## packages
library(tidyverse)
library(peacesciencer)
library(sandwich)
library(lmtest)
library(sjPlot)
library(patchwork)
library(coolorrr)
set_theme()
set_palette()
## create data in steps
## 1. country-year data of conflict initiation
## and peace spells
create_stateyears(
subset_years = 1950:2000
) |>
add_gml_mids() |>
add_spells() -> Data
## 2. Lake (2007) data for int'l hierarchy
haven::read_dta(
here::here("Data", "ISreplicationdataset.dta")
) -> lake_dt
## 3. merge the datasets
Data |>
left_join(
lake_dt
) -> Data15 Rules and Enforcement
The third pathway to peace that Blattman (2023) talks about is rules and enforcement—essentially, political order. When most people imagine political order, the state usually is what comes to mind. This is no surprise. The state is unique in that it has the supreme authority to both make and enforce rules within a particular territory. This ability gives the state the capacity to control violence, thus preserving peace. When a state is fragile or absent, violence often occurs with greater frequency.
However, the state isn’t the only institution that can control violence. There are many informal institutions at the local and international levels that have this power as well, which often arise in places where state authority is weak or nonexistent. Examples include Mafia-like criminal hierarchies which can control their subordinates and broker peace deals with rival groups, and international organizations which can do the same among countries. Beyond these examples, some institutions, such as honor (retributive) culture, are self-enforcing. While certainly imperfect, violence is much lower with these institutions than without.
These informal institutions are perhaps the most fascinating to study, because their source of legitimacy often isn’t legal, or as the political scientist David Lake (2007) puts it, “juristic.” Instead, rightful rule in these institutions is based on relational forms of legitimacy. By this, Lake (2007) means that the right to rule comes from a reciprocal relationship among actors. A hegemon (dominant power) exercises influence over subordinates, and in exchange the hegemon offers these subordinates some material benefit—usually security. So long as the hegemon delivers, subordinates are happy to cede some autonomy to it.
This idea of informal or relational hierarchy as a form of legitimate rightful rule, as opposed to juristic or legal theories of authority, is what Lake (2007) is most known for in political science. He applies this idea to international politics, where the conventional wisdom is that states in the international system exist under a condition of anarchy. Though it’s true that there is no world government that has legal authority to make and enforce rules, it would be a mistake to confuse the absence of a worldwide state for anarchy. Rather, Lake argues that international politics is inherently hierarchical, with regional or global hegemonic powers who exercise authority over subordinate countries. Whether it’s the British Empire or the U.S. lead Liberal International Order, history is full of examples of hierarchical relationships in international politics.
For Lake (2007), international hierarchy is more than a matter of fact; it has observable implications for the behavior of states. These implications speak directly to the arguments made by Blattman (2023) about rules and enforcement as a pathway to peace. Lake (2007) in his study develops a measurement strategy for quantifying how much a given country falls under the umbrella of U.S. security and economic hierarchy covering the period from 1950 to 2000. He proposes that the more countries fall under the authority of the United States, the less they will need to spend on their own defense. The reason lies in the relational nature of international hierarchy. In exchange for subordination to the U.S., the U.S. offers security. This reduces the need that individual countries have to finance their own defense.
Lake (2007) operationalizes (that’s a fancy way of saying “measures”) hierarchy along two dimensions: security and economic. He creates a U.S. security hierarchy index using measures of U.S. troop deployments per capita in different countries and the degree to which a country has military alliances with many different countries or solely with the U.S. He creates a U.S. economic hierarchy index using measures of the degree to which countries align their monetary policy with that of the U.S. and their level of trade dependence on the U.S. He then tests the relationship each of these measures has with defense spending per GDP in different countries over time. Lake finds that security hierarchy in particular corresponds with less defense spending on the part of other countries. This relationship doesn’t exist with economic hierarchy however, which Lake blames on either measurement error on his part in constructing his variables or else because economic subordination to the U.S. doesn’t guarantee that the U.S. will offer these countries security. Either way, it probably shouldn’t come as a surprise that hierarchy linked to security has the sharpest correspondence with security-related behavior on the part of subordinates.
Lake’s findings are important and suggest that hierarchy has observable effects in international politics. However, we can extend this argument to other behaviors on the part of states as well—behaviors that correspond more directly to the idea that rules and enforcement are a pathway to controlling violence. In the example to follow, I walk through how we can replicate Lake’s analysis and extend it to consider state aggression in the form of MID initiation.
15.1 Hypotheses
Lake (2007) makes a simple argument. Hegemonic powers such as the U.S. offer their subordinates material benefits, namely, security. In exchange, these subordinates bend to the preferences of the hegemon. This ability on the part of the hegemon to make and enforce rules among its subordinates is the very kind of political order that Blattman (2023) argues makes violence less likely. The existence of such an authority can mitigate each of the five reasons for war that Blattman discusses—unchecked leader interests, uncertainty, intangible incentives, misperceptions, and commitment problems. A hegemon can impose costs on states that disturb the peace and help to enforce bargains.
If this is true, then it follows that countries that fall disproportionately more under the umbrella of U.S. authority should be less prone to showing aggression toward other countries. In particular, this implies that the more countries fall under U.S. hierarchy, the less often they should initiate militarized interstate disputes (MIDs) with other states.
A key question, of course, is what kind of hierarchy counts with respect to violence? Lake’s analysis suggests that there may be something distinct about security hierarchy as opposed to economic hierarchy. This makes sense. U.S. authority with respect to security is probably most apt to influence security-related behaviors among subordinates—economic security, less so. Therefore, we should expect security hierarchy to have the closest correspondence to MID initiation:
Hypothesis 1: Security hierarchy should lower the likelihood of MID initiation.
Conversely, it probably should be the case that we’ll fail to find a strong relationship between economic authority and security-behavior. Therefore:
Hypothesis 2: Economic hierarchy should not influence the likelihood of MID initiation.
The next section introduces the data and offers some descriptive analysis.
15.2 Data
The below code creates the data necessary for testing the above hypotheses. It starts out, as usual, by telling R what packages to open. It then creates a base dataset of the universe of country-years from 1950 to 2000 and populates this data with variables related to MID involvement over time. Next, it reads in replication data from Lake (2007). This dataset is in the form of a Stata file. You can download it by going to this url: https://dataverse.harvard.edu/file.xhtml?persistentId=doi:10.7910/DVN/HVKGMZ/MG3TTY&version=1.0. This dataset has Lake’s measures of security and economic hierarchy along with a number of other variables that we can use as controls in our analysis. Once the data is read into R, since it has both a year and ccode column already, we can go ahead and join it to the MID dataset we created. The final object called Data is the dataset that we’ll use in the analysis.
Before we get to the main analysis, it may be instructive to look at some trends in the data. First off, let’s take a look at the measures of economic and security hierarchy. The below code creates a data visualization with two panels, each showing the distribution of economic and security hierarchy respectively using a histogram. From looking at the data, it’s clear that most countries in the international system fall under U.S. authority to some extent, but high levels of U.S. authority are rare.
Data |>
pivot_longer(
c(us_SH1995, us_EH1995)
) |>
ggplot() +
aes(value) +
geom_histogram(
color = "black",
fill = "gray"
) +
facet_wrap(
~ ifelse(name == "us_SH1995",
"Security",
"Economic")
) +
labs(
x = "Index values",
y = NULL,
title = "Frequency of security and economic hierarchy values",
subtitle = "Most countries do not fall subsantially under U.S. authority over time"
)
Levels of each dimension of authority have also been on a secular decline since 1950, as shown in the below figure. Here I’ve had R produce a time-series plot that shows years on the x-axis and levels of hierarchy on the y-axis. A smoothed generalized additive model is fitted to the data, which summarizes the expected average level of hierarchy along each dimension in the international system by year. Levels of each dimension of U.S. hierarchy are clearly much higher in 1950 compared to 2000.
Data |>
pivot_longer(
c(us_SH1995, us_EH1995)
) |>
ggplot() +
aes(
x = year,
y = value,
color = ifelse(
name == "us_SH1995",
"Security", "Economic"
)
) +
geom_smooth(
method = "gam"
) +
ggpal() +
labs(
x = NULL,
y = "Hiearchy Index",
title = "Variation in U.S. security and economic\nhiearchy from 1950 to 2000",
subtitle = "U.S. hiearchy has been steadly on the decline since 1950",
color = "Index:"
)
Finally, it’s worth checking whether these forms of hierarchy go hand-in-hand, substitute for one another, or are unrelated. The next figure shows a scatter plot with security hierarchy values for countries over time on the x-axis and economic hierarchy values for countries over time on the y-axis. A linear regression line is fit to the data to summarize the correlation between these measures. We can see a positive relationship in the data, suggesting that when countries fall under one kind of U.S. authority, they tend to fall under the other as well. However, it’s important to note that this relationship is noisy. There are many countries over time that fall substantially under U.S. security authority that only minimally fall under its economic authority, and vice versa.
ggplot(Data) +
aes(
x = us_SH1995,
y = us_EH1995
) +
geom_point(
color = "gray",
alpha = 0.5
) +
geom_smooth(
method = "lm",
color = "steelblue",
se = F
) +
labs(
x = "Security Hierarchy",
y = "Economic Hierarchy",
title = "The correlation between economic and\nsecurity hiearchy under the U.S.",
subtitle = "Economic and security hiearchy go hand-in-hand"
)
15.3 Analysis
To test hypothesis 1 and 2, we’ll estimate a logit model with MID initiation by a given country over time as the outcome and the measures of U.S. security and economic hierarchy as the main predictors of interest. We’ll also control for some additional factors in our regression model as well to adjust for their possible confounding relationship with these measures of hierarchy and MID initiation. These are similar variables to those controlled for by Lake (2007) in his own analysis. In particular, we’ll include a measure of the number of all other alliances a country has, country GDP per capita, quality of democracy as captured by Polity, and country military capabilities as captured by CINC scores. As we’ve also done throughout these notes, we’ll include a cubic peace spells trend in the model as well.
But first, before we get to this analysis let’s first attempt to replicate Lake’s original findings with respect to hierarchy and what Lake calls “defense effort,” which he measures by taking the ratio of country defense expenditures to country GDP. Lake uses a linear regression model in his analysis, but this approach is not necessarily the most appropriate given the shape of the data. Defense spending has a heavily skewed distribution and has some zero values for countries over time. A better statistical model for this outcome is a Poisson model, which is usually reserved for count data, but it also can be applied to continuous financial data as well. Usually, the recommendation is to use the quasipoisson family instead of the poisson family in R to estimate this kind of model. The latter makes some strong distributional assumptions, but the latter is a little more flexible in this regard.1
The following code block shows the code for estimating our Poisson model and it summarizes model estimates using coeftest() and reports robust standard errors clustered by country. This model includes the same control variables mentioned above plus a measure of whether a country is involved in any militarized dispute in a given year to adjust for the fact that, if a country is attacked for example, its defense spending will probably increase out of necessity. As we can see from the results, the findings are similar to Lake’s. Security hierarchy has a statistically significant and negative relationship with defense spending, while economic hierarchy has a mildly positive but insignificant relationship with defense spending. The other variables have pretty unsurprising relationships with defense effort.
## testing Lake's claim
glm(
def_eff ~
us_SH1995 +
us_EH1995 +
gmlmidongoing +
otherallies +
rgdpc_k +
polity2 +
cap,
data = Data,
family = quasipoisson
) -> fit_1
coeftest(
fit_1,
vcov. = vcovCL(
fit_1,
cluster = Data$ccode,
type = "HC0"
)
)
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -4.6074e+00 1.2860e-01 -35.8271 < 2.2e-16 ***
us_SH1995 -1.4649e+00 5.0359e-01 -2.9089 0.003627 **
us_EH1995 1.2176e-01 2.3940e-01 0.5086 0.611023
gmlmidongoing 7.1407e-01 1.3754e-01 5.1919 2.082e-07 ***
otherallies 2.0019e-02 9.8166e-03 2.0393 0.041423 *
rgdpc_k 6.1919e-05 9.7030e-06 6.3814 1.755e-10 ***
polity2 -3.1728e-02 1.3001e-02 -2.4404 0.014671 *
cap 5.7837e+00 8.9116e+00 0.6490 0.516335
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The following code produces a figure that summarizes the model predictions for security and economic hierarchy. It’s pretty obvious that security hierarchy strongly and negatively predicts defense effort, while economic hierarchy has no such relationship with defense effort.
## visualize
plot_model(
fit_1,
type = "eff",
terms = "us_SH1995",
vcov.fun = vcovCL(
fit_1,
Data$ccode,
type = "HC0"
)
) +
labs(
x = "US Security Hierarchy",
y = NULL,
title = NULL
) -> p1
plot_model(
fit_1,
type = "eff",
terms = "us_EH1995",
vcov.fun = vcovCL(
fit_1,
Data$ccode,
type = "HC0"
)
) +
labs(
x = "US Economic Hierarchy",
y = NULL,
title = NULL
) -> p2
p1 + p2 +
plot_annotation(
title = "Predicted defense spending per GDP",
subtitle = "Security hiearchy reduces military spending while\neconomic hiearchy modestly increases it"
) 
So we can replicate Lake’s findings, but can we also confirm whether hierarchy controls violence? The following code estimates the logit model described earlier. The model estimates are summarized using coeftest() and robust standard errors clustered by country. The results clearly support both hypothesis 1 and hypothesis 2. While falling more under U.S. security hierarchy leads to a reduction in the probability that a country initiates MIDs with other states in the international system, no such strong relationship is observed for economic hierarchy; though the estimate is negative.
## what's the effect on MID initiation
glm(
gmlmidonset_init ~
us_SH1995 +
us_EH1995 +
otherallies +
rgdpc_k +
polity2 +
cap +
poly(gmlmidinitspell, 3),
data = Data,
family = binomial
) -> fit_2
## summarize the output
coeftest(
fit_2,
vcov. = vcovCL(
fit_2,
cluster = Data$ccode,
type = "HC0"
)
)
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -2.2115e+00 1.1964e-01 -18.4841 < 2.2e-16 ***
us_SH1995 -9.6238e-01 4.0560e-01 -2.3727 0.0176566 *
us_EH1995 -2.0913e-01 2.0185e-01 -1.0360 0.3001805
otherallies 2.8296e-02 8.8854e-03 3.1846 0.0014497 **
rgdpc_k 9.8077e-06 9.6778e-06 1.0134 0.3108596
polity2 -1.8018e-02 1.1712e-02 -1.5384 0.1239515
cap 3.3044e+01 6.2881e+00 5.2551 1.480e-07 ***
poly(gmlmidinitspell, 3)1 -5.8148e+01 6.2030e+00 -9.3741 < 2.2e-16 ***
poly(gmlmidinitspell, 3)2 3.1370e+01 6.7794e+00 4.6273 3.705e-06 ***
poly(gmlmidinitspell, 3)3 -2.5443e+01 6.6414e+00 -3.8310 0.0001276 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The following code produces a figure that summarizes the predicted probability of MID initiation given levels of security and economic hierarchy. The predicted values show how much more security hierarchy is a strong predictor of country aggression compared to economic hierarchy. On the low end of security hierarchy, a country’s predicted probability of MID initiation may be as high as 8%. But among countries that have a score between 2 and 3 on the U.S. security hierarchy index, the predicted probability of MID initiation drops below 1%. Conversely, countries that barely fall under U.S. economic hierarchy are predicted to initiate MIDs 7% of the time. Countries that have up to a score of 2 on the U.S. economic hierarchy index are predicted to initiate MIDs just under 5% of the time. That’s only a predicted difference of approximately 2 percentage points. Moreover, the wide confidence intervals tell us that these predictions are not statistically different from one another.
## visualize
plot_model(
fit_2,
type = "eff",
terms = "us_SH1995",
vcov.fun = vcovCL(
fit_2,
Data$ccode,
type = "HC0"
)
) +
labs(
x = "US Security Hierarchy",
y = NULL,
title = NULL
) -> p1
plot_model(
fit_2,
type = "eff",
terms = "us_EH1995",
vcov.fun = vcovCL(
fit_2,
Data$ccode,
type = "HC0"
)
) +
labs(
x = "US Economic Hierarchy",
y = NULL,
title = NULL
) -> p2
p1 + p2 +
plot_annotation(
title = "Predicted likelihood of MID initiation",
subtitle = "Both types of hierarchy lower the probability of MID initiation\nbut the relationship with security hierarchy is sharpest"
) 
While economic hierarchy remains a weak predictor of MID initiation, it is interesting to note that its relationship with MID initiation is negative. This suggests that U.S. economic hierarchy may have a mild influence on violence, even if the overall impact is minimal and inconsistent. It’d be interesting to tug on this thread a little more, but, unfortunately, this is probably a task for another time.
15.4 Conclusion
Blattman (2023) argues that the presence of an authority that can make and enforce rules is an important condition for peace. While we often attribute this kind of power to the modern state, other forms of authority can operate in a similar way. In the analysis above we saw how international hierarchy can play a role similar to the state as a means of controlling violence. In particular, we saw that the U.S. role as a hegemonic power capable of providing security for its subordinates can promote peace by decreasing the likelihood that these countries initiate militarized disputes with other countries.
Of course, this analysis is highly contingent, and there are many things that we should probably do to check the robustness of these findings. Moreover, the U.S. is only one example of a hegemonic power. There are many regional powers that exercise their own level of authority among subordinates. China, in particular, is increasingly gaining power and influence on the world stage. Does it play a similar role as rule maker and enforcer among its own cadre of states? This is an interesting area of research, and a timely one as well, especially as concerns mount about the ability of the U.S. to continue in its role as leader of the Liberal International Order in the future.
By using
quasipoissonwe’re using a psuedo-Poisson maximum likelihood estimator.↩︎