Ludger J. Löning

# **Economic Growth, Biodiversity Conservation, and the Formation of Human Capital in a Developing Country**

The Case of Guatemala

Ludger J. Löning

## **Economic Growth, Biodiversity Conservation, and the Formation of Human Capital in a Developing Country**

Can education play a role in fostering economic growth and simultaneously decrease pressure on forests? The aim of this study is to show that it can. Human capital formation is a key element in a development strategy that includes natural resource conservation within the framework of sustained economic growth and poverty alleviation. Consequently, it is not by chance that Guatemala is experiencing both minimal per capital income growth and high deforestation while having one of the lowest educational levels in Latin America. However, since many assumptions about educational benefits are controversial and many aspects depend on broader issues, human capital formation can only be one piece in a multidimensional puzzle. This study is organized into three parts, each one of which can be read independently: first, a macroeconomic assessment of education and other factors involved in the country's growth trajectory; second, a rural analysis indicating the root causes of deforestation and the role education can play to slow down habitat loss; third, the highlighting of some elements indispensable to reform and to subsequent improvement of the quality of rural schooling.

Ludger J. Löning is presently working at an international financial institution in Washington D.C. He majored in economics and international relations at the Dresden University of Technology, l'Université Pierre Mendès France at Grenoble, and the University of Trier. After working three years as a researcher for the Ibero-America Institute of the University of Göttingen, he received his Ph.D. in economics at this University in 2004. The author has visited the Latin American Region extensively and worked as a consultant in this area for various organizations.

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Economic Growth, Biodiversity Conservation, and the Formation of Human Capital in a Developing Country

### **Gottinger Studien zur Entwicklungsokonomik Gottingen Studies in Development Economics**

Herausgegeben von/ Edited by Hermann Sautter

Band 13

Ludger Löning - 978-3-631-75357-6 Downloaded from PubFactory at 01/11/2019 05:58:33AM via free access Ludger J. Loning

Economic Growth, Biodiversity Conservation, and the Formation of Human Capital in a Developing Country

The Case of Guatemala

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#### **Bibliograflsche Information Der Deutschen Blbliothek**

Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Oaten sind im Internet Ober <http://dnb.ddb.de> abrufbar.

Open Access: The online version of this publication is published on www.peterlang.com and www.econstor.eu under the international Creative Commons License CC-BY 4.0. Learn more on how you can use and share this work: http://creativecommons. org/licenses/by/4.0.

This book is available Open Access thanks to the kind support of ZBW – Leibniz-Informationszentrum Wirtschaft. Zugl.: Gottingen, Univ., Diss., 2004

Printed with kindly support by the Spinnhutte GmbH and the lbero-America-lnstitut for Economic Research at the University of Gottingen.

D7

ISBN 978-3-631-75357-6 (eBook) ISSN 1439-3395 ISBN 3-631-52607-5 US-ISBN 0-8204-7309-X

© Peter Lang GmbH Europaischer Verlag der Wissenschaften Frankfurt am Main 2004 Aile Rechte vorbehalten.

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In Dankbarkeit, fiir meine Eltern

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#### Contents vii

### **Contents**

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#### **Acknowledgments**

Writing this thesis has been unusually pleasant. My gratitude for the opportunity to experience the generosity and hospitality of the people of Guatemala and its countryside, during three research visits, is deep but beyond words. That this study could not have been written without the help and support of many people is obvious. Some of them are mentioned in footnotes throughout this text, but some deserve special acknowledgment here.

My thesis advisor, Professor Hermann Sautter, supervised the often seemingly insurmountable task of putting some of my thoughts onto paper. His encouragement, thorough reading of pre-papers and generous flexibility to help me meet the time schedule, were essential for the accomplishment of this study. Equally, I am indebted to Professor Manfred Zeller, especially for the discussion on a previous paper about deforestation. I also would like to thank the German Research Association, which financed this study and the interdisciplinary Research Graduate Program on Biodiversity Conservation at the University of Goettingen. Of my colleagues from the Ibero-America Institute for Economic Research, I am particularly indebted to Isabel Giinther, Dierk Herzer, Jahir Lombana and Sebastian Vollmer, but also to Julia Johannsen from the Institute for Rural Development, and Michael Markussen from the Geographical Institute.

*Guatemaltecos* to whom I am indebted include Miguel von Hoegen for inviting me to the */nstituto de lnvestigaciones Econ6micas y Socia/es* at Rafael Landivar University, Ingrid Morjan de la Vega and her family for helping me to organize my research visits and to get an insider view of the Central American culture, Jorge Lavarreda from the *Centro de Investigaciones Econ6micas Nacionales* for his interest and support, Odgen Rodas and the *Plan de Acci6n Foresta/* for discussions and access to their Library, and Silvia Villatoro from *Banco de Guatemala* for her exceptional detective work at finding statistics. Finally, this thesis would not have been possible without Eduardo Somensatto and Maria Concepcion Castro from the World Bank Resident Mission, as well as Juan Alberto Fuentes from the United Nations Development Programme.

I want to thank them all.

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### **Table of Contents**

#### **Part One**

#### **Part Two**

#### **Part Three**

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#### **Illustrations**

#### **Text Tables**

#### *Part Two*

#### *Part Three*

#### **Text Figures**

#### *Part Two*

#### *Part Three*

#### **Text Boxes**

#### *All Parts*

#### **Overview and Summary**

A former head of the UN peace verification mission (MINUGUA) has qualified the prevailing social imbalances and ethnic divisions in Guatemala as being as ghastly as in the final stages of South Africa's apartheid regime. 1An overwhelming part of the population in Guatemala is thought to have Mayan origin, most living in poverty and at the margins of modern society. In addition to the enormous social distress, the country has the second lowest level of formal education in the Latin American hemisphere. After a civil war lasting three-decades, the per capita growth performance of Central America's largest economy is mediocre. The economy is still predominantly agricultural, with more than 1/ 2 of the country's labor force engaged in farming and forestry. Guatemala's richness in biodiverse forest resources was consecutively exploited during the course of its history. Currently, habitat destruction in Central America is higher than elsewhere in the world, and the annual deforestation rate in Guatemala is even higher than, for example, the rate for Brazil. Do these issues have something in common?

For the developing world, Auty (2001) argues that recent research reveals growing evidence that there may be a link between these items. Yet the literature does not allow drawing simple mono-causal explanations. The relationships stressed here are indeed puzzling phenomena. How and to what extend economic growth, human capital endowment, and the exploitation of biodiverse forests - or other natural resources - are linked to each other is not well explored. Similarly, Stedmann-Edwards (1998) finds many contradictions in this regard. However, only by understanding the factors that promote income generation, enhance social development, and drive people to make decisions to conserve their environment allows reasonable policy interventions to be proposed. The aim of this study is to fill *some* of these gaps and reinforce arguments from an empirical point of view. Sad to say, the Guatemalan case offers nearly a textbook example for exploring the chosen questions, in spite of not easily accessible data. Given the small size of the open economy and considering its heavy social contrasts, much appears to be clearer here than in other settings.

It should be made transparent from the beginning that due to the complexity of the issues involved, only *selected* avenues among these relationships can be documented. A focus of the present study lies on the role of human capital, i.e. formal education. Broadly speaking, there are two queries that can serve as a rough guidance throughout the study. First, the underlying question is whether human capital formation has the potential to promote economic growth and, at the same time, can slow down habitat loss. In documenting the correlation between economic growth, schooling and habitat conservation, the aim here is to point out

See Merrem (2001).

an interesting policy lever. Clearly, there is a substantial number of additional factors that must be taken into account as well. Second, if schooling proves to be significant, not only does the question arise about which level of education is important, but also of how to increase the access and quality of schooling in the complex setting of a developing country.

More specifically, the study consists of 3 independent parts. These parts follow individual research questions, use particular methodologies and come to distinct results. Although they are loosely connected, they should be read *separately* from another.

Part One investigates the impact of human capital on economic growth through the application of time series analysis and an extended growth accounting exercise. Apart from the elaboration of a data set and the application of an error-correction methodology, the contribution is twofold. First, very little analysis exists that analyzes the role of human capital on growth over a long time period and for an *individual* country. This study here presents such an analysis. Second, surprisingly rare in macro analysis, the study focuses on the contribution of different *levels* of education to growth.

To address the question of the role of education on growth, Part One is organized as follows. The first chapters briefly explore Guatemala's growth patterns over time and discuss the measurement of human capital to growth. After the construction of the relevant data, the following chapters display the results and test for robustness. The final chapter accounts for the sources of growth. The main findings indicate that both primary and secondary education appear to be a key factor for growth. In fact, human capital accumulation appears to explain more than 50 percent of the country's past growth trajectory. Interestingly, the macro evidence on the returns to education here is in line with micro studies. Part One also finds that the civil war and a resulting negative investment climate heavily affected the economy, and that complementary factors to human capital policies play a great role.

**Part** Two reveals that rural underdevelopment and low educational endowment are correlated with Guatemala's past agricultural growth polices. These policies, in tum, not only have hampered human capital accumulation and constrain long-term growth prospects, they also constitute a major origin for the causal structure of today's deforestation processes. To summarize a bit, Part Two is a general inquiry into the causes of deforestation and emphasizes the role of education. Given the *scant evidence* on the correlation between schooling and habitat loss, the detailed documentation and empirical analysis of this kind of relationship is a major innovation of the study. To address these questions, Part Two is divided into three main chapters: a conceptual analysis, a qualitative assessment of deforestation patterns in Guatemala, and an empirical analysis.

The conceptual analysis suggests that, in principle, the effects of schooling on habitat loss can be ambiguous. However, the empirical analysis reveals a more straightforward outcome. The empirics are based on three distinct analyses, compromising regional data, national household data and rather unique survey data from Guatemala's main agricultural frontier region: the Peten. Given its diversity in terms of endemic species, the analysis of this region allows a clearer look at the relationships between schooling, biodiversity loss, and other factors. The overall findings suggest that deforestation in Guatemala appears to be profitable and generally does *not* seem to follow subsistence-driven patterns. This questions a great deal of the current conservation policies. By contrast, basic primary schooling and, as a consequence, the higher probability of working in the non-farm sector have a strong potential to reduce habitat loss. However, many other factors are equally important. In particular, the effect of schooling and certain types of nonfarm employment may be increased via the investment in complementary measures, such as infrastructure facilities in terms of sanitation and electricity.

Part Three is finally concerned with the question of how a developing country can increase the access to and the quality of rural education. By contracting directly with local communities, and learning from successful experiences in other countries, Guatemala has recently employed a unique model of educational decentralization. This part is divided into three main chapters and builds on the previous analysis whose findings suggest that primary education is of particular concern.

The first chapter shows that after the transition to democratic rule and the formal ending of the civil war, somewhat surprisingly, Guatemala has made progress in expanding rural primary education. Although a lot remains to be done, the country offers an interesting case showing that it is possible to draw on small innovations. The second chapter explains the institutional structure of the program. Based on results from evaluation studies and a rough empirical analysis on school survey data, the final chapter assesses the impact of the community-managed schools. Overall, the program has been remarkably successful in expanding educational opportunities and may have generated positive externalities at the local level. However, the available data also shows that the quality of the program remains a concern and that community-managed schools are not the panacea to improve access and quality of schooling. Other issues, apparently beyond the scope of the school organization form, also play a great role, such as school infrastructure, availability of books and bilingual teacher training.

Before proceeding, a few comments are needed on the scope and limitations of this study. First, it does not address the issue of all the potentially conflicting and complex interactions between economic growth, poverty reduction, and the conservation of biodiverse forest resource. There is clearly a considerable amount

of tradeoffs that should be considered in *future research.* For example, somewhat simplistically, it may be reasonable to argue that over the long run, poverty declines with rising per capita incomes. If deforestation declines with rising income, it would follow that overall economic growth, particular in the rural areas, would act to reduce forest clearance and perhaps reduce rural resource degradation generally. However, rising per capita income may also generate a higher demand for agricultural products, provide resources for capital intensive projects in rural areas and allow subsidies for agriculture. These issues are *not* analyzed here.

Second, concentrating on the contribution of human capital to economic outcomes does not imply that other factors are less relevant and that schooling constitutes a remedy for solving all the oppressing problems of the country. In fact, the study explicitly attempts to analyze some of the fundamental determinants of growth and habitat conservation by placing emphasis on complementary issues.

Finally, it should be stressed that Guatemala constitutes a most challenging case for research. Throughout its history, as evidenced by UNDP (2002), there has been an impressive 'culture' of ignorance regarding the quality of scientific research as well as the collection of statistical data. In this vein, a considerable amount of the information for this study has been collected from disperse sources. In addition, some of the information comes from interviews, consultant's reports as well as the participation in workshops, conferences and field visits in various occasions during 2001-2003. Despite of a great deal of direct local assistance, helpful discussions on two earlier working papers, and the opportunity to learn from distinguished people, the author requests the reader to remain aware of potential uncertainties in a case study like this.

#### **Part One**

### **Human Capital, Productivity and Economic Growth in Guatemala: A Time Series and Extended Growth Accounting Analysis**

The following study addresses the question of Guatemala's long-run determinants of growth. As documented by Easterly (2001) and others, economic growth can be viewed as a very powerful ingredient for expanding opportunities for poor people. Growth depends on innumerable factors, including the accumulation of human capital. By contrast, as documented by UNDP (2000) and others, Guatemala's history is marred by the exclusion of an overwhelming part of its people from polices that promote human capital accumulation and allow for income generation outside agriculture. Per capita growth in Guatemala was only 1.3 percent over the past five decades. Under these circumstances, it is no wonder that, among various antecedents, the low performance of the economy in the context of an appalling inequality in the distribution of wealth, is widely regarded as the principal cause for the outbreak of the three-decade lasting civil war.

The signing of the Peace Accord in 1996 finally ended a conflict, which was very destructive to social and economic development. To remedy this situation, the *Acuerdos de Paz* (1998) outlined a broad socio-economic development agenda that contains many quantitative targets. One target is to achieve 6 percent real economic growth. Other targets of the agenda are predicated on the assumption that the country indeed attains such high growth rates. In this vein, it is important to find out about the quantitative role of human capital and other factors aiming to promote growth.

*"El crecimiento economico acelerado def pais es necesario para la generacion de empleos y su desarrollo social. El desarrollo social def pais es, a su vez, indispensable para su crecimiento economico y una mejor insercion en la economia mundial. Al respecto, la e/evacion def nivel de vida, la sa/ud de sus habitantes y la educacion y capacitacion constituyen las premisas para acceder al desarrollo sustentable en Guatemala.* "

Peace Accords, 1996

#### I. **Introduction**

This study examines the contribution of human capital to economic growth in Guatemala over the past 50 years. 2 The interest is twofold. First, for the country itself there are very few studies that thoroughly analyze past growth patterns, and there are no studies that empirically appraise the direct impact of education on growth. In general, evidence on human capital and growth comes almost entirely from cross-country analysis. Single-country studies, however, may be more illuminating since they overcome the heterogeneity problem and take into account the unique historical information for each country. Indeed, the original motivation of studying economic growth focuses on the time-seri'es dynamics of macroeconomic variables. Moreover, the cross-section focus may be inadequate if returns to education or the quality of education differ substantially across countries.

Second, this study focuses on the contribution of different levels of education to growth. This is an important aspect regarding the problems associated with measuring *average* years of schooling. Looking at education in a disaggregated way also proves more fruitful to the policy-maker since it indicates how resources should be divided between different education levels. Finally, the empirical analysis is based on an error-correction methodology, deals with endogeneity, and explores several data construction and robustness issues. All this may be relevant for future case studies as well.

This study, probably for the first time, constructs a reliable data set that accounts for the determinants of long-run growth in Guatemala. In terms of data

2 I especially want to thank Silvia Villatoro *(Banco de Guatemala)* for her assistance in compiling part of the data. I have benefited from interviews and discussions with Christian Dreger (Halle Institute for Economic Research), Felipe Jaramillo and Andy Mason (World Bank), Stephan Klasen, Dierk Herzer, Michael Grimm and Julian Weisbrod (University of Goettingen), as well as Paul Schreyer (OECD) and Oda Schmalwasser (Gennan Federal Statistical Office). Eduardo Somensatto and Maria Concepcion Castro (World Bank), Annando Morales (IMF), Estuardo Moran *(Banco de Guatemala)* as well as Pamela Escobar and Juan Alberto Fuentes (UNDP) equally deserve many thanks.

availability, the country constitutes a most precarious case. Despite these caveats, however, satisfactory and coherent time series data were obtained. The results based on a production function augmented for human capital reveal that a bettereducated labor force has a significant positive impact on long-run growth. Consistent with cross-country evidence, primary and secondary education appear to be most important for productivity growth, followed by tertiary schooling. These findings are in agreement with the micro evidence for Guatemala. Interestingly, the results also suggest that the effect of education in both micro and macro regressions is of similar magnitude.

This holds while changing the conditioning set of the variables, for example by considering trade openness. An interesting result is that *primary* schooling seems to be particularly affected by policies that promote competitiveness. This does *not*  suggest, however, that other schooling levels are unimportant. Rather it seems that in Guatemala, during the past decades, a sufficient coverage *and* quality of primary education were the minimum requirement to adopt foreign technologies. Overall, the econometric results have been found robust, even after controlling for endogeneity as well as for alternative data sources.

Finally, a modified growth-accounting framework is presented which takes into account quality changes of physical capital and differentiates by the level of education. It shows that the human capital variables explain more than 50 percent of output growth. Of these, secondary schooling was the main determinant of growth. Due to an environment of social and political conflict, however, productivity growth was slightly negative over the past decades. In addition, given the increase of average education and a decay of the quality-adjusted physical capital at the same time, there is evidence of a missing complementarity between the country's skills and its technology base. Ultimately, the empirical findings point towards the importance of an institutional and political environment conducive to growth.

This study is organized into eight chapters. The following chapter briefly assesses patterns of growth and some of the reasons that led to a low endowment of human capital. Chapter 3 discusses how to measure the contribution of human capital to growth over time. Furthermore, it provides an overview of relevant empirical findings. Chapter 4 is concerned with data compilation. Chapter *5*  introduces the empirical methodology and presents the main results, disaggregated by education level. Chapter 6 tests the robustness of the results. The regressions include several variables that help to explain the country's growth performance, for example measures for the quality of capital, trade, and military expenditures. Finally, based on the empirical estimates, chapter 7 accounts for the sources of growth. Chapter 8 concludes.

#### **II. Patterns of Growth in Guatemala**

To understand Guatemala's growth patterns, and hence the role of education, its turbulent political and social history must be taken into account. Average annual growth rates were about 3.9 percent between 1951 and 2002. According to Bailen (2001) this is in line with the neighbor countries.3 Due to rapid population growth, however, *per capita* growth in Guatemala has averaged only about 1.3 percent per year. A continuation of this growth rate implies that the average Guatemalan would need approximately 53 years to double his real income.

#### **Box 1. Guatemala: Growth with Low Productivity and Poor Social Development**

Relatively few studies focus on Guatemala's growth experience over a long time period. One of the most comprehensive assessments is a voluminous study by Gomez and Ordonez (1991 ). They focus on structural adjustment issues for the early 1990s, but their conclusions are still of interest. In particular, they claim that productivity in Guatemala was low because of manifold structural problems, including a deficient financial intermediation system and 'resistance' to technological change. That is, Guatemala's international competitiveness was traditionally based on a low-skilled labor force with consequently poor social development and little incentives for firms to increase productivity. In addition, a culture of rent-seeking among entrepreneurs as well as public institutional and financial weakness prevented significant change.

Historically, growth was not particularly pro-poor, i.e. favoring the rural or agricultural economy where the poor live. The elite domination and ethnic division failed to promote social and institutional development. Instead, growth in Guatemala's was accompanied by the exclusion of large parts of the society from wealth, and, as a consequence, accompanied by underlying social conflict. Poverty rates and inequality indicators are among the highest in the Latin American region. According to the World Bank (2003a) about 56 percent of Guatemala's population live in poverty in 2000.

Guatemala's recent growth experience can be divided into three broad episodes. Figure 1 visualizes annual GDP growth from 1951-2003, where selected

3 For example, growth has been lower than in Costa Rica (4.7 percent) but higher than in Honduras (3.7 percent), El Salvador (3.2 percent) and Nicaragua (2.1 percent).

*parallel* historical events are given from Lujan (2000).4 Table 1 presents the average output growth rates of primary, industry and service sectors for the period 1951-2003. In addition, there are three sub-periods. The growth rates of the primary sectors in Guatemala, which employ the majority of the rural and poor people, lagged behind other sectors for the *entire* time period. By contrast, in particular for the last decades, the growing sectors where those of electricity, communications and banking. Until approximately 1975, Guatemala appears to have had a reasonable growth performance, followed by a remarkable slowdown for the later periods. However, this requires closer examination.

#### **Figure 1. Guatemala: Economic Growth, Social Conflict and Politics, 1951-2003** (growth rates in percent)

Source: Author's elaboration based on data from Banco de Guatemala. Data for 2002 (2003) is preliminary (estimated). Historical events are taken from Lujan (2000).

*La 'edad de oro', 1951-1975.* During the first period Guatemala maintained reasonable growth rates. Ever since the 1954 coup, military governments were repeatedly in power, sometimes through fraudulent elections, sometimes by *coup d'etats.* In terms of its growth performance, this era is sometimes referred to as the 'golden period' but the denomination is *very* misleading. This is because the

4 The correlations do not necessarily imply causality. Moreover, in many Latin American countries growth rates during the decades of the 1950s and 1960s were quite volatile as well.

structural imbalances of the economy remained unchanged and ultimately gave rise to the explosion of civil strife. Annual growth was highly volatile - a fact most likely associated with the dependence on agricultural export growth as well as political events. For example, in I 956 a new constitution was drawn up and in 1963 Guatemala was preparing to enter into the Central American Common Market (MCCA). 5At first sight, Figure 1 suggests that the civil war's guerilla activities starting around 1960 - appeared to have an impact only on short-run growth. However, the later growth accounting exercise suggests that, indeed, the trend growth of total factor productivity (TFP) was negatively affected by the civil strife from the beginning.

#### **Box 2. Social Conflict and Guatemala's Growth Collapse**

A key study for understanding the Guatemalan growth collapse after 1975 is Rodrik (1999). His core idea is that the effect of the external shocks on growth are increased within the context of 'social conflict' and weak institutions for 'conflict management.' The term social conflict refers to the depth of social inequality and ethic fragmentation. Conflict management refers to democratic institutions, an effective judiciary and a non-corrupt bureaucracy. All of these adjudicate distributional competition within a framework of rules and accepted procedures. However, as in the case of Guatemala, the economic costs of shocks can be magnified by the associated distributional conflicts. These are triggered because social divisions run deep and governmental as well as democratic institutions are weak. Consequently, the productivity of resource utilization can be diminished in a number of ways. For example, by delaying adjustments in fiscal policies and key relative prices, including the real exchange rate and real wages. In addition, these adjustments may generate uncertainty in the economic environment and paralyze the economy for years. Cross-country econometric evidence supports this hypothesis. Rodrik finds that countries experiencing the sharpest drops after 1975 were those with divided societies and weak institutions. This seems indeed to be the case for Guatemala, and is an important finding not only in retrospect but also for the future.

*External shocks and the civil war, 1975-1985.* A second period starts shortly after the deterioration of the terms of trade and the international oil crisis. In 1976 a major earthquake affected Guatemala. After 1977, social tension culminated in a full-scale civil war that reached genocidal proportions in the early 1980s.

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5 An excellent review of the rise and fall of the Central American integration process for 1950-1999 can be found in de La Ossa (2000).

Consequently, growth declined dramatically. Apart from causing immense human sorrow, these events destroyed human life and physical capital. They also imposed high costs for long-run growth.

*Recuperation and stagnation, 1985-2002.* A third episode of growth begins approximately in 1985 when democracy was restored, albeit with civilian governments patronized by the generals. Although growth rates recovered, they have ever since followed a more or less stagnant pattern. A cornerstone in economic and social development in history was the signing of the Agreement of a 'Firm and Lasting Peace' in December 1996, the formal end to the civil war. Since the signing of the UN-sponsored Peace Accords, Guatemala has made progress by increasing investments in infrastructure and human capital. It has also made some efforts to improve public financial management, and in the area of tax revenues. However, UNDP (2003a) finds that the implementation of the Peace Accords has been uneven. Moreover, in particular during the past decades, Guatemala seems to be affected by electoral cycles. This issue has been investigated by Lopez-Calix (2002) who indeed finds weak empirical evidence supporting this hypothesis.

**Table 1. Guatemala: Sectoral Output Growth, 1951-2003** (in percent) *a1*

Source: Author's calculations based on data from *Banco de Guatemala.*

a/ Information for 2002 (2003) is preliminary (estimated).

Finally, GDP growth has declined continually since 1999. The processes behind this decline are not exactly understood. It is uncertain whether this represents a decrease in Guatemala's trend growth or a prolonged cyclical downturn. However, it is not unreasonable to argue that this decline is partly associated with high levels of violence, kidnappings (including the central bank governor) and social unrest. In addition, Guatemala scores poorly on most governance indicators, particularly those for corruption, the rule of law and the justice system, and political stability. The culmination of these factors ultimately seems to damage the climate for growth and investment.6

Somewhat paradoxical, over the past decades, Guatemala has experienced relative macroeconomic stability. Guatemala has a rather low level of external indebtedness, inflation has been held back, and after a process of (uncompleted) structural reforms the economy is now fairly open and with low levels of protection. Thus, contrary to other Latin American countries, macroeconomic mismanagement may presumably not be regarded as the main factor to understand Guatemala's modest performance in terms of per capita growth. Rather, other issues undermine Guatemala's long-run growth patterns.7 In addition to the factors already mentioned, one is low human capital endowment.

The current human capital base is essentially a product of past agricultural growth and eminently anti-distributional policies. The World Bank (2003a) and UNDP (2002) document that insufficient cheap labor, in particular for coffee, was the main barrier for the expansion of export crops during earlier periods. Hence, in order to create a low-wage labor force, the campesino and indigenous society was excluded from education. The plantation economy that resulted provided little incentives to accumulate human capital. Historically, the low level of schooling is also an outcome of a discriminatory education system. For the attentive observer, these issues are still felt today.

6 Hypotheses for the recent growth slowdown can be found in World Bank (2003b). These include restrictive macroeconomic policies, unfavorable external developments, the ending of the economic model relying on traditional agro-exports, and several political factors. As of June 2000, Guatemala is listed as noncooperative country in the OECD-backed 'Financial Action Task Force on Money Laundering.' Equally, fearing high levels of corruption and fraud, for example, the German Chamber of Commerce does not recommend investment in Guatemala.

7 During a very brief episode in the early 1990s, inflation increased and fiscal discipline eroded. More recently, the World Bank (2003b) presents arguments suggesting that short-run growth *may* be related to the cyclical stance of fiscal and monetary policies.

#### **Table 2. Guatemala, Central and Latin America: Comparison of Human Capital Indicators, 1998-2002**

Source: a/ World Bank (2003c). *bl* Cohen and Soto (2001). c/ UNDP (2003b). *di* Notice that Guatemala's public spending in education has increased recently. UNDP (2003a) reports a figure of2.6 percent in 2002. N.D. = no data available.

Table 2 shows that the country still performs poorly for indicators of education and health, and ranks highest among states in the region for child malnutrition, despite some improvements over time. 8 In addition, Guatemala spends less on education than any other country in the region. Based on household survey data comparing the education level of age cohorts, the Inter-American Development

8 Anderson (2001) provides a brief synopsis of recent developments in the education sector. The recent improvement of the education sector will be focussed in the 3rd part of this study.

Bank (2001) finds that the educational gap between Guatemala and other Latin American countries is widening.

Historically, it may be that a certain degree of development and growth in Guatemala was attainable with a skilled elite and a large amount of unskilled workers. Since the economy has diversified over time and is now less dependent on agriculture than before (Segovia and Larde 2002), the past exclusionary education policies may present an obstacle for future growth. On the micro level, there is evidence suggesting that insufficient human capital constitutes a constraint for production. For example, a firm survey by *Grupo de Servicios de Informaci6n*  ( 1999) indicates that for all firms the quality of skills ranks as the second most important constraint. For small firms, important for employment and income generation, the quality of skills is the main production constraint.

#### **III. Measuring the Contribution of Education to Growth**

The accumulation of human capital through education has long been acknowledged to be an important factor in the development process of a nation. Education is thought to be beneficial because it decreases inequality, improves the quality of life, and in particular it is a factor in rising the income level and facilitating economic growth. This chapter will concentrate on the latter effect and summarize some evidence on the relationship between education and growth.

#### **A. Augmented Solow Model and Endogenous Growth**

The existing literature contains a number of distinct conceptual rationales for the inclusion of human capital in models of economic growth. According to Sianesi and van Reenen (2003), the two main macro approaches are the augmented Solow model and the new growth theories.

#### *1. Augmented Solow Model*

One way to estimate the impact of education on growth is to adapt the Solow (1956) model. The augmented version extends the basic framework to allow human capital as an extra input to enter the production function. In particular Mankiw et al. ( 1992) show that traditional growth theory can accommodate human capital and provide a reasonable approximation for empirical analysis. At the economy-wide level, it may also take into account human capital externalities. Still, one of the key insights is that the factor accumulation affects the *level* of income, but per se is insufficient to achieve long-run *growth.* Long-run growth depends rather on growth in technological progress. Human capital accumulation may therefore have only a short-term impact on the rate of growth.

However, rates of accumulation are expected to have explanatory power for growth rates during the transition to an eventual equilibrium growth path. In particular, considering the case of Guatemala - presumably far away from a balanced growth process - consideration of transition could open up the possibility of assessing the macroeconomic role of education for economic growth within this framework. In addition, since the 'short run' in the context of growth theory is often thought of in terms of decades, these effects can be worthwhile policy objectives. Up to now, for the reasons clarified below, this approach has remained the workhorse of applied empirical research. The model is fairly flexible and allows for alternative specifications that can be adjusted to best match the available data.

#### *2. Endogenous Growth Approach*

Expanding these ideas, new growth theories emphasize the endogenous determination of technological progress, which is determined within the model.

Thus, long-run growth can be affected by government policies instead of being driven by exogenous technological change. With respect to human capital, the endogenous growth approach argues that there should be an *additional* effect over and above the static effect on the level of output. Models that explain long-run growth by focussing on technological progress and research and development, such as Romer (1990a) and Grossman and Helpman (199 l ), argue that domestic technological progress results from the search for innovations. The discovery of an innovation, undertaken by profit-maximizing individuals, raises productivity and is ultimately the source of long-run growth. This kind of model attributes growth to the existing *stock* of human capital. A second category is the model of Lucas (1988). It broadens the concept of capital and suggests that human capital *accumulation* may be an engine of growth itself, due to spillover effects that negate diminishing returns in production.

In particular, with respect to developing countries, one way of characterizing the role of human capital is the consideration of technology transfer from innovating countries. Already Nelson and Phelps (1966) suggested that education facilitates the adoption and implementation of new technologies, which are continuously invented. For example, countries with lagging technological capacity may be most able to catch-up if they have a large stock of human capital. In this case, the level of human capital effects growth by facilitating improvements in productivity. Also Lucas (1990) conjectures that physical capital does not flow from rich to poor countries because of a relatively low stock of complementary human capital.

In a rather influential study, Benhabib and Spiegel (1994) propose an empirical growth model in which human capital externalities can be considered in subsequent advances in education and in new physical capital via technology import. Their results indeed suggest that human capital impacts growth through two mechanisms. On the one side, human capital seems to influence the rate of domestically produced innovation, as proposed in the endogenous growth model of Romer (1990a). On the other side, in the spirit of Nelson and Phelps (1966), they claim that the human capital stock effects the speed of adoption of technology from abroad. More recently, in a generalized version of their model of technology diffusion - that allows for a nonlinear specification of total factor productivity growth - Benhabib and Spiegel (2003) find that a minimum initial human capital level is necessary to exhibit catch-up in productivity relative to the leader nation.

However, Pritchett (2001) agues convincingly that the finding of *only* a level effect on growth is rather puzzling. First, in the framework of endogenous growth, spillover effects of knowledge should be *in addition* to rather *instead* of the production effects of human capital. In other words, finding only spillover effects may be inconsistent with the micro evidence on the returns to education. Second, as will be stressed in more detail in the next section, Jones ( 1995) cnttc1sm of endogenous growth models applies here. That is, growth rates cannot be made a function of non-stationary parameters unless cointegration between the variables is accepted.

#### **B. Some Implications for Empirical Testing**

Distinguishing between the role of education as a factor of production, and as a factor that facilitates technology absorption and the production of knowledge, is significant. Any policy measure which raises the level of human capital may only have a one-and-for-all effect in the first framework, but will increase the growth rate of the economy for ever in the second one. In such cases, the estimated increase in productivity is not simply a phenomenon in the transitional period since an increase in the flow of education leads to a gradual increase in human capital stock. Implicit is the claim that by increasing the level of education the rate of economic growth will increase over time. Empirically, however, there is no consensus over which is the appropriate approach.

#### *1. Observational Equivalence*

A main problem for empirical testing at the macro level emerges from observational equivalence. This means that, despite a number of different ways of hypothesizing how human capital can affect growth, empirical analysis can yield similar predictions regarding the relationship between some human capital variables and some variables of income growth. In other words, apart from data uncertainty, the empirical research seeking to test these alternatives has been hampered by the use of relatively similar econometric specifications. Insofar, macro regressions do not readily allow testing one theory against another. Rather they tend to emphasize an expanded set of variables as suggested by the literature. Consequently, Romer (1990b) argues that the role of an endogenous growth framework is not to generate testable predictions, but rather to guide the process of data analysis.

#### *2. The Jones Critique*

A second criticism, especially relevant for the present study, is the seminal contribution of Jones (1995). Testing endogenous growth models in the context of time series implies establishing a relationship between a variable that is usually stationary - without drift - such as income growth, and a variable which is usually non-stationary, such as years of schooling. In other words, his results fundamentally call into question the implicit prediction of many endogenous growth models suggesting output growth should exhibit large permanent increases.

Time series data over a very long time period for the United States and other OECD countries reveal that the growth rates of GDP per capita in these countries exhibit little persistent changes, and can be characterized by more or less constant mean.

This observation imposes a testable prediction. According to endogenous growth models permanent changes in certain policy variables, such as schooling, or the number of scientists and engineers engaged in research and development, should have *permanent* effects on the rate of economic growth. Empirically, however, neither in the United States nor in other OECD countries does economic growth seem to exhibit such an effect. Incidentally, albeit for different reasons than in the OECD countries, these stationarity properties seem to be equally true for schooling and income growth in the Guatemalan data, as demonstrated in the Augmented Dickey-Fuller (ADF) tests in Appendix One.

#### **C. More Evidence on Education and Growth**

Empirical studies usually take the form of regression analysis and typically look at many more explanatory variables than human capital. A large number of papers have found one or more variables that correlate with growth. In fact, their number is very large and the question arises which combinations of these variables are actually robust. In the context of the present study, some of these findings will be outlined next.

#### *1. Weak Correlations*

While there is strong theoretical support for a key role of human capital in growth, Sala-i-Martin (2002), Easterly (2001) and in particularly Pritchett (2001) argue that the empirical relationship between education and growth is weak. 9 However, more specifically, Temple (2001) points out that fragile correlations in cross-country data may be due to measurement error and influential exceptions. Also, some kinds of relationships are more robust that others. For example, what is less clear and weak is the relationship of educational *growth rates* on output growth, the role of different education levels, and differences in effects of female and male education on growth. By contrast, some measures of health seem to be positively correlated with growth. In addition to human capital, many other factors have been found to be important for growth. Following Barro (2001), these include

9 Pritchett (2001) uses measures of the *growth* rate of human capital and finds a *negative* impact on output growth. Easterly (2001) argues that human capital accumulation is not a panacea. He emphasizes indirect ways that explain technological progress and factor accumulation by looking at the features of economies that facilitate them, such as government policies and structural issues.

institutions, such as free markets, secure property rights and the rule of law. Similarly, more open economies and countries with lower initial inequality appear to experience higher growth.

#### *2. Conditional Convergence*

One much debated prediction of neoclassical growth models is that of convergence. Poor countries should grow relatively faster than rich countries if countries are similar with respect to their structural parameters for preferences and technology. The cross-country studies by Mankiw et al. (1992), Barro and Sala-i-Martin (1995) and Barro (2001) find some evidence of convergence, albeit in a modified form. More specifically, among other things, convergence is found conditional upon a country's initial human capital stock. Therefore, a poor country on average may grow faster, but only if the poor country's human capital stock is above the amount initially expected at the level of per capita income.

#### *3. Reverse Causality*

Most of the evidence of some sort of relationship between education and growth is based on statistical *correlations.* From these correlations, it has been generally inferred that higher levels of education cause higher growth. One critique of these findings comes from Bils and KJenow (2000) who suggest reverse causation. Based on a calibrated micro-foundation model, they claim that faster growth induces people to stay longer in school. In other words, the channel from schooling to growth that is assumed to dominate in many models cannot explain all the observed correlation between education and growth. However, the reverse channel provides some explanation. Therefore, in an econometric framework, schooling should be treated as an endogenous input with respect to income. This implies making use of econometric methods for dealing with this problem.

#### *4. Few Individual Case Studies*

Recent research has mainly relied on cross-country regression analysis. However, the original motivation of studying economic growth focuses on the time-series dynamics of macroeconomic variables. In addition, the cross-section focus may be inadequate if rates of return to education or the quality of education differ substantially across countries. Unfortunately, with respect to human capital, there are very few studies that analyze a single country over a certain time period.

The exception is a study from Jenkins (1995) using time series data from 1971- 1992 for the United Kingdom. Still, the limited size of her time series sample makes it difficult to draw firm conclusions that can be generalized. Also Pissarides (2000) summarizes single case studies for India, Egypt, Tanzania and Chile. Part of

an OECD project, these studies were to provide a more thorough test of the relation between human capital and growth in a single country context. For the case of India, the study less plagued with methodological or data problems, the regressions show a significant contribution of human capital on industrial output growth. The estimate suggests that an increase in the average number of years of schooling by 1 year should raise output by about 30 percent.

#### 5. *Magnitude of the Education Effect*

In the augmented Solow model, the role of education can be inferred from estimates of the regression coefficients. However, with reference to the empirical research reviewed in Sianesi and Van Reenen (2003), there is no agreement on its magnitude. In principle, there would be positive empirical evidence in favor of a macroeconomic productivity effect of education if the elasticity of human capital resembles the share of human capital in factor income. As a measure of reference, one can calculate the share of human capital in labor income from back-of-theenvelope calculations.

For example, Mankiw et al. ( 1992) consider the minimum wage as the return to labor with no education. Historically, the minimum wage has been between 30 to 50 percent of average wage income in the United States. On this account, it would follow that the return to education equals about 50 to 70 percent in labor income, which is about 70 percent of total factor income. Obviously, the problem with this kind of calculation is that in developing countries the minimum wage is less enforced and less likely applicable.1° Pritchett (2001) therefore uses an estimation based on the distribution of wages. Either of these calculations suggest that the human capital coefficient should be at least 1 / 3•

#### *6. Effects of Education Levels*

Somewhat surprisingly, relatively few studies at the macro level address the question of level-specific education effects. The view that schooling does not have the same impact on economic growth at different education levels is based on the labor economics literature. Psacharopoulos and Patrinos (2002) provide a comprehensive review on the rates of return to education. International evidence suggests that returns vary according to the education level. Lower income countries tend to have higher returns to schooling. If education has economic externalities -

10 In Guatemala, the legal minimum wage currently amounts to approximately 3-5 U.S. dollars per day (UNDP 2003a). While the legal minimum wages are relatively high with respect to average wages, about 1/ 2 of workers in Guatemala earn less than the legal minimum wage. This is because of weak enforcement and the fact that selfemployed workers are not subject to the minimum wage regulation.

such as expanding well-being and the technological possibilities of the economy the true benefits of education may be better captured by the study of different education levels on economic growth. This is because the computation of rates of returns based on microdata can only measure the effects of education through individual's wages. However, this might not hold in macro analysis.

Within an endogenous growth framework one can also derive a distinct role for each education level. The intuition here is that primary education provides individuals with basic cognitive skills that enhance productivity in the production of final goods, but only post-primary education facilitates the absorption of new technologies, and enables individuals to contribute to the production of knowledge. Empirically, in the framework of the augmented Solow model, treating each education level as a separate input into production can quantify the role of primary, secondary and tertiary schooling. While the standard approach in the literature is to consider an aggregate measure of human capital, there are some exceptions that will be briefly reviewed now.

Barro and Sala-i-Martin (1995) regress the growth rate of GDP per capita for a large sample of countries on initial income and a set of control variables. Four measures of educational attainment are always present. These are average years of male secondary and higher schooling as well as average years of female secondary and higher schooling. The male education variables have a jointly significant impact on growth. The female variables enter sometimes with a negative sign. One possible interpretation, advocated by Barro, is that females are discriminated in the formal labor markets. Another explanation for this rather 'puzzling' finding could be simply due to collinearity of the education variables. 11 Other regressions include average years of female and male primary education. None of these variables are found to be significant. Barro (200 l) has continued to investigate the relations between education and growth using the same methodology. An important finding here is that school *quality* is much more important to growth than its *quantity.*  Overall, the studies do not make very clear the effect of education levels on growth given the negative contribution of secondary female schooling, and the insignificant result for primary education.

11 Klasen (2002) argues that the education variables are generally correlated. Empirically, this makes it difficult to identify individual effects of female and male education. However, the negative effect for female secondary education disappears once regional dummy variables are incorporated into econometric models. This finding may be due to East Asia's large initial gender gaps in the 1960s, and the combination of low economic growth and comparatively lower gender gaps in Latin America.

Another paper that investigates the link between education levels and growth is Petrakis and Stamatakis (2002). In a cross-country regression with a relatively small sample size they consider three groups of countries: advanced, developed and less developed. The empirical results suggest that the link of education and growth varies with respect to a country's level of development. Primary education is more important in less developed countries, while higher education seems dominant in advanced countries. In fact, there is some similarity with Gemmel ( 1996) who also distinguishes between primary, secondary and tertiary schooling for these three groups of countries. He argues that the effects of human capital on growth are most apparent at the primary and secondary levels in developing countries, but at the tertiary level for OECD countries. Unfortunately, the findings in both studies do not allow one to assess with certainty the role of secondary education. In fact, it sometimes enters with a negative sign.

Finally, based on a framework similar to Benhabib and Spiegel, Papageorgiou (2003) is also concerned to empirically determine the contribution of primary and post-primary education on growth. In a cross-country regression he finds that primary education contributes mainly to the production of final output, whereas post-primary education contributes to the adoption and innovation of technology. When the data is divided into subsamples, the results are less encouraging. However, the implicit claim is that for the poorest countries human capital acts mainly as input into final production and, to a lesser extent, as a facilitator for innovation. The relative contribution of human capital to innovation seems to increase with country wealth. Overall this is an interesting study. Nevertheless, the analysis ignores the Jones (1995) critique, and the conclusions are ultimately derived from a priori assumptions.

#### **D. Summing-Up**

Empirical results often do not allow for a clear-cut measurement of the macroeconomic role of education on growth, and theory seems to be much ahead of empirics. Cross-country evidence suggests that the relative importance of education level varies by the degree of a country's development. Results that come close to a priori expectation of the magnitude of human capital on growth seem to share three properties. First, a specification of the underlying regression that is based on a production function. Second, in particular regarding human capital, empirical data of reasonable quality. And finally, a functional form of the regression equation that tends to reduce econometric problems.

Attempts to measure empirically the impact of education on growth can be divided into two broad categories. The augmented Solow model originates the first class, while the second group is inspired by an endogenous growth approach. However, this is rather a conceptual framework for thinking about growth, which can be useful in the analysis of data, but does not generate a set of easily testable equations nor sharp quantitative predictions. In the light of observational equivalence and given the problems associated with testing endogenous growth models in a time series context, the following analysis will be based on a production function augmented for human capital. Nevertheless, some attention will be given to variables that proxy for trade openness and technological innovation, and their joint impact on education.

#### **IV. Data Compilation in a Post-Conflict Country**

Guatemala is definitely deficient in easily accessible data. Thus, to identify the macroeconomic impact of education on economic growth, a primary task is to overcome information constraints. It is important to note that a significant fraction of the economic activity in Guatemala can be found in the informal sectors. Since this lack of documentation does not influence all factors equally, there remains a potential bias that cannot always be traced.

However, satisfactory and coherent results can be obtained. A sizable amount of information, although not easily accessible, can be compiled from disperse or bulky individual files. Even for local experts, this is a challenging task. The lack of a consistent compilation of data to allow a serious analysis of growth patterns hampers inter-temporal comparisons and, more generally, research of development patterns for the country. Given these constraints, so far, there is very limited empirical research on virtually any macroeconomic topic in Guatemala.

The following paragraphs describe the data needed for the analysis that follows. These are measures for the human and physical capital stock and the labor force, and quality indices for human and physical capital. Information other than that reported in this chapter is listed in Appendix one. The time series are mainly from *Banco de Guatemala,* and, in the case of educational statistics, from the Ministry of Education and the United Nations Educational, Scientific and Cultural Organization.

#### **A. Human Capital Stock**

The human capital stock of Guatemala is defined by average years of schooling evident in the labor force. 12In line with most empirical analyses, this study assumes that years of schooling provides a reasonable approximation of the human capital stock, although it should be briefly stressed that the indicator is incomplete for several reasons.

*(1) Education as proxy variable.* Human capital is multifaceted and includes a complex set of human attributes. As a consequence, the genuine level of human capital is hard to measure in quantitative form. At best, average years of schooling can be regarded as a proxy for the component of the human capital stock obtained in schools. Therefore, in a later robustness test, life expectancy at birth will be

12 The use of labor force instead of total population data is due to problems regarding the Guatemalan population data for the 1980s. By contrast, the labor force proxy used here is assumed to take into account some of the effects of the civil war, i.e. migration and displacement.

included in the regressions. Life expectancy is commonly viewed as a companion indicator to educational capital that captures the effect of health.

*(2) Quality changes.* Average years of schooling measurements do not take into account quality changes within the education system. Quality changes may complicate comparison of schooling effects on growth over time as well as making comparisons with other countries difficult. CIEN (2002) and the World Bank ( 1995c) argue that the quality of the education system in Guatemala is rather low. Unfortunately, in terms of data availability, it proves impossible to include quality changes of education in this study.

*(3) Aggregation bias.* Average years of schooling raise human capital by an equal amount regardless of whether a person is enrolled in a primary, secondary or tertiary school. This is an important point because by defining human capital by average years of schooling, one implicitly gives the same weight to any year of schooling acquired by a person. This completely disregards the findings of the microeconomic literature on wage differentials. For example, Psacharopoulos and Patrinos (2002) suggests that the rates of return to education could be decreasing with the acquisition of additional schooling. Therefore, in order to capture the impact of education on growth better, a more complete picture will be presented by analyzing the role of primary, secondary and tertiary schooling.

After making some modifications to account for the statistical circumstances in Guatemala, the following procedure for constructing estimates of the human capital stock is used, based on the attainment census method advocated by Barro and Lee (2001 ). The use of a perpetual inventory method that employs census and survey information on educational attainment as benchmark figure can be seen as a major advantage over previous methodologies. The benchmarks are taken from various national censuses and surveys, see Table 3. Guatemalan statistics report distributional attainment stratified by age and sex in five cases: no formal education, first cycle of primary, second cycle of primary, first cycle of secondary, second cycle of primary and tertiary education. The data has been summarized into 4 broad categories, that is, no school, some primary, some secondary and some tertiary education.

The procedure starts to construct current flows of adult population, which are added to the initial benchmark stocks of the labor force (taken for 1950 from the Barro and Lee 2001 data set). The formulas for the three levels of schooling for the labor force aged 15 and over are as follows:

$$\begin{array}{cc} \text{(I)} & \mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\prime$$

$$\text{(2)}\qquad\mathsf{HN}\_{\mathsf{I},\mathsf{t}}=\mathsf{HN}\_{\mathsf{I},\mathsf{t}-\mathsf{1}}\cdot\langle\mathsf{1}-\mathsf{S}\_{\mathsf{t}}\rangle+\mathsf{L}\mathsf{1}\mathsf{S}\_{\mathsf{t}}\cdot\langle\mathsf{PRI}\_{\mathsf{t}-\mathsf{1}}-\mathsf{S}\mathsf{EC}\_{\mathsf{t}}\rangle$$

$$\text{(\textbf{3})}\qquad\mathsf{\mathsf{HN}}\_{\text{2,t}} = \mathsf{\mathsf{HN}}\_{\text{2,t-1}} \cdot \left(\mathsf{1} - \delta\_{\text{t}}\right) + \mathsf{L15}\_{\text{t}} \cdot \mathsf{SEC}\_{\text{t}} - \mathsf{L20}\_{\text{t}} \cdot \mathsf{TEC}\_{\text{t}}.$$

$$\begin{array}{cc} \text{(4)} & \mathsf{HN}\_{\mathsf{3},t} = \mathsf{HN}\_{\mathsf{3},t-1} \cdot \left(\mathsf{1}-\mathsf{S}\_{t}\right) + \mathsf{L}\mathsf{2O}\_{t} \cdot \mathsf{T}\mathsf{ES}\_{t-1} \end{array}$$

where

	- **L** = number of the economically active population
	- 0.,,1 = mortality rate of the human capital stock.

The mortality rate for the economically active population aged 15 and over is estimated from:

$$(\mathsf{S})\_{\mathsf{t}\leftarrow\mathsf{t}} = \frac{\mathsf{L}\_{\mathsf{t}\leftarrow\mathsf{t}} - (\mathsf{L}\_{\mathsf{t}} - \mathsf{L}\mathsf{1}\mathsf{S}\_{\mathsf{t}})}{\mathsf{L}\_{\mathsf{t}\leftarrow\mathsf{1}}}$$

and assumes that the mortality rate is independent of the level of schooling attained, which is not entirely correct. The term Li-L 151 describes the number of survivals from the previous period, which are subtracted from Li. 1in order to estimate the total number of missing persons. Equation (5) as such describes the proportion of the labor force which did not survive from the previous period. The formulas can be rearranged to create the final equations that were used to generate the attainment ratios, hrj, for the four broad levels of schooling for the economically active population aged 15 and over:

$$\text{(6)}\qquad\hbar\mathbf{r}\_{\text{0,t}} = \frac{\mathsf{H}\mathsf{N}\_{\text{0,t}}}{\mathsf{L}\_{\text{t}}} = \hbar\mathbf{r}\_{\text{0,t-1}} \cdot \left(\mathbf{1} - \frac{\mathsf{L}\mathsf{L}\mathsf{S}\_{\text{t}}}{\mathsf{L}\_{\text{t}}}\right) + \frac{\mathsf{L}\mathsf{L}\mathsf{S}\_{\text{t}}}{\mathsf{L}\_{\text{t}}} \cdot \left(\mathbf{1} - \mathsf{P}\mathsf{R}\mathsf{L}\_{\text{t-1}}\right) \tag{6}$$

$$\text{(17)}\qquad\hbar\mathbf{r}\_{\mathbf{i},\mathbf{t}}=\frac{\mathsf{H}\mathsf{N}\_{\mathbf{i},\mathbf{t}}}{\mathsf{L}\_{\mathbf{t}}}=\hbar\mathbf{r}\_{\mathbf{i},\mathbf{t}-1}\cdot\left(\mathbf{1}-\frac{\mathsf{L}\mathsf{L}\mathsf{S}\_{\mathbf{t}}}{\mathsf{L}\_{\mathbf{t}}}\right)+\frac{\mathsf{L}\mathsf{L}\mathsf{S}\_{\mathbf{t}}}{\mathsf{L}\_{\mathbf{t}}}\cdot\left\{\mathsf{PRI}\_{\mathbf{t}-1}-\mathsf{S}\mathsf{B}\mathsf{C}\_{\mathbf{t}}\right\}\right)$$

$$\text{(8)}\qquad\hbar\mathbf{r}\_{2,\text{t}}=\frac{\mathsf{H}\mathsf{N}\_{2,\text{t}}}{\mathsf{L}\_{\text{t}}}=\hbar\mathsf{r}\_{2,\text{t}-1}\cdot\left(\mathbf{1}-\frac{\mathsf{L}\mathsf{L}\mathsf{S}\_{\text{t}}}{\mathsf{L}\_{\text{t}}}\right)+\frac{\mathsf{L}\mathsf{L}\mathsf{S}\_{\text{t}}}{\mathsf{L}\_{\text{t}}}\cdot\mathsf{S}\mathsf{E}\mathsf{C}\_{\text{t}}-\frac{\mathsf{L}\mathsf{L}\mathsf{0}\_{\text{t}}}{\mathsf{L}\_{\text{t}}}\cdot\mathsf{T}\mathsf{E}\mathsf{R}\_{\text{t}}\,.$$

Data Compilation in a Post-Conflict Country 27

$$\text{L(\Theta)} \qquad \mathsf{htr}\_{\mathsf{3},\mathsf{t}} = \frac{\mathsf{HN}\_{\mathsf{3},\mathsf{t}}}{\mathsf{L}\_{\mathsf{t}}} = \mathsf{htr}\_{\mathsf{3},\mathsf{t}-\mathsf{1}} \cdot \left(\mathbf{1} - \frac{\mathsf{L}\mathsf{1}\mathsf{S}\_{\mathsf{t}}}{\mathsf{L}\_{\mathsf{t}}}\right) + \frac{\mathsf{L}\mathsf{2}\mathsf{O}\_{\mathsf{t}}}{\mathsf{L}\_{\mathsf{t}}} \cdot \mathsf{T}\mathsf{ER}\_{\mathsf{t}}.$$

The procedure requires school enrollment ratios that are crucial for exact calculations, but the proper accounting for Guatemala is not easy. Even though net enrollment ratios would be more precise for estimating the accumulation of human capital, gross enrollment ratios are used, as only this data is available. As reported in Appendix One, the ratios are taken from various yearbooks of the Guatemalan Ministry of Education (MINEDUC) for the 1990s, the United Nations Educational, Scientific and Cultural Organization (UNESCO) for earlier periods, and other sources available for Guatemala. The data for primary, secondary and tertiary enrollment ratios have been found consistent over time. Interpolation techniques were used to fill gaps in the data, but the use of this approach was kept to a minimum. The tertiary enrollment time series were more difficult to compile and required greater use of interpolated estimates.

**Table 3. Guatemala: Education Level of Labor Force, 1950-2002** (in percent) *a1*

Source: Compiled from census and survey data, ENCOVI and ENEI figures are from UNDP Guatemala. a/ Brackets indicate uncertain figures. Discrepancies are due to rounding.

In general, the estimated attainment data compares favorably with the census and survey information. The less accurate fit for 1981 is here believed to be due to large measurement errors or the possible manipulation of the census, which took place during the peak of the armed conflict in Guatemala. Consequently, this discrepancy was not smoothed over. Equally, data for 1998 differs slightly from the estimate. This is due to the fact that the survey largely oversamples the urban population of the economy in that year. Given the simplicity of the assumptions of the underlying model, however, the overall results have been found quite satisfactory.

In any case, simply employing gross enrollment ratios would overestimate the accumulation of human capital. Gross enrollment ratios are defined as the ratio of total enrollment in the respective schooling level to the population of the age group that is expected to be enrolled at that level. Thus, gross enrollment ratios can exceed I and therefore exaggerate the true amount of enrollment when students repeat, which is often the case in Guatemala.13 In response to this problem and in order to benchmark the estimated educational attainment data with census and survey information, the gross enrollment ratios have been adjusted by a depreciation factor for the respective education level, as reported in Loening (2002).

Finally, the formula to construct the measure for the human capital stock combines the estimated attainment data with the information on the duration of each schooling level. It is given as:

$$(10) \qquad \mathsf{h}\_{\mathsf{t}} = \sum\_{\mathsf{j=1}}^{3} \mathsf{h} \mathsf{r}\_{\mathsf{j},\mathsf{t}} \cdot \mathsf{d}\_{\mathsf{j},\mathsf{t}}$$

where h1 stands for the average years of schooling, hrj is the estimated attainment ratio of the labor force and dj is the average number of years of education received in the respective schooling level j. Average education values have been calculated from the *Encuesta Naciona/ Socio-Demograjica* (ENS) from 1989 and are assumed to have remained constant over time. This may result in a slight overestimate of the human capital stock for the period prior to 1989 and underestimate the average years of schooling for later periods. However, data from more recent household surveys suggest that this assumption may not be a large source of error.

How do these calculations compare to other sources? The correlation coefficients between the estimated average years of schooling here and those provided by Cohen and Soto (2002), Barro and Lee (2001), and Nehru et al. (1995), using different techniques and data sources, all exceed 0.95 in the case of Guatemala. Figure 2 compares the results. The time series shown by the solid line harmonizes to a large extent with alternative estimates at different points of time.

13 The use of net enrollment ratios is hampered by large data gaps. Also, net enrollment ratios introduce large measurement errors if there are under- or overaged children starting at each level of education, see Barro and Lee (2001). In Guatemala students who start late constitute a significant fraction of total enrollment - in particular for primary schooling.

Unlike the Barro and Lee data set, there is no implausible jump for 1980. The Cohen and Soto (2002) estimate provides the closest approximation. Additionally, not shown by Figure 2, the average years of schooling estimates here come close to values obtained from census and survey data. For example, Psacharopoulos and Arriagada (1986) report that mean education in the labor force was in the order of 1.7 for 1964. Edwards (2002) reports a value of 4.3 years for 2000.14

**Figure 2. Guatemala: Average Years of Schooling in Labor Force, 1950-2002**

Source: Author's calculations, as well as Barro and Lee (2001), Cohen and Soto (2001), and Nehru et al. (1995) education data.

A closer look at Figure 2 yields two important descriptive outcomes. First, the data suggests that mean education evident in the labor force slightly declined during the early 1990s. This outcome is associated with the disastrous effect of the civil war on the country's human capital base. Those disadvantaged cohorts from the 1980s entered later into the labor force. Second, there has been substantial increase in the average years of schooling within the economically active population since 1998. This can be attributed to improvements within the education system and increased attention to education after the signing of the 1996 Peace Accords.

14 According to the estimate here, average years of schooling was in the order of 1.86 years in 1964 and 4.63 in 2000. See Appendix One.

Even so, as it can be appreciated from Figure 2, this increased attention to education only has compensated for the loss of educational capital caused by civil strife. Consequently, recent educational progress does not represent a major improvement regarding the long-run growth of the country's human capital base. In this context, it is worth recalling that educational attainment in Guatemala remains lowest compared to other Latin American countries.

#### **B. Labor Force**

The measure of labor quantity here is the economically active population. For Guatemala there are several estimates. The National Statistic Institute (INE) provides calculations different from those of the Ministry of Work, both of which date back to 1980. Based on census and survey data, estimates for selected years have also been provided by the United Nations Development Programme (UNDP) for Guatemala. The labor force is usually defined as the working and job-seeking population, but the different calculations do not always reveal what underlies the specific assumptions and age definitions used for calculations. To develop a consistent time series of the economically active population, the International Labor Organisation (ILO) has used information on age specific labor force participation rates and population statistics. Unfortunately, for the reasons clarified below, these estimates are unreliable.

*(]) Data discrepancies.* First, there is no agreement either on the level or on the growth rates of the labor force. Virtually all data is different from each other. For example, UNDP (2003a) reports a total labor force estimate of about 2.84 million for 1989, as compared to 2.54 million from INE or 2.95 million from ILO. Second, as typical for estimates in other countries, labor force data should show some cyclical fluctuations as labor responds to higher output growth. Official estimates for Guatemala, however, are remarkably free of *any* fluctuations and follow a monotonous trend. This suggests reliance on population statistics or use of interpolation techniques.

*(2) Omission of the civil strife.* Most importantly, these estimates do not take into account migration flows and the consequences of the civil war on the economically active population. Especially the last point devalues official estimates. According to the Commission for Historical Clarification (1999), the internal military conflict left an estimated 200,000 civilians dead and another 1 million displaced, for a total population of about 10 million. Such an immense impact of the civil strife should be reflected somewhere in the statistics D but it is not.

In the absence of reliable information about the economically active population from these sources, labor is here proxied by the number of private contributors to the Guatemalan Social Security System (IGSS). The reliance on the number of private contributors to the Social Security System in order to account adequately for the economically active population is also adopted in an IMF study for the case of El Salvador by Morales ( 1998), and for Guatemala by Prera ( 1999). The numbers representing the labor force are calculated by assuming that the social security contributors account for approximately 25 percent of the total labor force. The participation rate has a negligible impact on the later calculations and is based on a historical mean value. 15

**Figure 3. Guatemala: Labor Force, 1950-2002** (millions of workers)

Source: Author's calculations based on *Banco de Guatemala* (2003), INE and ILO data.

Although a broad approach may limit the precision of calculations, the regressions in chapter 5 and 6 show that the variable has a high explanatory power on growth. Moreover, as can be seen from Figure 3, the estimated values give a more reasonable picture than the data from official sources. Notice that the *level* of the economically active population, but not its growth rate, is basically in line with ILO or INE calculations. In 1980s, when the civil war had already taken genocide

15 UNDP (2003a) reports a participation rate of 24.5 percent (2002). Based on INE data, as reported by Global Info Group (1999), this compares to 27.6 percent (1995), 29.9 percent (1990) and 28.2 percent (1985).

proportions, the labor force dropped dramatically by about 660,000.16 For recent years, the estimate for the economically active population derived from IGSS statistics comes close to INE data.

#### **C. Physical Capital Stock**

Internationally, the Perpetual Inventory Method **(PIM)** is a common way to estimate capital stock, but there are uncertainties associated with the calculation. In general, due to the lack of information about the initial capital stock, questionable validity of assumptions about the rate of depreciation, and lack of information about the utilization of capital, estimates should be taken with care. With these reservations in mind, the PIM was used to construct the physical capital stock for Guatemala. The following paragraphs present two distinct calculations, one with aggregated and another with disaggregated investment data.

#### *1. Estimate with Aggregated Investment Data*

The physical capital stock that is used throughout the subsequent analyses is computed using the PIM with aggregated investment data. The procedure argues that the stock of capital is the accumulation of the stream of past investments:

$$\begin{pmatrix} \mathbf{1} \ \mathbf{1} \end{pmatrix} \qquad \mathsf{K}\_{\mathbf{t}} = \mathsf{K}\_{\mathbf{t}-\mathbf{1}} \cdot \mathsf{(1} - \mathsf{\delta}\_{\mathsf{k}} \text{)} + \mathsf{I}\_{\mathbf{t}} \ \mathsf{k}$$

where K is the capital stock, I gross fixed capital formation, Oi<. the annual depreciation rate of the capital stock, and t an index for time. The initial value of the capital-output ratio for 1950 is taken from the Nehru and Dhareshwar (1993) data set. 17Information about gross fixed capital formation was provided directly by the Economic Research Department of the *Banco de Guatemala.* The data is compiled using the somewhat dated 1953 UN System of National Accounts, which is currently under revision. 18In line with other studies for Latin America, such as Loayza et al. (2002) and Morales (1998), the overall depreciation rate is assumed at

18 UNDP (2002) provides a brief summary of the associated empirical consequences and causes that prevented an actualization of the Guatemalan National Accounts.

16 It should be emphasized that the reliance on IGSS data may understate the drop of the economically active population during the 1980s. This is because the working population in the informal and rural sectors - typically not captured by the social security system - was particularly affected by violence and displacement policies.

17 The potential error of the estimate of initial capital stock diminishes over time due to depreciation. Based on international data, Nehru and Dhareshwar (1993) offer an estimate of the capital stock for Guatemala that was taken as a benchmark.

5 percent. This is still a rather high estimate when compared with more commonly used thumb values.

However, regarding the armed conflict, which has lasted for 36 years, and several periods of high violence in Guatemala, it was found useful to adopt a high depreciation rate in order to account for both capital *destruction* and *distraction*  from productive use. For example, the latter may have resulted in unprofitable military spending, several forms of non-productive investments, or temporary spare capital because of infrastructure deficiencies. As to be shown in the following chapter, the results of the regression analyses are not sensitive to moderate adjustments in the depreciation rate. In terms of data availability over a long time period, and given the robustness to alternative assumptions about depreciation, the capital stock series with aggregated investment data is adopted in the later regression analyses.

#### *2. Estimate with Disaggregated Investment Data.*

Based on the PIM, Moran and Valle (2002) present a second approach for Guatemala. In their model the capital stock is estimated for eight broad asset groups for 1971-2000. However, presumably because of too high depreciation rates for public and private construction, they seem to underestimate the genuine level of the capital stock. 19 Following their methodology but applying different depreciation rates and taking into account the initial benchmark estimate from Nehru and Dareshwar (1993), a second capital stock series has been calculated with disaggregated investment data for the period 1970-2002.

The initial values are obtained from a pre-estimate starting in 1950. The data gaps for the sectoral composition of the eight assets groups prior to 1970 are filled in by extrapolation techniques. These values, however, do *not* enter in the later regression or growth accounting exercise. They only provide reasonable initial values for the disaggregated capital stock. Table 4 presents the assumed average life service lines for each of these assets groups. The average service life for a given class of asset is considered to be identical for all kinds of economic activities. The service lives are arrived at by considering the nature of these asset groups, consulting experts, and a careful review of the average service lives used by other countries, as reported in OECD (2001b).

19 In addition, the following results of the quality index for the physical capital stock differ. This may be due to the possibility of an oversight in the logarithmic transformation by Moran and Valle (2002), as was pointed out in a personal communication with Estuardo Moran, *Banco de Guatemala,* October 15, 2003.

Source: Based on OECD (2001b) and expert consultation.

Based on average service life estimates, geometric depreciation rates are applied. With geometric depreciation, the market value in constant prices is assumed to decline at a constant rate within each period. The implicit depreciation factor for each asset group is set at a value that ensures that the initial value will have been reduced to 10 percent of the original value by the time it reaches the end of its expected service life. The main drawback of geometric depreciation is that it will never exhaust the full value of an asset. That is, the depreciated value of the asset falls asymptotically, approaching, but never reaching, zero. While the infinity problem is somewhat troublesome, geometric depreciation has the practical advantage of being suited better for benchmark estimates, such as in the present study.

#### **D. Quality Indices of Capital and Labor**

Based on the previous calculations, quality indices can be elaborated. The quality index of the labor force will only be used in the later growth accounting exercise since it already reflects improvements in human capital. However, the estimate for the quality of capital enters into the regressions. The following paragraphs are concerned with the construction of the indices for the quality of capital and labor, respectively, and a brief comparison over both indices for 1970- 2002. The capital and labor quality indices yield interesting outcomes.

#### *1. Quality of Capital*

One can calculate a quality index of capital by using the disaggregated capital stock data. The estimate follows the methodology advocated by Laurits et al.

( 1980) and Rold6s (1997). For the case of Guatemala, this means that changes in the index of quality of capital, zq, are computed as a weighted average of investment of the four broad asset groups. These are (1) public and private construction, (2) imported capital goods and investment in machinery and equipment, (3) domestically produced capital goods, and ( 4) cultivated assets and major improvements to land. The formula used is:

$$
\Delta(12) \qquad \Delta \mathsf{log}\mathsf{z}\mathsf{q}\_{\mathsf{t}} = \sum\_{l=1}^{4} \mathsf{v}\_{\mathsf{t},\mathsf{t}} \cdot \left< \Delta \mathsf{log}\mathsf{K}\_{\mathsf{t},\mathsf{t}-1} \right> - \left< \Delta \mathsf{log}\mathsf{K}\_{\mathsf{t}-1} \right>
$$

where K; is the respective capital stock and the weights v; are the relative capital rental rates. The index reflects changes in the composition of capital. If *all*  components of the capital stock are growing at the same rate, quality remains unchanged. If *components* of the capital stock with higher capital rents are growing more rapidly, quality increases. Since data on the rental rates v; is not readily available for Guatemala, estimates of these are, following Rold6s ( 1997), based on the arbitrage relation:

$$\mathbf{(13)}\qquad\mathbf{\dot{\mathbf{v}}}\_{\mathbf{t},\mathbf{t}}=\left(\mathbf{1}+\mathbf{r}\_{\mathbf{t}}\right)\cdot\mathbf{P}\_{\mathbf{l},\mathbf{t}}-\left(\mathbf{1}-\mathbf{\dot{\mathbf{s}}}\_{\mathbf{Z},\mathbf{l}}\right)\cdot\mathbf{P}\_{\mathbf{\dot{t}},\mathbf{t}+1}$$

where P; is a price index, 62,; the depreciation rate, and r1 is the economy-wide real interest rate. The price indices for the respective asset groups are taken from the Moran and Valle (2002) database. In order to take into account the volatility of the real exchange rate, which effects directly the relative price of the four types of capital, and to correct for measurement bias, the final series are smoothed by a 3 year moving average.

#### *2. Quality of Labor*

To quantify labor quality, an index hq is computed as a weighted average of labor within different levels of education. This formulation is consistent with the growth accounting literature that makes adjustments for education. It allows a more accurate indication of the contribution of labor to production. The index hq is defined as follows:

$$\mathbf{(14)} \qquad \mathsf{hq}\_{\mathfrak{t}} = \sum\_{\mathfrak{t}=1}^{3} \mathsf{w}\_{\mathfrak{t}} \cdot \left(\mathsf{L}\_{\mathfrak{t},\mathfrak{t}} \,/\mathsf{L}\_{\mathfrak{t}}\right)$$

where L; is the labor force with education level j (primary, secondary and tertiary) and w; are the weights for the respective schooling level. The weights measure how the productivity effect of schooling varies with the level of education and are taken from the later regression analysis (Table 6). Interestingly, they correspond

approximately with the private returns to schooling at each education level, as presented by Psacharopoulos and Patrinos (2002) for Guatemala.

Following OECD (2001a) another possibility to compute an implicit labor quality index would be to assume direct relations between skills and occupations, to rank occupations by their skill intensity and then use information on the occupational distribution of labor over time. In this case, skilled labor and less skilled labor have to be weighted by their respective relative labor productivity to account for differences in skills. For the case of Guatemala, similar to equation (14), this can be done by weighting labor inputs of different industries with the share that each type of labor occupies in total labor compensation.

#### **Figure 4. Guatemala: Comparison of Labor Quality Indices, 1970-2002**

(in percent, relative to base year 1970)

Source: Author's calculations based on *Banco de Guatemala* (2003) **data** (implicit labor quality index), and human capital stock estimate for labor quality index (hq).

However, it should be kept in mind that this kind of implicit differentiation of labor is a rather incomplete substitute for labor quality. It can only take into account some of the quality changes of labor input and does not allow the sources of the change to be identified. Moreover, the eight industry categories available from *Banco de Guatemala* (2003) statistics only apply to the *formal* sector. As such, they ignore approximately 75 percent of the population working in the informal and rural economy. Placing less emphasis on educational improvements in *primary* schooling - the working population of the IGSS is typically better

educated than the population in the informal and rural sectors - the implicit labor quality index is biased downwards.20 Nevertheless, for illustrative purposes, Figure 4 compares both indices. What is striking is the apparent similarity between both measures of labor quality despite completely different sources of data. This suggests that the time series properties of the human capital stock and its respective weights may be of reasonable quality.

#### *3. Comparison of Both Indices*

Finally, Figure 5 compares the estimated indices of the quality oflabor, hq, and capital, zq. The descriptive analysis yields three important outcomes. First, the index of labor quality presents a clear upward trend, reflecting improvements in educational capital and a shift to more skilled jobs. However, as a consequence of the civil strife, labor quality slightly declined during the early 1990s but begins to increase again after 1998.

#### **Figure S. Guatemala: Indices of Capital and Labor Quality, 1970-2002**

(in percent, relative to base year 1970) a1

Source: Author's calculations. a/ Changes in capital quality reflect the fact that investment with comparatively higher rental rates (imported capital goods as well as machinery and equipment) decreased during the civil war but eventually climbed up again.

20 This is because primary school enrollment has increased substantially over time (see Table 3).

Second, the quality of capital has decreased over time. In particular after 1977, the data suggests that capital quality declined dramatically. In the mid 1990s, the advent of the Peace Accords led to an improvement, followed, however, by a stagnant pattern. In any case, for the period under observation, the quality of Guatemala's capital stock declined by about 20 percent. The exact reasons underlying the deterioration are unclear and require further research. Prominent explanations are the destructive impact of the internal military conflict, and a negative investment climate due to an unstable policy environment and lack of good governance.

Third, a comparison of both indices shows an apparent gap between the evolution of the quality of capital and the quality of labor. This could imply that the deterioration of quality of capital is associated with, among other factors, the decreased output growth during the last decades. In other words, there is a missing complementarity between the country's skills and its technology base. The next chapter will take a closer look at the empirical determinants of growth in Guatemala.

#### **V. Empirical Evidence for Guatemala**

This chapter presents the main empirical evidence regarding the relationship between education and growth in Guatemala. Section 1 introduces the empirical methodology. Section 2 reports the findings for average years of schooling and growth. Given the apparent shortcoming of aggregate measurements of human capital, section 3 examines separately the effects of primary, secondary and tertiary schooling on growth. Finally, section 4 compares the returns to education at the macro level with the microeconomic evidence.

#### **A. Methodology**

The empirical methodology for the following sections is based on the human capital augmented growth model of Mankiw et al. (1992). This model considers human capital as an independent factor of production. It can be represented in a Cobb-Douglas production function with constant returns to scale:

$$(1\ \mathsf{S})\qquad\mathsf{V}\_{\mathsf{t}} = \mathsf{A}\_{\mathsf{t}} \cdot \mathsf{K}\_{\mathsf{t}}^{\;\;\;\alpha} \cdot \mathsf{H}\_{\mathsf{t}}^{\;\;\;\mathsf{B}} \cdot \mathsf{L}\_{\mathsf{t}}^{\;\;\;(1-\alpha-\beta)}$$

where Y ref resents output and A is the level of technology or total factor productivity. 1 K, H and L are physical capital, human capital and labor. Multicollinearity between capital and labor is avoided by standardizing output and the capital stock by labor units, which also impose the restriction that the scale elasticity of the production factors is equal to unity. Converted into a logarithmic expression, the production function can be estimated in its structural form:

$$(16)\qquad\log\mathsf{y}\_{\mathsf{t}} = \mathsf{log}\mathsf{A}\_{\mathsf{t}} + \mathsf{a}\cdot\mathsf{log}\mathsf{k}\_{\mathsf{t}} + \mathsf{\beta}\cdot\mathsf{log}\mathsf{h}\_{\mathsf{t}} + \mathsf{u}\_{\mathsf{t}}\,\mathsf{k}\_{\mathsf{t}}$$

where the lower case variables y = Y /L and k = KIL are output and physical capital in intensive terms, and h = WL stands for average human capital. At first glance, the formula already appears suitable for estimation. However, some problems arise since it is well known that most macroeconomic time series contain unit roots and that the regression of one non-stationary series on another is likely to yield spurious results. As reported in Appendix one, the data for the case of Guatemala is no

21 Further research may focus on a specification less restrictive than a standard Cobb-Douglas production function to allow a higher degree of precision for the determination of the technical coefficients. For example, factor shares are not necessarily constant, and the elasticity of substitution can be less than 1. A potentially interesting avenue is Jones (2003). He presents a production function that exhibits a short-run elasticity of substitution between capital and labor that is less than l, and a long-run elasticity that equals to l.

exception. The estimation bias can be removed by transforming the time series to stationarity. This can be done by first differencing. In any case, this will create its own problems, notably because of the risk of losing valuable information on the long-run relationships of the variables.

One approach to dealing with this dilemma is to employ an error-correction model which combines long-run information with a short-run adjustment mechanism. This methodology has been used successfully in alternative growth studies. Examples of this are Nehru and Dareshwar (1994), Morales (1998), and Bassanini and Scarpetta (200 I). The error-correction model can be estimated in different ways. Banerjee et al. (l 993) show that the generalized *one-step* errorcorrection model is a transformation of an autoregressive distributed lag model. As such, it can be used to estimate relationships among non-stationary processes. Based on Hendry's ( 1995) concept of general-to-specific modeling, the errorcorrection model of the human capital augmented production function for Guatemala can be specified as follows:

$$\begin{aligned} \text{(17)} \qquad \begin{aligned} \text{A} \log \text{y}\_{t} &= \text{\text{y}}\_{1} \cdot \text{A} \log \text{k}\_{t} + \text{\text{y}}\_{2} \cdot \text{A} \log \text{k}\_{t-1} \\ &- \text{\text{y}}\_{3} \cdot \text{(\text{log}} \,\text{y}\_{t-1} - \text{a} \cdot \text{log} \text{k}\_{t-1} - \text{\text{\textdegree}} \cdot \text{log} \,\text{h}\_{t-1} - \text{\text{\textdegree}} \,\text{A} \text{\textdegree}\_{t-1} \end{aligned} \end{aligned}$$

For Guatemala, in line with much empirical cross-country research, the shortrun effects of schooling on growth have been found insignificant and are as such excluded from the regressions. This suggests that only the *level* of human capital has a long-run effect on economic *growth.* As it stands, the equation can be estimated by ordinary least squares (OLS) or instrumental variables (IV) techniques, but the coefficients cannot be formed without knowledge of a and ~- However, one can estimate the re-parameterized form:

$$\begin{aligned} \text{(18)} \qquad & \begin{aligned} \text{(18)} \qquad \Delta \mathsf{log}\,\mathsf{y}\_{t} = \mathsf{c} + \mathsf{y}\_{1} \cdot \Delta \mathsf{log}\,\mathsf{k}\_{t} + \mathsf{y}\_{2} \cdot \Delta \mathsf{log}\,\mathsf{k}\_{t-1} \\ &+ \mathsf{y}\_{3} \cdot \mathsf{log}\,\mathsf{y}\_{t-1} + \mathsf{y}\_{4} \cdot \mathsf{log}\,\mathsf{k}\_{t-1} + \mathsf{y}\_{5} \cdot \mathsf{log}\,\mathsf{h}\_{t-1} + \sum\_{\mathsf{t}} \mathsf{\mathsf{\mathsf{\mathsf{d}}}\_{\mathsf{j}} \cdot \mathsf{d}\mathsf{un}\,\mathsf{mm}\,\mathsf{m}\mathsf{y}\_{\mathsf{j},t} + \mathsf{u}\_{t} \end{aligned} \end{aligned}$$

Estimates of the parameter "(3 can now be used to calculate the required elasticities a and ~- The loading coefficient "'3 contains additional information because it can be interpreted as a measure of the speed of adjustment in which the system moves towards its equilibrium on the average. In addition, Banerjee et al. ( 1998) argue that in a single equation framework a significant coefficient serves as a test for cointegration. Notice that the technology parameter, A, is allowed to change overtime as a function of different variables, Z:

$$\mathfrak{a}(19) \qquad \mathfrak{l}\mathfrak{o}\mathfrak{A}\_{\mathfrak{t}} = \mathfrak{f}(\mathbb{Z}\_{\mathfrak{t}})$$

where in its simplest formulation the technology level is proxied by a constant term, c, and a series of dummy variables. In a later chapter, proxy variables with respect to growth of trade openness, bad governance, time trends and other variables will be included in the equation. The majority of the following regressions include three dummies.22 First, a 1963 impulse dummy captures a positive one-off effect stemming from expectations regarding the Central American Common Market (MCCA). Second, a 1982 impulse dummy takes into account a negative one-off effect stemming from the peak of internal war. Third, a 1977 step dummy which models a structural change in the long-run relationship of the variables. A Chow breakpoint test does not reject the null hypothesis of no structural change during that year (p = 0.000). In fact, the 1977 dummy is always negative, very significant, and most likely corrects for the deviations resulting from the civil strife. Interestingly, this finding is consistent with the quality index of the capital stock series showing a decreasing trend since 1977.

#### **B. Average Years of Schooling and Growth**

Table 5 shows the results for the average years of schooling specification. The adjusted R2 of the error-correction model is rather high and indicates a good data fit. Test statistics do not indicate any serial correlation or misspecification at conventional levels. The residuals have been found to be normally distributed and to follow stationary patterns. If not mentioned otherwise, these properties apply equally to subsequent regressions.

The loading coefficient is highly significant and suggests a moderate speed of adjustment towards the long-run growth path, equal to about 25 percent of the deviations per year. After any specific shock to the economy it would, on the average, take approximately 10 years to reach the level of output consistent with long-run growth (with differences to be less than 10 percent). In the subsequent regressions, however, the magnitude of the coefficient- but not its significancewas found to be fragile with respect to the econometric specification. The asymptotic critical values of the t-ratio for the coefficient are taken from Banerjee et al. (1998). The significance level suggests a cointegrating relationship of the

22 Evidently, the Guatemalan time series are full of distortions, for example the 1976 earthquake and major political events. However, a sparse inclusion of dummy variables is the preferred econometric formulation. Other settings will be described in the following chapters. It is important to emphasize that the basic results are not sensitive to the dummy variables. That is, the omission of the impulse dummies ( 1963 and 1982) does have little impact on the qualitative results. However, it is important to model the structural break.

variables.23 The results are satisfactory considering the distortions caused by the internal military conflict and the simplicity of the assumptions used to construct the time series in the context of data uncertainties. At first sight, this seems astonishing. However, the good performance of the model may be due to the small size of the economy, and that the overall data uncertainties are not as severe as is commonly believed.

The most striking result is that human capital, as measured by average years of schooling, has a highly significant, positive and strong impact on long-run ~rowth. Column I reports the implicit long-run coefficients estimated by OLS.2 Since education levels are likely to respond to growing employment opportunities and increased income, column 2 shows the regression results when IV techniques are applied. In this case, lags of the explanatory variables are used as instruments. Compared to the OLS estimate, the quality of the results does not vary much with the IV estimation. The estimating parameters are in both cases significantly different from zero and the regressions, as test statistics indicate, show a satisfactory performance. However, the absolute value of the human capital coefficient is slightly reduced. By contrast, the implicit elasticity of the capital coefficient is sharply reduced. The endogeneity problem, thus, does not distort the estimate but has an impact on the magnitude of the coefficients. In the IV specification, the estimated long-run effect of a 1 percent increase of average schooling on GDP per unit of labor is 0.33 percent. As such, it is roughly consistent with a priori expectations on the magnitude of the factor share of human capital. The results in terms of the human capital augmented Cobb-Douglas production function are approximately as follows:

$$(\mathcal{D}0) \qquad \mathsf{Y}\_{\mathsf{t}} = \mathsf{A}\_{\mathsf{t}} \cdot \mathsf{K}\_{\mathsf{t}}^{1/3} \cdot \mathsf{H}\_{\mathsf{t}}^{1/3} \cdot \mathsf{L}\_{\mathsf{t}}^{1/3}$$

where the reported parameter values will serve as the base in a later growth accounting exercise. Notice that despite different methodologies the capital elasticity is broadly in line with empirical analyses which estimate a Cobb-Douglas production function for Guatemala (see Box 3). The capital elasticity, however, was found to be sensitive regarding the setting of the dummy variables. By

23 Notice equally that the human capital parameters are highly significant and compare favorably with the critical values provided by Pesaran et al. (2001). This is reassuring given the small sample size of *50* observations and the consequently low power of the ADF tests, where the stationarity properties of the repressors may not be known with certainty.

24 The long-run coefficients can be obtained by dividing the estimated parameter through the value of the loading coefficient, for example 0.084/0.241 • 0.35 l. Discrepancies are due to rounding.

contrast, the human capital coefficient was robust. These issues will be explored in more detail in the following analyses.

#### **Table 5. Production Function for Guatemala: Average Years of Schooling Specification, 1951-2002**

a/ Lags of the independent variables are used as instruments. b/ Asymptotic critical values of the t-ratio are from Banerjee et al. (1998). c/ A Breusch-Godfrey test finds no evidence for the presence of first, second and third order correlation in the residuals.

t-statistics in parenthesis. \*\* Significant at 1 %, \* significant at 5%. Source: Author's calculations.

N 51 50

#### **Box 3. Empirical Growth Studies for Guatemala: A Review**

There are no studies for Guatemala that empirically assess the direct impact of education on economic growth over time. However, some standard growth accounting regressions exist that partially confirm the findings of the present study.

Prera (1999) and the World Bank (1996) came up with rough capital share estimates of about 0.4 and 0.6, respectively, while estimating a Cobb-Douglas production function. The World Bank provides neither a detailed methodology nor its data sources. The study from Prera faces several constraints regarding these issues. Particularly the fact that he ignores the existence of unit roots within the time series context and the low significance of the estimated parameters places doubt on the reliability of the results. Moran and Valle (2002) face the same problems. In addition, their parameter estimates must be considered carefully because of a short time period. The capital share is estimated about 0.3. Segovia and Larde (2002) find a similar capital share using a first differences specification. Although the methodologies and data sources differ, the results partially suggest that the capital share for Guatemala is in agreement with empirical studies for other developing countries. According to Bosworth et al. (1996), capital shares are typically considered to be in the order of 0.3-0.4.

Some growth accounting studies for Guatemala also exist. Results differ and no firm conclusions can be drawn. The main discrepancies stem from the assumed or estimated factor shares, distinct time periods and, in particular, from data issues. Most studies rely on international data sets. They make no adjustments for the quality of inputs and are not concerned too much about data problems in the light of the civil strife. In general, studies tend to find that the role of total factor productivity growth was moderate and decreasing for recent periods. (with the exception of Bail en 2001, see for example Bosworth et al. 1996, Edwards 2000, Gregorio 1992, Loayza et al. 2002, Moran and Valle 2002, Nehru and Dhareshwar 1994, Segovia and Larde 2002, Prera 1999, and World Bank 1996).

Particularly interesting is the work of Sakellariou ( 1995) who claims to use the Lucas (1988) model of endogenous growth. While analyzing microdata from the 1989 household survey, Sakellariou tests external effects of education on wage differentials. Unfortunately, the study suffers from a limited number of industry categories and human capital variables. Consequently, the regressions tum out to be statistically insignificant and strong conclusions cannot be drawn. However, Sakellariou goes as far as finding that the analysis does not reject the hypothesis that external effects of human capital investment could be present in Guatemala.

Finally, there are two additional findings of interest. First, even in the IV estimate, physical capital accumulation has a rather high impact on short-run growth. This suggests that measures to stimulate investment, for example by improving the investment climate, are likely to have an immediate impact on shortrun growth. Second, the interception is significantly negative. Since the constant is expected to proxy for technology, a negative parameter in the sense of 'technological regress' is hard to understand. However, a loose interpretation for this finding would be that during the past 50 years, on average, the economy was not particularly efficient. One reason for that might be the conflicting political and social environment of Guatemala.

#### **C. Schooling and Growth by Education Level**

Using education data by levels may be preferable for a number of reasons. In particular, the growth impact of different forms of educational capital may vary. Columns 1-6 in Table 6 present the results of the production function augmented for human capital. The education level of the labor force enters separately into the estimation. The share of the labor force with primary, secondary and tertiary education is used here as the relevant unit.

It may be argued that *average years of schooling* by level of education should be used instead of labor force *participation.* In any case, with the given data, this would not change the results. Ideally, one would also include primary, secondary and tertiary education into the same equation in order to assess their joint impact on growth. However, due to stron& collinearity, the estimation only supports the inclusion of one education level.2 As can be appreciated from the test statistics the regressions perform quite well. Notice that the estimate for primary education includes a time trend starting in 1985, the year of Guatemala's transition to civilian rule. The inclusion of the trend variable was motivated to avoid serial correlation in the residuals, but does not have an impact on the magnitude of coefficients.

Table 6 presents both OLS and IV estimates. The endogeneity problem seems to be more pronounced for primary education, and in particular for physical capital. However, the qualitative results do not vary substantially. In all specifications the schooling variables are highly significant and positively correlated with growth. Interestingly, the significance levels increase with secondary and tertiary education. Regarding the long-run elasticities, the accumulation of primary schooling appears

25 In principle, the inclusion of a time trend for 1999 and an interaction term for secondary and tertiary schooling would allow incorporating all three levels of education at a time. Tentatively, such an exercise yields similar qualitative results on the impact of each level of education on growth - albeit primary schooling becomes insignificant. In addition, due to the multicollinearity problem, this specification was found to be rather sensitive and performs less well than the results displayed in Table 6.

to be most important for growth, followed by secondary and tertiary education. This finding should *not* be interpreted as implying that other levels are unimportant. This is particularly true given the tight connections between the various forms of educational capital and the retrospective character of the empirics.

Nevertheless, the evidence is in line with the limited cross-country studies on this topic. Recall that Gemmel ( 1996), Petrakis and Stamatakis (2002) and Papageorgiou (2003) plausibly suggest that the importance of post-primary education increases with the level of development. Similarly, de Ferranti et al. (2002) argue that in countries classified as adopters, such as Guatemala, policies should first focus on a critical threshold level of primary schooling, coupled with open trade policies. The intuition is here that different stages of technological transition require distinct policy priorities. A sufficient coverage *and* quality of primary education are regarded as the minimum prerequisite to adopt technologies. By contrast, in countries where basic skill requirements are fulfilled and firms are making significant adaptations or innovations, the creation of more specialized skills ought to be the priority. In addition, the results here partially confirm the earlier micro-level evidence for Guatemala. 26

Finally, it is interesting to observe the changes of the physical capital coefficients by level of education. In the IV specification for primary and secondary schooling, capital only enters as weakly significant. By contrast, the coefficient for physical capital becomes very significant and alters its long-run elasticity if tertiary education is entered into the estimate.

To the extent that this effect does not merely reflect statistical arbitrariness, a possible interpretation would be that the productivity of physical capital is affected by tertiary schooling. These findings support the conjecture of Romer ( 1990b) that the level of scientific education should be correlated with the rate of growth and the share of output devoted to investment in physical capital. It should be kept in mind, however, that the reliability of tertiary education data is comparatively poor in Guatemala. Moreover, according to Anderson (2001), low quality and internal inefficiency plague university education. Hence, some care should be taken before drawing too strong conclusions from the observed changes.

26 For Guatemala, Psacharopoulos and others have extensively investigated the returns to schooling, sometimes by level of education. Such exercises are summarized in Psacharopoulos and Patrinos (2002), Haeussler (1993) and World Bank (1995c). The studies generally report high private returns to primary schooling, but are merely based on ENS (1989) or earlier data, and typically do not care about sample selection bias.

### **Table 6. Guatemala: Effect of Schooling on Growth by Level of Education, 1951-2002** tT1 3

Note: The regressions include a 1977 step dummy and impulse dummies for 1963 and 1982, significant at I%. a/ Asymptotic critical values of the t-ratio are from Banerjee et al. ( 1998). b/ A Breusch-Godfrey test finds no evidence for the presence of first, second and third order correlation in the residuals.

t-statistics in parenthesis. \*\* Significant at I%, \* significant at 5%.

Source: Author's calculations.

#### **D. Mincerian Human Capital Specification**

An important question is how the effect of schooling at the macro level compares with the microeconomic evidence. The macro returns could be higher because of externalities from education. For example, if post-primary schooling leads to technological progress that is not captured in the private returns to education, or if education produces externalities in the form of the reduction of crime, more informed political decisions, better health and so on. To reconcile the macro effect of schooling with the micro level, Cohen and Soto (200 I) estimate the following production function:

(21) yt =At· Kr· HM(l-a)

where Y is output, A total factor productivity, **K** physical capital, and HM human capital. As first suggested by Bils and Kienow (2000), the micro evidence derived from a log-linear Mincer (1974) formulation can be used to specify the aggregate human capital stock as follows:

$$(\mathfrak{Z}\mathfrak{Z})\qquad\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathsf{\mathcal{\prime\mathsf{\mathsf{\mathcal{\mathsf{\mathsf{\mathcal{\prime\mathsf{\mathcal{\prime\mathsf{\mathcal{\prime$$

where hm1 is the human capital per worker, h1 is average years of schooling and 'I' corresponds to the returns to education. This Mincerian approach has become popular in the literature since the work of Bils and Klenow. 27 The specification is a straightforward way of incorporating human capital into the production function in a manner that is consistent with the standard semi-logarithmic formulation for estimating returns to schooling at the micro level.

Nevertheless, Temple (2001) argues that the parameter 'I' may not be interpreted as the social returns to schooling because it does not incorporate the opportunity costs of the resources used in educational provision. Still, it remains of considerable interest since an empirical estimate provides a way of either confirming or rejecting the importance of education suggested by micro studies.

For the Guatemalan case, the econometric specification is similar to the previous equations. The production function is first converted into a logarithmic expression:

$$(\mathbf{23}) \qquad \log \mathbf{y}\_t = \log \mathbf{A}\_t + \boldsymbol{\alpha} \cdot \log \mathbf{k}\_t + (\mathbf{1} - \boldsymbol{\alpha}) \cdot \boldsymbol{\Psi} \cdot \mathbf{h}\_t$$

Then, the production function is transformed into an error-correction formulation, which allows the long-run schooling parameter to be identified:

27 The working paper version was circulated prior to 2000. A caveat here is the missing role of experience.

$$\begin{aligned} \text{(24)} \qquad & \begin{aligned} \text{(24)} \qquad & \Delta \log \mathsf{y}\_{t} = \gamma\_{1} \cdot \Delta \log \mathsf{k}\_{t} + \gamma\_{2} \cdot \Delta \log \mathsf{k}\_{t-1} \\ & -\gamma\_{3} \cdot (\log \mathsf{y}\_{t-1} - \alpha \cdot \log \mathsf{k}\_{t-1} - \langle 1 - \alpha \rangle \cdot \Psi \cdot \mathsf{h}\_{t-1} - \log \mathsf{A}\_{t-1}) + \mathsf{u}\_{t} \end{aligned} \end{aligned}$$

Finally, the error-correction model is re-parameterized and includes a series of dummy variables:

$$\begin{aligned} \text{(25)} \qquad & \Delta \log \mathsf{y}\_{t} = \mathsf{c} + \mathsf{y}\_{1} \cdot \Delta \log \mathsf{k}\_{t} + \mathsf{y}\_{2} \cdot \Delta \log \mathsf{k}\_{t-1} \\ & + \mathsf{y}\_{3} \cdot \mathsf{log} \, \mathsf{y}\_{t-1} + \mathsf{y}\_{4} \cdot \mathsf{log} \mathsf{k}\_{t-1} + \mathsf{y}\_{5} \cdot \mathsf{h}\_{t-1} + \sum\_{j} \mathsf{s}\_{j} \cdot \mathsf{dummy}\_{j,t} + \mathsf{u}\_{t} \end{aligned}$$

Notice that the implicit return to schooling can be calculated with knowledge of a and *13 •* In principle, this approach would also allow the productivity effect of schooling to be differentiated by education level, as mentioned by WoBmann (2003). Unfortunately, the results here were found unstable for disaggregated education data. This is presumably due to the missing logarithmic transformation of the schooling variables.

Insofar, the specification provides an attractive way for comparing macro and micro evidence on the returns to schooling, but in a time series context tends to produce fragile parameter estimates. Nevertheless, when using aggregated data on human capital the regressions perform quite satisfactorily. Table 7 presents the results. Controlling for endogeneity does not distort the empirics. In the IV specification 1 additional lsear of schooling increases income per worker by approximately 18.4 percent. 8

This number suggests that the macro return to schooling in Guatemala is rather high, but it compares favorably with earlier microeconomic evidence. For example, the World Bank (1995c) reports a private return to schooling of 14.9 percent for Guatemala.29 There is evidence for much lower returns in the informal sectors and for decreasing patterns over time, but the magnitude of the coefficient is echoed in Funkhouser (1997). An estimate from Haeussler (1993) based on 1989 survey and Ministry of Education data suggests that, depending on the schooling level and underlying assumptions, the social return to schooling lies in a band between 13-19 percent. Finally, these results also confirm the cross-country evidence from Cohen and Soto (2001 ). They essentially find that in macro and micro regressions the effect of education on income is of similar magnitude.

28 According to the Table, the implicit return to schooling can be calculated as follows: (0.034/0.240)/(1-0.240)"" 0.184. Discrepancies are due to rounding.

29 Based on ENCOVI (2000) survey data the World Banlc (2003a) reports an overall rate of return of 6 percent.

#### **Table 7. Production Function for Guatemala: Mincerian Human Capital Specification, 1951-2002**

a/ Asymptotic critical values of the t-ratio are from Banerjee et al. (1998). b/ A Breusch-Godfrey test finds no evidence for the presence of first, second and third order correlation in the residuals.

t-statistics in parenthesis. \*\* Significant at I%, \* significant at 5%.

Source: Author's calculations.

#### **VI. Additional Explanatory Variables and Robustness Check**

This chapter seeks to answer some basic questions. How much confidence should be placed on the previous results? Evidently, given certain data restrictions and distortions caused by the civil war, a key issue is if the previous findings can be used to derive firm policy conclusions. In addition, another important aspect is considered: does the conditioning information set cause the schooling coefficients to change?