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Andrew Yeoum SID: 305147021 BUSS7902 Final Report Introduction This project is an exercise in modernization theory, which posits that a strong and positive relationship exists between economic development and democracy, with the causal direction running from the former to the latter. Understanding the relationship between these two variables and the causal direction of the relationship remains one of the major and ongoing endeavors of political science inquiry. Are rich countries more likely to be democratic because democracy makes countries rich, or is development conducive to democracy? Modernization theory is one of the most important and established theoretical areas in the field of comparative politics, and arguably the only work in the field that has ever truly earned the accolade of “theory” (McClintock, 2005). This being the case, the hypothesis is a much-tested one, but its empirical and methodological approaches remain contested. Much dispute also stems from issues related to 1

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Andrew YeoumSID: 305147021

BUSS7902 Final Report

Introduction

This project is an exercise in modernization theory,

which posits that a strong and positive relationship

exists between economic development and democracy, with

the causal direction running from the former to the

latter. Understanding the relationship between these two

variables and the causal direction of the relationship

remains one of the major and ongoing endeavors of

political science inquiry. Are rich countries more likely

to be democratic because democracy makes countries rich,

or is development conducive to democracy? Modernization

theory is one of the most important and established

theoretical areas in the field of comparative politics,

and arguably the only work in the field that has ever

truly earned the accolade of “theory” (McClintock, 2005).

This being the case, the hypothesis is a much-tested one,

but its empirical and methodological approaches remain

contested. Much dispute also stems from issues related to

1

Andrew YeoumSID: 305147021

conceptual and definitional disagreements on economic

development, on the one hand, and the nature of democracy

itself on the other, and how these two variables are

defined and measured as independent or dependent

variables.

The purpose of this project is to test a particular

variant of modernization theory, one that was put forward

by political scientist Adam Przeworski in his much cited

1997 article in World Politics, “Modernization: Theories and

Facts”. Using time-series cross-sectional regression,

Przeworski (1997) argued that indices of development,

such as economic growth, industrialization and

urbanization were poor indicators of why countries

actually make the transition to democracy, but they may

go a long way in explaining why democracies endure and

consolidate. The goal of this project is to test whether

this theory holds true approximately 22 years from the

exit year of his data, 1990, to a recent year, 2012. If

democracies with higher levels of economic development

are quantatively assessed to have generally better levels

of democratic development, then the theory holds. The

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Andrew YeoumSID: 305147021

independent variable will focus on only one, but arguably

the most illuminating, indicator of economic development

– per capita income measured through Gross Domestic

Product (GDP). The dependent variable is the countries

that are considered, as of 2012, to be democracies in at

least the formal, electoral sense. In defining the

variables in such a manner, this paper seeks to test the

hypothesis that countries with higher per capita incomes

are more likely to enjoy better states of democracy. The

hypothesis is thus a relational one, rather than causal.

It seeks to ascertain whether a strong, positive

relationship exist between high-income countries and

their levels of democratic consolidation. It is intended

that the existence of such a relationship will illustrate

the significance of economic development to a nation’s

democratic consolidation. More precisely, it will show

that higher (per capita) income levels are a good

indicator for the state of democracy in democratic

countries.

Background to the problem

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Andrew YeoumSID: 305147021

In what is now a classic article in the American Political

Science Review, the sociologist Seymour Martin Lipset (1959)

argued that there is a correlation between economic

development and democracy. He argued that rich countries

are much more likely than poor countries to be

democracies, or in his own words, “The more well-to-do a

nation, the greater the chances that it will sustain

democracy”.1 Distinguishing among stable democracies,

unstable democracies, unstable dictatorships, and stable

dictatorships both in Europe and the Americas, Lipset

showed how these regime types correlated with indices of

wealth, industrialization, education, and urbanization.

Part of the reason that this became called

‘modernization’ theory is that it presumed that economic

development and modernization caused democracy. The

contemporary debate over modernization theory has in many

respects circled around Lipset’s original research

agenda. Lipset’s argument was widely accepted in the

1960s, then contested in the 1970s after the breakdown of

democratic regimes in Latin America’s wealthier nations,

1 See Seymour Martin Lipset, “Some Social Requisites of Democracy” (1959) 53 (1) American Political Science Review 69-105.

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and ultimately reaffirmed in the 1990s as these and many

other nations made the transition to democracy. In many

of these cases, transitions seemed to follow impressive

periods of economic development.

Critics of Lipset took issue with the theory’s

relatively unproblematic picture of social change,

arguing that it was too linear, teleological and too

optimistic. One of the most important critics of Lipset

was Dankwark Rustow (1970), who criticized modernization

theory for focusing only on ‘environmental factors’ like

income, economic growth and urbanization. Rustow argued

that just because greater wealth and democracy happened

to appear at the same time in some places – correlation –

that didn’t mean that wealth caused democracy. The

decisions made by individuals, social groups, political

leaders and institutions were just as important. These

were very important in Latin America in the 1970s, he

argued, helping to explain why some countries became

democratic in the region and others did not.

Samuel Huntington (1968), in his seminal work Political

Order in Changing Societies, argued that modernization theorists

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Andrew YeoumSID: 305147021

were right in seeing economic development as unleashing

profound social changes, but wrong in assuming those

changes would necessarily be benign or progressive. 2 He

argued that there is nothing inevitable about economic

development leading to democratic change. Indeed,

whatever the threshold at which development is supposed

to undermine authoritarian regimes, dictatorships

survived for years in countries that reached the upper-

middle or even high-income brackets. Nevertheless,

Huntington (1968) was in general agreement with Lipset,

and he laid out four key intervening variables between

development and democracy: (1) A higher level of

education, literacy, and media sources are all more

likely in a wealthy society; (2) Political disputes and

corruption are less costly, and a more prosperous society

gives people diverse and broader options; (3) Society is

too complex for an authoritarian system; (4) Stable

middle class is the best support for a democracy.

Within modernization theory, the question of why,

exactly, development leads to and/or sustains democracy

2 Samuel P. Huntington, Political Order in Changing Societies (Yale University Press, 1968).

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Andrew YeoumSID: 305147021

has been the subject of intense debate. Some of the more

recent literature on modernization theory has focused

their inquiry almost exclusively on exploring the

intervening variables or the causal mechanisms involved.

Economic development, after all, does not in and of

itself causes democratic institutions to emerge

automatically when a country attains a certain level of

GDP. Some prominent political scientists in this area is

(Inglehart and Welzel 2005) argued that economic

development is conducive to democracy to the extent that

it, first, creates a large, educated and articulate

middle class who become accustomed to self-expression and

thought, and second, transforms people’s values and

motivations. His view that mass cultural and attitudinal

changes are the crucial intervening variables between

economic development and political outcomes drew heavily

on the vast amount of data he collected from societies

containing 85% of the world's population through the

World Values Survey. Other scholars (Carles Boix 2003 and

Acemoglu and Robinson 2005) have examined the ways in

which economic inequality and stratification influence a

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Andrew YeoumSID: 305147021

country's regime type (although they disagree over the

precise role played by inequality and stratification

patterns).

Alongside these endless empirical studies of the

correlation between wealth and democracy and its

intervening variables, Przeworski’s contribution to the

debate becomes highly significant. In reassessing

Lipset’s original thesis, Przeworski pointed out that

before any testing of hypotheses are even attempted, a

very important distinction must be made between the

processes of democratic transition, on the one hand, and

democratic consolidation, on the other. This distinction,

he argued, is crucial because it affected the

implications of empirical outcomes. A certain factor, say

variable X, may be an explanatory factor in both the

transitional phase and consolidation phase, but another

factor, variable Y, may go towards explaining the former

phase but may be irrelevant as an explanatory factor in

the latter phase, and vice versa.

Przeworski argued that the first wave of

modernization theory had erred in its failure to

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Andrew YeoumSID: 305147021

differentiate the dependent variable between the

establishment of democracy (“democratization”) and its

sustainability (“consolidation”). Much of the literature

on modernization theory tended to conflate these two

distinct stages of democracy into a single, unproblematic

dependent variable. He noted that the fragility of

democratic norms and values in many so-called

“democratized” nations with some of the trappings of a

formal democracy (e.g. holding elections) attested to

both the difficulty and importance of consolidating

democracy. According to Przeworski, this is where

economic development enters as the crucial independent

variable to explain the dependent variable defined as

consolidated democracy, as oppose to mere

democratization. In fact, he asserted, evidence showed

that economic development played an important role in

fostering the former but not the latter (i.e. it explains

why democracy endures, but not why it emerges). A 1997

study (Przeworski and Limongi 1997) of 135 countries

examined between 1950 and 1990 showed that for democratic

countries with a GDP per capita of USD 7,001 or above

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Andrew YeoumSID: 305147021

(the high income threshold in 1990), the statistical

probability of them descending into authoritarianism was

zero. That probability increased monotonically for the

democracies falling into the lower income brackets. In

other words, above $7,001, democracies could

theoretically expect to last forever, and indeed not a

single high-income democracy during the 40-year period

ever fell.

Methodology

The type of study undertaken was a two-variable cross

sectional linear regression, using the sample regression

model. The temporal dimension involved a stationarized

series for a single time-unit, year 2012. The spatial

dimension concerned nation states as the units of

analysis. Using the variables, data sets and sampling

explained below, this project was conducted in three

phases. The first phase involved the regression of

democracy scores and per capita GDP of the sample

countries and charting them on a scatter plot, with the

values of the dependent variable (Y) displayed on the

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Andrew YeoumSID: 305147021

vertical (intercept) axis and the values of the

independent variable (X) on the horizontal (slope) axis.

The pattern was a positive one, running from lower-left

to upper-right, i.e. the more rightward values on the

horizontal axis, the higher values on the vertical axis.

The parameters of the regression model were estimated

using the ordinary least-squares (OLS) estimator. To

assess the overall fit between the regression model and

the dependent variable (“goodness of fit”) the second

phase involved measuring the uncertainty of the OLS

regression line via coefficient of determination, or -

squared statistic ). The third phase involved

hypothesis testing via the test of significance approach.

Being a directional hypothesis test with a positive

expectation, the one-tailed t test was more appropriate

for this study than the two-tailed test.

The basic idea of two-variable regression is that we

are fitting the “best” line through a scatter plot of

data that represent the democratic countries. This line,

which is defined by its slope and y-intercept, serves as

a statistical model of reality. Theories about political

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Andrew YeoumSID: 305147021

phenomena, by their very nature, are necessarily

probabilistic rather than deterministic (Kellstedt and

Whitten 2009). Ultimately, this project is trying to

explain processes that involve human behavior, which is

complex and bound to involve random elements. It is not

expected that all of the data points to line up perfectly

on a straight line, so the values of our dependent

variable is construed as having both a systemic

component, , and a stochastic (or random)

component, . In two-variable regression, information

from the sample data is used to make inferences about the

underlying or unseen population of interest, which in our

case are all democratic countries in the world. Thus,

and are described as parameter estimates, and can be

written in terms of expectations: E (Y| )

, and the estimated stochastic component, the “residual”

or the sample error term, can be rewritten as .

But how “good” the estimated regression line is of true

population regression function (PRF) depends on specific

assumptions – aside from the fact that it is linear in

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Andrew YeoumSID: 305147021

the parameters – about how the stochastic are

generated.

Assumptions and Limitations

In estimating the regression model, a large set of

assumptions is made about the unseen population model.

The statistical analysis of the model in this study made

the following assumptions about the stochastic terms

and about our model specification.

Assumptions about : the assumption that the

independent variable ( ) is uncorrelated with the

disturbance term is automatically fulfilled in our

case since the GDP figures for per capita income,

the variable, is obviously non-stochastic, i.e.

its value is a fixed number. The assumption that

values are measured without error in turn assumes

that any variability from our regression line is due

to , and not to measurement problems in . There

are obvious problems with this assumption since many

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potential errors exist in any GDP measurement (e.g.

economic activities that are hard for governments to

measure), but it assumes, for the purposes of

estimating our OLS model, that the denominator (i.e.

population) in our calculation, GDP of countries for

2012, is measured exactly correctly.

No Bias: the random term represents all

factors not included in the model, and assumes that

they are unrelated to the variable explicitly

introduced in this model, the values of per capita

GDP. Thus, given the value of , the expected value

of the disturbance term is zero: .

has variance : Homoscedasticity: it was assumed

that the variance of each is constant, or

homoscedastic: . In other words, in assumes

that the democracy scores for each countries (the

values represented by the DI scores, discussed below

in “Variables and Data”) are spread around their

mean values with the same variance.

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Andrew YeoumSID: 305147021

No Autocorrelation: it is assumed that there is no

correlation, or systemic relationship, between two

error terms. This assumption of autocorrelation,

expressed, , means the error terms

are random. It assumes that any two DI scores for

countries are uncorrelated because only vary as

varies (since and ’s are fixed GDP numbers), and

so if ’s are uncorrelated, the ’s will also be

uncorrelated.

Correct Model Specification: it is assumed that the

model is correctly specified and that there cannot

be some other variable(s) (s) that may also affect

the democracy scores. In reality, there may be

additional variables that can be theorized to be

causally related to democratic consolidation, and to

realistically make the specification assumption, all

such variables should be included in the model.

Since the statistical model of reality is served

only by the two-variable regression line this study

must be construed as being simply the first (but

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Andrew YeoumSID: 305147021

important) step toward the multiple regression

model. The latter model, however, is beyond the

scope of this study and it is acknowledged that an

obvious shortfall is the inability to account, or

control for, (s) as we measure our independent

variable of interest and our dependent variable .

A further limitation worth mentioning is that the model

in this study does not account for intervening variables,

or the causal mechanism, involved between the two and

variables introduced in the study. That is, even if one

can assume for a moment that higher income levels cause

higher levels of democratic development, a more complete

explanation may add that causes because leads to,

or is at least correlated with, for example a growing and

educated middle class or that prosperity contributes to

political stability in general, conditions that are often

seen as necessary (although not sufficient) for

democratic consolidation.

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Variables and Data

As discussed earlier, the independent variable, defined

in this study as per capita income, is a continuous

variable and is measured as GDP per capita in current

United States Dollars (USD) using the 2012 calculations

provided by the World Bank in its online database, World

Databank. GDP per capita is the market value of all goods

and services produced inside a country at a given time

divided by the population of that country, and so is

effectively a per capita measure of the total income

received by all sectors of an economy within that country

at that given time. The GDP indicator is thus related to

national accounts and is not a measure of wealth or

living standards.3 A limitation with the GDP figures used

in this study is its nominal measurement in USD market

exchange rates, and so the World Bank’s calculations do

3 The GDP indicator has been criticized for its numerous limitations,and is not unproblematic when it comes to measuring a country’s levelof economic development. The limitations are too manifold and multifaceted for a detailed treatment here, but it may suffice to note that the GDP framework does not directly account for levels of real wealth, productivity, industrialization, urbanization, standardsof living and quality of life, or economic sophistication and complexity. It is, however, strongly and positively correlated with these indices of development and still remains a frequently used de facto indicator of a nation’s economic development.

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not reflect a country’s real, or purchasing power parity

(PPP) GDP and its relative price levels.

The dependent variable is defined as the “state of

democracy” (SOD), measured using the Democracy Index (DI)

compiled by the Economist Intelligence Unit (EIU). The DI

measures the state of democracy in 167 countries based on

60 indicators grouped into five different categories:

electoral process and pluralism, civil liberties,

functioning of government, political participation, and

political culture. The DI then assigns a numerical score

to countries and places them into one of four regime

types: full democracies (8.00-10.00), flawed democracies

(6.00-7.99); hybrid regimes (4.00-5.99); and

authoritarian regimes (0.00-3.99). In order to

operationalize the dependent variable, the measurement

metric of SOD was treated and measured as a continuous

variable by ignoring the DI’s categorization of regime

types and focusing only on its numeric scores so as to

give SOD equal unit differences, i.e. so that any

increase in the value of SOD always mean that it is more

democratic, whereas if the DI regime types were also

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Andrew YeoumSID: 305147021

adopted, SOD would be an ordinal variable whereby a

country with one-unit increase from say 6.05 to 7.05

would still be classified as a “flawed democracy”.

Quantifying “democracy” and levels of democratic

development through the use of numeric indexes is not

without its own problems, and remains a contentious issue

in the field of comparative politics, not least because

democracy is itself one of the most contested

definitional concepts in the social and political

science. Aside from methodological considerations, the

quantification of democracy is further complicated by

disagreements that exist along ideological, ideational,

or even ontological lines (Scmitter and Karl 1991). In

spite of these problems, quantitative measurements of

democracy can be seen to have a functional advantage, and

numerous non-partisan organizations rigorously study

countries around the world and apply variables to

determine whether a democracy exists, and to determine

its quality and the extent to which it is considered

durable.

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The US-based Freedom House publishes its annual

Freedom in the World (FIW) report (which assigns numerical

scores and then classifies countries as “free”, “partly

free” and “not free”) and the Center for Systemic Peace

maintains the Polity data series (see Polity IV for latest

version). The US National Endowment for Democracy also

conducts research and fields expert opinions.

Supplementing these are the World Values Survey (WVS) and

the work of other polling organizations such as Pew and

Gallup, which routinely measure the attitudes and values

of people around the world as they pertain to preferences

and proclivities for types of governments.

The choice of the EIU’s DI over other numeric

indexes measuring “democracy” and its ancillary elements

came from consideration of the “thin” and “thick”

components of democracy in comparative politics (Coppedge

2005). At the most fundamental (or thin) level, democracy

is simply a system of governance with popular sovereignty

or majority rule. Also known as “electoral democracy”,

this definition describes the processes by which a

government derives its authority or mandate. But this

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represents only one side of the equation, and a (thick)

designation of democracy factors into account other

constitutive elements that go towards a “liberal

democracy”, such as governance by rule of law,

accountability and the protection of civil liberties.

Though how these two basic components of democracy –

electoral and liberal – are represented may differ, it is

widely accepted that a truly democratic system of

governance must comprise both.

The FIW and the EIU’s DI both express this critical

combination of the thin and thick components of

democracy. Other indicators such as the widely used

Polity data series (Polity IV) simply measure a state’s

level of democracy based on evaluations of elections (its

competitiveness, openness and level of participation), a

minimalist criterion many consider thin and narrow. In

turn, the DI was chosen over FIW because the latter’s

measurements of thick components like the state of

political freedoms and civil liberties was deemed not

“thick” enough. FIW surveys do not encompass sufficiently

or at all some features that determine how substantive

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democracy is or its quality. Freedom is an essential

component of democracy, but not sufficient. Indeed, FIW

emphasizes the formal existence of liberties rather than

the actual exercise of freedom, according to (Przeworski

2003, 277) who gave the following example:

Look at the United States…It’s a country where half

of the population doesn’t vote, even in presidential

elections; where barriers of entry to politics are

enormous; in which practices which in other

countries would be considered political corruption

are ubiquitous; where the same two parties speak in

a commercially sponsored unison; a country in which,

at least for black American males, being free means

only being out of jail; the oldest democracy in the

world which has the highest rate of incarceration in

the world.

In the FIW surveys, two crucially important substantive

elements of democracy, political participation and

functioning of government, are taken into account only in

a marginal and formal way. In contrast, the EIU’s DI

treats these two elements as “necessary components” that

go towards a “full and consolidated democracy”, and was

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thus deemed preferable to the FIW’s more formalistic

measure of substantive democracy.

Population and Sample

The question being asked in this paper is whether higher

per capita income levels bear a strong positive

relationship with the “state of democracy” in democratic

countries. The population of this study therefore

encompasses all “democracies” in the world, i.e.

countries that are already democratic in at least the

electoral sense.

The sampling frame for the dependent variable is the

DI’s list of 167 countries, which as mentioned above,

groups the countries into four categories: full

democracies (8.00-10.00), flawed democracies (6.00-7.99);

hybrid regimes (4.00-5.99); and authoritarian regimes

(0.00-3.99). Countries are given overall and categorical

scores from 0–10 (a snapshot sample provided in Table 4

below). This project uses only the overall scores. The

frame for the independent variable is the list of 192

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countries listed in the World Bank’s DataBank under its

“GDP per capita (current US$)” indicator. The DataBank

lists the level of GDP per capita measured in current USD

according to country and by year (from 1980-2012) grouped

into five-year brackets from 1982 onwards (a snapshot

sample of the frame list can be seen below in Table 3).

As mentioned earlier, the time unit for this project is

the year 2012 only.

Since we are only interested in democratic

countries, the sample selected from these frames are all

the states listed in the DI with a numeric score of 6.00

and above, and for which income data was available on the

World Bank database. GDP figures for some DI-based

democratic countries were unavailable for the particular

year we were interested in (e.g. New Zealand and Israel

for 2012), and others like Taiwan is excluded in the

DataBank due to its de facto legal status. This left us

with a sample of 75 DI-based democratic countries for

which DataBank had figures for, out of DI’s sample frame

of 79 democracies (i.e. those with DI scores of 6.00 and

above).

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Results

Table 1 below is the computed output of the regression

analysis using StatPlus, represented in Table 2 by an Excel

scatter-plot chart showing the OLS regression line and

its goodness-of-fit measured by the coefficient of

determination (the equation and -squared statistic is

highlighted).

TABLE 1.

TABLE 2.

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Hypothesis Testing: One-Tailed Test

The most common form of statistical hypothesis tests

about the parameters from an OLS regression model is a

two-tailed test that the slope parameter is equal to

zero. First the sample slope parameter is observed, which

is an estimate of the population slope, then from the

value of this parameter estimate, the confidence interval

around it, and the size of our sample, we evaluate how

likely it is that we observe this sample slope if the

true but unobserved population slope is equal to zero. If

the answer is “very likely”, then we conclude that the

population slope is equal to zero.

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Andrew YeoumSID: 305147021

In reality, though, most political science

hypotheses are that a parameter is either positive or

negative and not just that the parameter is different

from zero (Gerring 2012). Our theory is that the higher

the levels of economic development as measured by GDP per

capita, the better will be the democracy scores for the

democratic countries. In other words, it is a

directional hypothesis where we expect to see a positive

relationship between GDP per capita and democracy scores,

meaning that we expect to be greater than zero. When

our theory leads to such a directional hypothesis with a

positive expectation, a realistic set of hypotheses is

expressed as:

: 0

: 0

where is the null hypothesis that GDP has no effect on

DIS, and is the (one-sided) alternative hypothesis

that GDP does have true effect on DIS. As is the case

with the two-tailed test, these two rival hypotheses are

expressed in terms of the slope parameter from the

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Andrew YeoumSID: 305147021

population regression model. Using the one-tail row from

the t-table in Appendix 1, we find that for 75 degrees of

freedom (d.f.), we have the following critical t values:

Level of Significance Critical t

0.01 2.3771

0.025 1.9921

0.05 1.6654

To test which of the two hypotheses are supported, we

calculate the t value where is set equal to the value

specified in the null hypothesis (in this case zero

because : ), which we represent as :

The computed t statistic is 11.70255. Since this t value

exceeds 1.6654, we can easily reject the null hypothesis

at the 5% level of significance. In fact, it far exceeds

the critical t value even at the 0.01% level of

significance. In other words, there is sufficient

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Andrew YeoumSID: 305147021

evidence to conclude that income (GDP per capita)

increases SOD.

Goodness-of-Fit: R-Squared Statistic

The findings above illustrate that the estimated

intercept and slope coefficients are individually

statistically significant (i.e. significantly different

from zero). This suggests that the sample regression

function fits the data reasonably well. The goodness of

that fit was measured as the coefficient of

determination, . The computed statistics for our two-

variable model of democracy score is 0.64921. It

indicates that our model accounts for about 65% of the

variation in the dependent variable. Since can at most

be 1, and in our case is measured as a percentage of a

properly stationarized (rather than time) series, the

computed should be interpreted as high. It explains

almost 65% of the variation in democracy scores in 2012

with just one measure of the economy, GDP per capita.

When we start to think of all the different (Z) variables

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Andrew YeoumSID: 305147021

– such as external influences, individual and group

agency, culture, ideology, values, historical or

geopolitical factors – that may potentially be involved

but not in this simple model, this level of accuracy is

rather impressive. In fact, it can be suggested that this

tells us something remarkable about democratic

consolidation or levels of democratic development – that

per capita income levels (and by extension, the economy)

is extremely important.

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APPENDIX 1: t-table (α is the probability of Type I error)4

α (1 tail) 0.05 0.025 0.01 0.005 0.0025 0.001 0.0005α (2 tail) 0.1 0.05 0.02 0.01 0.005 0.002 0.001

df61 1.6702 1.9996 2.3890 2.6589 2.9127 3.2293 3.457362 1.6698 1.9990 2.3880 2.6575 2.9110 3.2269 3.454563 1.6694 1.9983 2.3870 2.6561 2.9092 3.2247 3.451864 1.6690 1.9977 2.3860 2.6549 2.9076 3.2225 3.449165 1.6686 1.9971 2.3851 2.6536 2.9060 3.2204 3.446666 1.6683 1.9966 2.3842 2.6524 2.9045 3.2184 3.444167 1.6679 1.9960 2.3833 2.6512 2.9030 3.2164 3.441768 1.6676 1.9955 2.3824 2.6501 2.9015 3.2144 3.439569 1.6673 1.9950 2.3816 2.6490 2.9001 3.2126 3.437270 1.6669 1.9944 2.3808 2.6479 2.8987 3.2108 3.435071 1.6666 1.9939 2.3800 2.6468 2.8974 3.2090 3.432972 1.6663 1.9935 2.3793 2.6459 2.8961 3.2073 3.430873 1.6660 1.9930 2.3785 2.6449 2.8948 3.2056 3.428874 1.6657 1.9925 2.3778 2.6439 2.8936 3.2040 3.426975 1.6654 1.9921 2.3771 2.6430 2.8925 3.2025 3.425076 1.6652 1.9917 2.3764 2.6421 2.8913 3.2010 3.423277 1.6649 1.9913 2.3758 2.6412 2.8902 3.1995 3.421478 1.6646 1.9909 2.3751 2.6404 2.8891 3.1980 3.419779 1.6644 1.9904 2.3745 2.6395 2.8880 3.1966 3.418080 1.6641 1.9901 2.3739 2.6387 2.8870 3.1953 3.4164

4 Full version available on <http://www.statstodo.com/TTest_Tab.php> .

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