplementary Table 9, columns 1 and 2), changing the imputation
method (Supplementary Table 9, column 3) and stratifying the model
(Supplementary Table 9, column 4). We find that our results are overall
very robust. An additional placebo test does not show evidence of spuri-
ous diffusion25. Furthermore, we find the best model fit for a lag time of
1–2 years (Supplementary Table 11). Additional evidence suggests that
the marginal effect of a new policy decreased with the total number of
existing policies (Supplementary Table 10 and Supplementary Fig. 5a).
We use this insight on ‘saturation’ as motivation to estimate a non-linear
model that we then use for all simulations (Supplementary Fig. 5b).
Overall, the results of the empirical analysis suggest that between
1988 and 2021, carbon pricing policies diffused internationally. We
next examine how much this diffusion could contribute to reduc-
tions of GHG emissions globally. Specifically, we use our estimated
model to quantify the emission reductions that can be attributed to the
adoption of carbon pricing in a given country, distinguishing between
direct (domestic) emissions reduction and indirect (foreign) emission
reductions due to diffusion. All results are based on the empirical
estimates from the econometric analysis, but we assume a constant
baseline hazard, which means that all differences in the probability
of policy adoption between countries can be attributed to the spatial
lag and country characteristics. Given the probabilistic nature of our
model, we conduct Monte Carlo simulations. All simulations start in
2022 from the carbon pricing policies adopted by the end of 2021. For
every country without a carbon price, we conduct 30,000 simulations
in which this country adopts carbon pricing in 2022. We then compare
the results with results from counterfactual simulations in which this
country does not adopt carbon pricing in 2022. This comparison allows
us to attribute policy adoption in other countries to the diffusion of
one specific policy.
We find that indirect emission reductions are as large as or even
larger than direct emission reductions in most countries. Specifically,
from 2022–2050, about 70% of countries (97 out of 138) have larger
indirect than direct cumulative emission reductions (Fig. 2a). Further-
more, we find that indirect emission reductions are far more equally
distributed across countries than direct emission reductions (Fig. 2b).
This result also suggests that the total reductions in emissions from
policy adoption and diffusion are more equally distributed than only
direct domestic emission reductions.
For simplicity, we assume that carbon pricing policies reduce
GHG emissions by the same rate r = 1% per year in all countries relative
to a situation without a carbon pricing policy. This rate is conservative
compared to known reductions in emissions in existing ETSs and esti-
mated reductions for carbon taxes (Methods). In a sensitivity analysis,
we vary the value of this parameter between 0.1% and 10% and find that
this changes the number of countries with larger indirect than direct
emission reductions by only a few percentage points (Supplementary
Fig. 7). We do not find evidence that later adopters tended to adopt
systematically more or less stringent polices than earlier adopters (Sup-
plementary Fig. 6). Furthermore, we find similar results for alternative
proximity metrics (Supplementary Fig. 8).
Table 1 | Results of empirical analysis of policy adoption
1988–2021 with Cox proportional hazard models
Policy
Carbon price
Tax
ETS
Column
1
2
3
Spatial lag of carbon pricing
0.9152***
0.3423
0.8619***
(−0.2251)
(−0.2885)
(−0.1816)
log real GDP per capita PPP
0.4782
0.5221
−0.4602
(−0.4226)
(−0.388)
(−1.0017)
Government effectiveness
−0.2327
−0.0758
0.5461
(−0.4439)
(−0.3869)
(−1.177)
Regulatory quality
1.4777***
0.6952*
1.7684**
(−0.4559)
(−0.3969)
(−0.8692)
Reserves of oil
0.0093
0.0192
−0.0492
(−0.1408)
(−0.1917)
(−0.3266)
Government expenditure
0.3199
0.0399
0.014
(−0.2221)
(−0.441)
(−0.5959)
Gov. expenditure for welfare
0.1914
0.4893
0.9689**
(−0.2184)
(−0.373)
(−0.4885)
Democracy index
0.6016
0.7486
−0.3912
(−0.5236)
(−0.645)
(−0.8534)
Emission intensity
0.3478**
0.3392***
0.1653
(−0.1393)
(−0.1189)
(−0.2152)
Growth rate of debt to GDP ratio
0.2975*
0.4281***
0.3717*
(−0.1785)
(−0.1558)
(−0.2175)
AIC
173.4
219.3
81.8
log-likelihood
−76.7
−99.7
−30.9
Number of observations
5,322
6,061
5,295
Countries
167
188
159
Policies
25
26
11
Column 1 shows the main specification. Columns 2 and 3 show results for only carbon taxes
and only ETSs, respectively. Results are based on the gravity-IO proximity metric. Results for
other metrics are shown in Supplementary Table 7. Results excluding subnational policies
and for different ways of dealing with Europe are shown in Supplementary Table 8. See also
additional robustness tests in Supplementary Table 9. AIC, Akaike information criterion;
PPP, purchasing power parity. Standard errors clustered by country are in parentheses.
Significance is based on a two-sided t-test: *P < 0.1, **P < 0.05, ***P < 0.01.

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We find that indirect emission reductions are largest throughout
the Middle East and in South Asia and Southeast Asia (Fig. 2a,c). The
proximity metrics suggest that countries with large indirect emission
reductions tend to be relatively centrally located, are members of
similar international organizations to large emitters and are
also located physically close to countries with relatively large emis-
sions and no carbon pricing policies as of the end of 2021. To further
investigate these determinants of indirect emission reductions, we
calculate for every country its ‘network centrality’ on the basis of the
proximities and GHG emissions of all countries (equations (9–11)).
We find that network centrality can explain about 13% of the variation
in indirect emission reductions across countries, which increases to
43% if we take into account the emissions of other countries, and to
58% if we better account for the ‘cascading nature’ of policy diffusion
(equation (11)).
In the last part of the analysis, we examine how diffusion affects
the future geographical coverage of carbon pricing policies. To
this aim, we conduct similar Monte Carlo simulations starting in
2022 and continuing until 2100. Both scenarios start from exist-
ing policies. In the first scenario, we use our empirically estimated
relationship between the spatial lag of carbon pricing and the prob-
ability of policy adoption. In the second scenario, we set international
policy diffusion to zero. All other parameter values are chosen as in the
previous exercise.
We find that policy diffusion substantially increases the geographical
coverage of carbon pricing over the time period 2022–2050 (Fig. 3).
In our simulations, by 2050 carbon pricing policies will be in place in
about 50% of countries, 21 percentage points more than without diffu-
sion. By 2100, the difference increases to more than 30 percentage points
(Fig. 3a). In a sensitivity analysis, we multiply the baseline hazard and the
diffusion term in the model with factors between 0.5 and 2. Both para
meters have a positive effect on the number of countries with a carbon
price (Fig. 3b). Similarly, the effect of diffusion increases with either of
the two parameters. For example, as the factor of the baseline hazard is
increased from 1 to 2, the additional global coverage of carbon pricing
due to diffusion by 2050 increases from 21 to 32 percentage points.
These results add a key detail to the global benefits of interna-
tional policy diffusion. From the perspective of an individual country,
policy diffusion can add substantial global emission reductions to
domestic emission reductions. From a global perspective, however,
a high baseline probability of policy adoption and/or a strength of
mutual influences (both in historical perspective) are required to reach,
for example, 80% coverage by 2050. Because most of the countries
that adopt carbon pricing late in our simulations have relatively low
domestic emissions, the projected global coverage of pricing policies
is generally higher in terms of global GHG emissions than in terms
of countries, and the results are less sensitive to the two parameters
(Supplementary Fig. 11).
a
b
c
10
–3
10
–2
10
–1
10
0
10
1
10
–3
10
–4
10
–5
10
–2
10
–1
10
0
10
1
Direct emission reductions (Gt CO2eq)
10
–2
10
–1
Indirect emission reductions (Gt CO2eq)
Emission reductions (Gt CO2eq)
0
10
20
30
40
Number of countries
Direct
Indirect
–100
–50
0
50
Longitude (degrees)
100
150
–60
–40
–20
0
20
40
60
Latitude (degrees)
Indirect emission reductions (Gt)
0.25
0.20
0.15
0.10
0.05
0
Fig. 2 | Direct and indirect emission reductions from carbon pricing policies
on the basis of Monte Carlo simulations of future policy adoption. All panels
show cumulative emission reductions from simulated policy adoption in
2022–2050. a, Scatter plot of direct and indirect emission reductions. Dashed
black line indicates where indirect emission reductions are larger than direct
emission reductions. G20 economies are shown in blue. Countries with a carbon
price by the end of 2021 are omitted. b, Histogram of direct and indirect emission
reductions. c. Map of indirect emission reductions. Countries with a carbon
pricing policy by the end of 2021 are shown in dark grey. CO2eq denotes CO2
equivalent. Base map adapted from World Bank Official Boundaries under a
Creative Commons license CC BY 4.0.

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Discussion
The main contribution of this paper is the quantification of reductions
in GHG emissions that can be attributed to the international diffusion
of carbon pricing policies. These indirect emission reductions can be
interpreted as a quantitative measure of the international leverage of
a country in terms of global GHG emission reductions due to future
diffusion of its policy. Overall, our results suggest that the magnitude
of indirect emission reductions can be substantial. With our empiri-
cally estimated parameters, future indirect emission reductions will
be larger than domestic emission reductions in 63% of countries that
did not have a carbon pricing policy in place by the end of 2021. This
evidence for large positive spillovers of domestic climate policy adop-
tion provides additional support for the adoption of stringent climate
policies, especially in countries in which climate policies might so far
have been deemed to have relatively little importance because of a
relatively small domestic economy.
Our results speak to a long-standing debate about free-riding in
global environmental policy26. According to this theory, unilateral
climate policy weakens the incentives of other countries to implement
climate policy themselves. In this paper, we show that free-riding is
not the only possible reaction of countries to unilateral climate policy
in the case of carbon pricing policies. Instead, we find that these policies
diffuse internationally. We consider this as evidence consistent with the
idea that leadership in climate policy can send a credible signal about
the willingness to cooperate to other countries, supporting the forma-
tion of global climate coalitions that have been proposed27,28. Similarly,
ex-ante modelling studies have repeatedly predicted carbon leakage29
as a consequence of leadership. Empirical studies, however, find that
leakage is a very minor or no concern30–32. Similar to other studies that
examine the evidence for free-riding in climate policy33, our results
provide a possible (partial) explanation for this lack of leakage.
We find large indirect emission reductions especially for countries
in close proximity to large emitters without a carbon pricing policy.
This includes several countries on the Arabian peninsula and in South
and Southeast Asia. Our analysis of network centrality as a determi-
nant of countries’ international leverage suggests that the ‘cascading’
nature of policy diffusion is important to explain some of these results.
Notably, we find that countries have become more similar over the last
30 years in terms of their international leverage, suggesting that the
benefits from policy diffusion have also become globally more equally
distributed (Supplementary Fig. 10).
The results for emission reductions from the simulations for a specific
country should, however, not be considered as precise estimates because
of some necessarily neglected heterogeneity. Specifically, some of the
empirically estimated parameters are likely to differ between countries
with large uncertainty, including the effectiveness of future carbon pricing
policies. To assess the robustness of our results, we conduct a sensitivity
analysis in which we change this and other parameters. Furthermore,
owing to the construction of the scenarios, indirect emission reductions
simulated for a specific pioneering country are not additive with those
simulated for another pioneering country. This means that our estimates
for individual countries can in some sense be considered as upper bounds.
Theories of policy diffusion propose several mechanisms through
which the adoption of a policy in one jurisdiction can influence the
adoption of the same or a similar policy elsewhere. These mechanisms
are often referred to as learning, competition, emulation and coer-
cion25,34–39. Previous literature on climate policies has especially focused
on emulation and learning10,11. Somewhat consistent with this, we do
not find evidence that shared export markets have been important for
international diffusion, which suggests that the role of international
competition is limited. Furthermore, our results suggest that interna-
tional organizations contributed to policy diffusion, owing possibly to
international coordination and exchanges of information—consistent
with the role of emulation and learning—and possibly to compliance
with international norms10. We consider this to be an encouraging
finding for present and future attempts to increase the geographical
coverage of carbon pricing policies through international relations.
Previous qualitative research also suggests that certain design
attributes of carbon pricing policies have diffused because of emula-
tion13,40. Future research might examine the overall relevance of the
diffusion of policy design using similar quantitative methods. For
example, we consider it plausible that international diffusion also
matters for ratcheting up the stringency of existing climate policies;
for example, increases in carbon prices.
Online content
Any methods, additional references, Nature Portfolio reporting sum-
maries, source data, extended data, supplementary information,
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Baseline hazard (relative to estimate)
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Difusion parameter (relative to estimate)
31
(+4)
35
(+8)
39
(+12)
43
(+16)
46
(+19)
49
(+22)
52
(+25)
34
(+6)
40
(+12)
45
(+17)
49
(+22)
54
(+26)
57
(+29)
37
(+8)
44
(+15)
50
(+21)
55
(+26)
60
(+31)
39
(+10)
48
(+18)
55
(+25)
42
(+11)
51
(+21)
58
(+28)
44
(+13)
54
(+23)
47
(+14)
57
(+25)
60
(+32)
63
(+34)
66
(+37)
60
(+30)
64
(+34)
68
(+38)
70
(+41)
64
(+33)
68
(+37)
71
(+41)
74
(+43)
62
(+30)
67
(+35)
71
(+39)
74
(+43)
77
(+45)
65
(+32)
70
(+37)
73
(+41)
77
(+44)
79
(+47)
a
b
+21%
Global coverage of carbon pricing policies (% countries)
with difusion
versus without difusion
2000
2020
2040
2060
2080
2100
Year
0%
10%
20%
30%
40%
50%
60%
70%
Share of countries with carbon price
1989–2021
2022–2100, with difusion
2022–2100, without difusion
Fig. 3 | Future global coverage of carbon pricing policies from Monte Carlo
simulations of future policy adoption. All panels show the future number of
countries with carbon pricing policies as a share of all countries for simulations
starting in 2022 from existing policies by end of 2021. a, Time series of future
policy adoption for parameter values set to empirical estimates, for simulations
with and without diffusion. b, Share of countries with carbon pricing policies
by 2050 for different parameter values of the baseline hazard and the diffusion
coefficient. Red square indicates empirical estimates. See Supplementary Fig. 11
for results in global GHG emissions.

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acknowledgements, peer review information; details of author contri-
butions and competing interests; and statements of data and code avail-
ability are available at https://doi.org/10.1038/s41558-023-01710-8.
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Methods
Empirical analysis of policy diffusion
We use econometric models to identify policy diffusion in the data
on past policy adoption. To do so, we estimate a model that relates
adoption of a policy in a country i at time t to the adoption of the
same policy in other countries j = 1, …, Nc, j ! = i prior to time t (with Nc
being the number of countries in the sample). This is a common
empirical strategy to identify policy diffusion and has been used in
the literature on climate policy7,20,21,41. Technically, the model accounts
for the mutual influences between countries with spatial lags, which
are calculated as a weighted average of prior policy adoption in all
other countries. We use alternative weighting schemes based on geo-
graphical proximity, trade and international institutional linkages,
which we consider as representing some of the alternative diffusion
mechanisms cited in the main text.
The choice of our model is informed by two characteristics of
our dependent variable. The first characteristic is that any possible
future policy adoption is unobserved, which means that our dependent
variable is right-censored. Specifically, at the time of analysis, policy
adoption is only recorded in the Carbon Pricing Dashboard of the World
Bank up until April 2022, which means that 2021 is the most recent year
in our sample. The second characteristic is that our dependent variable
is binary, taking on only values 0 or 1. Both these characteristics are
common in survival analysis, which is also referred to as event history
analysis, and can be addressed with proportional hazard models.
We thus follow previous work on policy diffusion and model policy
diffusion with semi-parametric Cox proportional hazard models20,21,38,41.
As compared to parametric proportional hazard models, the Cox model
does not require an assumption about a specific functional form of the
survival function, and the results can therefore be considered more
robust to model mis-specification42. Formally, we estimate models of
the general form
h (t, Xi,t, Wi,t) = h0 (t) exp (Xi,t−1βX) exp (Wi,t−1βW)
= h0 (t) exp (Xi,t−1βX + Wi,t−1βW)
(1)
The hazard function h(.) of a country i in year t represents the
probability that the policy is adopted by that country in that year con-
ditional on it not yet being implemented at time t − 1. This hazard rate
is composed of a baseline hazard rate h0(t) and a second partial hazard
term that includes the time-dependent matrices Xi,t−1 and Wi,t−1. In the
Cox model, the functional form of the baseline hazard is not prescribed
a-priori and not necessarily smooth, but estimated on the basis of
the patterns of policy adoption in the data. For robustness, we also
estimate a stratified version of the model with different baseline
hazards h0,k(t) whereby the six continents are indexed by k.
For both the left-hand side and the right-hand side of equation
(1) we model policy adoption Yi,t as a binary variable that takes on the
value 1 for all years t, t + 1, …,T if a policy has been adopted before or
in year t. To account for autocorrelation, we cluster standard errors at
the level of individual countries.
The model is estimated from panel data on countries’ adoption of
climate policies by maximizing a likelihood function. Unbiasedness of
the estimated coefficients relies on the proportional hazard assump-
tion. This assumption is satisfied if conditional on all explanatory vari-
ables the hazard ratio of two countries is constant over time. We address
possible violations of this assumption with our set of control variables
and with stratification, and conduct statistical tests of Schoenfeld
residuals23. The control variables are discussed further below.
The matrix Xi,t−1 accounts for possible domestic influences in
country i in year t − 1. All explanatory variables are lagged by one year
to address concerns about reverse causality.
The matrix Wi,t−1 is a weighted average of policies Yj,t−1 ∈ {0,1}
adopted in other countries j = 1, …, Nc, i ! = j at time t − 1, also referred
to as a spatial lag. Other countries are weighted on the basis of a
certain metric of proximity between countries. In mathematical terms,
we calculate
Wi,t =
∑
Nc
j=1,j≠iwi,j,tYj,t
∑
Nc
j=1,j≠iwi,j,t
(2)
where the weight wi,j,t quantifies how much country j influences country
i in year t on the basis of a specific metric. These weights wi,j,t are con-
structed from several alternative data sources. For trade, we use data on
annual bilateral trade flows from the International Monetary Fund (IMF)
and calculate the export share xi,j,t and import share mi,j,t for every pair
of countries in the data (i, j) and every year t. We then use these shares
as weights; that is, wi,j,t = xi,j,t and wi,j,t = mi,j,t for exports and imports,
respectively. Note that the weights are generally not symmetric for a
pair of countries; that is, wi,j,t ! = wj,i,t.
For indirect trade links, we compare the vectors of export shares
of every pair of countries (i, j) for every time step t, xi,k,t and xj,k,t, and
calculate the L1 norm of the difference between the two vectors:
wi,j,t =
∑k∉{i,j} ||xi,k,t −xj,k,t||
Nc −2
(3)
For geographical proximity, we calculate the distance between
centroids of countries and use the inverse distance di,j as weight:
wi,j =
1
di,j
(4)
Furthermore, we construct an additional metric that is based
on geographical proximity but also takes the size of countries into
account. This is motivated by the hypothesis that policies in larger
economies have a stronger effect on policy adoption elsewhere. The
size of countries is expressed by the GDP of a country. In mathematical
terms, we define another set of weights
wi,j,t =
log GDPj,t
di,j
(5)
where di,j is again the distance between countries. A country is therefore
considered more influential for domestic policy adoption the closer it
is in space and the larger its economy is. This metric is closely related
to gravity models of international trade that make similar assumptions
about the factors that determine trade between countries43.
We also consider shared membership in international organiza-
tions as important for policy diffusion. For this metric, we use data on
membership of individual countries in international organizations
from the Correlates of War database. For the sample of countries and
years of our data, the dataset includes 431 international organizations
with at least one member. For the weights w we calculate for every pair
of countries how many memberships in international organisations are
shared. That is, we divide the number of international organizations in
which both countries are members by the number of organizations in
which any of the two or both countries are members:
wi,j,t =
∑k{i ∈Ok,t ∧j ∈Ok,t}
∑k{i ∈Ok,t ∨j ∈Ok,t}
(6)
with the sets of member countries of the international organisation k
in year t denoted as Ok,t.
The datasets on trade and memberships in international organiza-
tions do not cover all years for all countries. Specifically, the dataset on
trade tends to cover only the more recent years, whereas the dataset on
international organizations covers only the years up to 2014. To keep a
consistent sample throughout the empirical analysis without making

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Article
https://doi.org/10.1038/s41558-023-01710-8
assumptions about time trends or relationships between variables, we
fill missing values by keeping values constant at the beginning and at
the end of our sample period. The datasets overlap for 188 countries,
which is our main sample of countries in the analysis. The largest coun-
tries not included in the sample are Venezuela and North Korea. A map
of countries can be found in Supplementary Fig. 1.
For domestic control variables, we consider a large number of
possible variables. Informed by the literature (for example, refs. 6,21,
22,44–49), they include GDP per capita, the growth rate of GDP per
capita, government debt as a share of GDP, emissions of CO2 per GDP,
the service and the industry shares of GDP, the import and export
shares of GDP, reserves of fossil fuels, a variety of governance indica-
tors from the World Bank such as government effectiveness, control
of corruption and regulatory quality, air quality, government expendi-
ture for welfare as share of GDP, public belief in climate change, and
indices of democracy. In total, we collect data from 9 different sources
(Supplementary Table 1) for 21 variables (Supplementary Table 3).
Many of these variables have missing values, for earlier years
and for certain countries (Supplementary Table 2). This results in a
dilemma. On the one hand, we want to consider as many domestic
influences as possible to avoid omitted variable biases. On the other
hand, for the analysis of diffusion it is important to have a relatively
complete set of countries owing to the geographical dimension of the
phenomenon. As a way out of this dilemma, we use iterative multiple
imputation to fill the missing values. To limit the extent of extrapola-
tion across countries, we first use multiple imputation to fill missing
values for countries for which at least one observation of that vari-
able exists. We also include the year as a possible predictor to model
country-specific time trends. In the second step, we fill missing values
of all other variables and countries. Our only criterion to consider a
country for our analysis is thus the availability of at least one observa-
tion of real GDP provided from the World Bank, which is the case for
211 countries, including all 188 countries for which we also have data
for our spatial lags (Supplementary Fig. 1). As a robustness test, we also
construct a dataset in which we only keep values constant for every
country and variable, without any other imputation. We find that with
this method we can construct a set of 145 countries for which data on 17
variables are available. Reassuringly, we find that our main results are
robust to this alternative method (Supplementary Table 9, column 3).
The choice of which of the domestic control variables to include in
our model represents a trade-off. We do not want to exclude important
variables to avoid omitted variable biases, but including too many vari-
ables, many of which are highly correlated, leads to multicollinearity.
To find a good trade-off, we use a two-step procedure. In the first set, we
use Lasso regression in combination with 10-fold crossvalidation, the
latter of which addresses concerns of over-fitting, to identify a set of
important predictors. This yields a set of ten most important variables
(Supplementary Table 4). In addition, to gain further insights into the
relative importance of these variables, we also estimate a Lasso model
with higher penalty parameters α.
In the second step, we examine multicollinearity for these ten vari-
ables using the variance inflation factor (VIF). We find that for a model
with all ten variables, the typical upper limit for VIF of 10 is exceeded
by one variable (Supplementary Table 5). We hence stepwise drop vari-
ables from the model until the upper limit is satisfied. At every step, we
focus on the variable with the highest VIF and examine its correlation
with all other variables. We then drop the variable itself or the most
strongly correlated variable depending on which of the two variables
is considered as more important by the additional Lasso regressions
in Supplementary Table 4. We thus stepwise drop the industry share
of GDP.
This yields our preferred model specification with nine control
variables for domestic influences on climate policy: GDP per capita,
government effectiveness, regulatory quality, reserves of oil, govern
ment expenditure, government expenditure for welfare (health,
education and social protection), a democracy index, emission inten-
sity of the economy, and the growth rate of the debt to GDP ratio. The
influence of all the remaining variables is examined in robustness
tests. The results of these robustness tests are reassuring, as our main
estimates for the spatial lag of carbon pricing are barely affected by
any of the domestic influences (Supplementary Table 9).
Modelling the effect of policy diffusion on GHG emissions
In the second step of the analysis, we use our empirical estimates to
calculate the expected reductions in CO2 emissions that can be causally
attributed to policy diffusion. For this purpose, we use the estimated
coefficients of all control variables and the spatial lag and feed them
into Monte Carlo simulations of policy adoption and policy diffusion
using the model in equation (1).
We construct counterfactual scenarios that allow us to quantify
the emission reductions that can be attributed to diffusion. For every
country i, we compare a scenario A in which country i adopts carbon
pricing in year t with a scenario B in which country i does not do so. For
each of the two scenarios, we calculate the hazard rate of policy adop-
tion at time t + 1 for all other countries j = i based on equation (1). The
difference between the hazard rates of the two scenarios A and B can
then be considered the additional hazard of policy adoption in country
j that can be attributed to policy diffusion from country i.
The Monte Carlo simulations are based on equation (1). We assume
the actually implemented carbon pricing policies for the year t = 2021
and let the simulations run from 2022 onwards. That is, we simulate the
adoption and diffusion of climate policies from 2022 to 2050. To do so,
at every time step 2022 ≤ t ≤ 2050 we update the spatial lag Wj,t of every
country, calculate its hazard of policy adoption and use this hazard to
draw from a probability distribution to determine whether the country
adopts or does not adopt the policy at this time step.
We conduct 30,000 simulations for every country for scenario B
and 100,000 simulations for scenario A, which is the counterfactual
of scenario B for all countries. The simulations of scenario B result for
every country i in one matrix of probabilities of policy adoption of
country j in year t, PB
i,j,t with ∑
2050
t=2022PB
i,j,t ≤1∀i, j. The simulations of sce-
nario A result in another matrix PA
j,t that again satisfies ∑
2050
t=2022PA
j,t ≤1∀j.
Because there is no difference between the counterfactuals, this matrix
PA
j,t is the same for all countries i. On the basis of these probabilities, for
every country i we subsequently calculate the expected direct emission
reductions and the expected indirect emission reductions due to
policy diffusion. To map the probabilities of policy adoption onto GHG
emissions, we assume that a carbon pricing policy reduces emissions
by the same percentage r = 1% per year in all countries. A similar assump-
tion, namely that climate policies and carbon pricing policies are
similarly effective across countries, has been made in the literature
before our study50,51. The assumed value of 1% per year is slightly
conservative relative to estimated emission reductions from carbon
pricing policies 2003–2016 of about 3% per year51. Existing ETSs with
gradually tighter caps on emission permits also allow for a comparison
of this number. For example, in the EU ETS, between 2013 and 2020
the number of permits was reduced by 1.74 % per year. In California,
over the same period the cap was decreased by between 2% and 3.3%
per year.
Because we use the same value for the parameter r for direct and
indirect emission reductions from policy adoption, our results with
regard to their relative sizes are relatively robust to changes in the
parameter. We confirm this with a sensitivity analysis in which we
vary the rate between 0.5% and 10% per year, showing that this rate
does not substantially affect our comparison of indirect and direct
emission reductions (Supplementary Fig. 7). Reassuringly, we do not
find clear time trends in the data on economy-wide average carbon
price among past policies, which suggests that there has not been a
systematic difference in stringency between followers and leaders
(Supplementary Fig. 6).

Nature Climate Change
Article
https://doi.org/10.1038/s41558-023-01710-8
Formally, for every country i we calculate the direct emission
reductions from 2022–2050 of implementing the policy in year 2022 as
̂R
direct
i,2050 = ∑
2050
t=2022 [Ei,t −Ei,2022 (1 −r)
t−2022]
(7)
where r is the effectiveness of carbon pricing as in the section above.
For indirect emission reductions that can be attributed to policy dif-
fusion from country i to other countries, we use the probabilities of
policy adoption PA
j,t and PB
i,j,t of the scenarios A and B respectively. In
mathematical terms, we take the difference between the expected
emission reductions between the two scenarios:
̂R
indirect
i,2050
= ∑j≠i[∑
2050
ξ=2022[ (PB
i,j,ξ −PA
j,ξ) ⋅
∑
2050
t=ξ [Ej,t −Ej,ξ (1 −r)
t−ξ ]]]
(8)
The indirect emission reductions are influenced by a country’s
proximity to other countries and the emissions and existing car-
bon pricing policies of those other countries. To understand the
importance of these different influences, we use common metrics to
quantify the centrality of a node in a network and adjust them for our
purposes. Our first measure of centrality is the closeness centrality
for directed graphs:
Centrality Ai = ∑
Nc
j=1,j≠iwj,i
(9)
Our second measure also takes the emissions E of other countries
into account:
Centrality Bi = ∑
Nc
j=1,j≠iwj,iEj
(10)
Our third measure takes the emissions of other countries into
account on which a country has an indirect influence (through a third
country). For this third metric we calculate
Centrality Ci = ∑
Nc
j=1,j≠iwj,i (∑
Nc
k=1,k∉{i,j}wk,jEk)
(11)
Data
We use data on carbon pricing from the Carbon Pricing Dashboard of
the World Bank. The dataset includes pricing policies at the national and
subnational level (Supplementary Table 2). We assign subnational
pricing schemes to the corresponding countries and focus on the first
carbon pricing policy in every country. For a robustness test, we ignore
subnational pricing policies. Furthermore, for another two robustness
tests we keep only either carbon tax or ETS policies in the sample. For
the analysis of price levels, we combine this dataset with the World Carbon
Pricing Database52. Data on GHG emissions are from a previous report53.
For the explanatory variables we use 9 different sources (Supplementary
Table 2) for 21 raw variables (Supplementary Table 3). We use iterative
multiple imputation to fill missing values (see Methods). Descriptive
statistics of all covariates are shown in Supplementary Table 3. Our main
sample covers 188 countries from 1988–2021 (Supplementary Fig. 1).
Reporting summary
Further information on research design is available in the Nature Port-
folio Reporting Summary linked to this article.
Data availability
All data are publicly available and were obtained from the following
sources: Carbon Pricing Dashboard of the World Bank (https://car-
bonpricingdashboard.worldbank.org/); World Carbon Pricing Data-
base (https://github.com/g-dolphin/WorldCarbonPricingDatabase);
World Development Indicators of the World Bank (WDI) (https://
databank.worldbank.org/source/world-development-indicators);
World Governance Indicators (WGI) (https://info.worldbank.
org/governance/wgi/); GHG emissions from ref. 53 and https://
doi.org/10.5281/zenodo.5566761; reserves of fossil fuels from the
Energy Intelligence Agency (EIA) (https://www.eia.gov/); Global Debt
Database (GDD) (https://www.imf.org/external/datamapper/data-
sets/GDD); Government Finance Statistics (GFS) (https://data.imf.
org/?sk=a0867067-d23c-4ebc-ad23-d3b015045405); Expenditure by
Function of Government (COFOG) (https://data.imf.org/?sk=5804c5e1-
0502-4672-bdcd-671bcdc565a9); Democracy Index (Polity5) (https://
www.systemicpeace.org/polityproject.html); and public belief in
climate change from Gallup (https://news.gallup.com/poll/117772/
awareness-opinions-global-warming-vary-worldwide.aspx).
Code availability
A replication package is available at https://github.com/mlinzze/
climate-policy-diffusion.
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Acknowledgements
We are grateful to the following for comments and suggestions (IMF,
unless otherwise noted): S. S. Aiyar, M. Aufhammer (UC Berkeley),
M. Bangalore (LSE), H. Berger, S. Black, W. Chen, S. Fankhauser (Oxford
University), F. Jaumotte, T. Kliatskova (World Bank), V. Kluyev and
V. Thakoor; and participants of internal seminars at IMF and LSE, the
summer conference of the Association of Environmental and Resource
Economists and the annual conference of the European Association of
Environmental and Resource Economists. M.L. acknowledges financial

Nature Climate Change
Article
https://doi.org/10.1038/s41558-023-01710-8
support from the UK Economic and Social Research Council (ESRC)
with grant number 2300776. For the purpose of open access, the
authors have applied a Creative Commons Attribution (CC BY) licence
to any Author Accepted Manuscript version arising. All remaining
errors are our own. The views expressed in this paper are those of the
authors and do not necessarily represent the views of the IMF or its
executive board or management.
Author contributions
M.L., A.M. and G.S. designed the research. M.L. collected the data
and conducted the analysis. M.L., A.M. and G.S. wrote and revised
the manuscript.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version
contains supplementary material available at
https://doi.org/10.1038/s41558-023-01710-8.
Correspondence and requests for materials should be addressed to
Manuel Linsenmeier.
Peer review information Nature Climate Change thanks
Sam Fankhauser, Pravesh Raghoo, Jakob Skovgaard and
Yves Steinebach for their contribution to the peer review
of this work.
Reprints and permissions information is available at
www.nature.com/reprints.

    Scientific Research Study Methods:

Answer: This study uses a global dataset on carbon pricing policies, country connections and previously shown variables to explain which countries introduce carbon pricing. The study consists of two parts. In the first part, we empirically estimated the probability that a country would introduce carbon pricing depending on previous policies in other countries and the connections between countries regarding geographic proximity and shared membership in international organizations. The study uses proportional hazard models that address the binary nature of policy adoption and the probability of yet unobserved future adoption. In the second part, we used the statistical results to simulate international policy diffusion and calculate the indirect greenhouse gas emissions reductions from diffusion. To this aim, Monte Carlo simulations incorporating the probabilistic empirical estimates were used. The indirect emissions reductions are only calculated for countries that have not yet introduced carbon pricing.