and hold government officials accountable, thereby reducing corruption. Therefore, the negative effect of women's representation in government on corruption is spurious and vanishes when one includes a measure of democracy in the regression, which is empirically confirmed by Sung (2003). Swamy et al. (2001) draw attention to the "level of discrimination against women" as another possible omitted variable that drives both female participation and corruption. They claim that in countries that are more corrupt there is more discrimination against women and argue that in countries where traditions and clientelism prevail, there is a preference for men in power.

In this paper, we focus on the effect of discrimination against women on corruption in a society as we have a new measure of society's attitude towards gender inequality to empirically test this relationship. Swamy et al. (2001) do not explain how this relationship operates, but several papers deal with this issue in a direct or indirect way (Tripp, 2001; Inglehart et al., 2002; Rizzo et al., 2007). These authors claim that society's attitude towards women influences how a political system functions and that it affects the positions women take in this system. Assuming that the level of corruption depends on the functioning of the political system, one could argue that society's attitude towards gender inequality has an impact on corruption.

The study of Tripp (2001) focuses on women's movements as a countervailing force to prevailing practices of corruption in Eastern and South Africa. 2Political reforms at the beginning of the 1990s, including free and competitive elections, a multi-party system and freedom of expression and association were not enough to give women access to powerful positions and to curtail the practices of patronage, clientelism and personal rule. Women could enter the system, but they were excluded from male-dominated networks and therefore from the benefits of clientelism. However, political reforms allowed the formation of social forces. The disadvantaged women organized in autonomous movements, which were broadbased, multi-ethnic and multi-religious. These movements cross-cut cleavages and started to demand transparency and the removal of clientelistic networks.

A similar perspective is adopted by Inglehart et al. (2002) and Rizzo et al. (2007) who state that when a society favors gender equality, there is more tolerance in general, more personal freedom and individual autonomy. The absence of these values inhibits political reforms towards a democratic system. The study of Inglehart et al. (2002) finds that gender equality is the most important part of"self-expression values" appearing in post-industrialization societies which directly contribute to both democratization and to a greater representation of women in politics. Focusing on Arab and non-Arab Muslim countries, Rizzo et al. (2007) shows that even if democratic political institutions like elections, political parties or checks

2Waylen (1993) makes a similar point for Latin America.

and balances are put in place, gender inequality can prevent these institutions from functioning well.

We empirically test on a sample of developing countries the relationship between social institutions related to gender inequality and the level of corruption, and contribute to the literature discussed above. We focus on public corruption, which refers to the misuse of public office for private gain. It comprises grand corruption, which refers to activities of top officials and big companies, and petty corruption, which refers to the activities of people at the lower end of hierarchies (Pardo, 2004). To proxy society's attitude towards gender inequality or what Swamy et al. (2001) call "level of discrimination against women" we introduce social institutions related to gender inequality into the analysis. Social institutions are long-lasting norms, traditions and codes of conduct that shape gender roles and influence the opportunities of women and men in a society. As suggested by e.g. De Soysa and Jutting (2007) and in Essay 2, these guiding principles of human behavior affect development outcomes and should not be neglected in the study of a society. We measure social institutions related to gender inequality with the subindex civil liberties proposed by Essay 1, which is based on variables from the OECD Gender, Institutions and Development Database (Jutting et al., 2008). This subindex captures society's attitude with regard to gender roles based on the freedom of women to participate in social life.

Our aim is to investigate whether society's attitude towards gender inequality matters for corruption once one accounts for the representation of women in parliament and business as well as the political system of a country. The hypothesis is that in a society where women's participation in social life is restricted, there is a higher level of corruption.

Even after controlling for democracy and political and economic participation of women, as well as for other factors, we find a robust and significant relationship between the subindex civil liberties and the level of corruption. We show that social institutions related to gender inequality are an important factor for the study of corruption. In societies where women are deprived of their freedoms to participate in social life, corruption is higher. As should be clear from the various existing theories the exact causal mechanism behind this relationship is not obvious and it cannot be established in this study since we conduct a cross-sectional analysis. This implies that one needs to carefully investigate the context, as tackling corruption might require more than pushing democratic reforms and increasing female representation in political and economic positions.

The rest of the paper is organized as follows. Section 3.2 describes the the data used, the empirical estimation and the main results, which are discussed in section 3.3.

## **3.2 Empirical Estimation and Results**

#### **3.2.1 Data**

The definition of all variables and descriptive statistics are presented in Tables 3.1, 3.2 and 3.3. Measuring corruption is a complex task as it has many faces. There is public corruption, which refers to the misuse of public office for private gain, and corruption that comprises the collusion between firms or misuse of corporate assets (Svensson, 2005). Other authors differentiate between grand and petty corruption. Grand corruption refers to activities of topofficials and big companies. Petty corruption refers to the activities of people at the lower end of hierarchies (Pardo, 2004).

We use two different measures of public corruption in our estimations comprising grand and petty corruption. The first measure is the Corruption Perception Index (CPI) of Transparency International. 3The CPI measures the level of corruption in a country. It is based on various data sources, business surveys and expert panels about perceptions of corruption, and is a comprehensive measure that covers the different forms of grand and petty corruption in business, politics and administration. It is continuous and ranges from O meaning high corruption to 10 meaning low corruption (Lambsdorff, 2006).

The second indicator is the Corruption in Government Index from the International Country Risk Guide (ICRG) provided by the Political Risk Services.4 The ICRG index assesses the political risk associated with corruption and focuses in particular on those types of corruption that lead to instability in the political system as they distort the economic and financial environment, put foreign investments into risk and reduce the efficiency of government and business because people come to power not because of their ability but through patronage and clientelistic practices. *5* Hence, this measure gives the extent of political risk of instability that is assumed to increase with corruption. Therefore, it is only under certain conditions an indicator of the level of corruption. Whether the political risk of instability caused by corruption coincides with the level of corruption depends on the degree of tolerance towards corruption (Lambsdorff, 2006). The ICRG corruption index is a continuous variable that ranges from O to 6 with O meaning high risk and 6 indicating low risk.

The subindex civil liberties (Subindex Civil lib.) is one of five composite indices (the others being subindex family code, subindex son preference, subindex physical integrity, subindex ownership rights) that measure social institutions related to gender inequality, and were presented in Essay 1. These social institutions are conceived as long-lasting norms,

3Data are available at http://www. transparency. org/policy \_research/ surveys\_ indices/cpi.

4http://www.prsgroup.com/.

5http://www.prsgroup.com/ICRG\_Methodology.aspx\#PolRiskRating

traditions and codes-of conduct that find expression in traditions, customs and cultural practices, informal and formal laws and guide people's behavior and interaction. They shape gender roles and therefore the social and economic opportunities of men and women. We use the subindex civil liberties in this study as it covers those social institutions that directly shape the opportunities of women to participate in social life. It therefore reflects better their opportunities to gain power in politics and economics than the other subindices related to gender inequality. Indeed, we find that the subindex civil liberties is the only subindex that is significant in the regression analysis. The subindex civil liberties is built out of two variables of the OECD Gender, Institutions and Development Database (Morrison and Jutting, 2005; Jutting et al., 2008), which are freedom of movement and freedom of dress. Freedom of movement measures the level of restrictions women face in moving freely outside their own household. Freedom of dress measures the extent to which women are obliged to follow a certain dress code in public, for example being obliged to cover their face or body when leaving the house. Both variables are ordinal taking the values 0, 0.5 and 1 with O indicating no restrictions and 1 indicating high restrictions on women. 6 They are proxies of civil liberties in a sense that when women are restrained to leave the house it is difficult to imagine that they can actively participate in social, political and economic life. Wearing a veil might be a form of self-determination and expression, and different traditions, styles and customs are connected to it. However, *forced* veiling is incompatible with agency, as it might be a sign of subordination in a society and might hinder interactions with other human beings either as women cannot interact because they wear a veil or they can only interact if they wear a veil (Macdonald, 2006; Milallos, 2007). The subindex is the rescaled weighted sum of the two variables with the weights obtained from polychoric principal component analysis (Kolenikov and Angeles, 2009). The subindex goes from O (no gender inequality) to 1 (high gender inequality). As the subindex civil liberties does not cover developed (OECD) countries, the subsequent empirical analysis focuses on developing countries.

The variables that are contained in the subindex could be considered as proxies for religion and therefore one could think that the subindex civil liberties might be a proxy for religion as well. When investigating the variation of the subindex over religion, one observes that there is more variation within Muslim majority countries than in countries with

6The variable freedom of dress takes the value 0 if less than 50% of women are obliged to follow a certain dress code, 0.5 if more than 50% of women are forced to follow a certain dress code, and I if all women are obliged to follow a certain dress code, or if it is punishable by law not to follow it The variable freedom of movement is 0 ifless than 50% of women face restrictions on their movement outside the home, 0.5 if more than 50"/c, of women face restrictions on their movement outside the home, and I if women can never leave home without restrictions (i.e. they need a male companion).

either Christian majority or countries without Christian or Muslim majority (Table 3.5).7 To further examine whether the subindex measures Muslim religion, we plot the subindex civil liberties against the percentage of Muslim population in a country (Figure 3.1 ). It is true that countries having less than 50% Muslim population tend to have lower values on the subindex civil liberties with the exception of India which scores 0.6 with about 15% of Muslim population. For countries with more than 50% Muslim population the subindex shows more variation. Noticeably, there are several countries that have more than 70% of Muslim population and the value O on the subindex civil liberties. 8 Consequently, there is no perfect correspondence between the subindex and the percentage of Muslim population. Nevertheless, in the regressions we include a Muslim and a Christian dummy (Muslim and Christian) to control for the impact of religion, the left-out category being countries that have neither a majority of Muslim nor a majority of Christian population.9

To account for female representation, which is highlighted by e.g. Swamy et al. (2001) and Dollar et al. (2001), we include three measures of female representation. We take data from World Bank (2009a) on the proportion of female legislators (Parliament), the female share in professional, technical, administrative and managerial positions (Managers), 10 and women's share oflabor force (Labor force).

To capture democracy we choose the Electoral Democracy index (Electoral democ.) of Freedom House (2008) that takes the value 1 if there are competitive, universal, free and secret elections and a multiparty system. An alternative measure is the Polity2 index of the Polity IV Project that we use to check the robustness of the results as Polity2 measures more closely liberal democracy (Marshall and Jaggers, 2009). 11 Unfortunately, it covers

7The variable freedom of movement varies over all three religious categories, while the variable freedom of dress has almost no variation in countries having a Christian majority or countries without Christian or Muslim majority, except for India and Sri Lanka.

8 Albania, Azerbaijan, Gambia, Guinea, Kyrgyz Republic, Mali, Morocco, **Niger,** Senegal, Sierra Leone, Tajikistan, Tunisia, Turkmenistan, Uzbekistan

9As Muslim religion is related to the subindex we also use the percentage of Muslim population instead of the two religion dummies in the regressions. The results are unchanged.

10Both indicators have been criticized (Bardhan and Klasen, 1999; Dijkstra, 2002). In some countries, for example communist ones, parliaments lack power and the representation of women in these parliaments does not reflect actual power of women. Moreover, female representation in parliament measures only representation at the national level and ignores women's participation at other levels of the state and in civil society. A similar problem is attached to the representation of women in senior economic positions that only measures formal sectors. In addition, this indicator does not fluctuate much over years. However, given that there is a lack of data available for women's representation at the local and societal level as well as for informal economic participation and to be comparable to other studies, we use both measures.

11Current data for the Polity IV Project can be found at

http://www.systemicpeace.org/polity/polity4.htm.

fewer countries than the Electoral democracy index. 12 Dollar et al. (2001), Swamy et al. (2001) and Sung (2003) use either the Civil Liberties index13, the Political Rights index or the Freedom of the Press index of the Freedom House project as regressors in their empirical analysis to measure or to refine the measurement of democracy. It needs to be stressed that these measures are not without methodological problems as they include questions about bribing and other forms of corrupt behavior and are therefore by construction correlated with corruption. The Civil Liberties index includes questions on corruption that restrains free and independent media. The Political Rights index includes questions related to corruption in government. The Freedom of the Press index includes questions on the impact of corruption and bribery on content of the press. Moreover, Sung (2003) uses a rule oflaw index that is also problematic as rule of law is closely related to the prevalence of corruption. Therefore, only the Electoral Democracy index of Freedom House (2008) is included in our regressions to account for democracy.

As additional controls we include:

12We use averages over ten years to capture stability of democracy. For the 121 countries for which both Electoral democracy and Polity2 are available, the Pearson Correlation Coefficient between them is 0.90 and significant.

13Tbe Civil liberties index from Freedom House (2008) measures civil liberties in general and is not to **be**  mixed up with the subindex civil liberties related to gender inequality.

14US\$, PPP, base year: 2005.

• a dummy indicating whether a country has never been a colony (Not colony) and a dummy measuring whether a country was a British colony (British colony) based on Correlates of War 2 Project (2003) as corruption might also be linked to the history of colonialism (Swamy et al., 2001).

The subindex civil liberties reflects the information available around the year 2000 and is not expected to change rapidly over time as social institutions are long-lasting and change only slowly and incrementally. For this reason, we use in the case of all other variables averages of the existing values over time to minimize the loss of observations due to missing values and to obtain a more stable value for the indicators used. For the corruption indicators representing our response variables we take averages over the years 2001 to 2005 for the CPI and over the period 2000-2004 in the case of the ICRG. For the other regressors we use averages over ten years (1996-2005), with the exception of ethnic fractionalization as changes in the ethnic composition of a country in less than 20 years are rare (Alesina et al., 2003). Concerning the two democracy variables, choosing averages over ten years has the advantage of capturing the stability of a democratic system, which has been highlighted by Treisman (2007) as important for corruption. In addition, having a difference of five years between response variable and the regressors might help to alleviate endogeneity and capture delays until possible effects can be observed.

#### **3.2.2 Empirical Estimation**

We empirically test with multiple linear regressions whether the subindex civil liberties *si,*  which measures the freedom of social participation of women, is correlated with a response variable *Yi* capturing the level of corruption, after controlling for other factors that have been described in the literature as possible determinants of corruption. 15 As was discussed previously, we consider that social institutions related to gender inequality are relatively stable and long lasting. Therefore, we assume that they do not depend on the response variable for the period considered. 16

We run regressions as

$$
\Delta y\_i = \alpha + \beta s\_i + \text{control variables}\_i + \varepsilon\_i \tag{3.1}
$$

15Before conducting the multiple linear regression analysis, we account for the importance of GDP for corruption. We first run a simple linear regression of each corruption measure on log GDP. We then compute the estimated residuals from this regression and use them as the dependent variable in a new simple linear regression where the subindex civil liberties is the only regressor. For both CPI and ICRG we obtain a negative and significant coefficient for the subindex civil liberties which suggests that the subindex is able to account for something that goes beyond GDP when explaining corruption.

16In general, social institutions, i.e. normative frameworks, change only slowly and incrementally.

using information at the country level. We are mainly interested in testing the null hypothesis that coefficient */3* is zero at a statistical significance level of 10%. The control variables included to attenuate omitted variable bias are described in Table 3.1. We acknowledge, however, that it is impossible to entirely rule out this problem.

To reproduce the findings from the literature, we first run a regression without the subindex civil liberties to focus on the effects of democracy and representation of women, which have been largely discussed. In a second step, we add to the regressions the subindex civil liberties as a measure of society's attitude towards gender inequality, as it can be argued that it is a variable that has been omitted in the previous regressions (Swamy et al., 2001). We run each specification for the two measures of corruption and use each time one of the two alternative measures of democracy. At the end, we present four regressions for each corruption indicator.

Preliminary regressions not reported here suggest that heteroscedasticity is a possible issue in our data and that there are influential observations that could drive the results. If our model is well specified, the OLS estimator of the regression parameters remains unbiased in the presence ofheteroscedasticity, but the estimator of the covariance matrix of the parameter estimates can be biased and inconsistent, making inference about the estimated regression parameters problematic. Violations of homoscedasticity can lead to hypothesis tests that are not valid and confidence intervals that are either too narrow or too wide. To deal with heteroscedasticity, we run the regressions with OLS and 'heteroscedasticity-consistent' (HC) standard errors. As our sample sizes are less than 150, we use HC3 robust standard errors proposed by Davidson and MacKinnon (1993), which are better with small samples.17

For all the regressions, we check whether the results concerning the subindex civil liberties are stable in three ways. First, it is clear that in the multiple regressions, the estimate of the effect of our main variable, the subindex civil liberties, depends on the values of the other explanatory variables included (Mukherjee et al., 1998). We also try a simpler model to confirm that the estimated coefficient of the subindex civil liberties is negative and statistically significant. In this smaller model and based on the arguments presented before, we include as additional regressors the variables capturing the representation of women in so-

17Simulation studies by Long and Ervin (2000) have shown that HC standard error estimates tend to maintain test size closer to the nominal alpha level in the presence of heteroscedasticity than OLS standard error estimates that assume homoscedasticity. These authors recommend the use of HC3 robust standard errors, especially for sample sizes less than 250, as they can keep the test size at the nominal level regardless of the presence or absence of heteroscedasticity, with only a minor loss of power associated when the errors are indeed homoscedastic. We acknowledge that heteroscedasticity<onsistent standard errors are not a panacea for inferential problems under heteroscedasticity. As pointed out by some authors, there are limitations and trade-offs in these estimators (e.g. Kauermann and Carroll, 2001; Wilcox, 2001).

ciety, a measure of democracy, the log GDP, religion dummies and regional dummies. This has the advantage that less parameters have to be estimated with the available observations.

Second, we use bootstrap with I 000 replications to compute a Bias-corrected and accelerated (Bea) 90% confidence interval of the regression coefficients computed with OLS to confirm that the value zero is not contained in the confidence interval around */3* (Efron and Tibshirani, 1993). One of the main advantages of bootstrapping methods is that one does not make any assumptions about the sampling distribution or about the statistic. Third, we detect observations with high influence or leverage based on the first estimates (OLS with standard variance estimator) using Cook's distance. Cook's distance is a commonly used estimate of the influence of a data point when doing least squares regression, and it measures the effect of deleting a given observation. We exclude the countries identified as outliers from the sample if the value of Cook's distance is larger than *4/n,* with *n* being the number of observations, and re-estimate regression 3.1 on the restricted sample using HC3 robust standard errors.

One should consider that possible endogeneity of the regressors; (the subindex civil liberties), meaning thats; is correlated with the error term *e;* in the regression, might lead to an estimated coefficient of *s;* that is biased. Endogeneity might arise due to omitted variables, measurement error and simultaneity (Wooldridge, 2002). The control variables included in the regression **aim at** minimizing omitted variable bias, albeit one cannot rule out this problem. We do not find it plausible that there are measurement errors *ins;* which are related to the unobserved 'true' social institutions. Simultaneity could arise *ifs;* is determined simultaneously with the dependent variable *y;. AB* was discussed previously, social institutions related to gender inequality *s;* are relatively stable and long-lasting. Hence, it is unlikely that the response variable *y;* influences *s;.*

#### **3.2.3 Results**

Results for the CPI as the first measure of corruption are presented in Table 3.6. Specifications (I) and (2) do not include the subindex civil liberties. In both specifications, none of the democracy variables Electoral democracy and Polity2 are significant. From the three measures of representation of women only Parliament is significant and positively related to corruption in specification (I) where Electoral democracy is the measure of democracy. Of the control variables only GDP has a significant and positive coefficient. In specifications (3) and (4) the subindex civil liberties is added as a new regressor to the former specifications. Its coefficient is negative and significant in both. Both democracy variables as well as the measures for participation of women in the economy are not significant. Only Parliament carries a positive and significant coefficient when Electoral democracy is used (specification

(3)). In the same specification (3) two control variables besides log GDP become significant: British colony and the regional dummy for ECA. For all four specifications the adjusted R square is around 0.5.

Table 3.7 shows the results when ICRG is used as the measure of corruption. For all 4 specifications (1-4), none of the variables reflecting representation of women and none of the democracy measures is significant. Interestingly, log GDP is also insignificant in all specifications, whereas it is always significant when the CPI is used as measure of corruption. Openness is the only control variable which is significant in all specifications. Important for the results of this paper, the subindex civil liberties is significant in specifications (3) and (4), and adding it to the corresponding regressions yields values for adjusted R-square that are noticeably larger than without it. It must be noted, however, that the obtained values for adjusted R-square for the regressions with the ICRG are lower than for the CPI (between 0.2 and 0.3 for the ICRG and around 0.5 for the CPI), suggesting that the model is not able to explain much of the variation of the political risk of instability due to corruption.

Using the smaller model yields similar results for the subindex civil liberties and the variables measuring representation of women and democracy. 18 These findings do also withstand the two other robustness checks. First, we confirm with Bias-corrected and accelerated (Bea) confidence intervals that in all cases the value zero is not contained in the 90% confidence interval around the regression coefficient of the subindex civil liberties. Second, excluding outliers (6 to 7 countries) and re-running specifications (3) and (4) for both corruption measures, the subindex civil liberties remains significant in all estimations. It is worth mentioning that for every restricted sample, the adjusted R-square is higher than in the corresponding complete sample. 19

Summarizing the results, when we do not include the subindex civil liberties we find that from all variables for representation of women only Parliament is significant in the case of the CPI as long as Electoral democracy is used as measure of democracy. If one uses Polity2 instead, Parliament becomes insignificant. None of the democracy measures used turns out to be significant. When we include the subindex civil liberties, the results for representation of women and the democracy variables stay unchanged. Neither representation of women, except Parliament in the case of CPI when Electoral democracy is used, nor the democracy variables are significantly related to corruption. The main result concerning the subindex civil liberties is that even after controlling for democracy and for measures of political and

18With the smaller model we also run three separate regressions for (i) Muslim majority countries, (ii) Christian majority countries, and (iii) countries without Christian or Muslim majority. As could be expected, the subindex civil liberties is statistically significant only in the regressions with Muslim majority countries, as in other countries there is not enough variation in the subindex.

19Results for all the robustness checks are not reported here, but are available upon request.

economic participation of women as well as for other factors, we find a robust and significant relationship between the subindex civil liberties, which reflects society's attitude towards gender inequality, and the level of corruption. Social institutions favoring gender inequality are associated with higher levels of corruption.

## **3.3 Conclusion**

The literature investigating the link between gender and corruption finds that there is a relationship between female representation in political and economic life and the level of corruption in a country. However, some studies warn that the observed relationship may be due to omitted variable bias. A possible variable that might influence both participation of women and corruption, is liberal democracy ( e.g. Sung, 2003). We introduce a further omitted variable that has either been neglected in the literature or not been adequately dealt with because of insufficient data. Swamy et al. (2001) refer to this as the "level of discrimination against women" and proxy it with the gaps in educational attainment and life expectancy between men and women. We use the subindex civil liberties, which we consider a better proxy of the "level of discrimination against women" as it captures social institutions that restrict women in their freedom to participate in public life and reflect society's attitude towards gender inequality. The subindex measures underlying institutions and not outcomes of these institutions as do the variables used by Swamy et al. (2001).

When we replicate the findings of the literature for our sample of developing countries without the social institutions indicator, the results support the hypothesis of Sung (2003) and others that, when liberal democracy (in our case measured with Polity2) is considered in the regression, the representation of women in political and economic life is insignificant. However, Sung's hypothesis is weakened by the fact that there is no statistically significant association between democracy and corruption. Consequently, our statistical results support neither Sung's arguments nor the arguments put forward by Swamy et al. (2001) and Dollar et al. (2001) that representation of women is negatively related to corruption. 20 These results make it difficult to interpret social institutions related to gender inequality as an omitted variable when one investigates the relationship between representation of women in society, democracy and corruption.21

20Once again, our sample includes only developing countries, while the other studies include developed countries as well.

21We have estimated with multivariate regressions, not reported here, whether there is ( 1) a relationship between democracy and the subindex civil liberties and (2) a relationship between representation of women in society and the subindex civil liberties in our sample of developing countries, but did not find significant results.

Once we include the subindex civil liberties as a regressor, the main finding is that after controlling for representation of women in political and economic life and for democracy, it has a robust negative and significant relationship with corruption. In countries where social institutions inhibit the freedom of women to participate in social life, the level of corruption is higher.

Admittedly, one has to be cautious with these results. Interpretations for these findings in the light of the theories discussed are difficult, and country or regional studies are needed. Measurement is another relevant issue as the concepts of social institutions, democracy, participation of women and corruption are all hard to operationalize. The measures used in this study could be contaminated by measurement error. Finally, it cannot be ruled out that another factor, which has been neglected from the analysis, shapes the results.

Nevertheless, we derive one policy implication from this study, which should be mainly targeted at developing countries. In a context where social institutions deprive women of the freedom to participate in social life, neither political reforms towards democracy nor the representation of women in political and economic positions might be enough to reduce corruption. How women are treated in a society is not only important for them, but has major implications for the functioning of the whole society.

#### **3.4 Tables**

Table 3.1 : Description and Sources of Variables

Table 3.1 -continued from previous page

#### Table 3.2: Descriptive statistics of variables used

Table 3.3: Pearson Correlation Coefficient between subindex Civil liberties and control variables

Table 3.4: Pearson Correlation Coefficient *(p)* between the Corruption Measures

Table 3.5: Variation of the subindex civil liberties over religion

Table 3.6: Linear regressions with dependent variable CPI

HC3 robust standard errors in brackets.

Regional dummies included in all estimations.

\* *p* < 0.10, \*\* *p* < 0.05, \*\*\* *p* < 0.01

HC3 robust standard errors in brackets.

Regional dummies included in all estimations.

\* *p* < 0.10, •• *p* < 0.05, ••• *p* < 0.01

## **3.5 Figures**

Figure 3.1: Scatter plot: Subindex Civil liberties and percentage of Muslim population

# **Part** II

# Regional growth convergence in Colombia

# **Essay 4**

# **Revisiting the regional growth convergence debate in Colombia using income indicators**

## **Abstract**

This paper investigates growth convergence across Colombian departments during the period of 1975 to 2000, following both the regression and the distributional approaches suggested in the literature, and using two income measures computed by Centro de Estudios Ganaderos (CEGA). We also discuss issues related to data provided by Departamento Administrativo Nacional de Estadisticas (DANE) used by previous convergence studies. Our results show no evidence supporting convergence using per capita gross departmental product, but rather persistence in the distribution. Using per capita gross household disposable income, we find some evidence of convergence, but only at a low speed, close to one percent per year. Furthermore, we find no evidence of the existence of different steady states for the two variables considered.

## **4.1 Introduction**

One of the most interesting and disputed questions in the economics discipline during the last half century has been whether or not poor countries tend to catch up with wealthier ones over time or if, on the contrary, the gap between the rich and poor widens. This question also reflects an interest in understanding the distribution of outcomes across countries and, implicitly, the determinants of growth (Durlauf et al., 2005).

Empirical research on this topic is based upon macroeconomic aggregates and has concentrated on testing the neoclassical growth model of Solow (1956) using the estimation method proposed by Barro and Sala-i-Martin (1991) to investigate whether economies with lower capital per person at a certain initial point in time tend to grow more quickly than economies with higher capital per person. If this is the case, there is convergence among economies over the long run.

The convergence question has also been studied within particular countries to analyze how much regional disparities diminish over time. The difference with cross-country convergence analysis is that in such cases it is risky to make assumptions across countries on key model parameters, such as technology, savings, and population growth rates. On the contrary, within a single country, it is plausible to assume that regions exhibit similarities in these and other variables, such as language, institutions, and preferences. This presumed homogeneity has lead researchers to assume that convergence is more likely to hold within, rather than across, countries (Barro and Sala-i-Martin, 2004).

Empirical research supports regional convergence within industrial countries over the long run. Typical examples are given by Barro and Sala-i-Martin (1992b) who find convergence across U.S. states between 1880 and 2000, across Japanese prefectures between 1930 and 1990, and between regions in eight European countries between 1950 and 1990 (see also Barro and Sala-i-Martin (1992a)).

In the case of Colombia, a heterogeneous country at the department level in economic, geographic, and cultural aspects, existing research is contradictory. While some authors argue that Colombia was a successful case of convergence in the second half of the twentieth century, others argue for the persistence of regional disparities.

The objective of this study is to investigate whether or not Colombia was a case of convergence at the department level between 1975 and 2000 using two different income variables: gross departmental product and gross personal disposable income. We consider that the second variable is more appropriate for measuring convergence in well-being.

The study is constructed around three main questions. First, the study evaluates whether departments converged between 1975 and 2000 and if so, if convergence results obtained using the regression approach contradict the results obtained with the distributional approach suggested by Quah (1997), using bivariate Kernel density estimators. Second, we determine if the assumption of a common steady state for all departments holds or whether there is evidence of heterogeneity in the model parameters. Finally, the study evaluates whether the presence or absence of convergence occurs simultaneously in gross departmental product and in gross personal disposable income.

An important contribution of the study is the first ever test of the convergence hypothesis using time-series cross-sectional Colombian data with different specifications to check the robustness of results. The results are based upon data from Centro de Estudios Ganaderos (CEGA) because those data provide the longest time series (25 years) computed with a consistent methodology. 1

To summarize our results, we do not find convergence in gross departmental product and find no evidence of different steady states across departments using that variable. When using gross personal disposable income, we find convergence, but a very slow one, and no evidence of different steady states. For both variables, when using the regression approach, we find that the best estimators can be achieved using pooled time-series cross-section data and assuming homogeneity in the parameters. Furthermore, considering both variables, we do not find a contradiction in results obtained using the regression and the distributional approaches. Using bivariate kernel density estimators, we find persistence in the distribution of gross departmental product and slight convergence in gross personal disposable income.

One important policy implication of our results is the need to periodically review whether or not departmental disparities diminish over time based on consistent time series constructed under a single methodology. We explicitly warn that linking different time series computed with different methodologies can lead to incorrect conclusions for interventions, such as poverty-alleviating policies and growth strategies. In keeping with previous studies on this topic ( e.g. Bonet and Meisel, 2006a), we consider important the need to have an explicit regional policy in Colombia to foster growth in departments lagging behind national averages, after conducting case studies to assess which policies could be most effective in each case.

## **4.2 Motivation and Background**

#### **4.2.1 Economic Background**

One remarkable characteristic of Colombia is the large income inequality which exists at different levels-between individuals, between rural and urban areas, and between departments. The country is currently divided into 32 departments and the capital district of Bogota. De-

1CEGA was a large research center financed by a private financial institution in Colombia.

partments may also be grouped into *5* regions: the Caribbean Region comprising departments with access to the Caribbean Sea; the Pacific Region, with departments in the west coast to the Pacific Ocean; the Central Region, covering the three branches of the Andes mountain chains; Orinoquia, comprising large plains to the south-east of the country; and Amazonia in the south, comprising the Colombian part of the Amazon rainforest (see the map of Colombia in Figure 4.1).

Economic growth over the last 30 years, which was low but stable compared to other countries in the region, comes together with a combination of a high incidence of poverty, inequality, and violence. In 2004, the percentage of people living below the poverty line (headcount index) was 52 percent and the Gini coefficient was 0.58. The homicide rate was 63 per 100,000 people. Evidence shows that growth slowed compared to long-term historical trends after 1970. In fact, after having achieved in 1970 a growth rate of3.l percent in per capita gross domestic product, growth between 1980 and 1990 occurred at an average annual rate of only 1.2 percent due primarily by the adverse effects of Latin America's debt crisis. In the 1990s, the average growth rate was similar (1.1 percent), driven by a boom and bust cycle throughout the decade, which concluded in a severe recession in 1999 (per capita GDP contracted by 5.5 percent (Table 4.1)). On the contrary, between 2002 and 2007, favorable external conditions, especially high commodity prices and confidence due to the easing of internal conflict, have contributed to the acceleration of the economy (Tenjo G. and Lopez E., 2003; Cardenas, 2007).

The heart of economic activity in Colombia lies in the Central or Andean Region which concentrates the largest proportion of population within the major cities. Bogota and the departments of Cundinamarca and Antioquia account for 42 percent of total GDP with Bogota having a high level of participation in total production (22 percent). This area concentrates not only manufacturing industry and commerce near the cities, but also coffee plantations and other large-scale agricultural areas.

The GDP of departments in the Caribbean Region is based upon mining, small-scale agriculture, and cattle farming. La Guajira and Cesar are the two largest producers of coal, while C6rdoba is the largest nickel producer. Despite having some departments rich in minerals, this region nevertheless has a high incidence of poverty, particularly in C6rdoba and Sucre.

The Pacific Region comprises, relative to the Colombian average, three poor departments and one wealthy one (Valle del Cauca). Choc6, which is the poorest department in this region and in the country, is predominantly rural and sparsely populated, with large tropical rain forests and humid areas. It is known as the rainiest area in the country (and even one of the rainiest worldwide) and is geographically isolated from the rest of the country due to a chain of mountains to the east and the ocean to the west. Transport of population living in the department is largely done by way of its abundant creeks and rivers; road infrastructure is minimal. The scarce literature explaining socio-economic factors in this department argues that the current distribution of population and the quality of institutions may largely be explained by the early settlement of an extractive economy during colonization, at which time colonizers brought slaves to exploit gold mines but did not establish themselves in the department (Bonet, 2007). As opposed to Choc6, Valle de! Cauca is the third largest departmental economy in the country after Bogota and Antioquia and has some of the most productive agricultural areas, as well as a high level of participation in the manufacturing sector.

During the last 30 years, production was driven in some departments by the discovery of important mineral resources, as is the case for the departments of Arauca and Casanare, which have the largest oil fields in the country.2 The same applies for La Guajira, which has the largest open coal mine in Latin America.

According to Meisel (2007b ), the burden of poverty in Colombia is geographically located in the coastal departments and inequality is greater between departments than within them. Meisel argues that the urban-versus-rural divide is not the relevant dimension upon which to design poverty-alleviating programs, but the departmental one. Moreover, Meisel affirms that the already-large disparities have increased over the past 15 years and will not spontaneously disappear merely as a result of market forces.

The level of empirical research addressing regional disparities in Colombia has increased gradually since the early nineties, inspired by the international debate on convergence and the methodology proposed by Barro and Sala-i-Martin (1991 ). Since then, approximately 20 papers have investigated whether departments, regions, or even major cities have converged over time. Important shortcomings in this field arise due to the absence of consistent timeseries data allowing for a long-term perspective. As a consequence, results frequently depend upon how the researcher combined the available time series, as well as on the methodology and control variables used, with no robust and undisputed evidence concerning departmental convergence.

Debate in this field in Colombia revolves around two issues: first, a methodological discussion as to whether or not to rely on the methodology proposed by Barro and Sala-i-Martin (1992a) or on the distributional approach proposed by Quah (1993b), and second, whether

2These departments are included in our sample as one group named Nuevos Departamentos (Nuevos), meaning new departments. The so-<:alled New Departments are distributed in the south-east lowland plains, the Amazon Region, and the Caribbean islands. Excepting the islands, these departments are large in extension but have low population densities.

one should use information generated by Departamento Nacional de Estadisticas (DANE), rather than by Centro de Estudios Ganaderos (CEGA).3

Early studies used Barro-type regressions. The pioneer work of Cardenas and Ponton (1995), combining early GDP data by department from the National Planning Department with those produced by DANE, concluded that between 1950 and 1990, Colombia was a successful case of convergence with a 4-percent speed of convergence, and that migration played an insignificant role in convergence. Alternative combinations of data from DANE yield different results, despite using the same methodology. For instance, Baron (2003) finds convergence during the eighties but not during the nineties. Research using kernel density estimators concluded that Colombia was a case of polarization with the existence of three groups: a wealthy one that diverges from the average national income, a middle income one that shows convergence inside the group, and a third one that grows more impoverished over time (Birchenall and Murcia, 1997). Using CEGA data, research points to polarization in favor of the capital district of Bogota, to the detriment of departments located in the peripheries (Bonet and Meisel, 2006b). Almost all studies focus only upon convergence in income, while only three ask for convergence in living standards using social indicators.4

The reader is then confronted with the question of whether Colombia is a successful case of convergence or rather an example of hopeless persistence unless strong regional redistributive policies are adopted. *5*

Intuitively, when observing the different geographic conditions of the country and the agglomeration processes around the largest cities, as well as the differences in infrastructure, it is unrealistic to expect that poor departments can catch up with leading departments in terms of per capita product, given that they lack basic infrastructure and have a minor manufacturing and government presence.

However, there are mechanisms that could have promoted convergence among departments in recent years. One of them is fiscal equalization through central government transfers. Starting in the mid eighties, the government implemented a decentralization program to reduce the burden of spending by the central government. This process accelerated with the new constitution of 1991 which established a new system of transfers in order to increase the efficiency of social expenditures, as well as the supply of social services, compensated municipalities with weak financial capacities, and increased political power and the participation oflocal governments in the implementation ofhealth and educational policies (Departamento

3DANE is the official statistical agency in Colombia (http://www. dane. gov. co/).

4A comprehensive list of convergence studies in Colombia can be found in Aguirre (2008). We deal with regional convergence in social indicators in Colombia in Essay *5.*

5Research using alternative methodologies and looking for linkages among regions found that Colombia has limited spatial interdependency (Haddad et al., 2008).

Nacional de Planeaci6n DNP, 2002; Rojas, 2003; Barrera and Dominguez, 2006). As a result, social spending increased from 7 to 15 percent between 1991 and 2001. Moreover, starting in the eighties, the model of industrialization through import substitution changed to the policy of liberalization of the economy, reduction of tariffs, and integration into the world markets in order to increase competitiveness, productivity, and economic growth. This shift also accelerated after the constitutional reform.

Another possible mechanism for convergence is migration. In general, the country underwent an important urbanization process in recent decades encouraged by industrialization around urban centers and a higher orientation towards export markets. Labor mobility was a combination between voluntary migration for economic gain (which profited from increasing returns to scale in the manufacturing sector) and forced migration due to violence, which migration helped enlarge informal markets. Migration from rural to urban areas accelerated during the twentieth century. The percentage of population which is urban changed from 59 percent in 1973 to 75 percent in 2005 due not only to a transformation from a predominantly agriculture-based economy to a services and industry-based one, but also due to conflict, violence, and a lack of opportunities in rural areas (Murad R., 2003).

In this context, the substantive question we try to empirically answer in this study is whether or not Colombia was a case of convergence at the department level between 1975 and 2000. Thus, if poor departments had greater growth rates than wealthy ones over time and the gap between them decreased. Our interest relies upon closing the debate on the existence of convergence across departments in Colombia by analyzing methodological issues and data sources that may have had affected results up to now. One important motivation of this study is the policy implication that can result as a consequence of wrongly assuming that departments converge automatically over time.

In order to explain the importance of the data used and the possible combinations of time series, we explain in the next subsection the available data sources and the relevance of two variables, gross departmental product and gross personal disposable income, arguing that the second one is more appropriate for measuring convergence for well-being.

#### **4.2.2 Data Issues Affecting Convergence Results in Colombia**

There are two different data sources of departmental accounts in Colombia: Department of Statistics (DANE) and Centro de Estudios Ganaderos (CEGA).

DANE provides per capita GDP by department for three different periods: one for 1980 through 1996 in constant prices as of 1975, one for 1990 through 2005 in constant prices as of 1994, and a final one for 2000 through 2005 in constant prices as of 2000. The first period was calculated applying concepts of the System of National Accounts of 1986 (SNA-86) and used an indirect method for collecting information. The second period was calculated using the System ofNational Accounts of 1993 (SNA-93) and combined direct and indirect methods for collecting information. 6 The third period did not include illicit crops in its estimation and is also based upon SNA-93.

The classification of sectors, transactions, concepts, and methodology changed considerably in the SNA-93 and allowed for the inclusion of illegal activities as part of the GDP (DANE, 2008).7 It must be noted that statistical offices use different techniques to produce consistent time series of national accounts, particularly when international guidelines change. 8 For instance, most (OECD) countries make regular revisions for short time periods (usually of about twenty years) to incorporate new available information and benchmark revisions, in order to provide users with consistent time series. In Latin America, only Chile and Peru offer consistent large time series of regional per capita GDP using statistical or interpolation methods (Serra et al., 2006).

In Colombia, DANE collected information for some overlapping years using both methodologies, but did not construct a consistent time series based only upon one. Although users do not have enough information to consistently recompute long time series, they tend to rebase series and connect them using growth rates, which can be problematic.9

Comparison of the series for the overlapping years shows different departmental growth rates and a different evolution of the logarithm of the standard deviation, explaining why convergence results change depending on how and when the researcher linked the different data series. Note in Figure 4.6 that the annual standard deviation of the logarithm of GDP of the three series of DANE yields different patterns. In the series of 1980 to 1996, the standard deviation increases sharply starting in 1990, while in the series from 1990 to 2005, it remains close to 0.36 until 1997 and falls thereafter. Concerning the third time series (2000 to 2005), the trend is similar to the series for 1990 through 2005, but the level of the standard deviation is higher.

6Direct methods take departmental information by product whenever data sources are available. Indirect ones use national aggregates and assign each department a percentage of those aggregates.

7The main changes concern the measurement of value-added taxes, the reclassification of transactions in the government sector, changes to the capital account, and productivity levels for the banking, energy, and insurance sectors.

8Techniques can be broadly classified into four groups: detailed reworlcing, proportion methods, interpolation between benchmarks, and indicator methods.

9F or instance, the Canadian statistical office explicitly prohibits users from simply re basing series using growth rates due to the large methodological differences derived from changing to SNA-93, and argues that only the statistics office in charge may compile series using detailed accounting and recomputing information according to the new procedures (Lal, 1999).

The CEGA project compiled information at the departmental level in Colombia from 197 *5*  to 2000 using SNA-93 and presented a simplified system of national accounts. The project used mixed methods for collecting information, classified some particular products differently than DANE, and did not include illicit crops in the agriculture category. Departmental results coincide between CEGA and DANE from 1990 onwards because both use SNA-93 (there are, however, important differences before 1990).

CEGA produced consistent time series of two key variables relevant for convergence analysis, gross departmental product, which we will call henceforth PDB, and gross departmental income, which we will refer to as IDB. The first variable reflects production by residents in each department, while the second reflects the primary income received by those residents. The difference between these variables is the net external income of residents.

CEGA also provided time series of gross household disposable income by department, which we will call IDBH, and which is the result of households' income after subtracting taxes on property and rental income and net payments to the social security, and adding other net current transfers. This variable is a more accurate measure of a population's welfare than per-capita PDB, as it reflects household income after taxes and net public and private transfers. 10

Due to the advantages of the CEGA database, and as this database provides the only two consistent time series covering a long time span, we present results and discussion on convergence for per capita PDB and IDBH. 11Our final data set covers the period of 1975 to 2000 for 23 departments, the capital district of Bogota, and the nine "New Departments" grouped into one observation, for a total of 25 units and 25 years. 12

To calculate yearly per capita figures of both PDB and IDBH, we use the latest available population data, computed after reconciliation of the census of 2005 with previous censuses. According to the census of 2005, population is less than what had been forecasted using the 1993 census due to a lower birth rate and increased external migration (DANE, 2007). Although in most of the departments population was overestimated, there are some particular cases in which the contrary situation applies.

We use yearly population data at the departmental level from DANE (2007) for the years 1985 to 2000, and for the years 1975 to 1985, we interpolated departmental population using

10Toe abbreviations used refer to the original names in Spanish: Producto Departamental Bruto (PDB), lngreso Departamental Bruto {IDB) and Ingreso Departamental Bruto (disponible) de los Hogares (IDBH).

11 As will be explained in the next section, it would be best to work with data expressed as per unit of effective worker, but due to data availability, researchers often use per capita figures.

12The New Departments have existed formally since the 1991 constitutional reform when nine former intendancies and commissariats were acknowledged as departments (Amazonas, Arauca, Casanare, Guainia, Guaviare, Putumayo, San Andres y Providencia, Vaupes, and Vichada ).

the annual growth rate from 1973 to 1985 based on the 1973 census. The obtained values show a consistent evolution of population by department once connected to the official estimates from 1985 onwards.

Box plots of per capita PDB and IDBH in logs are shown in Figures 4.2 and 4.3. Box plots of relative PDB and relative IDBH in logs are shown in Figures 4.4 and 4.5. By relative we mean that the variables are expressed as ratios to the national average of the corresponding year. We can see that the ordering of departments is similar in both types of graphs, in levels and relatively, particularly in the upper and lower ends. The five departments with the lowest per capita PDB are Choc6, Sucre, Cordoba, Nariilo, and Cauca, four of these being located on the Pacific Coast. Bogota, Valle, Antioquia, Nuevos Departamentos and Cundinamarca have the five highest PDBs. Concerning per capita IDBH, departments with the lowest values are almost the same, excepting Santander instead ofNuevos.

The box plots show large variability in per capita figures of Guajira in both PDB and IDBH and low variability for Bogota. This pattern is accentuated in figures relative to the average, as well as for the group ofNuevos and observing PDB. On the contrary, the log of per capita IDBH shows less variation and dispersion of values, but a higher difference between the richest and the poorest departments. Note also that the group ofNuevos Departamentos has large variability in PDB. That variability is not visible in IDBH. In the following two sections, we present two well-known approaches for testing for convergence-the classical approach to convergence analysis and the distributional approach.

## **4.3 The Solow Model and Its Estimation**

#### **4.3.1 The Solow Model**

Empirical testing of convergence across economies is based upon the neoclassical growth model developed by Solow (1956)13 in which economies have a transition dynamic towards the *steady state,* defined as a situation in which all variables per unit of effective worker remain unchanged over time. In the steady state, the ratio of capital to labor is constant given that the capital stock expands at the same rate as the labor force, and the capital expansion is sufficient to compensate for it.

The neoclassical growth model assumes diminishing returns to factors and constant returns to scale. Due to this assumption, real returns of factors adjust to bring about full employment of labor and capital. Technology is exogenous and is the only force that explains changes in output and capital per worker. Any capital-to-labor ratio different than the one

13The neoclassical model was also developed in the original works of Ramsey (1928) and Cass (1965).

needed in the steady state readjusts as time passes so that economies tend towards the steady state. The speed at which this happens is known as the convergence rate and is inversely related to the distance from the steady state (Durlauf, 1996).

Under the framework of the neoclassical growth model, smaller initial values of the capital-to-labor ratio *k,* are associated with greater growth rates of the ratio production per worker. Robert Barro and Xavier Sala-i-Martin tested whether economies with lower capital per worker at a certain initial point in time grew more quickly in per-worker terms (Barro and Sala-i-Martin, 1991, 1992a,b, 2004; Sala-i-Martin, 1996), using the following equation:

$$\log[\hat{Y}(t)] = (1 - \exp^{-\beta^{\star}t})\log(\hat{Y}^{\star}) + \exp^{-\beta^{\star}t}\log[\hat{Y}(\mathbf{0})]),\tag{4.1}$$

where *t* represents time, */3\** indicates how rapidly an economy's output per effective worker *Y* approaches its steady-state value *Y\** in the neighborhood of the steady state. The corresponding definition of */3\** with a constant saving rates is */3\** = (1 - *a)(x+n+* S), where *a* is a constant representing the share of capital in production, *n* is the rate of population growth, *x* is the rate of exogenous growth, and *S* is the depreciation rate. The speed of convergence is measured by how much the growth rate decreases as the capital stock increases in a proportional manner. 14 Equation 4.1 implies that the average growth rate of per-capita output *Y*  over an interval from an initial time 0 to any future time *T* (higher than 0) is

$$\frac{\log[Y(T)/Y(0)]}{T} = x + \frac{(1 - \exp^{-\beta \cdot T})}{T} \log[\hat{Y}^\*)/\hat{Y}(0)],\tag{4.2}$$

where xis the rate of technological progress or the steady-state growth rate. 15 Equation 4.2 also shows that the effect of the initial position *Y(O)* is conditioned on the steady-state position *Y\** (conditional convergence) (Barro and Sala-i-Martin, 2004). The approach suggested by Barro and Sala-i-Martin (2004) is known as the regression approach or as the classical approach to convergence analysis (Sala-i-Martin, 1996; Magrini, 2004). There are two alternatives for applying this concept - testing for absolute convergence or for conditional convergence.

#### **4.3.2 Absolute Beta-Convergence**

The concept of absolute beta-convergence (also known as unconditional convergence) is relevant for a group of closed economies that are structurally similar; they have the same

14Note that /3' is not the same as *{3.* It is the convergence rate in the proximity of the steady state and is determined by ( I - a) for given values of x, n, and /j.

15Equation 4.2 indicates that the coefficient (I - exp-/JT)/T declines, the higher Tis for a given /3, and as long as /3 is positive. Therefore, the average growth rate *ofY* decreases as *T* • ~(and thusx) dominates the average growth rate. In contrast, for a given *T,* a higher /3 implies a higher coefficient (I - *exp-/JT)/T.*

values of the parameters *x, s, n,* and *o,* and thus they have the same production function steady-state values *k\** and *Y\*.* The only difference is the initial quantity of capital per person *k(0),* which reflects past disturbances (wars, transitory shocks to production, etc.). Hence, economies with lower values of *k(0)* and *Y(0)* have unambiguously greater growth rates of *k* and *Y.* The estimation equation for absolute convergence is equation 4.2, omitting the *Y\**  term:

$$\frac{\log[Y\_{l,t}/Y\_{l,t-T}]}{T} = a - \frac{(1 - \exp^{-\beta T})}{T} \log[Y\_{l,t-T}] + \omega\_{l,T},\tag{4.3}$$

where *w;1,r* represents the effect of the error terms *w1* between dates *t* and *T,* i is the corresponding subscript for each region or country, and *a= x+* (1 - exp-f:lr) log(Y\*). Absolute convergence arises when the term multiplying the initial income is negative, and implies that poor economies tend to grow more quickly than wealthy ones. One can estimate a regression with non-linear least squares (NLLS) to obtain the speed of convergence */3* directly.

#### **4.3.3 Conditional Convergence**

Conditional beta-convergence arises by allowing for heterogeneity across economies, particularly by dropping the assumption that all economies have the same parameters and the same steady state. 16 The main idea is that the further an economy is from its own steady-state value, the more quickly it grows:

$$\frac{\log[Y\_{i,t}/Y\_{i,t-T}]}{T} = a - \frac{(1 - \exp^{-\beta T})}{T} \log[Y\_{i,t-T}] + \gamma X\_i + \omega\_{\boldsymbol{\theta},T},\tag{4.4}$$

where *X;* is a set of variables that proxy for the steady-state level of income (Y;\*). Empirical studies show little evidence of unconditional convergence for large and heterogeneous samples of countries. Instead, they tend to find conditional convergence in economies with similar structural characteristics (Barro and Sala-i-Martin, 1991) with speeds of convergence usually around 2 percent. However, there is no agreement on which variables to include as proxies for the steady state, and their selection depends mostly upon the researcher interest. An extensive review made by Durlauf et al. (2005) shows a list of about 145 different regressors used in convergence literature and points out that most of them have been found to be statistically significant. These regressors are classified by Durlauf et al. (2005) into 43 distinct growth theories or growth determinants, raising doubts about their usefulness.

16Under the asswnption of different parameters, Equation 4.3 would provide biased estimates because the steady-state level of income *Y,\** would be correlated with the explanatory variable log[Y;1-r]. To solve this problem, Barro and Sala-i-Martin (1992a) suggest incorporating into the regression a set of variables *X;* as proxies for the steady-state level of income (Y,') and testing for conditional convergence.

#### **4.3.4 Parameter Heterogeneity: Are There Different Steady States?**

An alternative way to estimate conditional beta-convergence is to remove the assumption of parameter homogeneity, as suggested by Canova and Marcet (1995) and Maddala and Wu (2000), using time-series cross-sectional (TSCS) data. 17 Advocates of this approach argue that the Barro-type growth regressions create biases in the estimated coefficients by pooling data whenever there is heterogeneity in the parameters. Moreover, cross-sectional regressions lead to a waste of information, since they ignore unit-specific time variations in growth rates and prevent the estimation of a steady state for each region or country separately ( e.g. Lee et al., 1997; Temple, 1999; Pritchett, 2000; Durlauf, 2001; Brock and Durlauf, 2001; Masanjala and Papageorgiou, 2004). 18

Canova and Marcet (1995) propose a way to model heterogeneity and calculate steady states for each unit *without* proxying for the steady state of income with additional variables. The model allows calculation of the speed of adjustment for each unit to its own steady state. A weakness of the approach is the need for the time dimension *t* to be large; otherwise, estimates will have large standard errors and their small sample distribution may strongly deviate from the asymptotic one. Using cross-country data, they find an average speed of adjustment to be close to 11 percent, but reject the hypothesis of equal steady states for all cross-sectional units. 19 Using an iterative Bayesian approach with a similar cross-country data set, Maddala and Wu (2000) find average annual convergence rates of around *5* percent and further argue in favor of different steady states for each country.

The estimation relies upon transforming equation 4.2 in discrete time as follows:

$$
\log(\wp\_{i,T}) = \mathfrak{a} + \mathfrak{p}\_T \log(\wp\_{i,0}) + \mathfrak{p}X\_i + u\_i,\tag{4.5}
$$

where *y;,1* is *relative* output per worker, which will be defined below, *pr=* exp-llT, *t* = 0, 1,2, ... , *T,* and the variables *X;* are introduced to allow for shifts in the limit of the steady state means *ofy;.* The key to allow for parameter heterogeneity relies in dropping the assumptions that */3;* = *f3* and *a;= a\/;.* The first assumption is expressed by *p; =/ p;* that is to

17For a description of time-series cross-sectional data, see, for example, Beck (200 I) and Beck and Katz (2007).

18 As indicated by Masanjala and Papageorgiou (2004), parameter heterogeneity in growth regressions has at least three interpretations: there are (i) multiple steady states, i.e., the parameters of a linear growth regression are not constant across countries **(e.g.** Durlauf, 1996), (ii) omitted growth determinants (e.g. Durlauf and Quah, 1999), and (iii) nonlinearities of the production function, i.e., the identical Cobb-Douglas aggregate production function may **be** unsuitable. After investigating the third interpretation, Masanjala and Papageorgiou (2004) conclude that using more general constant elasticity of substitution aggregate production functions does not explain away heterogeneity across countries, and they consequently suggest shifting attention to the other two interpretations.

19 According to Shioji (1997) their convergence rates are high due to the type of Bayesian approach and the short period used (10 years).

say, the convergence rates among all economies are allowed to be different. After grouping *a;* = *a+ yX;,* the final estimation is

$$
\log(\wp\_{i,t}) = \mathfrak{a}\_l + \rho\_l \log(\wp\_{i,t-1}) + \mathfrak{u}\_{l,t}.\tag{4.6}
$$

Note that both Canova and Marcet (1995) and Maddala and Wu (2000) use relative per worker (capita) outputy;,1 for the estimation, defined as *Yi,1,* i.e., per capita output ofregion i in period *t,* divided by the national average of output per capita in year *t.* A value higher ( or lower) than 1 means that the region has a higher (or lower) per-capita outputthan the national average. Usingy;,1 instead ofY;,1 has the advantage that the linear trend term disappears, as it is assumed that in steady state all *y;,1* should grow at the same rate of technological progress, although the levels may vary. It also corrects for problems of serial and residual cross-unit correlation and avoids specifying a process for growth, that is, whether it is trend or unit-root with drift (Maddala and Wu, 2000).

For each region, Equation 4.6 is an AR(l) process of *log(y;,t).* If IPI < I, the time series is stationary and given that *E(log(y;,1))* = *E(log(y;,1\_i)),* one could estimate the expected value as

$$
\hat{E}(\log(\mathcal{y}\_{l,l})) = \frac{\mathfrak{d}\_l}{1 - \mathfrak{H}\_l},
\tag{4.7}
$$

where *fx.;* and *p;* are obtained from regressions based on Equation 4.6.

According to Maddala and Wu (2000), the condition IPI < 1 ensures that region iconverges towards its own steady state and is equivalent to the definition of beta-convergence in Barro and Sala-i-Martin (1992a). As long as IP I < I, the speed of adjustment of each unit to its own steady state is given by 1 - *p;.*

Concerning the empirical estimation, and as discussed by Maddala and Wu (2000), equation 4.6 can be estimated by (i) pooling the data and assuming that V; *a;= a* and *p;* = *p,* (ii) running 25 separate regressions, one for each department, allowing for 25 *a;* and *p;,* or (iii) through shrinkage estimators that assume that *a;* and *p;* have two components, one fixed and one random. Additionally, one could estimate Equation 4.7, assuming that there is a fixed number of groups, allowing, for example, for three values of *a* and *p,* in other words, *a1,*  a2, a3 and *p1,* p2, p3. The departments that belong to each group should be identified with the appropriate method.

We will estimate equation 4.6 following all the alternatives presented.

#### **4.3.5 Sigma-Convergence**

An alternative to evaluating beta-convergence is to focus on whether there is a reduction over time in the dispersion of real per-capita income across entities, indicating a more equitable distribution of income. This is called sigma-convergence and arises when for *T* > 0

$$
\mathfrak{G}\_{l+1} < \mathfrak{G}\_{l},
\tag{4.8}
$$

where <T1 is the standard deviation ofreal per-capita income in period t (Sala-i-Martin, 1996). The existence of beta-convergence tends to generate sigma-convergence. However, there are cases in which shocks affecting each entity differently lead to the existence of betaconvergence but the lack of sigma-convergence. The example given by Sala-i-Martin (1996) in this regard is clear. Assume two economies, one rich and one poor. The initial poor economy grows so quickly that in the final period its distance from the rich one is the same as before, except that now the poor economy is the wealthier. In such a case, the resulting standard deviation would be the same in the initial and final period. One would observe beta-convergence, given that the poor economy is growing more quickly than the rich one, but no sigma-convergence. Hence, sigma-convergence is an indicator of dispersion of the overall entities, but does not tell much about mobility of each one. Beta-convergence is thus a necessary, but not sufficient, condition for observing sigma-convergence.

## **4.4 Distributional Approach: Quah's Critique**

One important critique to the standard regression approach was raised by Danny Quah (Quah, l 993a,b, 1996, 1997), who argues that neither beta nor sigma-convergence can deliver useful answers to the question of whether poor countries or regions are catching up to wealthier ones. Quah argues that the classical approach does not give any information about mobility, stratification, or polarization, and suggests that the typically obtained 2-percent speed of convergence is a statistical artifact that arises in moderate size samples for reasons other than convergence (Durlauf et al., 2005). In his analysis using cross-country data, Quah finds some evidence of convergence clubs, but also evidence of poor countries becoming progressively poorer and wealthy countries, even wealthier.

Quah initially suggested working with a sequence of income distributions and, after discretizing the space of income values, counting the observed transitions into and out of the distinct cell values to construct a transition probability matrix (Quah, l 993a,b ). Later, Quah (1997) argued that the discretization could distort dynamics if the underlying observations are indeed continuous variables. He proposed thinking of the distinct cells as tending towards infinity and towards the continuum, with the transition probability matrix tending to a matrix with a continuum ofrows and columns, that is, becoming a stochastic kernel.20

The methodology is based upon tracking the evolution over time of the entire crosssectional distributions across regions through the estimation of kernel densities for "relative" variables, which means that the variables of interest are expressed as being relative to the national average, allowing abstraction from changes in the mean when one evaluates how the distribution changes.

Before we define how we proceed to test for convergence using the distributional approach, we briefly present some concepts needed for our estimation.21

For the distributional approach, all variables are expressed relative to the Colombian value. Additionally, we take the logarithm of the relative variable, as it facilitates the comparison to the national level. Expressed in logs, a relative value equal to 0 indicates that the department has the same value as the country, while a value that is, for example, equal to -0.05 means that the value of the department is 5 percent lower than the national value.

A univariate kernel density estimate may be regarded as a generalization of a histogram:

$$\hat{f}\_h(q) = \frac{1}{mh} \sum\_{l=1}^n \kappa \left( \frac{q - Q\_l}{h} \right), \tag{4.9}$$

where *IC* is a kernel, m is the number of observations, and *h* > 0 is the bandwidth, also called the smoothing parameter.22 In the context of growth convergence, we are interested in checking whether we find unimodality or multimodality in the estimated densities of the logarithm of relative income, and in what way the estimated densities change between the starting and the final period.

Bivariate kernel density estimation requires two-dimensional data and a two-dimensional kernel. Here, *Q* = *(Q1,* Qzf and the kernel *K* maps JR2 into lR+. The estimate is

$$\hat{f}\_H(q) = \frac{1}{m} \sum\_{i=1}^m \frac{1}{\det(H)} K\{H^{-1}(q - Q\_i)\},\tag{4.10}$$

where *K* is a bivariate kernel function, m is the number of observations, and *H* is a symmetrical bandwidth matrix.

For the analysis of convergence, we estimate the bivariate kernel density for the relative variable in two periods and check whether or not a large portion of the probability mass remains clustered around the 45-degree diagonal, which would indicate persistence in the

20For a technical derivation of a stochastic kernel see Quah (1997, section 4).

21A review of the statistical principles of univariate and multivariate kernel density estimations can he found, for example, in Hllrdle et al. (2004).

22Kernel refers to any smooth function satisfying the conditions *rc(q)* > 0, *J rc(q)dq* = I, *J qrc(q)dq* = 0, and *a;= J q2rc(q)dq* > 0 (Wasserman, 2006).

distribution. We present the 3D representation of the estimated bivariate density and a contour plot showing the highest density regions.

## **4.5 Empirical Estimation and Results**

We empirically test for convergence in PDB and IDBH, using both the classical and distributional approaches to convergence, as we are interested in checking if, in the Colombian case, there is a contradiction of the results obtained when employing both approaches, as suggested by the existing literature on Colombia. We do not use population weights in our calculations, as we are interested in investigating whether or not departments that were Jagging behind have been able to catch up, and consider this to be a pertinent question in the Colombian case where departments are important political entities, with elected local governments and separate department assemblies.

Our empirical analysis begins with the classical approach, testing for sigma and betaconvergence. In the case of beta-convergence, we test absolute and conditional convergence. Conditional convergence is tested with cross-sectional regressions with control variables and also with AR(l) regressions using time-series cross-sectional data for relative income, starting with a pooled model that assumes homogeneity in the parameters and then allows for heterogeneity.

We then follow the distributional approach and compute univariate and bivariate kernel density estimators for relative income in 1975 and 2000.

#### **4.5.1 Sigma-Convergence**

Results of sigma convergence are presented in Figure 4.7. As may be observed, there exists evidence of sigma-convergence in IDBH but not in PDB. From 1975 to 1984, the standard deviation of the log of both variables remains close to 0.40. From 1985 onwards, IDBH decreases and has a value close to 0.32 in 2000. On the contrary, PDB remains around 0.40. Thus, the distribution of IDBH has become more equitable, while the distribution of PDB has not.

#### **4.5.2 Absolute Beta-Convergence**

Figure 4.8 shows a weak inverse relationship between the growth rate of per-capita PDB between 1975 and 2000 and its value in I 975. Cross-sectional regression results based upon Equation 4.3 and using NLLS are shown in Table 4.2. We use HC3 robust standard errors as proposed by Davidson and MacKinnon (1993) to account for possible heteroscedasticity, considering that the number of observations is small (Long and Ervin, 2000). The estimated speed of convergence is 0. 7 percent, but it is not significantly different from Oat the 5 percent level. The adjusted R-squared of the regression is extremely low (0.01) suggesting that this model does not explain departmental PDB growth rates. These results do not change if one excludes Choc6, Nuevos, and Guajira, which have a large influence on results, as suggested by Cook's distance computed after the first regression (Figure 4.9).

In the case of IDBH, Figure 4.10 shows a stronger negative relationship between the growth rate of per-capita IDBH between 1975 and 2000 and its value in 1975. This is confirmed with the regression presented in Table 4.3, where the estimated speed of convergence is 1.2 percent and statistically significant. The adjusted R-squared is 0.35. Excluding Guajira, as suggested by Cook's distance, and then rerunning the regression yields similar results.

Hence, we find evidence of absolute beta-convergence using IDBH, but not using PDB.

#### **4.5.3 Conditional Beta-Convergence Using Control Variables**

As explained in Subsection 4.3.3, one may drop the assumption that all economies have the same parameters, and hence the same steady state, and try to proxy for the steady-state level of income with a set of variables *X;,* running regressions based upon Equation 4.4.

There is no agreement as to which variables to include as proxies for the steady state with cross-sectional data (Durlauf et al., 2005). We use variables that are based upon theoretical arguments and our choice is limited by data availability at the departmental level. We use the logarithm of population growth and a variable based upon saving rates.23 Additionally, we use three variables proxying for human capital: log oflife expectancy in 1975, log ofliteracy in 1973, and log ofnet enrolment rate in 1985. Several specifications for the average growth rate of per-capita PDB are shown in Table 4.4 and for per-capita IDBH in Table 4.5.24

Results for PDB show that the speed of convergence remains statistically insignificant in all the specifications, including the variables proxying for the steady state, as was the case with absolute convergence. We find no evidence of conditional convergence using PDB data.

In the case of IDBH, where we find evidence of absolute convergence, once we include variables *X;* proxying for the steady-state level of income, the speed of convergence turns insignificant. We find no evidence of conditional convergence using IDBH data.

23 As the saving rates that are available from CEGA (2006b,a) include values that are negative, we add a constant to all values, so that the transformed data are all positive and we can compute the logs.

24The number of departments included depends upon data availability.

### **4.5.4 Beta-Convergence Using Time-Series Cross-Sectional Data**

Recall that with TSCS data, the regression is based upon Equation 4.6, defined in subsection 4.3.4as

$$\log(\wp\_{t,t}) = \alpha\_t + \rho\_t \log(\wp\_{t,t-1}) + \mathfrak{u}\_{t,t}, \eta$$

which uses the measure ofrelative income *y;,1,* that is, income of each department expressed as the ratio to the national average. One may estimate the equation in several ways. First, we begin by pooling the data, assuming homogeneity in the parameters. Second, we use linear mixed models where the parameters are assumed to have a fixed component, common to all departments, and a random part. Third, we estimate 25 separate ordinary least squares (OLS) regressions for each entity. Finally, we assume that there are several groups of departments which share the same *a* and *p,* and explore this issue with finite mixture models.

In all cases, the key issue is whether the estimated value for *p* is lower than 1, which would suggest that there is economic convergence.

#### **Pooled Data and OLS**

The assumption of *a;* = *a* and *p;* = *p V;* in Equation 4.6 is equivalent to assuming that there is a common steady state to all departments. Hence, the results are comparable to those obtained using cross-sectional data when we tested for absolute beta-convergence in subsection 4.5.2.

Tables 4.6 and 4.7 present the results for PDB and IDBH using TSCS pooled data and estimating with OLS. In both cases, the estimated *p* is less than 1 (0.989 for PDB and 0.986 for IDBH). However, it must be noted that while the value 1 is not included in the 95 percent confidence interval of *p* for IDBH, it is included for PDB, confirming the evidence of absolute convergence in IDBH, but not in PDB.

For IDBH the implied estimated speed of convergence /3, computed with the estimated *p*  value, is 1.4 percent, similar to and only slightly higher than the one observed using crosssectional data (1.2 percent) in Section 4.5.2.

#### **Mixed Models**

We follow here a frequentist approach for the estimation ofEquation 4.6. Following Maddala

$$Z\_{i} = \begin{pmatrix} \log(\mathcal{y}\_{i,1}) \\ \vdots \\ \log(\mathcal{y}\_{i,T}) \end{pmatrix}, \quad X\_{i} = \begin{pmatrix} 1 & \log(\mathcal{y}\_{i,0}) \\ \vdots & \vdots \\ 1 & \log(\mathcal{y}\_{i,T-1}) \end{pmatrix}, \quad b\_{i} = \begin{pmatrix} \alpha\_{i} \\ \rho\_{i} \end{pmatrix}, \text{and} \quad U\_{i} = \begin{pmatrix} u\_{i,1} \\ \vdots \\ u\_{i,T} \end{pmatrix}.$$
  $\text{with } i = 1, \dots, N \text{, where } N \text{ is the number of regions in the data.}$

We consider the autoregressive regression model

$$Z\_l = X\_l b\_l + U\_l, \quad l = 1, \ldots, N,\tag{4.11}$$

with the assumptions *U;* ~ *N(0,* <Jf J), and *b;* ~ *N(µ, L),* where *J* is the identity matrix and *L* is a nonzero covariance matrix.25 We further assume that the *U;* are independent across the *N* equations, and that *b;* and *U;* are independent for different regions.

We work with a linear mixed model (McCulloch and Searle, 2001). If we write *b;* as *b;* = *µ+71;,* with *1j;~N(0,L),* wecanrewriteZ;,(i= l, ... ,N) as

$$Z\_i = \ \ X\_i(\mu + \eta\_i) + U\_i$$

$$= \ X\_i \mu + X\_i \eta\_i + U\_i \tag{4.12}$$

$$=\quad X\_{l}\mu + \omega\_{l},\tag{4.13}$$

with *w;* ~ *N(0,* il;), il; being the variance covariance matrix defined as

$$
\Delta \Omega\_l = \mathcal{X}\_l \Sigma \mathcal{X}\_l^{'} + \sigma\_l^2 I. \tag{4.14}
$$

In Equation 4.12, the vectorµ represents the fixed effects and 1j; represent the random effects. In linear mixed models, fixed effects are used for modeling the mean of the response variable and the random effects are used to model the variance-covariance structure of it (McCulloch and Searle, 2001). The parameters in our linear mixed model are thenµ, *L,* and <Jf. The last two parameters are in fact variance components, as presented in Equation 4.14.

One can obtain an estimator for *µ* and best-linear unbiased predictors for the random effects 1j; with maximum likelihood or restricted maximum likelihood (REML).26 Here, we prefer REML for three reasons: (i) the estimators are based upon taking into account the degrees of freedom for the fixed effects in the model, (ii) because of its unbiasedness in the case of balanced panels, and (iii) as REML estimators seem to be less sensitive to outliers in the data.27 With the obtained values *forµ* and 1j;, one could compute predicted values for the *N* different *a;* and *p;.*

We are interested in the estimation of the fixed effects. As was mentioned before, the literature suggests that in some cases, the estimated speed of convergence can be substantially higher than the one obtained by assuming there are no random effects. We also compare the results with those assuming homogeneity in the parameters using likelihood ratio tests

25Toe results of the estimation assume no special structure of the matrix l:.

26For the algorithms used for obtaining maximum likelihood and restricted maximum likelihood estimates in the case of a linear mixed model, see Pinheiro and Bates (2000).

27For a review oflinear mixed models and a discussion of the estimation with maximum likelihood and REML, see McCulloch and Searle (2001).

and the Akaike information criterion (AIC) in order to investigate if a more flexible model allowing for heterogeneity in the parameters should be preferred.

Results for PDB are presented in Table 4.8. The estimated coefficients for the fixed effects are similar to the coefficients estimated when assuming homogeneity in the parameters (Table 4.6). In the case of *p,* the estimated value for the linear mixed model is 0.984, close to the value 0.989 obtained with OLS and assuming no random effects. It must be noted that the standard error of the fixed effect of *p* is higher than for the coefficient estimated in the model assuming homogeneity in the parameters. The estimated standard deviations of both random effects are quite low, especially the one for *a,* with a value close to 0, suggesting there is no evidence of different steady states. The value for the Akaike information criterion for the linear mixed model is larger than for the simpler model, assuming parameter homogeneity, and hence the simpler model is preferred. This is also corroborated by a likehood ratio test.

Table 4.9 shows the results for IDBH. Once again, the coefficients for the fixed effects are close to the ones obtained with the model in the previous section, in which we assumed parameter homogeneity (Table 4.7), with *p* equal to 0.986 in both cases. The estimated standard deviations of both random effects are low, in particular the one for *a,* which is close to 0, giving no support for the existence of different steady states. The AIC suggest that the simpler model is better, which is confirmed with a likelihood ratio test. 28

#### **Separate Regressions for Each Department**

We also treat all departments as separate entities and run an AR(!) regression for each one. These separate regressions shed light upon the effect of past values on current values, but due to the low amount of observations for each department (25 years), estimations are not reliable. In Table 4.12, we present results for PDB. The slope coefficient *p* is lower than I for all departments but has large standard errors and is not significant at the 5-percent level for Cauca and Boyaca.29 The resulting speeds of convergence are implausibly high with values ranging from 10 to 60 percent in the case of PDB, a result influenced by the fact that the period only covers 25 years. Results for IDBH are similar (Table 4.13).

The graphical analysis of each time series is more informative. In Figure 4.12, we plot the individual time series for relative PDB in logs for all departments. We observe that in almost all departments, the values change little over time and the series seem stationary. They remain either above or below the national average with the exception of Guajira and

28 Although it is possible to calculate the implied speed of convergence for each department, the interpretation is difficult. For illustrative purposes, we present them in Tables 4.10 for PDB and 4.11 for IDBH. The associated speeds of convergence have a larger variability for PDB than for IDBH. The average speed of convergence is 1.6 percent for PDB and 1.4 percent for IDBH).

29The expected value can be calculated when Ip I < I, i.e. when the time series is stationary.

Nuevos. The time series do not become closer to the national value over time, except for Guajira, indicating a lack of economic convergence among departments.

Results for IDBH (Figure 4.13) show that most of the time series seem stationary. Interestingly, the wealthiest department, Bogota, moves slightly closer to the national average, as does as the poorest department, Choc6. Guajira, although becoming closer to the national average, still remains below it.

#### **Mixture Models**

In the previous sections, we estimated a model assuming that *a* and *p* are the same for all departments. We then allowed these parameters to be different for each department, in the context of a linear mixed model, where the parameters are assumed to have a fixed component, common to all departments, and a random part. Then, we estimated 25 separate AR(l) regressions, one for each department.

Another possibility is that there are several groups of departments which share the same *a*  and *p.* We explore this possibility with a finite mixture model, as described in Leisch (2004) and Griin and Leisch (2008). These types of models can be applied, assuming that observations originate from various groups, where the group affiliations are unknown. Finite mixture models with a fixed number of components are estimated with the expectation-maximization (EM) algorithm within a maximum likelihood framework.

We assume three groups and fit the model with the statistical software R (R Development Core Team, 2008) and the package *fiexmix* (Leisch and Griin, 2008). Results for PDB and IDBH are presented in Tables 4.14 and 4.15. We show estimated *a* and *p* for each group of departments, as well as the departments composing each group.

Results for PDB (Table 4.14) show that Group 1 includes many of the poorest departments (e.g., Choc6, Sucre, Nariiio, and C6rdoba), Group 2 is composed ofNuevos Departamentos and La Guajira, and Group 3 includes the richest departments ( e.g., Bogota, Valle, and Antioquia). 30 Estimated values for *a* and *p* are similar for Groups 1 and 3, with *a* being negative and close to O and *p* being close to 0.99, a result that is similar to the estimated value obtained in subsection 4.5.4, assuming homogeneity in the parameters. The implied speed of convergence for these two groups is close to 1 percent. If one believes in the validity of the estimated expected value of the time series, one would expect that departments belonging to Group 1 would remain well below the national average over time, while those from Group 3 would remain below, as well, but would be closer to it. As was discussed before, Nuevos Departamentos and La Guajira experienced high growth rates between 1975 and 2000, as-

30Mixture models are only identifiable up to a permutation of the component labels (Leisch, 2004). The names, Group 1, Group 2, etc., have no special meaning here, and the order of the groups is irrelevant

sociated with the production of oil and coal. The model captures this, suggesting that both departments are far from their steady states, showing a large implied speed of convergence (10 percent), and predicting that both would remain above the national average.

Concerning IDBH (Table 4.15), the grouping of departments is similar as above, with Group 1 including many of the poorest departments and Group 3 including the richest ones. Group 2 now includes Nuevos Departamentos, La Guajira, and Sucre. Groups 1 and 3 have values for the estimated *a* that are quite similar to one another, and close to 0. Values for the estimated *p* are also similar with 0.98 for Group 1 and 0.99 for Group 3, both being close to the estimated value obtained, assuming homogeneity in the parameters (Subsection 4.5.4). Nuevos Departamentos, La Guajira, and Sucre have values for *a* and *p* that are different than those from the other two groups (-0.01 for *a* and 0.96 for *p).* Once again, the model suggests that these departments are far from the steady state, with an implied speed of convergence of 4 percent, which speed is greater than that for Groups 1 (2 percent) and 3 (1 percent). Once again, with an analyzed time period of only 25 years, it is questionable whether one should rely upon the estimated expected values.

#### **4.5.5 Kernel Density Estimators**

All the results for kernel density estimations were computed with the statistical software R (R Development Core Team, 2008) and the package *ks.31* For both univariate and bivariate kernel density estimations, we use Gaussian kernels and smoothed cross validation bandwidth selectors32 (Jones et al., 1991; Duong and Hazelton, 2005). In the univariate case, and as suggested by Bowman and Azzalini (1997), we use for both years the same bandwidth, which is computed as the mean of the two selected bandwidths obtained for each year separately. In the bivariate case, the smoothed cross validation is unconstrained, meaning that we do not impose that the (nonsingular) bandwidth matrix *H* has to be diagonal in Equation 4.10. Hence, we are able to handle correlation between components, as we allow kernels to have an arbitrary orientation (Wand and Jones, 1995). As we are especially interested in checking whether a large portion of the probability mass remains clustered around the 45 degree diagonal, this flexibility is relevant for us. If we were to impose a diagonal matrix *H,*  only kernels which are oriented to the coordinate axes would be allowed.

Univariate kernel density estimations of the logarithm of relative departmental PDB for the years 1975 and 2000 are shown in Figure 4.16. Both densities seem unimodal and are

31.b- is currently the most comprehensive kernel density estimation package in R (Duong, 2008). All the estimations were done with the function *kde.*

32We have also tried direct plug-in methods as suggested by Sheather and Jones (1991) and obtained results that are not very dissimilar.

very similar. Thus, according to this figure, there were almost no changes in the distribution. Table 4.16 shows the results of a formal bootstrap test of equality of the estimated densities for both years. We cannot reject the hypothesis that the two densities are identical. Bivariate kernel-density estimators are presented in Figures 4.17 and 4.18. Both figures make clear that most of the mass is concentrated along the 45-degree diagonal and hence support persistence in the distribution. Departments with a relative PDB that was above (or below) average in the year 1975 tend to remain above (or below) average in 2000. Two interesting cases are La Guajira and Nuevos Departarnentos, as they show some mobility. Nuevos Departarnentos was close to the national average in 1975 and is clearly above the average in 2000, while La Guajira was clearly below the national average in 1975 and is quite close to it in 2000.

Turning to results using the logarithm of relative departmental IDBH, Figure 4.19 presents the univariate kernel estimators for the years 1975 and 2000, showing a slight shift of the distribution to the right in 2000. The distribution narrowed between 1975 and 2000 and the two modes observed in 1975 in the left and right tails of the distribution almost disappeared in 2000. However, according to the bootstrap test of equality of the estimated densities for both years, we cannot reject the hypothesis that the two densities are identical (Table 4.16). Bivariate kernel-density estimators are presented in Figures 4.17 and 4.18. Bivariate kernel density estimators in Figures 4.20 and 4.21 show some mobility, as well. In the contour plot (Figure 4.21), the mass of the distribution rotates slightly clockwise, suggesting mild convergence in the distribution.

## **4.6 Conclusions**

Returning to the questions raised at the beginning of the study, we do not find absolute or conditional convergence in PDB using the regression approach. The distributional approach shows persistence in the distribution, i.e., relative to the average, each department remains in the position where it was located in 1975. Results of both methods point in the same direction - there is no convergence but persistence in PDB does exist.

Analysis of IDBH shows absolute convergence using the regression approach. After testing different models allowing for parameter heterogeneity, we found that there is no evidence of the existence of different steady states. The pooled model using TSCS provides our preferred estimators. Bivariate kernel density estimators show some improvements in the distribution. However, the changes are small and consistent with the low speed of convergence of around 1 percent.

Different factors explain our results. Differences in geography, infrastructure, and population density among departments are relevant factors to explain lack of convergence in

PDB, as are differences in production structures and value added by department. Excepting for the mining departments, the different production structures remained almost unchanged between 1975 and 2000 (Table 4.17).33 However, mineral exploitation in Colombia is relatively recent, going back only to the mid eighties, and this fact explains why the group of Nuevos and the department of La Guajira are the only initial poor departments that grew more quickly than the wealthier departments, according to PDB data. Previous literature had already pointed to the fact that once the mining departments are excluded, any hint of convergence disappears (Birchenall and Murcia, 1997) and that departments with a high share of agricultural production had the lowest growth rates (Bonet, 1999). Three departments concentrated at least 50 percent of PDB in both evaluated years: Antioquia, Bogota, and Valle de! Cauca. These three departments combined produced 65 percent of the manufacturing output in 1975 and 60 percent in 2000. The stability of the shares in other sectors is also remarkable, indicating departmental concentration and low mobility of production factors across the country.

At least two of the assumptions of the Solow model, which is the usual theoretical framework for studying convergence, seem problematic for application to the Colombian case. First, the neoclassical model assumes mobility of factors, which is in this case constrained by geographic, climatic, and infrastructural issues, as well as by the internal conflict issue. For instance, several productive sectors periodically suffer from attacks by violent groups, not only on physical capital, but also human capital through kidnapping and extortion. Second, the assumption of constant returns to scale is an oversimplification that does not hold for all sectors in the economy. As has been argued by World Bank (2009b ), while returns to scale in agriculture tend to be constant, those in manufacturing and services are increasing.

The slow convergence observed in IDBH could be explained by recent redistributive policies. Recall that per capita IDBH is a measure of households' income after subtracting taxes on property and rental income and net payments to the social security, and adding other net current transfers. We must also note that Colombia has experienced higher public spending in social sectors and infrastructure. Literature dealing with the direct link between convergence and public spending is scarce, but suggests that it affected the relative position of some departments, although not the distribution as a whole (Ardila Rueda, 2004), and that efficiency of public spending has been decreasing over time, mainly due to political interests and corruption.

33Nuevos Departamentos increased its participation in the Colombian mining sector from 11 percent in 1975 to *55* percent in 2000 (Table 4.17).

**Summary of Results**

*Note:* Results for conditional beta convergence with TSCS data and for the distributional approach based on relative values, i.e., ratios to the national level.

Increased social spending has also benefited from mining sector revenues which are distributed across all departments through the fiscal system. 34 IDBH of mining departments is still very low and did not exhibit the high growth rates observed in PDB.35 One reason for this is that fiscal decentralization began in the late eighties and the reforms are thus still too recent to be fully evaluated. A second reason is that financial resources from mining sectors are not efficiently spent because of corruption and are not sufficient to compensate for the low starting point in income of these departments. Recall that in 1975, La Guajira was the second poorest department in Colombia and that a large part of its population is indigenous and poorly linked to the departmental economy. Previous research suggests that even if rev-

34Oil revenues are divided between direct and indirect revenues and correspond to about eight to 25 percent of total extracted crude oil income. Direct revenues are those given to producing departments, municipalities, and ports of exports basically to finance investment in social sectors, and account for about 76 percent of oil revenues. Indirect revenues are those distributed among non-producing departments (Hernandez, 2004 ).

35Producing departments are obliged to spend at least 50 percent of the received mining revenues on social investment until having achieved certain minimum thresholds for infant mortality, health care, education, water, and sanitation. Indirect revenues are distributed according to projects presented through territorial entities (Law 14 I of I 994 ).

enues of coal exports in La Guajira were distributed efficiently and without any corruptionrelated loss (corruption levels seem to be particularly high in mining departments), IDB of that department would still be about 60 percent of national IDB in 2000 (Meisel, 2007a).

Although overall public spending has increased, the transfer system bears some disadvantages for poor departments. Evidence shows that after totaling all public revenue (not only that directed to social sectors), there is no fiscal equalization in Colombia and the system is regressive; wealthy municipalities have the highest shares of public funds.

Two other issues have to be taken into consideration for interpreting the results of both PDB and IDBH. One is that in 2000, our last year of analysis, the country was experiencing a large economic crisis which affected public and private finances. Transfers from the central government were thus also affected by the crisis. A second issue is related to the domestic conflict. Between 1998 and 2002, violence escalated dramatically when the groups involved in the war were fighting one other for control of strategic areas. Sanchez and Palau (2006), who deal directly with this last issue, argue that decentralization policies, political and fiscal, affected the interests of armed groups and even strengthened them through the sharp increase in local resources. The higher political autonomy at the local level increased the ability of armed groups to intimidate politicians and to extract rents from public funds. Guerrillas relocated in strategic zones with greater levels of prosperity, the facility for processing illicit drugs, and an intimidated local population (Sanchez and Palau, 2006).

One of the policy implications of this study is the necessity of monitoring the efficiency of social spending and enforcing decentralization policies so that a faster convergence in IDBH can be achieved. Concerning convergence in PDB, reallocation of productive sector resources is not easy to achieve and could yield to efficiency losses, but the state can, for example, encourage the accumulation of human capital and improve infrastructure in lagging departments, which would help attract investments in the long run. Additionally, it is crucial to find a way out of the internal conflict to foster factor mobility in Colombia, particularly in those areas without significant state presence. We consider it vital to have an explicit regional policy in Colombia to foster growth in departments lagging behind national averages, after conducting case studies to assess which policies could be most effective in each case.

Finally, for monitoring convergence across departments in the future, it is essential to have consistent time series constructed under a single methodology. Unfortunately, the work done by CEGA for the period 1975 to 2000 was not continued for the years after 2000. Such a project is of high policy relevance for the country.

## **4.7 Tables**

Table 4.1: Colombia. Gross Domestic Product (Constant Million Pesos of 1994), Per Capita GDP and Population. 1980-2006.

*Source:* Own calculations based on National Accounts and Census 2005, DANE

Table 4.2: Beta Convergence Using Cross-sections and Non Linear Least Squares. Dependent Variable: Average Growth Rate ofpc PDB 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

*Source:* HC3 standard errors calculated according to Davidson and MacKinnon (1993).

Table 4.3: Beta Convergence Using Cross-sections and Non Linear Least Squares. Dependent Variable: Average Growth Rate ofpc IDBH 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

*Source:* HC3 standard errors calculated according to Davidson and MacKinnon (1993).

Table 4.4: NLLS Regressions. Dependent Variable Average Growth Rate ofpc PDB. 1975-2000. , ...

• *p* < 0.05, •• *p* < 0.01, ••• *p* < 0.001 (j

Note: HC3 robust standard errors (Davidson and MacKinnon, 1993) in brackets. 0

Table 4 .5: NLLS Regressions. Dependent Variable Average Growth Rate ofpc IDBH. 1975-2000.

• *p* < 0.05, •• *p* < 0.01, ... *p* < 0.001

 Note: HC3 robust standard errors (Davidson and MacKinnon, 1993) in brackets.

Table 4.6: OLS Linear Regression. TSCS Data. Dependent Variable */og(y;,1).* Relative Per capita PDB. 1975-2000.

Table 4.7: OLS Linear Regression. TSCS Data. Dependent Variable *log(y;,1).* Relative Per Capita IDBH. 1975-2000.

Table 4.8: Linear Mixed Model (REML). TSCS Data. Dependent Variable: *log{y;,1* ). Relative Per Capita PDB. 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Table 4.9: Linear mixed model (REML ). TSCS Data. Dependent Variable: */og(yu).* Relative Per Capita IDBH. 1975-2000.

Table 4.10: Implied Convergence Rates Using TSCS Data and Linear Mixed Models (REML). Per capita PDB. 1975-2000

Table 4.11: Implied Convergence Rates Using TSCS Data and Linear Mixed Models (REML). Per capita IDBH. 1975-2000

Table 4.12: Autoregressive Processes of Order 1. Dependent Variable: *log(yu* ). Per Capita PDB. 1975-2000. I~

*Source:* Own calculations based on data from CEGA. Constant prices of I 994. 0 *Note:* Expected values (a/ ( I - p)) calculated only for *p* significant at *5%* level and lower than I.

 - (") Vl

Table 4.13: Autoregressive Processes of Order I. Dependent Variable: *log(yu).* Per capita IDBH. 1975-2000.

*Note:* Expected values *(a /* ( I - p)) calculated only for *p* significant at 5% level and lower than I.

Table 4.14: Mixture Model with 3 Components. Fitted with ML. Dependent Variable: *log(y;,1* ). Relative Per capita PDB. 1975-2000.

Table 4.15: Mixture Model with 3 Components. Fitted with ML. Dependent Variable: *log(y;,1* ). Relative Per Capita IDBH. 1975-2000.

Table 4.16: Bootstrap tests of equality of univariate density estimates, Income indicators

Test proposed by Bowman and Azzalini ( 1997). I 000 replications.

*Source:* Own calculations based on data from CEGA.

## **4.8 Figures**

Figure 4.1: Map of Colombia.

*Source:* Instituto Geografico Agustin Codazzi.

*Labels in its order of appearance:* International Limit, Departmental Limit, Country Capital, Capital District, River, Water.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Figure 4.3: Box Plot: Log of Per Capita IDBH. 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

#### Figure 4.4: Box Plot: Log of Relative Per Capita PDB. 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Figure 4.5: Box Plot: Log of Relative Per Capita IDBH. 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Figure 4.6: Sigma Convergence. GDP by Department.

*Source:* Own calculations based on data from DANE.

Figure 4.7: Sigma Convergence. Per Capita Gross Departmental Product (PDB) and Gross Personal Disposable Income (IDBH). 1975-2000 .

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Figure 4.8: Beta Convergence. Per Capita PDB. 1975-2000 .

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Figure 4.9: Beta Convergence without Nuevos, Choc6 and Guajira. Per Capita PDB. 1975- 2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Figure 4.10: Beta Convergence. Per Capita IDBH. 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Figure 4.11: Beta Convergence without Guajira. Per Capita IDBH. 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Figure 4.12: Log of Relative **PDB** by Department. 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

I I Q z *(j*  i I

.....

V,

N

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

Figure 4.14: Log of Relative PDB. All Departments. 1975-2000.

Figure 4.15: Log ofRelative IDBH. All Departments. 1975-2000.

*Source:* Own calculations based on data from CEGA. Constant prices of 1994.

*Source:* Own calculations based on data from CEGA. Variables in logs

Figure 4.17: Relative Per Capita PDB Dynamics. Years 1975 and 2000. Constant Prices of 1994.

*Source:* Own calculations based on data from CEGA. Variables in logs

Figure 4.18: Relative per capita PDB Dynamics: Contour Plot. Years 1975 and 2000. Constant Prices of 1994.

*Source:* Own calculations based on data from CEGA. Variables in logs *Note:* Contours are drawn at 30%, 60% and 90%. The points represent the 25 observations. Points outside the contour level curves are identified. A 45 degree line is added to the plot.

Figure 4.19: Univariate Kernel Density Estimators of Relative per Capita IDBH. Years 1975 and 2000. Constant Prices of 1994.

*Source:* Own calculations based on data from CEGA. Variables in logs

Figure 4.20: Relative Per Capita IDBH Dynamics. Years 1975 and 2000. Constant Prices of 1994.

*Source:* Own calculations based on data from CEGA. Variables in logs

Figure 4.21: Relative per Capita IDBH Dynamics: Contour Plot. Years 1975 and 2000. Constant Prices of 1994.

*Source:* Own calculations based on data from CEGA. Variables in logs *Note:* Contours are drawn at 30%, 60% and 90%. The points represent the 25 observations. Points outside the contour level curves are identified. A 45 degree line is added to the plot.

# **Essay 5**

# **Regional growth convergence in Colombia using social indicators**

## **Abstract**

This paper investigates convergence in social indicators among Colombian departments from 1973 to 2005. We use census data and apply both the regression approach and the distributional approach (univariate and bivariate kernel density estimators). Using literacy rate as a proxy for education, we find convergence between 1973 and 2005, but persistence in the distribution between 1975 and 2000, when we use the infant survival rate and life expectancy at birth as proxies for health. Additionally, using data from Demographic and Health Surveys, we find some evidence of convergence in the rate of children that are well-nourished between 1995 and 2005.

## **5.1 Introduction**

The majority of studies on convergence use macroeconomic aggregates to study whether poor countries are catching up with wealthier countries, and are particularly interested in the speed at which this process occurs, when it does occur. A large part of the empirical analysis of convergence is based on the neoclassical model developed by Solow (1956) and the estimation procedure suggested by Barro and Sala-i-Martin (1992a). Most of these studies use cross-sectional regressions based on per capita gross domestic product (GDP) to investigate if poor regions have higher rates of growth as they develop than wealthier areas.

In recent years, some authors have also tested if there is convergence in living standards, given that it is well-being that really matters, and arguing that per capita GDP is not the appropriate indicator for it. 1 For example, Neumayer (2003) and Kenny (2004) conclude that even in the absence of convergence in per capita GDP, there is convergence in living standards among poor and rich countries, a phenomenon praised by Neumayer as one of the greatest success stories of development in the last century.

This argument seems to be valid for cross-country analysis, but few studies exist investigating regional convergence in living standards in developing countries. Within a particular country, convergence analysis is important, not only to focus development assistance towards regions lagging behind in economic growth, but also to evaluate the efficiency and scope of public policies. Lack of convergence and the persistence of inequalities inside a country can lead to political instability, social unrest, and violence, given that people are concerned not only with their own improvements, but also with meeting the living standards of the wealthiest regions (Kenny, 2004). In Colombia, high regional inequality in living standards is one of the possible underlying causes of the ongoing domestic conflict, which is fueled by drug trafficking and corruption, particularly in isolated regions with a low level of governmental presence and a high incidence of poverty.

Over the past 30 years, Colombia has witnessed important reforms in social areas, particularly in health care and education. These reforms were marked by increased governmental intervention during the mid seventies, such as the creation of a national health care system and vaccination campaigns to eradicate tropical diseases like malaria, and, in the early eighties, policy formulations to reduce mortality and increase primary education. At the beginning of the nineties, decentralization accelerated in order to reduce the fiscal burden on the central government, making municipalities more responsible for generating and administrating their own resources, and partially moving the provision of health services to the private sector (Hernandez and Obregon, 2002).

1 In this paper, we will refer indistinctly to non-income indicators, social indicators, quality-of-life variables, and living standards.

The link between decentralization policies and the improvement in living standards in Colombia is a topic of extensive debate. While some researchers argue that the health policies have categorically failed, others conclude that they have been successful, although recognizing that there is still a large margin for improvement, particularly given that the system in place is still too recent to make a general judgement (Homedes and Ugalde, 2005; Barrera and Dominguez, 2006). Evidence shows that even though social spending increased considerably and reforms were designed to compensate municipalities with weak fiscal capacities, fiscal equalization has not been achieved.

Although Colombia has experienced improvements in living standard indicators at the national level, particularly those related to health, education, and access to public services, there is evidence of a heterogeneous distribution of improvements. Thus, investigating regional convergence in social indicators is relevant, as it is a relatively under-researched topic. Out of20 research documents about regional convergence in Colombia produced in the last 15 years (Aguirre, 2008), only two published articles that deal with convergence in nonincome indicators (Aguirre, 2005; Meisel and Vega, 2007).

The objective of this study is to analyze whether departments that were lagging behind in social indicators in the 1970s were able to catch up by the year 2000. We use both the regression approach suggested by Barro and Sala-i-Martin (1991), among others, and the distributional approach pioneered by Quah ( 1997) to test for convergence in three variables, based on census data. Using literacy rate as a proxy for education, we find regional convergence between 1973 and 2005, but persistence in the distribution between 1975 and 2000 when we use the infant survival rate and life expectancy at birth as proxies for health. Additionally, using data from Demographic and Health Surveys (DHS), we find convergence between 1995 and 2005 in the percentage of children that are well-nourished.

This paper is divided into six sections. After this introduction, we argue in section 5.2 that it is fundamental to focus upon indicators other than income and that the analysis of convergence at the department level is relevant for Colombia. We present two methods to empirically test for convergence in section 5.3. Section 5.4 describes the data used and the details of our empirical estimation. Results are presented in section 5.5 and discussed in section 5.6.

## **5.2 Motivation**

The importance of analyzing social indicators, instead of focusing only upon income, has been extensively discussed in the work of Amartya Sen, who argues that *social opportunities*  are one of the five types of instrumental freedoms that contribute to the overall freedom people have to live as they choose (Sen, 1999). Social opportunities are understood to be the arrangements that a society makes which influence the individual's substantive freedom to live better, such as providing education and health care, which are important, not only for the the citizens in the conduct of their private lives, but also for more effective participation in societal economic and political activities.

Public policies have a crucial influence on social opportunities ( e.g., they can influence longevity through epidemiological policies and education through the provision of the corresponding facilities). Thus, it is important to shift attention to elements that affect individual well-being and freedom but which are not captured by income statistics (Sen, 1997).

Particular attention shall be given herein to health status when analyzing social inequalities. Sen (1998) argues that mortality is a key economic indicator, given that it mirrors the success or failure of a society. Indicators like the infant survival rate, which responds very rapidly to public health polices, are central to that kind of analysis (Mazumdar, 2003). Along the same lines, indicators referring to the level of nutrition reflect one of the most basic needs for survival, namely access to adequate food (Sen, 2002).

In Colombia, awareness of the influence and scope of the government on health and education gradually increased in the second half of the *20'h* century, and has translated into programs, as well as legislation, aimed at achieving universal access to health care and primary education. Policies for both sectors experienced important changes in the last quarter of the century, reflecting the transition from a centralist system to a locally managed one.

In the seventies, polices on education focused upon reducing illiteracy and increasing the coverage of primary education, particularly in rural areas, where public schools and teachers were almost nonexistent. 2 However, rural areas continued to lag behind. Adult education and literacy campaigns continued through the eighties, together with the expansion of secondary and pre scholar education.

Due to macroeconomic imbalances at the end of the eighties, the government initiated a decentralization program to reduce the financial burden on the central government, and transferred substantial revenues and responsibilities to local administrations. The country has been praised as a leading example of fiscal decentralization, which policy had the objective of increasing social expenditures and efficiency in social sectors, as well as financially compensating territories with weak fiscal capacities. This process accelerated with the new constitution in 1991 (Rojas, 2003; Barrera and Dominguez, 2006). As a result, social spending increased from seven to 15 percent of GDP between 1991 and 2001. Concerning education, evidence shows that reforms were beneficial for the urban sector, but less so for

2With society facing limited resources, secondary and tertiary education was left largely to the private sector under the argument that spending in public universities would favor middle and upper income groups.