External Debt & Economic Growth

Transcription

1 w.gmaika Mälardalen University School of Sustainable Development of Society and Technology Thursday, May 28, 2009 External Debt & Economic Growth By Diego R. Calvo Johannes H. Stefanoudakis Juan Marcelo Tames Blanco Supervisor: Christos Papahristodoulou Mälardalen University Box 883 SE Västerås Sweden Tel. +(46)

2 Abstract Throughout the years most countries have incurred in borrowing money in order to finance many of their operations. Those loans and their accumulation have either benefited or impaired those countries ability to grow. In this report we examine several factors that affect the gross domestic product (GDP) and their levels of impact with the sole purpose of inferring the relationship between debt and GDP. In addition, we will propose a cut-off point from which additional debt results in negative growth. 2

3 Acknowledgements If I have seen further it is by standing on the shoulders of giants Isaac ewton, Letter to Robert Hooke, February 5, 1675 Diego R. Calvo Dedicated to Virginia Calvo, Sheyla & Nicole Rosales Roger, Annika & Darcie Vaughan Maria Damaris Calvo & Carlos A. Granados Raymond & Birgitta Davis Special thanks Barry Rudolph Boyko Vasilev & Aniko Cakarevic Walker & Ross Family Sune & Berit Ludvigsson Terrie Alexander & Tim Miller Barbara Denk Johannes H. Stefanoudakis Dedicated to Tina Gianna Nikolaos Stefanoudakis Christofer Stefanoudakis Special thanks Nikos Spinos & Family First and most important, I want to thank God for the strength and courage that guided me through my life to reach this point. To my uncle Roberto Blanco who gave me the unique opportunity to come and study in Sweden. To my mother Elena Blanco whose unconditional support and infinite love never let me give up. To my girlfriend Lindsay Calle who has always been there for me when I needed to remember my objectives, ambitions and motivations. Special thanks to my closest friends Diego R., Franklin, Juan Pablo, Abraham and the rest of my family. - Marcelo Tames We would also like to thank Christos Papahristodoulou for the guidance and support he provided during this project. 3

4 Contents Abstract Introduction Problem Area Aim and Limitations... 6 The Choice of External Debt... 6 Data Integrity... 6 Missing Factors Affecting Our Model... 7 Time Lag... 7 Money usage & External Factors... 7 Statistics vs. Theoretical background... 7 Interest Rates Methodology malfunction Theoretical Background Debt and Growth Relationship The regression equation Statistics of the Regression The Coefficients R-squared Adjusted R-squared Durbin-Watson Statistic Akaike and Schwarz Information Criterion Definitions and Techniques Basic Definitions Variables Econometrics & techniques Ordinary Least Squares Method (OLS) Unit Root tests Granger Causality Co-integration Field Work Data analysis with EVIEWS Unit Root Test results Granger Causality Tests Results Regression Analysis Regression coefficients

5 5.3 Statistics of the Regressions R-Squares Adjusted R-squares Durbin-Watson Statistics Akaike Information Criterion Schwarz Information Criterion (BIC) Debt and Growth results Conclusion References Appendixes Appendix 1: Countries of study Appendix 2: Unit root results Appendix 3: Granger Causality test results Appendix 4: Statistic results per country Appendix 5: Regression Results Appendix 6: Individual Graphs

6 1. Introduction 1.1 Problem Area There has been very little theoretical information regarding the effects of total external debt on the economic growth of a country as a result the information that we have manage to put together is based on empirical studies. Theories on economic growth suggest that even though certain amounts of debt are good for the economic growth of a country, there is an amount of debt, after which any extra amount added, affects growth negatively. In order to be able to investigate the effects of external debt on growth, we will examine a total of 30 randomly chosen developing countries over a period of 33 years ( ). The countries we chose for our research are stated in Appendix 1 and they are presented according to their position in the human development index put together by the United Nations Development Program. The data series for each country were obtained from the IMF, World Bank, Pennsylvania University and the ations Masters databases. For each country we examine the following variables 1 with the first one being dependent and the rest independent: GDP per capita (current $US) Debt service to exports Population increase Investments Openness to trade Debt-to-GDP ratio Debt-to-exports ratio 1.2 Aim and Limitations The aim of this paper is to examine whether there exist an inverse U-shape relationship between external debt and economic growth after a certain debt-to GDP ratio. In other words, we will try to verify the existence of a non-linear relationship between those two variables explaining how big is the impact of debt on growth and through which channels this impact takes place. However in our research we need to establish some limitations and assumptions because of two main reasons. Firstly, to explain possible errors in our estimates and where they came from. Secondly, to avoid having to deal with factors that are not possible to include in or model. The Choice of External Debt We chose to examine the effects of external debt on growth due to the lack of solid theoretical models describing this relationship. The external debt was presented in terms of total public and private external debt. Public debt is owed by the governments and is indirectly considered debt of the citizens. Private debt is that money owed by individuals and business within a country. We make no inference regarding the effects of internal debt since an increase of internal debt is at the same time an investment made by the citizens of that same country. Data Integrity The problem sometimes is lack of information and some other times the vast amount of deviating sources to use. Many organizations internet websites presented raw data but we continuously found cases in which figures between sources veer by large quantities. Hence, 1 See p.13 section 3.2 for details 6

7 we need to assume that the sources that we end up working with output accurate figures or as close to real data as possible. Missing Factors Affecting Our Model There exist many variables affecting GDP in different proportions. Some of those include, secondary school enrolment rates, interest rates, fiscal balance, terms of trade growth, inflation, currency fluctuation and initial income per capita. Even though they are of high importance, they were not included in our model due to lack of data. The exclusion of those variables could account for the incoherent values obtained for some countries, i.e. Togo. Time Lag When a country borrows funds from an exterior source it will end up investing those funds in projects that have a positive net present value. These funds become part of the debt during that same year but the benefits will not be consolidated until years later. Since most countries incur in to debt and see the benefits of their investment during deferent time lags we will need to assume that all of them start and conclude their investment during periods up to five years. Money usage & External Factors We will have to assume that the resources borrowed were properly used and factors such as corruption and funds allocated to the wrong cause did not represent a threat to the consistency of our analysis. Another important assumption is that our data sample size is large enough to outperform the effect of natural disasters, armed conflicts and other social and political disruptions to a country s economical structure. Statistics vs. Theoretical background There are some cases where the statistical results obtained from the analysis do not perfectly fit the theory underlying the data behaviour. As a result efforts are made to maintain a balance between the weights put on the statistics and the theoretical background. Interest Rates Interest rates play a very important role in the relationship between external debt and economic growth. If interest rates are not constant but rather increase for higher debt levels the chances of repayment become more unlikely, for an already struggling economy, creating a chain of debt accumulation. Still, the time series are not adjusted for any sanction to the borrowing country. 1.3 Methodology malfunction The first part of this paper is devoted to the theoretical background. Here we will introduce from basic concepts to the mathematical and economical frameworks be used during the entire research. In the second part of our paper, we present the analysis of the data for each of the chosen countries, what kind of inputs we will analyse and why. For the analysis shown in this part we will use the variables mentioned above together with the use of econometric techniques such as Cointegration, Granger Causality, Unit root and Ordinary Least Squares method (OLS) to make the final inferences. After the complete analysis we will present our results. These include numerical as well as graphical figures. We explain why we obtained those results and what they mean for some of those countries. In this part we also explain how these results support the theories about external debt and economic growth. Finally we will condensate our research in a summary of the results with a proper conclusion for them and a general inference of the group as a whole. 7

8 2 Theoretical Background 2.1 Debt and Growth Relationship From recent literature regarding economic growth and debt such as from Pattillo, Poirson and Ricci (2002), Rubio, Ojeda and Montes (2003) and Cordella, Ricci and Ruiz-Arranz (2005), we know that low levels of debt have a positive effect of growth. There is also evidence that after some certain point of debt stock the effect on growth becomes negative. There is strong evidence that the channel through which debt affects growth is investment and by reducing the investment flow there is a direct negative effect over growth; causing less efficient investments since investors tend to assign resources to short-term projects 2. Nonetheless, Presbitero (2006) points out the important role of the productivity factor as another channel that correlates external debt and growth. The question still remains, why high levels of debt result in negative growth? Theory suggests that there are various reasons that could lead to this result. A first assumption we could make regards political economic considerations that can lead to over-borrowing, low growth as well as capital flight. Another strongly supported assumption is that of debt-overhang. This describes a situation where the debt stock of a country exceeds the country's future capacity to repay it and occurs when the cost of debt is combined with a fall in a country's trade and economic health. As a result there is decreased spending on education, health, and infrastructure which puts the country in even worse economic shape. 3 Paul Krugman defines the debt overhang as the presence of an inherited debt which is so large that creditors don t expect to be paid back completely any longer. 4 Figure 1 presents the Debt Laffer Curve of external debt, expected payments and amortizations. For small amounts of debt, from the origin to point A, the expectation of not getting paid is almost nil. Therefore the marginal expected debt repayment with relation to the debt stock is one. However, after that point the expected debt repayment expands at a lower rhythm in relation to the debt accumulation due to the fact that it s less probable the country debtor will be able to handle bigger amounts of debt. This means that the risk of not getting paid is greater than zero 5. This risk may vary from country to country according to the level of their debt s interest rate. Under such circumstances, the expected debt repayment reaches its maximum value, point B, and then starts falling as the debt stock reaches higher levels making the marginal impact of debt harmful for the creditor. This is because of their awareness that higher amounts of debt will only decrease the size of the following payments. 2 Pattillo, Poirson and Ricci (2002), External Debt and Growth, June p Investopedia, a Forbes digital company, Retrieved May 3th, 2009, from 4 See Krugman (1988) 5 See Pattillo (2002, p. 33). 8

9 Source: Flores, Fullerton, Olivas (2007) Empirical evidence on foreign debt, investment, and growth in Mexico, The debt Laffer curve can be extended to a curve that actually shows the contribution that external debt has in the economic growth of a country. We can see the representation of the curve in Figure 2. There we can imply that the relationship between external debt and growth is not linear and that reasonable levels of debt actually contribute to the economic growth of a country while excessive levels turn out to be destructive. This means that too much debt would lead to zero or even negative economic growth. Some other assumptions include distortionary types of taxation and investor s uncertainty about how much debt will be serviced with the country s own resources.

10 Previous empirical studies among developing countries have verified the existence of this non-linear relationship. Specifically it is an inverted U-shape with debt-to-gdp on the x-axis and GDP growth on the y-axis. In a recent paper 6, strong evidence was found supporting this idea. Specifically they found that there exists a point, after which any extra amount of debt would affect growth negatively. The average turning point of debt-to-gdp ratio that they estimated was around 35-40% of the GDP and % of the exports. Furthermore, there is a geometric relationship between figures 1 and 2 which is shown in Figure 3. There we can find that at a certain point, the increase in debt, affects negatively the creditors expectations of being paid back completely. By looking closely at the Figure, we can derive that, when the expected payment of the debt increases proportionally less than the debt stock, the distortions are such that extra amounts of debt start decelerating the GDP growth rate. Moreover, if the debt accumulation achieves higher levels such that the debtor starts diminishing or failing to make its regular amortizations, any extra debt increment will be translated into negative contributions to the GDP growth rate. 6 Pattillo, C. Poirson H., & Luca, R., External Debt and Growth 10

11 2.2 The regression equation For testing the non-linear assumption we will use Group Unit root, Granger Causality, OLS and the following regression equation: y it = c + β i1 X it + β i2 D it + β i3 (D it ) 2 + ε it where y it is the growth per capita, X it are the control variables, D it are the debt variables, c is a constant. The β i s are the regression coefficients and ε it is the residual error. In the next section we explain thoroughly what these coefficients mean and what we expect their sign to be. The control variables include: debt service to exports, population growth rates, openness to trade, investment rates. The debt variables are composed by total external debt to exports, total external debt to GDP and their squares. Using the Ordinary Least Squares method, the regression equation mentioned above and performing regressions for all our data we will be able to calculate the intercept c and the β i s for all of the variables. 2.3 Statistics of the Regression Each regression outputs several statistics as well as the coefficients for the equation. Below we will present explanations for the most relevant indicators, that Eviews provides us with, followed by the formulas used to compute them. The Coefficients The coefficients measure the marginal contribution of the independent variables to the dependent variable, holding all other variables fixed 7. They are calculated by using the standard OLS formula: b = ( ) X y R-squared The R-squared or coefficient of determination statistic is used to describe how well the independent variables used in the model, will predict the dependent variable. More precisely, it shows how much of the dependent variable s variance is explained by the independent ones. R-square can take values between 0 and 1. Obtaining an R 2 equal to one, would indicate that the model fits perfectly. =1 ( ) ( ) h = / Adjusted R-squared The adjusted- R 2 has the same interpretation as R 2 with one important difference; it takes into account those variables that do not help in predicting the dependent variable. If is considerably lower than R 2 it probably indicates lack of variables that enable a proper measurement of the variation in the dependent variable. =1 (1 ) 1 7 EViews 5 User s Guide Copyright Quantitative Micro Software, LLC 11

12 Durbin-Watson Statistic This statistic is used to measure the serial correlation of the residuals. There are many issues if serial correlation is detected within the model. First of all, the OLS method is no longer efficient for describing the data. Secondly, the S.E is generally underestimated. Finally, if we have lagged variables on the right hand side of the regression equation the OLS will turn out biased and inconsistent. A value of 2 in this statistic indicates no serial correlation. Studies of Johnston and DiNardo (1997) on the Durbin-Watson statistic indicate a value lower than 1.5 is sign of positive serial correlation. = ( ) / Akaike and Schwarz Information Criterion Akaike Information Criterion (AIC) is a method used for choosing the best econometric model for the data. It presents the figures that indicate the amount of data lost while modeling. = 2 +2 h = 2 1+log(2 )+log Schwarz Criterion or Bayesian information criterion (BIC), as well as the AIC, is also used for choosing the model that best fits the curve but defers from AIC in the magnitude of the penalty for additional coefficients. = 2 ) +( It can be deduct from above due to the close relation of these two statistics and their properties each of these values needs to be as small as possible. 12

13 3. Definitions and Techniques 3.1 Basic Definitions Before we start investigating the effects of debt on growth there are a few important concepts that we have to consider for understanding the variables used and what the results mean. We start by defining gross domestic product (GDP). That is the total market value of all final goods and services produced within a country in a specific year. In our study case we have not deducted depreciation of assets, depletion and degradation of natural resources. It is measured in current US dollars. Single year exchange rates taken at the end of each year were used for converting into dollars. GDP growth is defined as an increase in production levels of goods and services. Through our research the most important variables for our calculations are: Total External Debt: That is, the outstanding amount of those current and not contingent liabilities owed to non-residents of a country. 8 Population: Accounts for all residents regardless of legal status or citizenship. Refugees not permanently settled in the country of asylum are generally considered to be part of the population of their country of origin. 9 Exports of goods and services: include all transactions made between the residents of a country and the rest of the world. They are measured in current dollars and as a percentage of GDP. 11 Openness to Trade: is calculated as exports plus import, divided by GDP. By using it we take into consideration that a country s growth is affected by how open it is to trade. Debt Service: Total debt service is the sum of principal repayments and interest actually paid in foreign currency, goods, or services on long-term debt, interest paid on short-term debt, and repayments (repurchases and charges) Variables In the previous section we have defined each variable we use in our report. However, before we continue with the testing and analysis of our time series data we should clarify what their abbreviations stand for. For each country we have a set of debt and control variables with the following explanations: GDP: TPOP: Gross Domestic Product Total Population As presented by economic theories such as the Solow Model, we expect population to have a negative impact on economic growth through productivity. This happens if an increase in population is combined with fixed levels of capital and as a consequence there would be less capital available for each worker. 8 The Organization for Economic Co-operation and Development. Retrieved April 23th, 2009, from 9 World Development Indicators. (2008). World Bank. 10 World Development Indicators. University of Michigan, Retrieved May 3th, 2009, from 13

14 DS: I V: OPS: EXoG&S: TED: However, when a country borrows capital, it does it in order to avoid the negative effect of population with the fixed capital. Therefore, the effect is unclear and depends on the debt rate being larger or lower than the population increase rate. Total Debt Service The variable of debt service is also used in our model and we expect to see a negative relationship with growth since high amounts of debt service hinder investment into productive activities within a country. Investment share of Gross Domestic Product Assuming that all capital taken as debt resulted in successful investment we can deduct that economic growth will be affected in a positive manner by the factor. Openness to trade. A country with a higher degree of openness to trade would benefit from exports, imports and exchange of technological and scientific innovations. All this would lead to efficiency improvements, higher productivity and thus positive economic growth. Exports of Goods and Services. (% of GDP) Total External Debt. Total external debt to GDP and total external debt to exports are strictly related to debt and are the keystones of our model s analysis. 3.3 Econometrics & techniques If we were to test the model supposing a linear relationship between debt and growth, the results obtained would not be as accurate. This is because of the different effects on growth according to the debt level. Moreover, the results of other studies show better fit with nonlinear models. Ordinary Least Squares Method (OLS) One of the most commonly used methods in regression analysis is the Least Squares Method (LS or OLS) initially proposed by Carl Friedrich Gauss in It s a method for fitting a line to the data points. Its purpose is to estimate the intercept and the slope of the regression equation that best describes the data series. Unit Root tests One of the most important assumptions regarding the OLS model, which we use to test our regression equation, is that of data being stationary. A data series is said to be stationary if the mean, variance and autocorrelation structure do not change over time. 11 In the case where the data series are not stationary, the regression model is called spurious. A spurious regression occurs when a pair of independent series, but with strong temporal properties, is found apparently to be related according to standard inference in an OLS regression 12. This 11 Engineering Statistics Handbook, Retrieved May 20th, 2009, from 12 Granger, Hyung and Jeon. Spurious Regressions with Stationary Series. October

15 relationship states that under those circumstances, the OLS regression may generate invalid estimates. For example, the regression can show high R 2 and t-ratio values that could be meaningless from the economic point of view. As a result, we have to test whether our data are stationary or not. To do so we are going to perform a sequence of Group Unit Root tests (Levin,Lin & Chu t-stat, Breitung t-stat, ADF-Fisher Chi square, PP-Fisher Chi-square, Lm Pesaran and Shin W-stat) using Eviews. In the Appendix 2 we present a table with a summary of those results. Granger Causality One of the two techniques used in our econometric analysis is Granger Causality named after Nobel Laureate Clive Granger ( obel Memorial Prize in Economic Sciences, 2003). Granger causality is a technique used in testing whether a time series is useful for predicting another. In our case we will be able to check if External Debt and our control variables are better for describing growth patterns. Even though it is a very useful technique it involves some errors. First we have to stretch that Granger causality does not imply true causality. Second and most important is that this technique can be applied to only pairs of variables. Thus, if the true relationship involves 3 variables or more, it can lead to inaccurate results. Co-integration If we want to test a hypothetical relationship between two variables having unit roots, then cointegration is the best method. Since our data series are of limited length ( ), cointegration is a very powerful and accurate tool to use. The most commonly used methods for testing co-integration are: - The Engle-Granger two step method. - The Johansen procedure. - Phillips-Ouliaris co-integration test. Although this method is quite precise, it bears some error. This is due to the fact that this method assumes a constant co-integrating vector where in reality the long-run relationship between variables is likely to change. 15

16 4. Field Work 4.1 Data analysis with EVIEWS In section 2.3 of the report we introduced the concept of stationary data series and its importance to our model. As a result, the first step is to check for data stationarity by running the unit root tests we discussed above with the help of EVIEWS. We run a series of tests for each country. In the first set we check for the existence of unit root assuming a common unit root process and using the tests of Levin, Lin & Chu t-stat and Breitung t-stat. In the second set we assume individual unit root process and test for unit root using ADF-Fisher Chi square, PP-Fisher Chi-square and Lm Pesaran & Shin W-stat. A second step is to test for Granger Causality. That is, the independent variables granger causes the dependent one and vice versa. The third step in our analysis is to run the regressions using OLS for each of the countries. By studying the tables presented in Appendixes we can draw the following conclusions for the tests mentioned above. Unit Root Test results Using the unit root statistic we ested the null hypothesis (H 0 ) of non-stationarity. Testing the data using lags from 0 to 5 years, best results were obtained having 1 year lags. For the majority of the countries we have a 95% confidence level that the data series are non- stationary. Let us consider a few countries as an example. Using the Levin, Lin & Chu t-stat on Pakistan s data we have obtained a confidence level of 98%. The Breitung t-stat on Bolivia s data showed a level of 99%. Lm Pesaran and Shin W-stat resulted in a 96% confidence level for Algeria. Peru s data were tested with PP-Fisher Chi-square and showed a level of 96%. Using ADF-Fisher Chi square on Nigeria resulted in a 98% confidence level. For more information on the unit root results you can refer to Appendix 2. Co-integration was proposed by Engle and Granger (1987) who stated that a linear combination of two or more non-stationary series may be stationary. Those non-stationary series are then said to be co-integrated and in order to prove that, we run co-integration tests. However, running the unit root tests and having the results mentioned we proved that with 95% confidence our series are stationary. Thus, the test of co-integration is no longer valid and there is no need to check the existence of it. The decision on data stationarity was based on the results obtained from the Levin, Lin & Chu t-stat because we are more interested in rejecting the hypothesis of common unit root process. This process assumes the same unit root for all the variables and their time series. Figure 4 and table 1 summarize the obtained results. Being assured that our data is stationary we can now run the regressions and obtain the coefficients (β i ) for every country. The results are presented in the section 4. Confidence Countries Involved Level Algeria, Argentina, Benin, Bolivia, Brazil 99% Burundi, Chile, Ecuador, Honduras, Malawi, Nigeria, Rwanda, Sierra Leone, Sri Lanka, Togo, Venezuela Burkina Faso, Turkey, Colombia, 95% Costa Rica, Egypt, India, Lesotho, Malaysia, Pakistan, Peru 90% Chad, Indonesia, Mexico Figure 4 Table 1

17 Granger Causality Tests Causality tests indicate whether one variable is better explained and predicted with the help of another one. In section 2.3 we explained the test proposed by Granger and we performed such test on our 30 countries with the help of EVIEWS. Since every country s model consists of 9 different accounts, we considered unnecessary to check causality for every possible pair of accounts for all the countries. Therefore we run the tests for the Investments, GDP per capita and Debt to GDP ratio accounts, which lead to six different hypothesis of causality for each country. By looking at the results we conclude that there s not an absolute trend that holds for all the countries, but still there is a good amount of cases where causation is proven for all the accounts. For example, among the most remarkable individual results, we have obtained with a 99% confidence level that Chad s Investments Granger causes its GDP per capita. Also in Benin and Burundi, within the same confidence level, we found out that their Debt-to-GDP ratio Granger causes GDP per capita. There have also been cases where a two-way way causation occurs. For example, Malawi s Debt-to-GDP ratio Granger causes Investments and vice versa with a 95% confidence level. Out of the six different hypothesis tests calculated, there are two that prove causation more often among our pool of countries. These are GDP per capita Granger causing Investments and Debt-to-GDP ratio granger causing Investments. nts. As a result, we can refer to the investments account as a more sensitive one that relies partly on the behaviour of the level of the Debt-to-GDP ratio and GDP per capita and Figures 5 and 6 illustrate the results. This assumption is supported by the fact that investors use as a key indicator the health of a country s economy before they place their capital there. For more information on the unit root results you can refer to Appendix 3. Figure 5 Figure 6 Prob GDP Per Capita Doesn t Cause Investments Countries Involved Benin, Bolivia, Brazil, Chile, Ecuador, Indonesia, Malawi, 0 to 0,1 Pakistan, Sierra Leone, Sri Lanka. Colombia, Egypt, Togo, 0,1 to 0,2 Uruguay, Venezuela. 0,2 to 0,3 Mexico, Nigeria 0,3 to 0,4 Algeria, Chad, Turkey 0,4 to 0,5 Argentina, Burundi, Malaysia Burkina Faso, Costa Rica, 0,5 to 1 Honduras, India, Lesotho, Peru, Rwanda Table 2 Prob GDP Per Capita Doesn t Cause Investments Countries Involved Algeria, Ecuador, Indonesia, 0 to 0,1 Malawi, Nigeria, Pakistan, Sierra Leone, Sri Lanka 0,1 to 0,2 Chad, Honduras Benin, Bolovia, Costa Rica, 0,2 to 0,3 Malaysia, Peru, Togo, Venezuela Burkina Faso, Chile, Mexico, 0,3 to 0,4 Uruguay 0,4 to 0,5 Colombia, Egypt Argentina, Burundi, India, 0,5 to 1 Lesotho, Rwanda. Turkey Table 3

18 5 Results 5.1 Regression Analysis By performing the regressions for each country using the Ordinary Least Squares method, we were able to calculate the coefficients of our variables meaning, the β i s of the control and debt variables. Together with the coefficients, EVIEWS provided us with statistical information regarding the fitness of our model to each country s data as well as its accuracy. All the results are tested using a 0.05 significance level. We will now consider one of the countries and explain what those results say about the model used. Let s consider Venezuela as an example. The following information was obtained by performing the regressions in EVIEWS and by using the equation below. Log (GDP/capita) = c + β 1 log (DS/Exports) + β 2 log (Inv) + β 3 log (Ops) + β 4 log (Popinc) + β 5 log (TED/Exports) + β 6 log (TED/GDP) + β 6 log(ted/exports) 2 + β 8 log(ted/gdp) 2 Dependent Variable: LOG(VENEZUELA RB_GDP_POP) Method: Least Squares Date: 05/26/09 Time: 00:10 Sample (adjusted): Included observations: 32 after adjustments Convergence achieved after 113 iterations Backcast: 1971 Variable Coefficient Std. Error t-statistic Prob. C LOG(VENEZUELA RB_DS_EXPORTS) LOG(VENEZUELA RB_INV) LOG(VENEZUELA RB_OPS) LOG(VENEZUELA RB_POPINC) LOG(VENEZUELA RB_TED_EXPORT) LOG(VENEZUELA RB_TED_GDP(-1)) (LOG(VENEZUELA RB_TED_EXPORT))^ (LOG(VENEZUELA RB_TED_GDP(-1)))^ AR(1) MA(1) R-squared Mean dependent var Adjusted R-squared S.D. dependent var S.E. of regression Akaike info criterion Sum squared resid Schwarz criterion Log likelihood F-statistic Durbin-Watson stat Prob(F-statistic) Inverted AR Roots.89 Inverted MA Roots

19 5.2 Regression coefficients The first column of the table obtained from EVIEWS illustrates the control variables that are used in the model. Logs were used in each variable in order to smooth the data and account for extreme fluctuations. In some cases we see a (-1) inside the variable which accounts for time lags. The autoregressive (AR) and moving average (MA) terms were used in order to avoid the existence of serial correlation. The second column presents all the coefficients, β i s, that were computed by the software using OLS method. The important aspect here is what these coefficients mean in comparison to their probabilities, which lie on the last column of the table. As we mentioned in section 2.5 -The coefficients measure the marginal contribution of the independent variables to the dependent variable, holding all other variables fixed -. For example, in Venezuela s study case, the coefficient in front of TED/GDP is with a probability of Using a 5% significance level we can say that if we increase TED/GDP by 1% GDP per capita (the dependent variable) will increase by % with 99% probability. At the same time (TED/GDP) 2 will decrease GDP per capita by % at a 99% confidence level since that the coefficient is negative. An important observation between the coefficients of TED/GDP and its square is the signs. More specifically, in most cases, we have a small negative coefficient in front of (TED/GDP) 2 and at the same time, for the non-squared debt variable, the coefficient is big and positive. This implies that for small ratios of debt-to-gdp, the positive coefficient will outperform the negative one. On the other hand large ratios of debt-to-gdp will have the opposite effect which will affect GDP per capita negatively. Therefore the more debt we take the less growth we have, supporting our theory of negative impact on growth after a certain level of debt stock. 5.3 Statistics of the Regressions Each time a regression is performed on a data series we obtain a large amount of outputs; some of them are indicators of the precision by which our curve fits the data of a specific country. Since the analysis is based on 9 time series for each country, the amount of figures forced us to condensate those statistics in histograms that will allow a more visual approach to understand the accuracy of our regressions. The raw figures for all graphs of this section are presented in Appendix 4. R-Squares In Figure 7 we can observe that 91% of our R-square values are equal or higher than 0.8. This implies that 91% of the time our independent variables explain the variance of the dependent variable by 80% or more. The other 9% of the R-squares are in the range 0.65 to All those figures placed together lead to an average of 90.95% variance of the model explained by our independent variables. 19

20 Figure 7 Adjusted R-squares The difference between our R 2 and our figures has an average of Since both indicators are stated in percentage their difference is very small. Consequently it allows us to infer that our variables allow us to make good measurement of the variation in the dependent variable. The average for is 0.87 where 86% of the cases have an of at least 80% as seen the Figure 8, Figure 8 Durbin-Watson Statistics As we mentioned above, it would be very unlikely to have all the countries perfectly fit the model. Chad s results indicate the existence of certain degree of positive serial correlation. The rest of the countries have a D-W value between 1.6 and 2.2. Since, for our model we assume that values between 1.6 and 2.3 indicate no serial correlation our results support the accuracy of the use of OLS in our study.

21 Figure 9 Akaike Information Criterion During the numerous regression performed we managed to reduce the AIC from down to 7.7 to 4.23 and finally we ended up with an average of , being and the minimum and maximum values respectively. We can observe from the Figure 9 that 93% of all our values are negative and the other 7% remaining does not have a large size. The implication here is that our model fits very well the data of the counties studied. Figure 10 Schwarz Information Criterion (BIC) The BIC as well as the AIC gives a positive result. Even penalized stronger for the coefficients it does not distorts the indication of a good fit for our model. Figure 11

22 5.4 Debt and Growth results After obtaining the raw data series from IMF, World Bank and other databases we transformed each of the variables into GDP percentages and calculated the increase in population. In the next step we calculated all the ratios that form part of our model, those are: Total external debt-to-gdp, GDP per capita, total external debt-to exports and debt serviceto-exports. Having all the variables ready, we can now perform the regressions for each country. By using the regression equation we are able to calculate the coefficients for each variable β i. To calculate the optimal level of total external-to- GDP we have to compute the partial derivative of the regression equation with respect to TED/GDP variable. Let us consider the case study of Venezuela as an example. Below we present the regression equation, using the coefficients obtained from EVIEWS. Log (GDP/capita) = log (DS/Exports) log (Inv) log (Ops) log (Popinc) log (TED/Exports) log (TED/GDP) log(TED/Exports) log(TED/GDP) 2 The partial derivative will provide us with the following equation which we take equal to zero in order to compute the optimal level of total external debt with respect to GDP (TED/GDP) log(TED/GDP)*(TED/GDP) -1 = 0 Solving the above equation we can obtain the maximum amount of external debt that optimizes GDP growth. For Venezuela this level was found at approximately 35%. In a similar way we calculate the levels for all the countries of our study. The optimal debt-to-gdp ratios obtained from the regression equations were applied to the economic theory that is the basis of our thesis (the Debt Laffer curve theory). In order to do so we have gone back to the accounts obtained by modifying our raw data. Specifically, we have taken a look at the historical Debt-to-GDP ratios for each country and compared them with growth rate they have experienced in the same year. Moreover, we examine the points were the Debt-to-GDP ratio is around the optimal level found from our model. Also, we considered the development of investments and see that such ratio doesn t vary a lot over the years for most of the countries studied. We also found that the best time- lag for investments is one year. This might be because developing countries usually have high external debt levels and according to our theoretical background, investors tend to assign resources to short-term projects. Therefore we reckon investments to be constant. Least but not last, we will see high levels of GDP for the years when the Debt-to-GDP ratio is closer to our optimal value, but later in time we may observe suboptimal ratio levels and higher GDP. Many other factors affect GDP; For example, population growth influences GDP due to the fact that the working force is larger and production increases. However, we focus completely on the Debt-to-GDP ratio and GDP growth relationship. 22

23 In most cases, the results clearly support our theory since we observe how low levels of debt (in relation to the optimal level) contribute to the country s GDP growth. Then, for high levels of debt, there is a negative relationship between Debt-to-GDP ratio and GDP growth. We can better illustrate this in the following examples. Figure 12 presents the historical development of Debt-to-GDP, Investments and GDP per capita accounts for Venezuela from 1970 to We use a double Y axis graph illustrating percentages on the left and US dollars on the right. Figure 12 From our table of optimal debt-to-gdp ratios found in Appendix 5, we see that our regression model calculated an optimal level el for Venezuela of 35.17%. Such ratio was achieved by the country around the years of 1978 and If we follow the Debt-to-GDP and GDP per capita lines, we observe that between 1970 and 1975 the Debt-to-GDP ratio was quite low. Although the country managed to grow during that period, it was from 1978 that the Debt-toskyrocketed to levels as GDP ratio got closer to the optimal level and we can see how GDP high as almost $5000 per capita. However, the Debt-to-GDP ratio kept growing over the optimal level affecting negatively GDP growth. It was only in 1989 when the Debt-to-GDP ratio started falling from a critical level of 70% and the country started growing again. Table 1 and Figure 12 shows some interesting figures for Venezuela from 1996 to Year Optimum Ratio Debt to GDP ratio DTG ratio % change GDP GROWTH 50,53 6,48% -11% 41,24-18,37% 23% 40,99-0,62% 4% 41,53 1,32% 5% 35,81-13,77% 17% 31,53-11,95% 3% 39,10 23,99% -26% 45,21 15,63% -12% Table 1

24 We can observe that the Debt-to-GDP ratio increased in 1996 and GDP growth was -11%. From that point it started falling and the next year when the ratio had decreased by 18%, the country grew as much as 23%. Such a high growth level was resembled when the country reached our hypothetical optimumm level in That year the growth rate was 17% and later the Debt-to-GDP ratio started to rise rapidly from 2001 causing GDP growth to fall again. Figure 13 By looking to the corresponding figure, we can verify what Arthur Laffer proposed. When a country gets closer to its optimal Debt-to-GDP ratio, the GDP growth rate is high as well, if it s too low or too high, the country might still grow but wouldn t achieve its highest potential. Finally if the debt level keeps increasing, eventually the country may experience negative growth. We can briefly check another example by selecting another country from our pool. Table 2 and Figures 13 and 14 show the data and analysis for Burkina Faso. Year Optimum Ratio Debt to GDP ratio DTG ratio % change GDP GROWTH 18,48% 7,87% -10% 20,05% 8,53% -4% 24,85% 23,93% -11% 28,08% 12,99% -11% 33,03% 17,60% 4% 31,41% -4,89% 28% 34,91% 11,15% 13% 32,31% -7,47% 7% 27,42% -15,13% -3% 26,83% -2,15% 15% 30,77% 14,67% -2% 46,26% 50,35% -31% 47,79% 3,32% 1% 59,69% 24,89% -21% Table 2

25 From our table of optimal debt-to-gdp ratios found in Appendix 5, we see that our regression model calculated an optimal level for Burkina Faso of 34.63%. Such ratio was achieved by the country around the years of 1985 and Actually, if we follow the Debt-to-GDP and GDP per capita lines, we observee that from 1970 the Debt-to-GDP ratio was low and started growing in a healthy way helping GDP grow as well. Nonetheless, it was from 1985 to 1988 when the Debt-to-GDP ratio got closest to our optimal level and as you can see from Table 2 GDP grew at outstanding rates. This shows how keeping the Debt-to-GDP ratio around the optimal level results in excellent GDP growth rates. Here we can also point out that the investment level was kept around 10% over time, supporting our assumption of constant 1- year investment rates. In 1991, the Debt-to-GDP ratio went up to 46% and reached 59% two years later. As a result, we observe a fall in GDP and went sidelines, which was expected according to our theory. It was only in 2000 when the ratio started falling and GDP began rising as well. For more information about the rest of the countries refer to appendix 6. Figure 14 Figure 15

26 6 Conclusion Having run a series of test on the data obtained from various databases, as well as many regressions using econometric techniques, we were able to support the theories and assumptions about the importance and impact of external debt on economic growth. More specifically we reached the following conclusions. Regarding our time series, we have managed to smooth the extreme fluctuations of our data and with the help of Levin, Lin & Chu t-stat, we confirmed stationary data at a 95% confidence level. Unit root tests also suggested that the optimal time lag to be used in order to achieve stationary data and accurate results is one year. The next set of tests involves Granger causality statistics. The results indicated that for several countries causation exists among the variables. Also the theory that total external debt affects economic growth, through the investment channel, was verified by the fact that external debt-to-gdp ratio and GDP per capita granger cause investments for a significant amount of countries. The quadratic model used to describe the relation between the dependent and independent variables turned out to be a good fit for the data series. However, we need to stress that the degree of our model s fitness differs among countries. Nonetheless, the model indicated that on an average level, the optimal external debt-to-gdp ratio for those countries lies at 54%. Another important inference made from this model s results, is that it supports the quadratic relationship between external debt and growth. It illustrates that reasonable levels of debt actually contribute to the economic growth of a country while excessive levels turn out to be harmful. Last but not least, the regressions run with the use of Ordinary Least Squares method, provided results which support our assumptions about the contribution of the control variables in the prediction of GDP per capita. If we examine closely the regression coefficients obtained as an average of all countries, we can see how the underlying variables affect GDP per capita. Debt Service-to-exports has a positive coefficient implying that the higher the amount of debt serviced the better GDP per capita ends up. The positive coefficient of Investments verifies the assumption that new investments will result in higher GDP growth one year later. As we mentioned in section 3.1, an increase in population combined with less or fixed capital sources would result in negative GDP growth. The negative coefficient in front of population increase sustains that theory. The openness coefficient has a negative sign which can be explained by two main theories. The first one suggests that long term economic openness might cause productivity reduction. The reason is that no additional investments are made (seen as a flat rate over most of the countries) and innovations turn to be usual inputs. Alternatively we could imply that governments might try to protect the domestic production in cases of high openness, thus harming the GDP growth. To sum up we strongly support the theory that external debt can be beneficial for a country but only up to certain levels. After those levels additional debt results in negative contribution on economic growth. 26

27 7 References Cordella, Ricci & Ruiz-Arranz, Deconstructing HIPC s Debt Overhand, Washington,DC, International Monetary Fund EViews 5 User s Guide. Copyright Quantitative Micro Software, LLC Flores, Fullerton, Olivas, Empirical evidence on foreign debt, investment and growth in Mexico. Gujarati, D.N, 2003, Basic econometrics, 4th ed., Boston, McGraw-Hill Investment words. Retrieved April 20 2th, 2009,from Johnston, J., & Dinardo, J , Econometric Methods. 4 th edition. MCGraw Hill International Krugman, P., Financing vs. Forgiving a Debt Overhang, Journal of DevelopmentEconomics, number. 29, pp Pattillo, C. Poirson H., & Luca, R., External Debt and Growth Presbitero, A., The Debt-Growth exus: a Dynamic Panel Data Robert, P., & Rubinfeld, P., Econometric Models and Economic Forecasts, 4th edition,mcgraw-hill/irwin Rubio, Ojeda, Montes Deuda externa, inversión y crecimiento en Colombia. Ruey S. Tsay, Analysis of Financial Time Series, 2nd edition, Willey Interscience United Nations Human Development Program. Retrieved May, 3th, 2009, from University of Pennsylvania. Retrieved May 4th, 2009 from Wackerly, D., Mendenhall, W. III, Scheaffer, R., Mathematical Statistics with applications, Duxbury Resource Center Wapedia. Retrieved. May 4th, 2009, from Wapedia. Retrieved. May 4th, 2009, from Weil, D., Economic Growth, 2th edition, Pearson International Education 27