Scholarly article on topic 'Democracy and growth: Evidence from a machine learning indicator'

Democracy and growth: Evidence from a machine learning indicator Academic research paper on "Political Science"

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Abstract of research paper on Political Science, author of scientific article — Klaus Gründler, Tommy Krieger

Abstract We present a novel approach for measuring democracy based on Support Vector Machines, a mathematical algorithm for pattern recognition. The Support Vector Machines Democracy Index (SVMDI) is continuous on the [0,1] interval and enables very detailed and sensitive measurement of democracy for 185 countries in the period between 1981 and 2011. Application of the SVMDI yields results which highlight a robust positive relationship between democracy and economic growth. We argue that the ambiguity in recent studies mainly originates from the lack of sensitivity of traditional democracy indicators. Analyzing transmission channels through which democracy exerts its influence on growth, we conclude that democratic countries feature better educated populations, higher investment shares, and lower fertility rates, but not necessarily higher levels of redistribution.

Academic research paper on topic "Democracy and growth: Evidence from a machine learning indicator"

Accepted Manuscript

Democracy and growth: Evidence from a machine learning indicator

Klaus Gründler, Tommy Krieger

PII: S0176-2680(16)30022-2

DOI: doi: 10.1016/j.ejpoleco.2016.05.005

Reference: POLECO 1562

To appear in:

European Journal of Political Economy

Received date: Revised date: Accepted date:

29 June 2015 18 May 2016 31 May 2016

- European Journal of POLITICAL ECONOMY

Please cite this article as: Griindler, Klaus, Krieger, Tommy, Democracy and growth: Evidence from a machine learning indicator, European Journal of Political Economy (2016), doi: 10.1016/j.ejpoleco.2016.05.005

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Democracy and growth: Evidence from a machine learning

indicator

Klaus Gründlera'*, Tommy Kriegerb

a University of Würzburg, Department of Economics, Sanderring 2, D-97070 Würzburg, Germany b University of Konstanz, Department of Economics, Universitütsstraße 10, D-78457 Konstanz, Germany

Abstract

We present a novel approach for measuring democracy based on Support Vector Machines, a mathematical algorithm for pattern recognition. The Support Vector Machines Democracy Index (SVMDI) is continuous on the [0,1] interval and enables very detailed and sensitive measurement of democracy for 185 countries in the period between 1981 and 2011. Application of the SVMDI yields results which highlight a robust positive relationship between democracy and economic growth. We argue that the ambiguity in recent studies mainly originates from the lack of sensitivity of traditional democracy indicators. Analyzing transmission channels through which democracy exerts its influence on growth, we conclude that democratic countries feature better educated populations, higher investment shares, and lower fertility rates, but not necessarily higher levels of redistribution.

JEL classifications: O11; O47; P16; H11; C43

Keywords: Democracy; Economic growth; Panel data; Machine learning; Support Vector Machines

1. Introduction

Today, the belief in democracy and its positive effects on freedom, liberty, and wealth is widespread among citizens of different countries. Covering preferences of the vast majority of the world's citizens, the World Value Survey (2014) finds that 79 percent of the global population wish to live in a country that is governed democratically.1 This preference is not only prevalent in countries with a long democratic tradition (United States: 78.7 percent, Sweden: 91.9), but can also be found in Islamic states (Pakistan: 78.3, Malaysia: 86.6),

* Corresponding author Email addresses: klaus.gruendler@uni-wuerzburg.de (Klaus Griindler), tommy.krieger@uni-konstanz.de (Tommy Krieger)

1 See question V140 of the World Value Survey's 6th Wave, conducted between 2010 and 2014: "How important is it for you to live in a country that is governed democratically? On this scale where 1 means it is not at all important and 10 means absolutely important what position would you choose?" The above numbers refer to all respondents that respond to the question with a value of 7 or higher.

Preprint submitted to European Journal of Political Economy

June 2, 2016

African nations (Rwanda: 74.1, Zimbabwe: 86.1), South America (Chile: 83.4, Ecuador: 84.2), and Asia (China: 80.6, South Korea: 86.0). Beginning in December 2010, the unfulfilled desire for democracy in the Arab World (Egypt: 93.6, Yemen: 76.3) culminated in a wave of protests, riots, and demonstrations that spread throughout the nations of the Arab League and the surrounding area. Driven by a fatigue with authoritarian rule, the desire for the improvement in economic opportunities was one major trigger for the uprisings (see Campante and Chor, 2012).

While the majority of the citizens around the world seem to be quite confident that democracy brings with it an improvement in living standards, academics in the fields of political science and economics could not disagree more about the effect of democratization on economic growth. Gerring et al. (2005) summarize the related literature by concluding that "the net effect of democracy on growth over the last five decades is negative or null". More recently, some studies point to a positive effect of democracy on the income level (e.g. Acemoglu et al., 2014 and Madsen et al., 2015), whereas other studies still find no positive contribution (e.g. Murtin and Wacziarg, 2014).

In this paper, we provide evidence for a robust positive influence of democracy on economic growth. We argue that the ambiguity in the recent literature can first and foremost be traced back to the composition of existing democracy indicators. Available indices suffer from substantial methodological weaknesses, particularly with regard to the strategy employed to aggregate the underlying secondary data. As a result, existing indicators do not react with sufficient sensitivity to political events and regime changes.

This problem is amplified by the specification of the applied estimation techniques. A large number of recent studies eliminate unobserved heterogeneity via Within-Group estimations or difference GMM. However, while the first method yields a considerable dynamic panel bias (Nickell, 1981), the latter is accompanied by dramatic efficiency losses if additional orthogonality restrictions can be exploited (see Blundell and Bond, 1998). Even more crucial, when estimating empirical models using transformations that remove the information in the equation in levels, it is particularly necessary to utilize democracy indicators that react very sensitively to political events and regime changes. Otherwise, relying on the limited within-country information in the panel is likely to yield ambiguous results concerning the growth effect of democratization.

This paper addresses both challenges. In the first step, we introduce a novel approach to measure democracy which is based on machine learning algorithms for pattern recognition. The advantage gained via application of these algorithms is that they give computers the ability to learn without being explicitly programmed. Whereas the machine learning toolbox provides numerous promising instruments, Support Vector Machines (SVM) in particular have recently produced striking results in various branches of science, e.g. for categorization of cancer cells (Guyon et al., 2002) and identification of biomarkers of neurological and psychiatric disease (Orra et al., 2012). We transfer the SVM approach to the problem of democracy measurement, obtaining an index which we refer to as the Support Vector Machines Democracy Indicator (SVMDI). The indicator is continuous on the interval from 0 to 1, thereby considerably enhancing the level of detail. The most important improvement, however, is that the aggregation of the underlying secondary variables is not arbitrary, as

our SVM algorithm puts the problem of learning—i.e. the evaluation of country-years—into the context of an optimization problem. The SVMDI is available for 185 countries in the period from 1981 to 2011, covering countries representative of over 99 percent of the global population.

In the second step, we analyze the effect of the SVMDI on economic growth in a system GMM framework which addresses the econometric challenges described above. Our findings indicate a robust positive relationship between the SVMDI measure and economic growth. This result remains stable when changing the estimation technique to some recently applied strategies from the literature. In particular, accounting for waves of democratization via instrumental variable regressions using regional and cultural democratization trends as external instruments strongly supports the baseline outcomes.

We also provide an extensive comparative analysis of the results obtained by SVMDI and alternative democracy indicators. Given the inability of hitherto existing democracy indicators to react with sufficient sensitivity to political developments, the SVMDI is the only indicator that suggests a positive effect on growth in models that rely on the within variation of countries. This implies that even small steps in the transition process towards democracy are beneficial for increases in living standards. However, when using the system GMM framework of our baseline estimations, the positive association between democracy and growth emerges as a clear empirical pattern, even when relying on rough measures of democratization.

Finally, we investigate the transmission channels through which democracy effects income increases. We observe that democracy exerts its influence via better education, higher investment shares, and lower fertility rates. Meanwhile, we find little evidence for a redistribution-enhancing effect that would consequently contribute to an overall non-linear effect of democracy (see Barro, 1996). Hence, our results imply that higher degrees of democratization are always beneficial to growth.

The paper proceeds as follows: Section 2 discusses the ambiguity in terms of the effect of democracy on growth in recent studies. Section 3 critically analyzes the most commonly used traditional democracy indicators. In Section 4, we introduce the ideas behind Support Vector Machines and the SVMDI algorithm. This Section additionally provides an overview of the democracy level and its historical trends in the world, and compares the SVMDI to alternative indicators. Section 5 is concerned with the estimation strategy and the presentation of the empirical results. In Section 6, we examine the transmission channels of democracy. We conclude in Section 7.

2. The ambiguous effect of democracy in recent studies

The effect of democracy on growth is strongly ambiguous in recent studies, both theoretically and empirically. On the theoretical side, it has been argued that democratization may benefit growth, most importantly via better provision of public goods and education (Saint-Paul and Verdier, 1993, Benabou, 1996, and Lizzeri and Persico, 2004) or by imposing constraints on kleptocratic dictators and preventing political groups from monopolizing lucrative economic opportunities (Acemoglu et al., 2008 and Acemoglu and Robinson,

2012). In addition, Alesina et al. (1996) emphasize that increased political stability enhances national and foreign investment. Feng (1997) illustrates that democracy reduces the probability of regime changes, which indirectly benefits growth. However, a large body of literature emphasizes the possible negative effects of democratization, mainly as a result of a higher level of redistribution, which is assumed to reduce growth (see, for instance, Alesina and Rodrik, 1994 and Persson and Tabellini, 1994). In addition, Olson (1982) argues that sufficient organization of interest groups can lead to stagnation in democracies.

Empirically, cross-sectional analyses conducted by Barro (1996) and Tavares and Wacziarg (2001) suggest a (slightly) negative effect of democracy on growth. The investigation of Barro (1996) also provides evidence for a nonlinear relationship between the variables, where an increase in political rights at low levels of democratization benefits growth, but triggers a negative effect if a critical threshold of democratization is exceeded. Barro (2003) confirms the nonlinear effect using panel data, while other panel data analyses yield quite ambiguous results. Rodrik and Wacziarg (2005) find no significant effect of democratic transition on growth in the long-run, but emphasize short-run benefits and a decline in economic volatility. Likewise, Apolte (2011) reports ambiguous effects of democracy on prosperity in transition countries, tentatively arguing that basic constitutional rights and constraints on the government may be conducive to growth. Burkhart and Lewis-Beck (1994), Giavazzi and Tabellini (2005) and Murtin and Wacziarg (2014) find no robust indication of a positive relationship running from democracy to growth. Using semi-parametric methods, Persson and Tabellini (2008) report an average negative effect of departure from democracy on growth. Persson and Tabellini (2009) analyze the effect of democratic capital, measured by a nation's historical experience with democracy and by the incidence of democracy in its neighborhood. Whereas the results imply that democratic capital stimulates growth, Acemoglu et al. (2014) argue that the formidable challenge in this case is the difficulty of disentangling the impact of unobserved heterogeneity from the effect of democratic capital. Gerring et al. (2005) apply a similar approach, concluding that democratization facilitates income increases. Providing a dichotomous index of democracy, Acemoglu et al. (2014) find that the degree of democracy is positively correlated with future GDP per capita. The authors use regional waves of democratization in an IV approach to account for possible problems caused by endogeneity. A similar approach is employed by Madsen et al. (2015), who use the strength of democracy in linguistically comparable countries as an external instrument. Both approaches find a positive link between democracy and the level of income.

A different branch of literature is concerned with the reverse effect, i.e. the causal relationship of economic growth to democracy. This literature goes back to Lipset (1959), who finds a strong and positive correlation between the level of income per capita and the likelihood of transition to democracy. Recent studies, however, provide ambiguous results. While Acemoglu et al. (2008, 2009) suggest that growth does not contribute to the process of democratization, Murtin and Wacziarg (2014) endorse Lipset's modernisation theory.

3. Recent democracy indicators

The traditional way to create a democracy indicator follows three steps: First, it is necessary to choose a definition of democracy. Second, a number of instruments must be designed that are able to describe the properties of the theoretical concept. Finally, a suitable manner for combining the selected variables must be found for computation of the democracy index (Munck and Verkuilen, 2002).

In practical applications, however, a large number of problems arise in each of these steps. The first issue concerns the nature of democracy. With no generally accepted definition at hand, the interpretations range from minimal approaches primarily focusing on the election process (see, e.g., Dahl, 1971) to concepts that additionally incorporate human rights and social inequality (see, e.g., Rawls, 1971). As a result of this variety, the indicators deviate considerably in their underlying instruments. For instance, the popular index of Vanhanen (2000) only utilizes two dimensions—participation and competitiveness in elections—to characterize a democracy. The advantage of such a minimal concept is that data can be collected for a large number of countries and years, yielding a democracy indicator that covers a broad sample of observations. However, researchers employing democracy data need to acknowledge the inherent cost-benefit trade-off and must ensure that any substantial analytical conclusion drawn in the course of their investigation is consistent with the underlying data concept. In the case of the Vanhanen-index, the allure of large data coverage comes at a high cost. First, instrumentation of participation and competition via (respectively) voter turnout and the percentage of votes going to the largest party constitute, at best, poor measures of the corresponding attribute (for a detailed discussion, see Munck and Verkuilen, 2002). Second, the aggregate index is obtained by simply multiplying the two attributes, whereby Vanhanen (2000) does not offer any theoretical justification for the arbitrary assumption that equal weight ought to be assigned to the attributes.

A similar minimal concept is used in the index of Boix et al. (2013) that defines a country-year as democratic if it meets three conditions in terms of contestation and participation.2 The drawback of this approach, one inherent to each dichotomous indicator of democracy d{o,1>, is the lack of detail. In particular, the implicit assumption in empirical cross-country analyses is that each country with d{0,1} = 1 is equally weighted in the computation of estimates. With regard to the Boix et al. (2013) measure for the year 2010, this implies classifying Pakistan, Bangladesh, and Mali as having the same extent of democratization as the United States, Germany, and Canada.

Two measures of democracy have achieved a particularly high degree of popularity. These are the Polity IV score provided by Marshall et al. (2014) and the rating compiled by Freedom House (2014). Both approaches are neither dichotomous, nor continuous. For Polity IV and Freedom House the range of possible values runs from -10 to 10 and from 2 to 14, respectively. Although they differ in their purpose, both indices are quite similar in their

2These conditions are: (1) The executive is elected in popular elections and is responsible to voters, (2) the legislature or the executive are elected in free and fair elections, and (3) the majority of adult men have the right to vote.

construction, building on the evaluations of country experts who classify nations based on a set of predefined criteria. In both cases, however, the aggregation strategy is problematic. The Freedom House (2014) index aggregates scores for two attributes—political rights and civil liberty—by simply adding up the values of their respective underlying components. With regard to each of the two attributes, all components are added with equal weight without any theoretical justification of this aggregation strategy. In fact, equal weighting seems particularly inadequate in most cases.3 This failure to employ a reasonable aggregation rule is compounded by a number of conceptual and measurement problems that are discussed in detail in Munck and Verkuilen (2002) and Cheibub et al. (2010). Arbitrariness of the aggregation rule is also a fundamental deficiency of the Policy IV score (for a detailed discussion, see Treier and Jackman, 2008).

More recently, some scholars have attempted to achieve more reliable measures by synthesizing existing democracy indicators. For instance, Acemoglu et al. (2014) propose an approach based on four established indices to obtain a dichotomous indicator. According to the applied heuristic, a country-year is classified as democratic (d{0,i> = 1) if the rating of Freedom House (2014) is free or partly free and the Polity IV score provided by Marshall et al. (2014) is greater than zero. To address the issue that for certain observations only one of the underlying indicators is available, Acemoglu et al. (2014) use two additional indices (Boix et al., 2013 and Cheibub et al., 2010) to classify the country-years in question. As in the case of the Boix et al. (2013) measure, one main drawback of this method is that it enables only a binary classification of democracy, which does not allow for a nuanced distinction between different countries. Furthermore, a dichotomous indicator contradicts the broad consensus that cultivation of a democracy is a process which occurs over a longer period of time. Treating each country-year as equally (non)democratic neglects information about the process of democratization and results in a severe upward bias in empirical estimations (Doucouliagos and Ulubasoglu, 2008).

Pemstein et al. (2010) propose another, more technical method to combine established indices. The basic idea underlying this concept is to synthesize ten available democracy indicators via a Bayesian latent variable approach to obtain the Unified Democracy Score (UDS). A formidable challenge presented by the inclusion of such a large number of indicators is finding an appropriate way to deal with the fact that they differ substantially in terms of their number of evaluated countries and periods. For instance, the Polity IV score is available continuously for the time-period from 1945 to present, while other indices are available only for few periods. Nevertheless, the approach of Pemstein et al. (2010) includes all available information for each country-year, whereby the number of included secondary indicators varies from observation to observation. This, however, yields inconsistency in the UDS over time and across countries.4 In fact, a large number of the included national series imply

3For instance, it is questionable whether the decentralization of power is as important for democracy as the actual power exercised by elected representatives (Munck and Verkuilen, 2002).

4 Although for some country years the UDS was produced by drawing on information from ten democracy indicators, the majority of observations rely on an average of six underlying indicators which deviate in their composition for different country-years. This restricts comparison of UDS scores across countries and over time.

relatively constant democracy scores over time, only to be interrupted by a peak occurring almost every five years when analyzing the time period between 1950 and 1980. This peak is due to the index of Bollen (2001), which is only included in the UDS in the years 1950, 1955, 1960, 1965, and 1980.5 A very similar bias that affects the UDS of a considerable number of countries can be observed in the early 1970s, the time period when the Freedom House (2014) ratings were initially published.

The drawbacks discussed above may stand exemplary for the majority of the existing democracy indicators. While points of criticism include the low level of detail, subjectivity and arbitrariness in the conceptualization, and the selection of the instruments, the main concerns are the fairly low level of sophistication with regard to the aggregation process and the way in which the underlying components are weighted.

4. Measuring democracy using Support Vector Machines 4-1. Motivation

Compared with other macroeconomic series—such as, for instance, the inflation rate, the unemployment rate, or the growth rate—the quantification of democracy is considerably more challenging, since there is neither a commonly accepted definition of democracy nor a natural unit or scale by which it can be measured. The literature at hand has, however, arrived at the predominant consensus that it is preferable to measure the degree of democratization rather than quantify the stock of democracy, where the usage of scales with lower and upper bounds chosen a priori as benchmarks for the lowest (fully autocratic) and highest (fully democratic) possible degree is common. Mindful of this preference, traditional democracy indicators attempt to determine a number of requirements which a country has to fulfill to reach a certain degree of democratization, as opposed to trying to observe democracy directly.6 More formally, the degree of democratization dj,t E D C R of country i in period t can be expressed as a function F: X C Rm ^ D C R of the extent to which the country-year satisfies the selected conditions. Subsequently, we refer to these conditions as xi,t = (x1,t, ...,x1-mt) E X C Rm, where m denotes the number of requirements, i.e.

di,t = F (xit,...,smt) v(i,t). (1)

A basic property of the frequently used scales is that their range of values can be normalized to the [0,1] interval without the loss of essential information.7 Hence, we subsequently focus on the case in which the output space is normalized, i.e. D = [0,1]. This provides the advantage that each absolute change in the indicator can directly be interpreted as the change in the degree of democratization.

We have already explained in Section 3 that the low degree of sophistication with respect to the aggregation function F(0 is undoubtedly a substantial methodological weak point of

5See the online appendix of the paper for a graphical illustration of this effect.

6In this context, democracy is frequently interpreted as a latent variable (see, e.g., Pemstein et al., 2010).

7For instance, the Polity IV Index originally ranges from -10 to 10 (Marshall et al., 2014). It is possible to obtain a normalized score for each country-year Pit with the same information via computation of Pit2"o10.

existing democracy indicators. Hence, finding a suitable strategy to detect the unknown function FO without arbitrary assumptions is an essential step to improve the quality of democracy indicators. By using Support Vector Machines, we transfer the problem of aggregation into an optimization context, estimating the most appropriate function FO). In fact, machine learning algorithms and Support Vector Machines are explicitly designed for problems where the functional form is unknown and where researchers do not have any reasonable description of the functional relationship between the inputs and the desired response (see Steinwart and Christmann, 2008). To construct a statistical learning machine with Support Vectors (SV), two essential requirements must be met. First, we need a set of input characteristics that are available for all observations in the sample. Second, we need a limited number of observations with known output, on the basis of which the algorithm can learn (see Steinwart and Christmann, 2008).

Intuitively, our approach first identifies country-years that can be indisputably categorized as highly democratic or highly autocratic and uses them as observations with known output. Based on these a priori labeled observations and a set of observable characteristics, we compute the aggregation function FO via Support Vector regressions. The underlying attributes include different aspects of political participation, political competition, and civil rights. Finally, we obtain a continuous measurement of democracy, which we refer to as the Support Vector Machines Democracy Indicator (SVMDI). This indicator can be interpreted as the degree of democratization based on a continuous scale reaching from 0 to 1.

4-2. Machine learning and Support Vector Machines

The field of machine learning studies algorithms that operate on the basis of a model drawn from example inputs that is then used to make data-driven predictions or decisions (see, e.g., Bishop, 2006). The enormous advantage gained through application of such methods is that of providing computers with the ability to learn without being explicitly programmed (Samuels, 1959). Largely developed at AT&T Bell Laboratories, the Support Vector Machines (SVM) algorithm as a subfield of machine learning was designed to have a firm orientation towards real-world application. Hence, utilization of SVM has achieved very promising results in various branches of sciences. Application of SVM has proven highly effective in accomplishing such practical tasks as categorization of cancer cells (Guyon et al., 2002), classification of hyperspectral data in geophysics (Gualtieri, 2009), and identification of biomarkers of neurological and psychiatric disease (Orru et al., 2012). In addition, the algorithm has been used to categorize texts (Joachims, 2002) and to analyze hand written characters (Cortes and Vapnik, 1995).8

The machine learning toolbox consists of a wide range of different algorithms. In our application, we use two common methods of SV regression and SV classification. While the regression tool is essential for obtaining the desired aggregation function, SV classification is

8Thus far, little effort has been made to apply the SVM algorithm in the field of economics, where up until now its application has been restricted to financial topics and stock markets. For instance, Kim (2003) and Tay and Cao (2001) use SVM for financial time-series forecasting and Shin et al. (2005) apply the method in a bankruptcy prediction model.

used to conduct validity tests of our selections. This section provides a brief description of how to use Support Vector Machines for regressions, and the concept of SV classification can be seen to be closely related. It bears underscoring, however, that the mathematical literature on machine learning has developed considerably over time, which is why the following description concentrates primarily on its basic ideas. For readers with a broader interest in the mathematical and computational issues of SVM, we recommend the inspirational work of Vapnik (1998), Smola and Scholkopf (2004), and Steinwart and Christmann (2008).

The problem to be solved by the SV regression tool can be described as follows: Given a certain data set F = {(x1,y1);...; (xn,yn)}, where xi £ X C Rm and yi £ R, we want to find a function f: X C Rm ^ R with the property

f(Xi) = yi V i = 1,...,n. (2)

However, due to measurement errors and unobserved characteristics, achieving a perfect fit is generally not feasible. For this reason, the aim of SV regression is to compute a function f: X C Rm ^ R which approximates the "true" function f: X C Rm ^ R such that

1. the deviation between f(x») and yi does not exceed a given level e for each observation i, and (simultaneously)

2. the shape of f (•) is as flat as possible (Smola and Scholkopf, 2004).

Largely influenced by the Generalized Portrait algorithm (Vapnik and Lerner, 1963; Vapnik and Chervonenkis, 1964), the basic idea of SV regressions is to find a hyperplane in X that satisfies these two requirements. However, the functional flexibility of hyperplanes typically limits the possibility of obtaining precise approximations for all observations in the sample. As a result, the first condition is violated in most cases. To resolve this issue, Boser et al. (1992) suggest using a higher dimensional space H instead of X—called feature space—where shifting of the data is accomplished via a nonlinear feature map $(•) : X ^ H that is chosen a priori.

This procedure, however, gives rise to the question of how to treat the high-dimensional space H, since an appropriate map $(•) is typically unknown. In addition, this approach can easily become computationally infeasible with respect to polynomial features of higher order or higher dimensionalilty. Boser et al. (1992) propose a method to overcome this problem, which has become known as the kernel trick, largely building on the idea initially introduced by Aizerman et al. (1964). The approach circumvents direct construction of the hyperplane based on the data in H and relies instead on the dot products of the Support Vectors (Vapnik, 1998). This method is feasible if there exists an admissible kernel k: XxX4 R that satisfies a certain number of conditions.9 In our application, we use the Gaussian Radial Basis Function as a kernel, with the result that the corresponding feature space H becomes a Hilbert space of infinite dimension.

In this way, the optimal SV regression function can be calculated via

9See, in particular, the Theorem of Mercer (1909) and the Theorems of Schoenberg (1942) and Burges (1999). For a detailed overview and discussion, see Smola and Scholkopf (2004).

f(x) = (ai — a*) k(x, x») + b

where b denotes the intercept, and the Lagrange multipliers a = (ai,..., an)' and a* = (a*,..., a*n)' are computed by solving the optimization problem (Smola and Scholkopf, 2004)

ij=i i=i i=i

s-t- — a*) = 0 and ai,a* G [0,C].

with given cost parameter C and fixed margin e.

4.3. The SVMDI algorithm

In this section, we transfer the general approach of SV regression to the problem of quantifying the degree of democratization. In the first step, we need to specify a set of input attributes ( x) that capture the character of democracies and that are available for each observation in the sample. This selection is based on a broad concept of democracy, i.e. we do not exclusively focus on the core elements of political participation and political competition (as, for instance, proposed by Dahl, 1971), but also include civil liberty and independence of non-government institutions such as the judiciary and the press. In this sense we follow a large body of theoretical literature which argues that democracy requires more than just a free general election process (see, e.g., Rawls, 1971 and Diamond et al.,

In his well-known work, Vanhanen (2000) suggests quantifying the degree of political competition based on the share of power concentrated in the largest political party in the last general election. How to measure this share is, however, ambiguous. In fact, it seems plausible to either use the share obtained at the ballot box or, alternatively, to rely on the share of seats in the parliament. Both shares may be relatively similar in the majority of cases, but differ considerably with respect to certain country-years. For instance, the 2002 Turkish general election saw 34.28 percent of all valid votes go to the Justice and Development Party (AKP) chaired by Recep Tyyip Erdogan. This, however, led to their acquiring 66 percent of all seats in parliament (Carr, 2014). After analyzing the bibliography of Vanhanen (2000), we unfortunately found severe data inconsistencies in the competition dimension over time and across countries, for which reason we refrain from utilization of this database. Instead, we collect the necessary information from other sources that distinguish between both shares in the majority of cases. To obtain additional information concerning the degree of political competition, we further calculate the ratio of votes and the ratio of parliamentary seats between the strongest and second strongest parties. In total, we obtain four variables to characterize the competition dimension of democracy.10

10The secondary datasets used include African Election Database (2014), Carr (2014), IPU (2014), IDEA (2014), Nohlen et al. (1999, 2001); Nohlen (2005); Nohlen and Stover (2010), and World Bank (2014a).

1990).

The second attribute is political participation, which we include based on voter turnout (Vanhanen, 2000), the rating of political freedom provided by Freedom House (2014), and an indicator of political oppression and violence computed by Gibney et al. (2013).11 In addition, independence of the judiciary is reflected by the INJUD series from the database of Cingranelli et al. (2014), while the freedom of the press indicator is obtained from Freedom House (2014). Finally, the quality of civil liberties is evaluated by two expert-based ratings provided by Freedom House (2014) and Cingranelli et al. (2014). The attribute drawn from the Cingranelli et al. (2014) compilation is based on the mean value of five scores regarding essential human rights.

In light of the critique directed at traditional democracy indicators (see Section 3), we select these eleven variables cautiously with respect to the crucial issue of data quality. Whenever feasible, we avoid inclusion of aggregated data by drawing on the original series. In addition, by inclusion of various series from different sources, we counterbalance their individual weaknesses, at least to some extent. Yet it bears underscoring that the accuracy of the SVMDI depends on the attributes that are used as input variables.

In the second step, we select a subset of country-years L C F consisting of elements that can unambiguously be categorized as either highly democratic or highly autocratic. This selection of preliminary degrees of democratization lays the foundation for the SV algorithm. At this point, we follow the seminal work of Ragin (2000, 2008), which suggests using 0.05 (0.95) for highly autocratic (highly democratic) observations as appropriate bench-marks.12 In order to compile L, we follow Acemoglu et al. (2014) by using the Polity IV score (Marshall et al., 2014) as decision criterion. However, in our case, a country-year is labeled as democratic only if the Polity IV index assumes its highest possible value of 10. At the other end of the spectrum, we classify countries as autocratic if the Polity IV indicator is —7 or below, as suggested by Jaggers and Gurr (1995).13

Subsequently (step 3), a random generator selects tdemo and tauto elements of L and consolidates them into the training set Tz. To avoid arbitrary assumptions, both parameters are chosen by a uniformly distributed random number generator. The algorithm proceeds

11 By using different sources and variables, we try to counterbalance the methodological shortcomings of the input measurements, conceding that this strategy does not remove all issues. However, no better data is available for the large number of observations included in our sample.

12 Undoubtedly, the assignment of the thresholds is to some extent arbitrary, which is why we conducted the algorithm with several different thresholds, ranging from 0 to 0.1 (0.9 to 1). The results turn out to be relatively unaffected by the particular choice. In each case, the algorithm is able to detect substantial differences in the degree of democratization in both of the subsamples that have received a preliminary label. We illustrate this issue in Section 4.5 based on the example of Mongolia. Note also that the empirical results in terms of the democracy-growth nexus explored in this paper are not sensitive to different thresholds.

13 Since the selection of the Polity IV index as a criterion seems arbitrary, we check the robustness of the classification by using several other criteria based on other democracy indicators. These changes yield little differences in the resulting indicator, which is hardly surprising given the high agreement of established democracy indicators with respect to the top and the bottom of the global democracy distribution. As an additional internal validity check, we conduct SV classifications based on the input variables to examine if there are differences in the initial labels compared to those obtained by usage of the Polity IV indicator. This analysis reveals very little indication of any mislabeled country-years.

(step 4) by conducting a SV regression based on the observations in Tz, yielding a nonlinear function Ftz : X C R11 ^ [0,1].14 For computation of Ftz(•), we use the broadly accepted Gaussian Radial Basis Function (RBF) kernel, which has provided the most promising results in our robustness checks. In the fifth step, we use the estimated aggregation function Ftz(•) to assign a degree of democratization dit G [0,1] to all country-years included in our sample F.15 To prevent a potential selection bias, we compute ( = 1,..., 2000 iterations of the process from step 3 to 5. This bootstrapping procedure ensures numerical robustness with respect to our parameter selection, accounts for potential measurement errors in the underlying data, and enables the estimation of confidence intervals.16 The Support Vector Machines Democracy Index (SVMDI) is the average value over the 2000 iterations for each country-year, yielding a continuous measurement of democracy that ranges from 0 to 1.

For a given country-year (i,t), the SVMDI indicates the degree of democratization with respect to our liberal concept of democracy and the benchmark country-years included in the classification. Due to the availability of the underlying data, the SVMDI is computable for 185 countries in the period from 1981 to 2011. To account for a potential bias due to inexact quantification, potential measurement errors in the underlying data, and omitted variables, we compute confidence intervals for our SVMDI point estimates as urged by Treier and Jackman (2008). The lower (upper) bound of these intervals corresponds with the 5th (95th) percentile of the simulated distribution of the point estimate that is compiled for each country-year based on the 2,000 iterations. The SVMDI scores and the associated confidence intervals can be accessed in the online appendix of this article.

4.4. Democracy in the world

We now turn to a detailed illustration of the democratic tendencies in the world implied by our indicator. Figure (1) maps the SVMDI data in the post-2010 period. This presents a very heterogeneous picture: while countries in Europe, Oceania, North America, and—to a large extent—in South America possess high SVMDI scores, a substantial part of the nations in Africa and Asia are classified as being considerably less democratic.

An interesting pattern revealed by Figure (1) is that the degree of democratization shows a clear tendency towards regional concentration. If a country is (non-)democratic, we observe a high probability that the same applies to its neighboring countries. There are three remarkable exceptions to this general rule: surrounded by countries with very low SVMDI scores, Mongolia (SVMDI: 0.8755), Ghana (0.9295), and—to a lesser extent—Benin (0.8296)

14 To ensure that the estimated function can reach all values between 0 and 1 without penalization through the SV regression, we set the margin parameter e as equal to 0.05. In addition, we follow Mattera and Haykin (1999) and set the penalization parameter C equal to to 1. However, our robustness checks showed that the SVMDI is only weakly affected by the particular parameter choice.

15 From a theoretical perspective, it is possible that some of the predicted values are above the upper bound 1 or below the lower bound 0. To avoid such cases, we include an additional restriction in our implementation, ensuring scores between 0 and 1. In our application, only 0.2 percent of the estimated values lie outside the [0,1] interval.

16The combination of bootstrapping and SVM is frequently used in the literature (see, e.g., Alonso-Atienza et al., 2012, Jain et al., 2014 and Wang and Ma, 2012).

Figure 1 Democracy in the world (SVMDI), post-2010 period.

succeeded in establishing democratic structures. Overall, the figure suggests that the extent of democratization is quite polarized.

This polarization becomes particularly apparent when we consider the distribution of the SVMDI measure, illustrated in Figure (2). The data suggests a bimodal distribution, where the first mode is located at a very low level of democracy, and the second mode lies at a substantially higher degree of democratization. This pattern is typical when examining the degree of democratization across countries and occurs in a similar manner when analyzing alternative measures. The reason is that there exist a substantial number of countries with an SVMDI index close to zero. This group includes nations where civil war is prevalent— e.g. Sudan (0.0449), Syria (0.0633), and Afghanistan (0.0889)—and countries with absolute monarchies, such as Brunei (0.0477), Qatar (0.0504), and Swaziland (0.0515). On the other hand, there are numerous countries where strong democratic institutions have been established, particularly in Europe, North America, Oceania, and in some parts of Latin America. Figure (2) also demonstrates that democratization emerges as a clear empirical pattern in the SVMDI data. Whereas the relative fraction of non-democratic nations was extraordinarily high in the 1980-1984 period, the data approximate a more uniform distribution in the post-2010 period, where we observe a substantially higher number of democratic countries and a lower number of nations with poor SVMDI scores.

Figure (3) plots the SVMDI scores and the confidence intervals for Serbia, South Korea, Venezuela, and Argentina over the entire period from 1981 to 2011.17 The figure highlights the considerable progress in democratization during the 1980s and the early 1990s, which later became known as "Democracy's Third Wave" (see, for instance, Huntington, 1991, 2012). Beginning in Latin America in the early 1980s, the Third Wave washed over to Asia Pacific countries and reached its crest in Eastern Europe after the collapse of the Soviet Union. This development is clearly visible in the SVMDI data. Particularly noteworthy is the substantial progress achieved in South Korea and Argentina, both of which were classified as highly autocratic in the early 1980s. Similar movements towards democracy can

17Note that the Serbian SVMDI is composed of the scores of SFR Yugoslavia (1981-91), FR Yugoslavia (92-02), Serbia and Montenegro (03-05), and Serbia (06-11).

- 1980 ......... 2010

Figure 2 Democracy in the World, SVMDI data, kernel density estimates 1980—2010. Kernel is Epanechnikov.

be observed in Eastern Europe after the fall of the Iron Curtain in 1989. The Serbian path to democracy, however, was more tortuous than those of its Baltic and East-Central European neighbors. Only following the resolution of the armed conflicts in Bosnia and Herzegovina (1992-1995) and Kosovo (1998-99) was an increase in political rights and democratization initiated (see Nohlen and Stover, 2010). Still, democracy has not yet been cultivated in full, which is exactly reflected in the SVMDI of the country (Greenberg, 2014).

A further issue that has gained increasing attention is the fear of a potential "reverse" wave occurring in Latin America due to the importance of autocracy and military in the region's political culture, as well as the strong institutional position of its armed forces (see Zagorski, 2003). While similar movements were ushered in in large parts of South America during the 1960s and 1970s (e.g. in Argentina, Chile, and Uruguay), Venezuela was not affected by this cross-national reduction in democratic structures (Huntington, 2012). As a result, the Venezuelan SVMDI was well above the Latin American average in the early 1980s. However, beginning in the late 1980s, the stable democracy in Venezuela frequently came under attack, e.g. by multiple popular uprisings, the first of which began in 1989, followed by two coup attempts in 1992 and the eventual impeachment of President Carlos Andres Perez (1989-1994). As a consequence, the quality of the country's democratic institutions decreased considerably (Romero, 1996). The decline gathered momentum during the presidency of Hugo Chavez (1999-2013). In his first year in office, Chavez abolished the elected government and transferred its power to an assembly more loyal to his interests (Brewer-Carlas, 2010). The following years saw a clear tendency towards autocracy, which was promoted by the adoption of illiberal laws, the constraint of the freedom of the press, and the repression of the political opposition (Corrales, 2015).

1990 2000 2010

Confidence interval - Serbia

1980 1990 2000 2010

Confidence interval South Korea

to -to -^r -

1990 2000 2010

Confidence interval- Venezuela

1990 2000 2010

Confidence interval- Argentina

Figure 3 The path of democratization. SVMDI scores and confidence intervals of Serbia, South Korea, Venezuela and Argentina, whole period (1981-2011).

With the end of the military junta in 1983, Argentina succeeded in reestablishing its democratic institutions (Larkins, 1998). This development is reflected in the sharp increase in the SVMDI. However, while Argentina's democracy in the mid-1980s was more stable than that of previous regimes, democratic institutions became weaker during the 1990s (Levitsky and Murillo, 2008). In fact, President Carlos Menem (1989-1999) increasingly limited both the power of the congress and the independence of the Supreme Court (Larkins, 1998), resulting in Argentina's movement towards a delegative democracy shaped by weak control mechanisms between different state agencies (O'Donell, 1994). With the continuation of presidential dominance and centralization of power (Elias, 2015; Levitsky and Murillo, 2008), Argentina's political institutions remain weakened under the presidency of Nestor Kirchner (2003-2007) and his wife Christina Fernandez de Kirchner (2007-2015).

4-5. Relation to existing democracy indicators

One huge advantage of the SVMDI algorithm is that aggregation of the underlying attributes is less arbitrary than with recently used strategies, as it relies on weaker assumptions. In particular, unification of attributes is conducted via a nonlinear optimization problem rather than via crude aggregation rules or the implicit assumption of equal weights. In addition, combining information from different data sources compensates for weaknesses in conceptualization as well as for potential measurement errors in the underlying secondary

data. A direct result of these methodical improvements is a substantial increase in the level of detail in comparison with established approaches.

To demonstrate the superiority of the SVMDI algorithm, Figure ( 4) plots the democracy levels of Jamaica, Nicaragua, Venezuela, and Mongolia as gauged by SVMDI and several other indicators. Note that we have normalized all indices to values between 0 and 1 in order to ensure sufficient comparability of the measurements.18

First, consider the case of Jamaica. What is striking in terms of the classification of the Jamaican democracy is the considerable divergence between the trends observed in the early 1980s by the SVMDI and those identified by alternative measures. While the Polity scores and the Freedom House (2014) ratings do not change notably, the SVMDI score experiences a sharp decline in the year 1983. Given the political situation in that year, the result suggested by the SVMDI algorithm is much more plausible. In 1983, the "People's National Party"—until that time the largest opposition group in the parliament—boycotted the election, which resulted in the incumbent "Jamaica Labor Party" winning all seats in the parliament (Figueros, 1985). In fact, whereas 54 of 60 seats were completely unopposed, voting took place for six seats due to participation of minor parties. However, nationwide voter turnout was only 2.7 percent, which was the lowest value in the history of the country and the only time that it was below 50 percent (Wust, 2005). From that time until 1989, Jamaica was a de facto one-party state. Such a situation, however, should factor negatively into a democracy measure, as political pluralism in parliament is an important aspect of democracy, even in minimal concepts such as that proposed by Dahl (1971). Without the control and criticism provided by a parliamentary opposition, the ruling party is able to exercise power without supervision. In fact, the rule of Edward Seaga, Prime Minister of Jamaica from 1980 to 1989, became increasingly authoritarian, which led to widespread public protest during the election in 1989 (Wust, 2005).

The case of Nicaragua highlights a typical pattern of the Vanhanen (2000) index, which in the overwhelming majority of observations only changes (slightly) after elections have taken place. In Nicaragua, elections are held every five years. While the Vanhanen-index implies an increase in democracy in each electoral year, it remains unaltered during the interim period. In particular, with the exception of a minor decline in 2011, the index provides no indication of a decrease in the degree of democracy during the entire period. Likewise, the Polity score (Marshall et al., 2014) implies a similar period of flourishing democracy without any indication of an interruption. The dichotomous indicator of Acemoglu et al. (2014) changes only once, in 1990, the year when the first competitive election in the country took place (Williams, 1990). Contrary to the consensus that Nicaragua's democracy is far from being in full bloom (Walker, 2009), the indicator suggests strong democratic structures in the country. In contrast, the SVMDI displays a continuous loss of democracy since 2006, the year when Daniel Ortega came into his second presidency after years as a member of the opposition. Due to the increasingly autocratic governance of President Ortega—including,

18It is crucial to emphasize that the superiority of the SVMDI score in describing recent political developments is not limited to the illustrated countries, but can be observed with respect to the overwhelming majority of country-years included in the data.

1990 2000

Jamaica

SVMDI Polity IV

Freedom House UDS

1990 2000

Nicaragua

SVMDI Vanhanen

Polity IV

Acemoglu et al. (2014)

1990 2000

Venezuela

Boix et al. (2013)

Vanhanen

Acemoglu et al. (2014)

1990 2000

Mongolia

SVMDI Polity IV

Acemoglu et al. (2014) Vanhanen

Figure 4 Democracy in Jamaica, Nicaragua, Venezuela, and Mongolia. SVMDI and traditional democracy indicators, 1980-2011.

for instance, growing oppression of critical journalists and opposition members, as well as controversial constitutional amendments (Anderson and Dodd, 2009; McConnell, 2014)—a decreasing trend is more justifiable than a constant or even increasing level.

The third nation illustrated in Figure (4) is Venezuela. As highlighted in Figure (3) in the previous section, democratization in Venezuela experienced a decline during the past decades. This phenomenon is intensely discussed in the literature as a "reverse wave" of democracy. However, the breakdown of Venezuelan democracy is captured quite differently by traditional democracy indicators. Whereas the indices of Boix et al. (2013) and Acemoglu et al. (2014) attest to a thriving democracy until the end of the 2000s, the index of Vanhanen (2000) remains at a constant level of roughly 0.20 over the whole period between 1981 and 2011, indicating no notable decline in democracy at all. The SVMDI, however, illustrates that the antidemocratic trend in Venezuela had already begun during the 1990s, which is much more reflective of the existing literature (see, e.g., Zagorski, 2003 and Levitsky and Murillo, 2008).

The last country depicted in Figure (4) is Mongolia. The figure highlights that the SVMDI algorithm is able to detect differences between country-years which had originally obtained a label in step two, i.e. observations that are elements of L. Although Mongolia received a preliminary label for the period between 1999 and 2011, the figure clearly shows

that the degree of democracy has changed considerably during this time.19 What is striking about the figure is the sharp decline in the SVMDI of Mongolia in 2000. In this particular year, the ex-communist Mongolian People's Revolutionary Party (MPRP) won 72 of 76 seats, resulting in Mongolia's shift towards a one-party system (Severinghaus, 2001). Such a development, however, stands in contrast to our definition of democracy that—in line with a large body of literature—requires a multiple-party system. In fact, political competition is a central issue in theoretical and empirical concepts relating to democracy (see, for instance, Dahl, 1971; Vanhanen, 2000; Huntington, 2012). When the vote in the 2004 Mongolian parliamentary election was evenly split between the MPRP and the Motherland Democratic Coalition, Mongolia's SVMDI experienced a renewed increase. When relying on traditional indicators—such as Polity IV and the measures of Vanhanen (2000) and Acemoglu et al. (2014)—no changes in democratization are observable.

5. The empirical effect of democracy on growth

5.1. Estimation strategy

We now turn to the empirical investigation of democracy, as measured via the SVMDI algorithm, and growth. Our analysis uses a standard framework of empirical growth regressions to estimate the effect of democracy on growth, utilizing 5-year averages of all variables. Averaging the data is necessary due to the long-term perspective of growth theory, the need to disentangle short-term fluctuations and long-term effects, and the occurrence of gaps in the data for some of the covariates. Considering additive linkage of the variables, our basic dynamic panel specification is20

Vit = Oyn-1 + A hu + P Xit + Ydit + n + 6 + vu (4)

where yit is the log of initial per capita GDP in country i at 5-year period t, hit is human capital endowment, dit is the democracy index, and Xit includes the covariates of the regression. The selection of the covariates is based on the standard framework of Barro (2003, 2013), which has been proven to capture the empirical determinants of economic growth quite accurately in a number of studies. These variables include the logarithmic value of real per capita GDP in (t-1) to account for conditional convergence, denoted by log(GDPpc); the investment share (INVS); government consumption (GOVC); the inflation rate (INFL); the degree of openness (OPEN); and the log of the fertility rate, log(FERT). Human capital enters into the equation using average years of schooling (SCHOOLY) and log(LIFEEX),

19In order to make these slight differences computable, we only use a subset Tq C L with T| ^ |L| to estimate Ftz (•) in iteration Z and apply the SVM-regression based on all country-years available in the sample. This procedure enables detection of possible differences between country-years that have been classified as democratic (autocratic) in the second step.

20This specification is obtained by following the model structure developed in a number of recent empirical investigations, where the growth rate is modeled to evolve as yit — yit-1 = (0 — 1)yit-1 + ^hit + ^Xit + Ydit + n + £t + vit (see, e.g., Bond et al., 2001, Voitchovsky, 2005, and Halter et al., 2014).

the log of life expectancy at birth, to proxy education and health, respectively.21 We do not include measures of physical capital, as their calculation relies on arbitrary assumptions regarding depreciation and the initial value. Rather, we follow Barro (2003, 2013) in assuming that higher levels of log(GDPpc) and hit reflect higher levels of capital endowment.

Equation (4) also captures country-specific effects n and time effects of period t, denoted by £t, in order to account for the various institutional aspects of the countries. The term vit = uit — — n denotes the idiosyncratic error of the model.

A common and widely-used approach to account for both unobserved heterogeneity and endogeneity is to employ the estimator proposed by Arellano and Bond (1991). Define for reasons of lucidity that Vk = (kit — kit-1) and V2k = (kit-1 — kit-2), the basic idea of this approach is to adjust (4) to

Vy = dV2V + AVh + YVd + £ VX + V£ + Vv (5)

and then use sufficiently lagged values of yit, hit, dit, and Xit as instruments for the first-differences. However, first differencing Equation ( 4) removes the information in the equation in levels. This drawback is particularly severe with regard to the purpose of this paper, as the variation in democracy data stems to a large extent from the cross section rather than the time-dimension. This particularly holds for hitherto existing democracy indicators. Blundell and Bond (1998) and Bond et al. (2001) show that the standard first-difference GMM estimator can be poorly behaved if time-series are persistent or if the relative variance of the fixed effects n is high. The reason is that lagged levels in these cases provide only weak instruments for subsequent first-differences, resulting in a large finite sample bias. In addition, difference GMM magnifies gaps in unbalanced panels as it requires at least three consecutive lags for each of the variables. This requirement results in an asynchronous loss of observations because data availability is typically more limited in developing countries. However, we are particularly interested in observations concerning developing economies, as these country-years contain information regarding the growth effect of regime change in transition economies.

System GMM proposed by Arellano and Bover (1995) and Blundell and Bond (1998) provides a tool to circumvent the previously described biases, if one is willing to assume a mild stationary restriction on the initial conditions of the underlying data generating process.22 In this case, additional orthogonality conditions for the level equation in (4) can be exploited using lagged values of Vk and V2k as instruments. By these means, system GMM maintains some of the cross-sectional information in levels and exploits the information in the data more efficiently. Satisfying the Arellano and Bover (1995) conditions, system GMM has been shown to have better finite sample properties (see Blundell et al., 2000). To detect

21 The data used in the regression stem from commonly used data sources in empirical growth research. log(GDPpc), INVS, GOVC, OPEN and INFL are from PWT 8.0 as documented in Feenstra et al. (2015), SCHOOLY is from Barro and Lee (2013), log(LIFEEX) and log(FERT) are from World Bank (2014b).

22The assumption on the initial condition is E(niVyi2) = 0, which holds when the process is mean stationary, i.e. yi1 = n«/(1 — + V with E(vj) = E(vrji) = 0.

possible violations of these assumptions, we conduct Difference-in-Hansen tests for each of the system GMM regressions.23

Let ©it = [yit hit dit Xit], the moment conditions used for the regression in first-differences

E[(vit — Vit-1)©it-s] = 0 for t > 3, 2 < s < 3, and the additional moment conditions for the regression in levels are given by

E[(vit + ni)(©it-1 — ©it-2)] = 0 for t > 3.

We restrict the instrument matrix to lag 3. Roodman (2009a) illustrates the need to introduce such a restriction, as otherwise the problem of "instrument proliferation" may lead to severe biases. In principle, our specification can be estimated using one-step or two-step GMM. Whereas one-step GMM estimators use weight matrices independent of estimated parameters, the two-step variant weights the moment conditions by a consistent estimate of their covariance matrix. Bond et al. (2001) show that the two-step estimation is asymptotically more efficient. Yet it is well known that standard errors of two-step GMM are severely downward biased in small samples. We therefore rely on the Windmeijer (2005) finite sample corrected estimate of the variance, which yields a more accurate inference.

5.2. Baseline results

Panel A of Table 1 reports the results of the baseline regressions. The first column illustrates the effect of democracy measured by the SVMDI in a restricted model where the only covariate is the initial income level. The advantage of examining the effect of democracy in a very reduced specification is that the estimated parameter captures the full growth effect of democracy, leaving all possible transmission channels open. In addition, this estimation enables the investigation of SVMDI in a broad sample of 164 countries. The subsequent columns examine the effect of the SVMDI when additional controls are introduced; however, limited data availability for the covariates yields a decline in the number of countries included in the estimation. Panels B and C use exactly the same specifications as Panel A, but examine the influence of initial democracy in (t — 1) as well as nonlinear effects of democracy.

The result in Column (1) of Panel A provides a clear indication that democracy and income increases are positively and significantly related. The column rejects the hypothesis of convergence, reflecting the well-known argument in empirical growth research that convergence can only be detected when holding constant a number of variables that distinguish the countries (see, for instance, Barro and Sala-i Martin, 1992). For this reason, the subsequent columns gradually introduce a number of standard controls in empirical growth regressions. The motivation for including additional controls is twofold. First, Hansen's p-value points to an omitted variable problem in the reduced regression in Column (1),

23 A more detailed description of the estimator in the context of the empirical application can be found in Bond et al. (2001) and Roodman (2009b).

Table 1 The effect of SVMDI on growth, dependent variable is real per capita GDP growth.

(1) (2) (3) (4)

Panel A: Baseline regression results

Log(GDPpC) 0.00629 -0.00848** -0.0169*** -0.0181***

(0.00497) (0.00332) (0.00327) (0.00308)

SVMDI 0.0249*** 0.0292*** 0.0137* 0.00236

(0.00887) (0.0101) (0.00719) (0.00650)

INVS 0.111*** 0.0464 0.0453

(0.0337) (0.0330) (0.0317)

SCHOOLY 0.00261 0.00232* -0.000371

(0.00197) (0.00141) (0.00127)

Log(LIFEEX) 0.0992*** 0.0593***

(0.0181) (0.0176)

GOVC -0.00532 -0.00429

(0.0312) (0.0281)

INFL -0.00108 -0.00108

(0.000673) (0.000731)

OPEN 0.00737** 0.00302

(0.00317) (0.00342)

Log(FERT) -0.0332***

(0.00640)

Panel B: The effect of initial democratization

SVMDI(t - 1) 0.0243* 0.0349*** 0.0159 0.00643

(0.0139) (0.0124) (0.00992) (0.00768)

Panel C: Non-linear effect of democracy

SVMDI 0.126** 0.0742 0.0405 0.0203

(0.0488) (0.0508) (0.0289) (0.0259)

SVMDI SQUARED -0.107** -0.0503 -0.0295 -0.0195

(0.0497) (0.0511) (0.0287) (0.0260)

SLM p-val 0.0492 0.317 0.275 0.249

Observations 1,077 877 794 794

Countries 164 132 131 131

Hansen p-val 0.00000867 0.00847 0.718 0.981

Diff-in-Hansen 0.206 0.729 1.000 1.000

AR(1) p-val 0.0391 0.0730 0.110 0.113

AR(2) p-val 0.374 0.274 0.343 0.333

Instruments 40 78 154 173

Notes : Table reports two-step system GMM estimations. All estimations use period fixed effects and Windmeijer-corrections, robust standard errors in parentheses. The instrument matrix is restricted to lag 3. Test statistics refer to Panel A. Hansen p-val. gives the p-value of Hansen's J-test, AR(1) p-val. and AR(2) p-val. report the p-values of the AR(1) and AR(2) test. Diff-in-Hansen reports the p-value of the C statistic of the difference in the p-values of the restricted and the unrestricted model. The unrestricted model ignores the Arellano and Bover (1995) conditions. *p < .10, * * p < .05, * * *p < .01.

which may result in a bias in the estimated parameter. Second, we aim to investigate the mechanism through which democracy affects incomes by introducing potential transmission channels of democracy, as suggested by Tavares and Wacziarg (2001). As such, the newly introduced variables are "bad controls" in the sense that they are part of the causal effect we aim to estimate (Angrist and Pischke, 2009). For this reason, the more comprehensive model specifications neither capture nor attempt to capture the full growth effect of democracy. Rather, their comparison with the reduced model in Column (1) illuminates potential mechanisms through which democracy translates into growth.

When introducing the investment share and the average years of schooling in Column (2), conditional convergence in the form of a negative relationship between initial incomes and growth can be observed. What is remarkable in this estimation is the robustness of the effect of democracy, which remains significantly positive and maintains its magnitude. In Column (3) we incorporate life expectancy at birth, government consumption, the inflation rate, and the openness of countries. The effect of democracy remains positive and significant, but the estimated parameter shrinks slightly. The latter observation is in line with the findings of Doucouliagos and Ulubasoglu (2008), who show that inclusion of these additional covariates reduces the marginal effect of democracy on growth. Investigating bi-variate correlations between SVMDI and the newly introduced covariates, our data implies that democracies tend to have higher life expectancies (correlation: 53 percent) and a lower probability of hyperinflation (-31 percent). Each of these effects stimulates growth, which is why the column suggests a lower marginal impact of SVMDI. Finally, when introducing the fertility rate, the effect of democracy becomes insignificant. As democracies tend to have substantially lower fertility rates (correlation: -60 percent), the fertility channel appears to be a crucial transmission mechanism of democracy on growth. In countries where non-democratic structures are prevalent, the trade-off between the quantity and the education of the children is often resolved in favor of having more offspring. In light of binding budget constraints, families may consider this a substitute for missing social security systems.

The test statistics given in the lower part of Table 1 highlight the high degree of validity of our results. The AR(2) p-value illustrates that there is no second-order serial correlation in the residuals. In addition, once additional controls are introduced in Columns (2)-(4), the p-value of Hansen's J-test suggests that an omitted variable bias becomes increasingly unlikely. Finally, the Difference-in-Hansen statistics highlight the validity of the instrument subsets used for the level-equation, implying superiority of system GMM over difference GMM.

Overall, there is a clear indication of a positive effect of democracy measured by SVMDI on the growth rate. This effect remains positive and significant in Panel B, which investigates the impact of the initial democratization level via inclusion of SVMDI in (t— 1). Whereas the marginal effect in the reduced specification in Column (1) is remarkably stable in magnitude, the influence of initial democracy tends to be marginally stronger than current democracy in the subsequent regressions. As in Panel A, the effect of democratization vanishes once additional controls are introduced that account for the transmission channels of democracy, particularly the fertility rate.

Some authors have stressed a non-linear relationship between democracy and growth,

arguing that democracy enhances income increases at low levels of political freedom but depresses growth once a moderate level has been attained (see, e.g., Barro, 1996). In dictatorships, an increase in political rights may be growth enhancing due to the advantages arising from limitations on governmental power, increases in contractual freedom, and reductions in foreign trade barriers. At high levels of democracy, however, a further increase may eventually be an impediment to growth due to increases in redistributive efforts. Panel C deals with the examination of a possible nonlinear effect of democracy by inclusion of the squared SVMDI score. Whereas Column (1) provides indication of a parabolic influence of democracy on growth, the effect vanishes when additional covariates are incorporated. The Sasabuchi-Lind-Mehlum (SLM) test of Lind and Mehlum (2010) also indicates the presence of an inverted-U relationship in the reduced model, but does not detect a similar pattern in the more comprehensive specifications.

5.3. Sensitivity analysis I: Different estimation techniques

Subsequently, we explore whether our results are sensitive to the specified estimation strategy. Table 2 provides the results of two adjustments to Table 1. The first adjustment is first-difference GMM as proposed by Arellano and Bond (1991), and the second method uses Within-Group estimations. Both methods have been applied in recent studies concerning the effect of democracy on income increases (e.g. in Acemoglu et al., 2014, Rodrik and Wacziarg, 2005 and Gerring et al., 2005). The table reports three variants of each technique. The first specification is the reduced model of Column (1) of Table 1, while the second and third columns refer to the more comprehensive models reported in Columns (3) and (4) of Table 1. The columns are labeled in accordance with the variant of the baseline table that is used for specification.

Overall, the effect of democratization is remarkably stable across the regressions conducted in Table 2, strongly resembling the findings of the baseline estimations in significance and magnitude. One exception is the effect of SVMDI in the reduced model reported in Column (1), where Hansen's J-test again suggests an omitted variable problem. In addition, the Difference-in-Hansen test reported in Table 1 indicates that the additional moment conditions used in the system GMM estimation are valid, implying substantial efficiency losses when utilizing difference GMM. Note also that the number of observations declines from 1,077 to 913, as difference GMM requires observations for at least three consecutive periods. This technique draws on variations over time and eliminates the information in the equation in levels. Thus, when conducting difference GMM estimations, we expect the main effect of democracy to appear via the transition of non-democracies to democracies. Differencing the data, however, mainly yields losses of precisely the observations that we are interested in, i.e. observations from developing economies during the transition process. When introducing additional controls in Column (3), the positive and significant effect of SVMDI found in the baseline model reappears. This is a strong indication that democracy exerts its influence via a number of transmission channels which have opposing effects on growth. If we do not control for the effects of these variables, the estimated parameter of SVMDI captures the neutralizing effects of the transmission variables and becomes insignificant. In accordance

Table 2 The effect of SVMDI on growth, different estimation techniques. Dependent variable is real per capita GDP growth.

First-difference GMM Within-Group

(Arellano-Bond) (WG)

(1) (3) (4) (1) (3) (4)

Log(GDPpC) -0.128*** -0.0768*** -0.0741*** -0.0330*** -0.0589*** -0.0582***

(0.0310) (0.0135) (0.0138) (0.00610) (0.00857) (0.00832)

SVMDI 0.00957 0.0227* 0.0170 0.0267*** 0.0110* 0.00649

(0.0358) (0.0120) (0.0108) (0.00584) (0.00606) (0.00595)

INVS 0.0734** 0.0710** 0.0825*** 0.0723**

(0.0320) (0.0353) (0.0314) (0.0311)

SCHOOLY 0.00330 -0.00274 0.00823*** 0.00302*

(0.00470) (0.00516) (0.00164) (0.00172)

Log(LIFEEX) 0.0590 0.0299 0.131*** 0.120***

(0.0481) (0.0494) (0.0215) (0.0203)

GOVC 0.0309 0.0349 -0.00489 -0.00209

(0.0339) (0.0337) (0.0211) (0.0209)

INFL -0.000809 -0.000570 -0.000732 -0.000719

(0.000638) (0.000558) (0.000545) (0.000540)

OPEN 0.00306 0.00317 -0.00158 -0.00147

(0.00478) (0.00556) (0.00388) (0.00375)

Log(FERT) -0.0327 -0.0412***

(0.0219) (0.00857)

Observations 913 663 663 1,077 794 794

Countries 164 131 131 164 131 131

Hansen p-val 0.00231 0.118 0.114

AR(1) p-val 0.0467 0.107 0.109

AR(2) p-val 0.0649 0.217 0.227

Instruments 27 99 111

F Stat 20.12 29.91 31.50

F p-val 0.000 0.000 0.000

Notes: Table reports first-difference GMM (Arellano-Bond) and Within-Group (WG) estimations. Robust standard errors in parentheses. WG uses cluster-robust standard errors. The instrument matrix is restricted to lag 3. Hansen p-val. gives the p-value of Hansen's J-test, AR(1) p-val. and AR(2) p-val. report the p-values of the AR(1) and AR(2) test. F Stat gives the F statistic of the model, F p-val denotes the associated p-value. *p < .10, * * p < .05, * * *p < .01.

with the baseline results, the impact of democracy becomes insignificant once the fertility rate is introduced.

The Within-Group (WG) estimations also strongly support the results of the baseline table. This technique resembles the estimation strategy conducted by Gerring et al. (2005), Rodrik and Wacziarg (2005) and Papaioannou and Siourounis (2008). However, one concern is that introducing a lagged dependent variable in a WG model most likely results in a Nickell (1981) bias. In addition, WG does not account for possible problems caused by endogeneity, which are typically to be expected in growth regressions.

5.4. Sensitivity analysis II: Regional and cultural waves of democratization

We now turn to another branch of sensitivity analyses, conducting IV regressions in which SVMDI is instrumented with regional and cultural democratization. This technique, used in some more recent studies of the topic (see, e.g., Acemoglu et al., 2014 and Madsen et al., 2015), is motivated by the empirical observation that democratization often occurs in waves. Section 4.4 demonstrates that the SVMDI measure implies a multinational trend in democratization in the world during the 1980s and the early 1990s, which Huntington (1991, 2012) refers to as "Democracy's Third Wave". In addition, the renunciation of authoritarian regimes during the Arab Spring provides more recent experience with regional entanglements in the process of democratization. Spreading from one country to another, waves of democratization may be a satisfactory determinant of exogenous variation in democracy (Persson and Tabellini, 2009). We follow Acemoglu et al. (2014) in assuming that, conditional on covariates, democratization in neighboring countries should be uncorrelated with a country's national GDP.24 This allows for the creation of external instruments of democracy which capture the effect of democratization waves.

We use two different approaches to build our external instruments. The first approach is based on that of Acemoglu et al. (2014), instrumenting country-year {i,t} with jack-knifed average SVMDI of region r (denoted by Z\t) in which i is located. In order to satisfy the exclusion restriction, we leave out the value for i in the calculation of Z\t. The crucial challenge in computing Z\t is the accurate definition of the decisive regions. Whereas a narrower concept is more likely to include the countries that directly influence national demand for democracy, it bears the risk of leaving out information necessary for accurate instrumentation of national SVMDI scores. In addition, arbitrary classification of regions may cause a distortion in the results. For this reason, Table 3 uses two different definitions of region. The first (broad) definition refers to the country classification of the World Bank, the second (narrower) definition splits each continent into four disjoint regions, as illustrated in appendix A2.

The second approach weights the SVMDI of the countries by their cultural distance from i. We refer to this instrument as Z\t. While this procedure builds on the method proposed by Madsen et al. (2015), we use the cultural dimensions from Hofstede (2001) to

24 Whereas we could imagine plausible reasons why this assumption may be violated—e.g. due to a decline in regional trade or capital flows—Acemoglu et al. (2014) provide evidence that controlling for such effects has little impact on the estimation results.

Table 3 The effect of SVMDI on growth, IV estimations. Dependent variable is real per capita GDP growth.

Regional Democracy Regional Democracy Cultural Democracy

(World Bank) (Narrower definition) (Culturally-weighted)

(1) (4) (1) (4) (1) (4)

Panel A: 2SLS regression results

Log(GDPpC) -0.0537*** -0.0643*** -0.0482*** -0.0664*** -0.0354*** -0.0509***

(0.0106) (0.0128) (0.00831) (0.0116) (0.0115) (0.00804)

SVMDI 0.245*** 0.186** 0.166*** 0.0854*** 0.223*** 0.0458

(0.0536) (0.0774) (0.0314) (0.0287) (0.0602) (0.0451)

INVS 0.0847* 0.0842** 0.0650*

(0.0460) (0.0387) (0.0348)

SCHOOLY 0.000792 0.00231 0.00206

(0.00295) (0.00212) (0.00209)

Log(LIFEEX) 0.117*** 0.121*** 0.0946**

(0.0305) (0.0196) (0.0386)

GOVC -0.0384 -0.0282 -0.0418*

(0.0350) (0.0267) (0.0244)

INFL -0.000694 -0.000614 -0.00103

(0.000544) (0.000556) (0.000811)

OPEN -0.0164* -0.00963* -0.00787

(0.00901) (0.00513) (0.00566)

Log(FERT) -0.00758 -0.0259** -0.0385***

(0.0208) (0.0121) (0.0103)

Panel B: First-stage regression results

Democracy wave 0.5030*** 0.3929*** 0.5900*** 0.5160*** 0.5980*** 0.05182

(t - 1) (0.9224) (0.1200) (0.0809) (0.0961) (0.1585) (0.0495)

SW F-Stat 23.74 10.90 53.20 28.84 14.23 4.64

Stock-Yogo 5.53 5.53 5.53 5.53 5.53 5.53

Kleibergen-Paap 0.000 0.002 0.000 0.000 0.000 0.040

Observations 937 688 937 688 574 466

Countries 164 131 164 131 99 87

F p-val 0.000000424 1.28e-13 1.12e-10 1.64e-21 0.000611 2.83e-16

Notes: Table reports 2SLS estimations, where SVMDI is instrumented with regional and cultural democracy. All estimations include country fixed effects, cluster-robust standard errors in parentheses. Test statistics and number of included countries refer to Panel A. F p-val gives the p-value of the F Statistic of the reported model. Additional statistics reported in Panel B represent the Sanderson-Windmeijer F Statistic (SW F-Stat), the Stock Yogo critical value for 25% maximal IV size (Stock-Yogo), and the p-value of the Kleibergen-Paap test for underidentification (Kleibergen-Paap). Labels of the columns refer to the respective specification reported in the baseline estimations in Table 1. *p < .10, * * p < .05, * * *p < .01.

capture cultural diversity rather than linguistic differences. The advantage of Zrit is that the exclusion restriction may be more likely to be fulfilled, as culturally similar countries are not necessarily in the vicinity of one another. The creation of the instruments is described in detail in appendix A1.

The estimation strategy used in Table 3 follows Acemoglu et al. (2014) and Madsen et al. (2015), using 2SLS with cluster-robust standard errors and including country-fixed and period-fixed effects.25

Panel A of Table 3 reports the 2SLS results, with first-stage outcomes presented in Panel B. The results from this exercise strongly support the positive effect of democracy found in Table 1. However, when instrumenting SVMDI with regional democratization waves, the reduced models imply an increase in the marginal effect of SVMDI from 0.0249 in the baseline specification to 0.245 in Table 3. The results also seem to be relatively unaffected by the classification of regions r, as both the categorization of the World Bank and the narrower concept yield outcomes strongly comparable in their significance. However, when using the narrower classification of regions, the marginal effect is smaller. Instrumenting the SVMDI variable via culturally-weighted waves of democracy yields a heterogeneous picture. The marginal effect in the reduced model strongly resembles the effect detected in Column (1). Unlike in the estimations based on regional instruments, the SVMDI ceases to be significant once the fertility rate is introduced in the model.26

Panel B highlights a strong and significant effect of regional democratization waves in t — 1 on national SVMDI scores, suggesting that Zrt-1 is a valid instrument for SVMDI.27 The Sanderson and Windmeijer (2016) weak instrument F-test (SW) implies that regional and cultural waves of democracy are strong instruments for national democracy. Likewise, the Kleibergen and Paap (2006) test rejects the null of under-identification in each specification. However, the first-stage regressions also highlight that ZJt-1 is less valid than Zrt-1. In the reduced model, cultural waves of democratization are significantly related to national democracy. In the comprehensive model specification in the last column, we cannot find any contribution of cultural democracy waves to the SVMDI in country i. Meanwhile, the SW test points to a weak instrument problem.

Comparing the outcomes of Table 3 to a similar analysis conducted by Acemoglu et al. (2014), we find that utilization of SVMDI is superior to the application of a rough di-chotomous measure, as it yields much more significant results.28 This is in line with Elkins

25Whereas the authors of both studies use real per capita GDP as the dependent variable in their IV regressions, the dependent variable in Table 3 is again the growth rate of real GDP per capita to ensure comparability with the baseline results. Note that exact replication with inclusion of SVMDI as democracy variable yields quite similar results. Note also that the results of a more direct comparison to the baseline table achieved by inclusion of our external instruments in the System GMM estimations strongly resemble the baseline findings.

26Similar to the baseline results reported in Table 1, SVMDI significantly contributes to income increases in each specification other than model (4).

27We instrument SVMDI by only one lag of Zrt. As with Acemoglu et al. (2014), we find only slightly differing effects when using more lags of Z\t as instruments.

28 The same increase in significance occurs if we directly replicate the utilized specifications, using Log(GDPpc) as dependent variable.

(2000), who shows that graded measures of democracy are superior to dichotomous classifications in empirical political science research. In our case, the superiority is the result of the substantial increase in the level of detail enabled by the Support Vector approach. Even when controlling for regional democratization waves, the strong heterogeneity in the subset of democratic (autocratic) countries—which necessarily occurs when conducting a binary classification—results in a loss of information that causes a distortion in the estimated results. Note also that the IV approach is likely to suffer from a Nickell bias unless the (bold) assumption holds that E[Zrt_1eit] = 0 and eit is serially uncorrelated.

5.5. The effect of alternative democracy indicators on growth

Whereas the previous results provide strong evidence for a positive effect of democracy on growth when applying the SVMDI measure, we are interested in determining if these results are superior when compared with estimations which use alternative indices of democracy. Whenever the available indices lack observations for recent periods (e.g. Vanhanen and Lindell, 2012) or have not yet been made available (e.g. Acemoglu et al., 2014), we calculate missing values according to the algorithms reported in the original documentations. We conduct two different estimation techniques, difference GMM and system GMM.

Difference GMM has been used in a number of recent studies (e.g. in Gerring et al., 2005 and Acemoglu et al., 2014). The general idea of this technique, shown in Equation (5), is to eliminate unobserved heterogeneity by first-differencing the specified model, i.e. first-differencing Equation (4). However, this transformation removes the information in the equation in levels, so that the estimation relies solely on the within-country information. In the context of the relationship between democracy and growth, this means that the estimated parameter essentially captures the effect of democratization within countries, i.e. the process of transformation towards or away from democracy.

Panel A of Table 4 illustrates the results of the difference GMM estimations, replicating the specification of Column (3) in Table 2 using SVMDI and six commonly used democracy indicators. To exclude the possibility of a sample selection bias, the estimations rely on the set of observations that are available for all indicators. As in Section 5.3, the SVMDI detects a positive and significant effect of the democratization process within countries on their growth rate. However, neither of the alternative indicators suggests a similarly significant influence, a result which strongly resembles the effects identified in many recent studies.29 Since (non-)democratic countries differ in numerous historical, cultural, political, and institutional aspects, first-differencing the model requires indicators that react quite sensitively to political events in order to capture the effect of transition towards democracy within countries. As illustrated in Section 4.5, hitherto existing democracy indicators are unable to react with sufficient sensitivity to political events and regime changes. For this reason, raw measures of democracy—particularly dichotomous indices—provide little indication of an income-enhancing effect of democratization, as Table 4 clearly demonstrates.

29Note that this result also occurs if we use other model specifications, e.g. Column (4) of Table 2 and Columns (2)-(4) of the baseline estimations of Table 1.

Table 4 The effect of different democracy indicators on growth. Dependent variable is real per capita GDP growth.

SVMDI POLITY VANHANEN ACEMOGLU FREEDOM BOIX UDS

Panel A: Difference GMM estimations

DEMOCRACY 0.0252* 0.0006 0.0008 0.0082 0.0085 0.0075 0.0085

(0.0149) (0.0009) (0.0005) (0.0116) (0.0067) (0.0104) (0.0072)

Observations 616 616 616 616 616 616 616

Countries 122 122 122 122 122 122 122

Hansen p-val 0.214 0.170 0.0968 0.221 0.210 0.199 0.226

AR(1) p-val 0.118 0.120 0.116 0.122 0.115 0.120 0.115

AR(2) p-val 0.229 0.240 0.237 0.229 0.220 0.231 0.236

Instruments 99 99 99 99 99 99 99

Panel B : System GMM estimations

DEMOCRACY 0.0203** 0.0009** 0.0006*** 0.0119** 0.0058 0.0064 0.0070**

(0.0086) (0.0004) (0.0002) (0.0054) (0.0036) (0.0055) (0.0034)

Observations 737 737 737 737 737 737 737

Countries 122 122 122 122 122 122 122

Hansen p-val 0.946 0.924 0.904 0.945 0.959 0.930 0.949

Diff-Hansen 1.000 1.000 1.000 1.000 1.000 1.000 1.000

AR(1) p-val 0.121 0.120 0.118 0.122 0.119 0.122 0.118

AR(2) p-val 0.345 0.348 0.352 0.342 0.337 0.344 0.346

Instruments 154 154 154 154 154 154 154

Notes : Table reports two-step system GMM estimations. The specifications of the covariates refer to Column (3) of Table 2 (Panel A) and Column (3) of Table 1 (Panel B). All estimations use period fixed effects and Windmeijer-corrections, robust standard errors in parentheses. The instrument matrix is restricted to lag 3. Hansen p-val. gives the p-value of Hansen's J-test, AR(1) p-val. and AR(2) p-val. report the p-values of the AR(1) and AR(2) test. Diff-in-Hansen reports the C statistic of the difference in the p-values of the restricted and the unrestricted model. The unrestricted model ignores the Arellano and Bover (1995) conditions. *p < .10, * * p < .05, * * *p < .01.

Since most of the variation in traditional democracy indicators stems from the cross-section rather than the time-dimension, the utilization of additional orthogonality conditions proposed by Arellano and Bover (1995) and Blundell and Bond (1998) is beneficial, as these additional restrictions ensure that some of the information in the equation in levels is maintained. With respect to the estimation of the democracy-growth nexus, this implies that the estimated parameters also capture the between variation, i.e. the variation in the level of democracy between the countries in the sample. In addition, as difference GMM requires information from at least three consecutive periods in order for a country to be included in the estimation, the exploitation of the Arellano and Bover (1995) orthogonality conditions also yields an increase in the number of observations. This is crucial, as we might expect a loss of observations for developing countries in particular, which possess a higher within variation in democratization than advanced economies. Panel B of Table 4 reports the results of system GMM using the same model specifications as in Panel A. What we

observe is a change in the picture. The SVMDI index maintains its positive and strongly significant effect on growth. Additionally, four of the six alternative indices now point to a similar influence of democracy on growth.

Overall, the results of Table 4 broadly indicate that democracy is positively related to long-run growth. However, only the SVMDI indicates that the transition to democracy is beneficial to growth. From an economic perspective, this implies that small steps towards democracy already lead to long-run increases in living standards, even if political rights in the countries do not catch up with those of established democracies. Meanwhile, reverse waves of democratization are likely to be harmful to growth in the long-run. Once the econometric specification allows for the investigation of differences in the democracy level across countries, the positive effect of democracy can be observed as a clear empirical pattern, even if the model relies on raw measures of democracy.

6. The transmission channels of democracy

In line with Tavares and Wacziarg (2001), we previously suspected that political rights exert their influence on growth via a number of transmission channels. This section is concerned with a more in-depth analysis of these mechanisms.

Table 5 illustrates the effect of democracy on schooling, investment, redistribution, and fertility. Each of these variables plays an important role in the growth process; however, it is crucial to disentangle the effects of democracy from those of credit availability. Whereas democracy may increase schooling and investment via a more equal distribution of opportunities and fewer government interventions in the private sector, it simultaneously contributes to better credit availability. It has been emphasized in the growth literature that mitigation of credit market imperfections yields an increase in education and physical capital investments (see, e.g., Galor and Zeira, 1993; Galor and Moav, 2004). For this reason, we specify two models for each of the transmission variables: the first variant uses the variables of the specifications in Table 1, while the second variant additionally introduces private credit to GDP (CREDIT) as a proxy for credit availability.30 As expected, the correlation between SVMDI and CREDIT is high (50 percent).

The empirical framework follows Acemoglu et al. (2014), conducting Within-Group (Panel A) and 2SLS (Panel B) estimations. The latter once again uses regional waves of democratization as external instruments for domestic democracy. Due to the high probability of a potential Nickell (1981) bias in our "small" T panel, we do not include lagged dependent variables. SVMDI enters in the regressions with a lag of one period to ensure that causality runs from democracy to the transmission variables, rather than the reverse.

The first transmission channel in Table 5 is concerned with education. The results imply that wealthier economies exhibit a higher average level of school attainment. In addition, better health as measured by life expectancy enhances education. The trade-off between the quantity and the education of children is clearly visible, as we can observe a significantly negative impact of fertility on education. Controlling for these effects, the influence

30The data source is World Bank (2014b).

Table 5 The transmission channels of democracy

Schooling Investment Redistribution Fertility

(1) (2) (1) (2) (1) (2) (1) (2)

Panel A: Within-Group regression results

Log(GDPpc) 1.078*** 0.705*** 0.0136 0.00717 0.000527 -0.00594 0.000866 -0.0550*

(0.197) (0.196) (0.0216) (0.0229) (0.00597) (0.00545) (0.0342) (0.0329)

SVMDI(t - 1) 0.252 0.327** 0.0375*** 0.0362** 0.00356 0.00264 -0.107** -0.0494

(0.172) (0.149) (0.0140) (0.0155) (0.00368) (0.00407) (0.0426) (0.0341)

INVS 0.102 -0.0372 -0.0758*** -0.0755*** -0.310** -0.361***

(0.679) (0.680) (0.0207) (0.0211) (0.143) (0.133)

SCHOOLY 0.00277 -0.000336 0.00582*** 0.00505*** -0.116*** -0.120***

(0.00588) (0.00614) (0.00150) (0.00138) (0.0164) (0.0164)

Log(LIFEEX) 2.051** 1.579** 0.150* 0.154* 0.0275** 0.0222** -0.164 -0.175

(0.840) (0.767) (0.0826) (0.0907) (0.0117) (0.0111) (0.139) (0.132)

GOVC -0.900 -0.810 -0.120 -0.151* 0.00220 0.00232 0.0772 0.0735

(0.708) (0.681) (0.0927) (0.0867) (0.00912) (0.00886) (0.104) (0.0950)

INFL -0.0142** -0.0113 -0.000267 -0.00129** 0.000416 0.000397 0.000465 0.000798

(0.00679) (0.00743) (0.00140) (0.000618) (0.000284) (0.000315) (0.000741) (0.000653)

Log(FERT) -2.745*** -3.056*** -0.0681** -0.0834*** 0.0164** 0.0124*

(0.296) (0.286) (0.0295) (0.0299) (0.00681) (0.00653)

OPEN 0.0842 0.0995 -0.00415 -0.00877 0.00500 0.00447 0.00178 0.00948

(0.120) (0.109) (0.0106) (0.0100) (0.00344) (0.00331) (0.0215) (0.0185)

CREDIT 0.671*** 0.00412 0.0128** 0.121***

(0.218) (0.0184) (0.00578) (0.0430)

REDIST -0.688***

(0.189)

Panel B: 2SLS regression results

SVMDI(t - 1) 1.512*** 1.584*** 0.0722** 0.0825** 0.0138* 0.0135 -0.368*** -0.304***

(0.415) (0.417) (0.0301) (0.0367) (0.00774) (0.00868) (0.0962) (0.109)

Observations 688 666 572 666 572 556 688 666

Countries 131 129 124 129 124 122 131 129

R-Squared 0.613 0.650 0.243 0.206 0.129 0.149 0.538 0.576

F Stat 44.62 47.56 8.305 8.883 3.706 3.460 31.53 32.41

F p-val 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000

Notes: Table reports Within-Group and 2SLS estimations. Model specification of the 2SLS estimations is identical to the Within-Group variant. 2SLS uses regional democracy (narrower definition) as instruments, for a description see Section 5.4. Cluster-robust standard errors in parentheses. Test statistics refer to the Within-Group models. F Stat reports the F-test statistic of joint significance of the model, F p-val gives the p-value of the F-test. *p < .10, * * p < .05, * * *p < .01.

of democratization is positive in the Within-Group estimations and becomes significant in Column (2) when we introduce CREDIT. Likewise, SVMDI is significant in both specifications of the 2SLS estimations. The results imply that better credit availability softens the budget constraints of the household, thereby contributing to a higher level of education of individuals. However, even when controlling for this effect, democracy acts as an additional source of educational improvements.

The second transmission channel illustrates the effect of SVMDI on investment, which is positive in both the Within-Group and the 2SLS estimations. Apparently, democratic structures and political rights facilitate both national and foreign investments and capital inflows. These findings are in line with the well-known results of Perotti (1996), who finds that political stability—which is considerably greater in democracies (Feng, 1997)—has a huge impact on investment and growth. CREDIT has no significant effect on investment, suggesting that the positive contribution of the SVMDI stems largely from foreign investments, which are not necessarily financed by loans acquired in the target country. To examine a possible negative effect of an increase in political rights in countries with a medium or high level of SVMDI, Column (1) also incorporates the level of effective redistribution, measured by the difference of the Gini coefficient of household incomes before and after taxes and transfers.31 The results show a strongly significant impact of redistribution on investments, where a greater amount of redistribution is negatively related to investment activity. This, in principle, supports the hypothesis that a higher level of democratization may be an impediment to growth. However, this mechanism only comes into play if democracy enhances redistribution.

This redistribution-enhancing effect is investigated in the third branch of transmission analyses. We observe that redistribution is lower in countries with a higher average level of education. Meanwhile, countries with longer life expectancy, higher government consumption and higher fertility rates typically tend to redistribute more. Controlling for these effects, we find no additional contribution of SVMDI to redistribution in the Within-Group regressions, and only a weak positive effect in the 2SLS estimations. This implies that the strong bivariate correlation between SVMDI and REDIST (63 percent) is not due to an inherent causality running from democracy to redistribution, but is the result of numerous variables that are affected by democracy. The ambiguous effect of democracy on redistribution strongly resembles the recent findings of Acemoglu et al. (2013). However, Feld and Schnellenbach (2014) emphasize that the manner in which income is redistributed differs between countries, depending on their respective constitutional framework.

The last transmission channel deals with the effect of democracy on fertility. The first column highlights that democratization yields a significant decline in fertility rates. The process of democratization is often accompanied by a substantial increase in the size of social security systems and a reduction of uncertainty due to greater political stability, both of which reduce families' incentives to have children as a substitute for social protection. However, it is crucial to disentangle the different effects of democracy and credit availability, as is illustrated in Column (2). When holding constant CREDIT, the effect of democracy

31 Data source is the SWIID v5, documented in Solt (2009) and Solt (2016).

shrinks, but remains negatively and—in case of the 2SLS estimations—significantly associated with fertility. Better credit availability increases the fertility rate, as access to capital markets alleviates the otherwise binding trade-off between the quantity and the education of children.

Summarizing the findings, we observe that democracy exerts its influence on growth via better education, higher investment shares, and lower fertility rates. In contrast, we find only minor evidence for a redistribution-enhancing effect of democratization.32

7. Conclusions

Possessing reliable measurements of democracy is essential for achieving a sound understanding of democratization and its effects on political and economic outcomes. The overwhelming majority of existing indicators, however, are fraught with methodical problems. Not infrequently, scholars using such rough measurements will find that an inappropriate democracy indicator is the Achilles' heel of empirical analyses, particularly when working with panel data.

By maximizing comparability for the broadest possible sample of countries, the SVMDI algorithm facilitates empirical investigations of democracy. A direct result of this methodological improvement is a substantial increase in the level of detail in comparison with established approaches. In addition, the algorithm places the crucial question of how to aggregate the underlying attributes—undoubtedly the main weak point of alternative indicators—into the context of a nonlinear optimization problem, thereby obtaining much more consistent and plausible results. The unprecedented potential of machine learning enables researchers to make highly accurate classifications, and may also provide very promising results for various problems in the field of economics beyond its utilization for measuring democracy.

Using the SVMDI, we find a robust positive influence of democracy on long-run economic growth. Our results suggest that the ambiguity in recent studies stems from two main sources. First, in light of the diversity of political institutions across countries, the lack of a sufficient reaction of traditional democracy indicators to political events and regime changes only allows for a rough classification of democracy. Second, when using empirical models that rely on the within-country variation, the problem of inadequate and insensitive measurement of democracy becomes particularly severe.

When digging deeper into the democracy-growth nexus, we find only minor indication of a nonlinear relationship between the variables. The analysis of the transmission channels through which democracy exerts its influence on growth illustrates why: while democratic countries typically have better educated populations, higher investment shares, and lower fertility rates, we find little evidence of a redistribution-enhancing effect of democratization.

32 We also do not find any robust effect of democracy on health, even though both variables reveal a high bivariate correlation (53 percent). What we do find, however, is a significant impact of initial wealth on life expectancy. Whereas we would suspect that democratic countries provide better public health services, the estimations imply that incomes are much more decisive for health than regime type. However, life expectancy may be a poor proxy in this context, as changes in this variable may only occur a considerable amount of time after democratization has taken place.

Taken together, our results emphasize that democratic structures facilitate economic growth in the long-run, and that their implementation may be a beneficial strategy for less-developed countries. However, countries differ in numerous cultural, historical, political, and institutional dimensions. Isolating the growth effect of different aspects of democratic institutions may thus be an advantageous field of future research. Likewise, it would be beneficial to acquire a deeper empirical understanding of the transmission channels of democracy, particularly with regard to human capital, inequality, and redistribution.

Acknowledgments

We thank Toke Aidt (Editor), Luna Bellani, Norbert Berthold, Leo Kaas, Guido Schw-erdt, Heinrich W. Ursprung, and two anonymous referees for their valuable comments and discussions. We are also grateful for the very utile notes provided by the participants of the 9th Workshop of Political Economy (Ifo Institute for Economic Research Dresden) and the Annual Meeting of the European Public Choice Society (2016). Tommy Krieger is grateful for the support of the Graduate School of Decision Science (University of Konstanz).

Appendix

Appendix A1: Description of the external instruments used in the IV regression

Let R = {1,..., R} denote a set of regions, where each country i belongs exactly to one region r. In addition, let Nrt be the number of countries in region r at period t and dit denote the level of democracy in country-year {i,t}. Then the regional democratization wave—i.e.

instrumental variable Z[t—is calculated via

{j=i|r'=r,r'€R}

To build the culturally weighted instrumental variable of democracy, we use four of the cultural dimensions—Power Distance (PD), Individualism (IN), Masculinity (MC), and Uncertainty Avoidance (UA)—provided by Hofstede (2001) and calculate our instrument via a four-stage approach. First, we calculate the Euclidean distance

5i:i = ^/(PA - PDj)2 + (IN - INj)2 + (MC - MCj)2 + (UAi - UAj)2 (A.1)

for each set of countries {i, j}. Subsequently, we normalize iii- to the interval from 0 to 1 by applying the standard formula

- _ maXi,j } -

= fx T : rx T" '

which is used, for instance, for generation of the Human Development Index (see United Nations, 2013). In the third stage, we calculate the cultural weights A^- via

Ai,j = ^V (A.3)

to ensure that the weights sum up to 1 for each country i. Finally, the external instrument —which equals the culturally weighted democracy score for a particular country-year {i,t}—is computed as follows

Zt = ^ Ai,k SVMDIk,t. (A.4)

Table A2 Classification of regions in the IV regression.

I. ASIA

Central Asia

East-Southeast Asia Arabic Region

Oceania

Afghanistan, Armenia, Azerbaijan, Bhutan, Georgia, India, Iran, Kazakhstan, Kyrgyzstan, Maldives, Mongolia, Nepal, Pakistan, Sri Lanka, Tajikistan, Turkmenistan, Uzbekistan Bangladesh, Cambodia, China, Japan, Laos, Myanmar, North Korea, South Korea, Taiwan, Thailand, Vietnam Bahrain, Iraq, Israel, Jordan, Kuwait, Lebanon, Oman, Qatar, Saudi Arabia, Syria, Turkey, United Arab Emirates, Yemen

Australia, Brunei Darussalam, Fiji, Indonesia, Malaysia, New Zealand, Papua New Guinea, Philippines, Samoa, Singapore Solomon Islands, Tonga, Vanuatu

II. EUROPE

Central-Northern Europe

South-Southwest Europe East Europe

Balkan States

Austria, Belgium, Denmark, Finland, Germany, Iceland, Ireland, Luxembourg, Netherlands, Norway, Sweden, Switzerland, United Kingdom

Cyprus, France, Greece, Italy, Malta, Portugal, Spain Belarus, Czech Republic, Estonia, Latvia, Lithuania, Moldova, Poland, Russia, Slovakia, Ukraine Albania, Croatia, Bulgaria, Hungary, Kosovo, Macedonia, Montenegro, Romania, Serbia, Slovenia

III. AFRICA

North Africa Central-East Africa

West Africa

Southern Africa

Algeria, Egypt, Libya, Morocco, Tunisia Cameroon, Central African Republic, Chad, Djibouti, Eritrea, Ethiopia, Kenya, Somalia, South Sudan, Sudan Benin, Burkina Faso, Cape Verde, Cote d'Ivoire, Gambia, Ghana, Guinea, Guinea-Bissau, Liberia, Mali, Mauritania, Niger, Nigeria, Senegal, Sierra Leone, Togo Angola, Burundi, Comoros, Democratic Republic of the Congo, Republic of the Congo, Equatorial Guinea, Gabon, Lesotho, Madagascar, Malawi, Mauritius, Mozambique, Namibia, Rwanda, Sao Tome and Principe, Seychelles, South Africa, Swaziland, Tanzania, Uganda, Zambia, Zimbabwe

IV. AMERICA

North America Central America

South America

Caribbean

Bahamas, Canada, United States

Belize, Costa Rica, El Salvador, Grenada, Guatemala, Honduras, Mexico, Nicaragua, Panama

Argentina, Brazil, Chile, Colombia, Ecuador, Guyana, Paraguay, Peru, Suriname, Uruguay, Venezuela Antigua and Barbuda, Barbados, Cuba, Dominica, Dominican Republic, Haiti, Jamaica, St. Kitts and Nevis, St. Lucia, St. Vincent, Trinidad and Tobago

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Highlights

• We evaluate the impact of democracy on economic growth

• We use a novel approach to measure democracy based on a machine learning algorithm

• We detect a robust and significant effect of democratization on income increases

• Established democracy indices are not sufficiently detailed to reveal this relation