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Policy diffusion is the process by which a government’s decision to adopt a policy is influenced by the earlier decisions of other governments. Researchers study it by asking why a policy spreads across states, provinces or countries, and by testing whether adoption becomes more likely as other governments adopt. After reading this page you should be able to define the concept, separate it from purely internal causes of adoption, set up a basic event history model and report the result.
What is policy diffusion?
Policy diffusion describes adoption that is interdependent: whether and when one jurisdiction adopts a policy depends partly on what other jurisdictions have already done. The classic unit of analysis is a US state, but the same logic is applied to countries, cities and agencies. The concept is a close relative of diffusion of innovations in the sociological tradition, applied to governments rather than individuals or firms.
In the state-politics literature an innovation is defined as a program or policy that is new to the government adopting it, not necessarily new to the world (Walker 1969, as quoted by Berry and Berry 1990). A state that adopts a lottery in 1985 has innovated in this sense even if other states adopted decades earlier. A review of more than fifty years of political science research found hundreds of articles on the topic across American politics, comparative politics and international relations (Graham, Shipan and Volden 2013).
Policy diffusion vs. internal determinants
Berry and Berry (1990) frame the central question as what causes a government to adopt a new policy, and distinguish two families of answer:
- Internal determinants models explain adoption by a jurisdiction’s own characteristics, such as its fiscal condition, its politics or its election calendar.
- Regional diffusion models explain adoption by the behaviour of neighbouring jurisdictions that have already adopted.
Their main methodological point is that the two explanations should be analysed in one unified model rather than in isolation. In their study of state lotteries, the effect of neighbouring adopters was stronger when internal conditions (poor fiscal health, an election year) already favoured adoption. A model that includes only neighbours, or only internal factors, misattributes part of the effect.
Mechanisms of policy diffusion
The literature commonly groups the reasons for interdependence into four mechanisms: learning from other governments’ experience, economic competition, imitation, and coercion (see Shipan and Volden 2008, listed under Sources). Which one operates determines which variable you should measure. A competition mechanism, for example, points to economic neighbours or trading partners rather than geographic ones. Because a count of adopting neighbours cannot tell these mechanisms apart on its own, say in your write-up which mechanism your measure is designed to capture and which it cannot rule out.
How is policy diffusion measured? Event history analysis
The standard approach is event history analysis. It explains a qualitative change in a unit’s behaviour, the event, at a point in time. For policy adoption the event is adoption, and the dependent variable is the hazard rate: the probability that state i adopts in year t, given that it has not adopted before year t. Berry and Berry (1990) note that adoption is nonrepeatable, so a state leaves the sample once it adopts, and they estimated the model as a pooled cross-sectional time-series probit.
The model and every symbol
A discrete-time version can be written as:
P(ADOPTit = 1 | not yet adopted) = F(β0 + β1·NEIGHBORSit + β2·INTERNALit)
- ADOPTit: 1 if state i adopts the policy in year t, otherwise 0.
- F: the cumulative distribution function of the standard normal (probit) or the logistic (logit) distribution.
- β0: the intercept, which sets the baseline hazard when all predictors are zero.
- NEIGHBORSit: the number of bordering states that adopted before year t. Berry and Berry used the count of nearby previous adopters instead of predesignated regions, arguing that region boundaries are arbitrary. The hypothesis is that the probability of adoption rises with this count.
- INTERNALit: one or more internal-determinant variables (for example fiscal health or an election-year indicator), each with its own coefficient.
The data set is a state-year panel. Each state contributes one row per year from the start of the observation window until it adopts, then drops out. This set of rows is the risk set.
Worked example (hypothetical numbers)
The numbers below are invented to show the arithmetic. They are not results from any real study.
Risk set. Suppose a state adopts in year 5 of the window. It contributes five rows: ADOPT = 0 for years 1 to 4 and ADOPT = 1 for year 5. A state that never adopts contributes a row of zeros for every year. In real policy panels most rows are zeros: Berry and Berry report that only about 3 percent of the cases in their lottery sample are adoption events, which is why this is a rare-events problem.
Predicted hazard. Suppose a logit model gives β0 = -4.2 and β1 = 0.60 per adopting neighbour, with the internal variables held constant. The predicted probability is 1 / (1 + e-z), where z = β0 + β1·NEIGHBORS.
| Adopting neighbours | z | e-z | Predicted hazard |
|---|---|---|---|
| 0 | -4.2 | 66.686 | 1 / 67.686 = 0.0148 (1.5%) |
| 2 | -3.0 | 20.086 | 1 / 21.086 = 0.0474 (4.7%) |
| 4 | -1.8 | 6.050 | 1 / 7.050 = 0.1419 (14.2%) |
Odds ratio. Each additional adopting neighbour multiplies the odds of adoption by e0.60 = 1.82. Check with two neighbours: the odds are 0.0474 / (1 – 0.0474) = 0.0498, which equals e-3.0.
Interpretation
| What you see | Reading |
|---|---|
| Positive, significant coefficient on neighbouring adopters | Adoption becomes more likely as more neighbours adopt, consistent with diffusion once internal determinants are controlled. |
| Coefficient near zero once internal variables are added | Apparent clustering may reflect shared internal conditions, not influence between governments. |
| Neighbour effect larger when internal conditions favour adoption | An interaction pattern of the kind Berry and Berry (1990) found for lotteries; test it with an interaction term. |
| Probit or logit coefficient | Report predicted probabilities or odds ratios as well; the raw coefficient is not a percentage-point effect. |
Assumptions and common mistakes
- Ignoring the risk set. Keeping states in the data after they adopt treats adoption as repeatable. Drop them, as adoption is nonrepeatable.
- Arbitrary regions. Predesignated regions impose boundaries the data may not support; a count of adopting neighbours is the alternative Berry and Berry used.
- Analysing explanations separately. Fit diffusion and internal determinants together.
- Mistaking correlated adoption for diffusion. Neighbouring states may adopt in the same period because of a shared shock. Consider time effects or a measure tied to your hypothesised mechanism.
- Reading coefficients as probabilities. Convert to predicted hazards as in the table above.
How to report the result (APA style)
A reporting sentence using the hypothetical numbers above, with a hypothetical standard error of 0.15:
In a discrete-time logit model of state-year data, each additional previously adopting bordering state increased the odds of adoption (b = 0.60, SE = 0.15, odds ratio = 1.82, 95% CI [1.36, 2.45], p < .001), holding fiscal condition and election year constant.
Also state the unit and period, the number of state-years in the risk set, the number of adoption events, and how neighbours were defined.
How to estimate it in R, Python or Excel
R (probit, as in Berry and Berry; use binomial(link = "logit") for a logit):
fit <- glm(adopt ~ neighbors + fiscal_stress + election_year,
family = binomial(link = "probit"), data = panel)
summary(fit)Python (statsmodels):
import numpy as np
import statsmodels.formula.api as smf
fit = smf.logit("adopt ~ neighbors + fiscal_stress + election_year", data=panel).fit()
print(fit.summary())
print(np.exp(fit.params)) # odds ratiosExcel (predicted hazard from known coefficients, with the intercept in B1, the neighbour coefficient in B2 and the neighbour count in A5; the model itself is estimated in R or Python):
=1/(1+EXP(-($B$1+$B$2*A5)))In each case panel must contain one row per state-year at risk, with adopt coded 1 only in the adoption year.
Frequently asked questions
What is policy diffusion in simple terms?
It is the spread of a policy from government to government, where earlier adopters influence later ones. It is distinct from governments each adopting independently for their own reasons.
How do you tell diffusion from independent adoption?
Model both together. If the number of adopting neighbours still predicts adoption after internal determinants are controlled, that is evidence for diffusion; if it vanishes, the clustering may be internal.
Is a state’s first adoption always the first in the world?
No. In this literature an innovation only needs to be new to the adopting government.
Why is adoption modelled as nonrepeatable?
The event can occur once per unit. After adoption the unit is no longer at risk and leaves the risk set.
Where does this fit in a research design?
It is a quantitative, observational design for panel data. For related methods see types of regression analysis and, for estimating the effect of a single adopted policy, the synthetic control method. For background on the object being studied, see what is public policy.
Sources
- Berry, F. S., & Berry, W. D. (1990). State lottery adoptions as policy innovations: An event history analysis. American Political Science Review, 84(2), 395-415. Full text (read 2026-11-08).
- Graham, E. R., Shipan, C. R., & Volden, C. (2013). The diffusion of policy diffusion research in political science. British Journal of Political Science, 43(3), 673-701. Abstract (read 2026-11-08).
- Shipan, C. R., & Volden, C. (2008). The mechanisms of policy diffusion. American Journal of Political Science, 52(4), 840-857.
- Walker, J. L. (1969), as cited in Berry and Berry (1990).
