Inflation, monetary balances and the aggregate production function : the case of Colombia

The World Bank INU-55 Policy, Planning and Research Staff Infrastructure and Urban Development Department Report INU 55 Inflation, Monetary Balances and the Aggregate Production Function: The Case of Colombia by Robert Buckley and Anupam Dokeniya October 1989 DISCUSSION PAPER This is a document published informally by the World Bank. The views and interpretations herein are those of the author and should not be attributed to the World Bank, to its affiliated organizations, or to any individual acting on their behalf. FILE COPY Copyright 1989 0 TIve World Bank 1818 H Street, N.W. ALL Rights Reserved First Printing October 1989 This is a document published informally by the World Bank. In order that the information contained in it can be presented with the least possible delay, the typescript has not been prepared in accordance with the procedures appropriate to formal printed texts, and the World Bank accepts no responsibility for errors. The World Bank does not accept responsibility for the views expressed herein, which are those of the author and should not be attributed to the World Bank or to its affiliated organizations. The findings, interpretations, and conclusions are the results of research supported by the Bank; they do not necessarily represent official policy of the Bank. The designations employed, the presentation of material, and any maps used in this document are solely for the convenience of the reader and do not imply the expression of any opinion whatsoever on the part of the World Bank or its affiliates concerning the Legal status of any country, territory, city, area, or of its authorities, or concerning the delimitations of its boundaries or national affiliation. The authors are Robert Buckley, Sr. Economist, and Anupam Dokeniya, Researcher, Infrastructure and Urban Development Department, The World Bank. Helpful comments were made by WiLLiam Easterly, Emmanuel Jimenez, Kyu Sik Lee, Desmond McCarthy, Jacques Polak, Bertrand Renaud and Alan Walters. They, of course, are not responsible for any remaining errors. The views expressed are not those of The World Bank. The World Bank Inflation, Monetary Balances and the Aggregate Production Function: The Case of Colombia DISCUSSION PAPER  ABSTRACT The role of monetary balances in economic growth has long been a topic of macroeconomic research. Following the work of Sinai and Stokes (1972), a number of studies have given this perspective empirical content. By demonstrating the significance of the role of monetary balances in an aggregate production function, this work has shown that money and financial policy need to be carefully considered in studies of growth. This paper also examines the role of real money balances in an aggregate production function of a developing economy, Colombia. In addition to being a developing country, Colombia is also interesting to analyze in this way for a number of other reasons. First, although it has experienced high and variable rates of inflation, it has also introduced a competitive system of quasi-monetary balances that have been indexed for inflation. In fact, the success of this system appears to have played a significant role in the continued expansion of the Colombian financial system. Second, as one of the most extensively studied developing countries in the world, data on Colombia are more readily available than they are for other developing countries. In this respect, Colombia is one of the few developing countries for which an empirical study of the effects of financial policy on economic growth can be made. There is little empirical work on this topic, and Colombia represents an unusual opportunity to perform such analysis. Finally, the role that monetary balances may have played in economic growth in Colombia is of interest because indexed mortgages played a major role in this change in financial policy. Rather than deregulating the interest rate on deposits and thereby simply permitting a more competitive market for broadly-defined monetary balances, Colombia induced more competition. It did this by introducing indexed mortgages which provided higher yields on deposits than those available at commercial banks. In a sense, these indexed mortgages were similar to introducing a competitive "Trojan Horse" into the Colombian financial system. Other depository institutions had to compete with indexed mortgage lenders for deposits. Our results indicate that it was not the effects of finance on the composition of investment patterns that mattered. Rather, growth was stimulated by not only permitting but by inducing the financial system to be able to minimize the effects of high and variable inflation rates on the cost of monetary balances. Household access to credit for "low priority" investments played an important part in the process of inducing a cost-reducing, more competitive financial technology. While it does not appear that the forced investment schemes that still litter the financial system have made the best use of the resources mobilized by the more competitive deposit system, one can only speculate about what would have occurred if the resources were not in the financial system at all.  INFLATION, MONETARY BALANCES AND THE AGGREGATE PRODUCTION FUNCTION THE CASE OF COLOMBIA Table of Contents Page No. I. INTRODUCTION................. .... . . . . 1 II. INDEXED MONETARY BALANCES IN COLOMBIA. ........ . . . . 4 III. THE MODEL AND THE DATA............. .... . . . 10 IV. THE AUGMENTED PRODUCTION FUNCTION AND OTHER STUDIES OF COLOMBIAN ECONOMIC GROWTH.... . . . . . 14 A. Indexation and Economic Growth.... .... . . . . . 14 B. Income Distribution Issues........ ... . . . . 15 C. Financial Policy and the Sources of Growth.... . . . . 16 V. CONCLUSION.................... . . . . . . 18 APPENDIX I . . . . . . . . . . . . . . . . . . . . . . . . . 20 APPENDIX II . . . . . . . . . . . . . . . . . . . . . . . . . 21 TABLES Table 1 - Behavior of Monetary Aggregates and Inflation over the 1958-84 Period . . . 8 Table 2 - Estimates of the Parameters of the Cobb-Douglas Production Function, with and without Real Money Balances, Corrected for Autocorrelation, for the years 1958-1984........ ..... . . . . 22 Table 3 - Estimates of the Parameters of the Cobb-Douglas Production Function, with Real Money Balances (with and without Adjustment for Indexation and Inflation) Corrected for Autocorrelation, for the Years 1958-1984......... ... . . . 23 - 111 - Page No. TABLES (continued) Table 4 - Estimates of the Parameters of the Cobb-Douglas Production Function, with the without Real Money Balances, Corrected for Autocorrelation, for the Years 1958-1984. (Capital is Adjusted for Capacity Utilization and Labor is Adjusted for Change in Sex Composition and Education). ......... . . .24 Table 5 - Data for Colombia 1958-1984....... . . . . . . . 25 Table 6 - Natural Logarithmic Transformation of the Variables . 26 Table 7 - GDP of Colombia 1958-1984. . .......... . . .27 Table 8 - Capital Stock for Colombia 1958-1984..... . . . .28 Table 9 - Labor Force in Colombia 1958-1984..... . . . . . .29 Table 10 - Monetary Balances in Colombia 1958-1984..... . . .30 Table 11 - Real Monetary Balances for Colombia 1958-1984 . . . 31 Table 12 - Indexed Real Money Balances for Colombia 1958-1984 32 Table 13 - Regression with No Money Variable..... . . . . . . 33 Table 14 - Data Used for Using Solow's Approach to Find Components of Growth........ ..... . . 34 Table 15 - Data Used for Predicting the Values...... . . . . 36 Table 16 - Ratio of M2 (Broadly Defined Money) Over GDP . . . 37 Table 17 - Regression Results of Financial Deepening Over Time 38 Table 18 - Inflation Tax on Money Balances as a Share of Income. 39 FIGURE Figure 1 - Inflation Tax on Monetary Balances as a Share of Income . . . . . . . . . . . . . . . . . . . . . . 40 BIBLIOGRAPHY................ .... . . . . .41 INFLATION, MONETARY BALANCES AND THE AGGREGATE PRODUCTION FUNCTION THE CASE OF COLOMBIA I. INTRODUCTION 1.01 The role of monetary balances in economic growth has long been a topic of macroeconomic research, see, among others, Levhari and Patinkin (1968). Following the work of Sinai and Stokes (1972), a number of studies have given this perspective empirical content. By demonstrating the significance of the role of monetary balances in an aggregate production function, this work has shown that money and financial policy need to be carefully considered in studies of growth. More recently this type of empirical analysis has been extended to the production function of a developing country, Pakistan, by Khan and Ahmad (1985). Their results are consistent with the findings for the U.S. and Japan --that is, real money balances are an important factor of production. 1.02 This paper also examines the role of real money balances in an aggregate production function of a developing economy, Colombia. In addition to being a developing country, Colombia is also interesting to analyze in this way for a number of other reasons. First, although it has experienced high and variable rates of inflation, it has also introduced a competitive system of quasi-monetary balances that have been indexed for inflation. In fact, the success of this system appears to have played a significant role in the continued expansion of the Colombian financial system. See the World Bank (1987), and Barro (1975). 1.03 Over the 1974 to 1984 period, for example, Colombia was one of the few Latin American countries not to experience any significant reduction in broadly defined monetary assets as a share of GDP.11 In contrast to most other Latin American countries, Colombian monetary balances continued to grow more rapidly than did the economy without any significant interruptions. It would be interesting to determine whether this more competitive and buoyant financial system reduced the costs of this factor of production by such an extent that it affected the level of economic growth. 1/ Data on M2\GDP for Argentina, Brazil, Chile, Colombia, Mexico, and Peru for the 1974-84 period indicate that all of these countries except Colombia at least once experienced a substantial reduction in broadly-defined monetary balances as a share of GDP. The Colombian ratio was much less volatile, as well as almost monotonically increasing. In one year, 1979, there was a less than one percent decrease in M2/GDP. A log linear regression of M2/GDP-Aeu', where t-time, for each of the six countries for the 1974-84 period (Mexico only 1977-84) indicates that in Colombia the coefficient on time was positive and significant at the one percent level, and the R2 was equal to .68. The results for the other countries did not yield a significant time trend except for Brazil, but in Brazilian case, the coefficient was negative. Source for the data is International Financial Statistics. -2- 1.04 Second, as one of the most extensively studied developing countries in the world, data on Colombia are more readily available than they are for other developing countries. Indeed, this empirical analysis can be undertaken only because the time series data from two other studies, by Harberger (1969) and a Presidential Employment Study as reported in World Bank (1987) were developed, and in the former case updated. In this respect, Colombia is one of the few developing countries for which an empirical study of the effects of financial policy on economic growth can be made. As Fry (1988) shows, there is little empirical work on this topic, and Colombia represents an unusual opportunity to perform such analysis. 1.05 Third, work on the sources of growth in Colombia, by Elias (1978), Hanson et. al. (1985), indicates that one of the larger "unexplained" sources of growth in Colombia over the 1960-1980 period occurred during the period when financial sector policy innovations were introduced. Once again, it would be interesting to determine whether this higher level of technical change can be empirically related to the financial innovations. 1.06 Finally, the role that monetary balances may have played in economic growth in Colombia is of interest because indexed mortgages played a major role in this change in financial policy. Rather than deregulating the interest rate on deposits and thereby simply permitting a more competitive market for broadly-defined monetary balances, Colombia induced more competition. It did this by introducing indexed mortgages which provided higher yields on deposits than those available at commercial banks. In a sense, these indexed mortgages were similar to introducing a competitive "Trojan Horse" into the Colombian financial system. Other depository institutions had to compete with indexed mortgage lenders for deposits. The central way that they could do this was through paying more competitive interest rates on financial instruments. Over the 1972-84 period, for example, commercial bank certificates of deposit had an ex post average real return of 2.5 percent, after having yielded an average negative 6.5 percent real return for the previous 14 years. 1 1.07 This kind of increased competition for funds may have a number of desirable allocative effects. However, it could also cause mortgage borrowers to "crowd out" other investments, as suggested by Carrizosa et. al. (1982). In many developing countries financial regulators proscribe the supplying of mortgages by the formal financial system because of this latter concern. In this respect, the study is one of the first attempts to analyze empirically the possible macroeconomic effects of providing households access to mortgage credit at competitive interest rates. 1.08 Coherent with the preliminary nature of our research, the econometric specification of the study is similar to the original Sinai and Stokes approach. 2/ The rate of return over the 1958-71 period are ex post rates inferred from Carrizosa et. al. (1982); the data for the later period are from Correa (1986). Berry and Urrutia (1976) also provide data on real deposit rates and a discussion of the broader effects of mortgage lending policies in the pre-indexation period. - 3 - Indeed, the approach taken is very much in the spirit of the original Solow (1957) article on aggregate production functions and the sources of growth. That is, we hope that we are not pushing the data beyond what can reasonably be inferred from such aggregate measures. Nevertheless, despite the more heuristic than strictly quantitative nature of the analysis, we think that our results provide robust if imprecise evidence that a more competitive deposit and credit market played an important role in Colombia's economic growth. 1.09 The plan of the paper is as follows. The next section reviews the effect that inflation can have on the cost of monetary balances and the way that indexation affects these costs. Then, the Colombian experience with inflation, indexation, and increased financial competition is described. The effects of inflation on monetary aggregates and what we term "equivalent units" of this factor of production are examined and compared to the levels that would have been obtained in the absence of indexation. In Section III the data and empirical results are presented and discussed. Section IV reviews previous analyses of Colombian economic growth in light of the findings, and discusses the policy implications of our findings. A final section summarizes. II. INDEXED MONETARY BALANCES IN COLOMBIA 2.01 For households, the transaction costs of expenditures can be minimized if transaction balances can be placed into highly liquid deposits that are not affected by changes in the inflation rate. For the most part, the savings and time deposits offered by the Colombian Caja Ahorra de Vivienda (CAVs), savings and housing corporations, have been such instruments. While in recent years ceilings on the amount of adjustment for inflation have reduced the real return on these deposits, the record of their largely positive ex post return since 1972 has built confidence in the use of such instruments. 2.02 The CAVs were created in 1972 by a series of decrees by the Pastrana government. The government relied upon Constitutional authority relating to the disposition of personal savings and their development played a major role in the government's development strategy.11 Their design and implementation were placed under the direction of Laughlin Currie.Al These institutions were introduced into a financial system which had allocated a contracting share of national resources to the formal financial sector and which operated parallel to a thriving and growing informal sector. For example, over the 1965-69 period credit outstanding as a share of GDP averaged 15 percent, whereas it averaged 19 percent in the preceding five year period. In contrast, by the 1980-84 period, the net credit outstanding as a share of GDP averaged 36 percent, and there is indirect evidence that the level of economic activity in the informal sector had secularly contracted.5' 2/ See Berry and Soligo (1980) for a discussion of the development strategy and Sandilands (1980) for a discussion of the CAVs creation and their early regulation. / Currie was formerly the chief advisor to both Mariner Eccles, Chairman of the Federal Reserve Board, and President Roosevelt. He also directed the first World Bank mission to Colombia in 1949. ./ The informal sector generally has three important dimensions: finance, employment and housing production. In contrast to many other Latin American economies, each of these aspects of the informal sector appeared to contract during the 1970s. See the World Bank (1987), p. 70 for further discussion of the expansion of the formal financial sector in the 1970s mentioned in the text. With respect to housing, Urrutia (1985) p. 64 documents the very significant formalization of the housing stock that took place over the 1970s. The World Bank (1983) p.19-23 provides a discussion of labor participation over the 1960s and 1970s saying that in the latter period the employment expansion would appear to be the highest achieved by a big country over a comparable period. After 1972 employment in the informal sector continued to grow more rapidly than did employment in the formal sector. However, it grew at a less rapid rate than in the 1958-72 period even though total employment expanded much more rapidly in the second period. Over the period 1958-72 the share of the labor force in the informal sector showed an increasing trend, expanding in all the years except - 5 - 2.03 As financial intermediaries, the CAVs represented both a liberalization and a further specialization of an already highly segmented and controlled financial system. They were a liberalization because they financed mortgages at positive ex ante real interest rates that were initially fully indexed for inflation, and they paid their depositors a similarly indexed real return. However, because they were the only intermediaries allowed to index both their credit and their liabilities to a unit of constant purchasing power, called UPACs, they were also a further specialization of the financial system. This specialization increased over time through a series of regulations that governed the share of the CAV portfolio that had to be lent for certain loan sizes, the interest rate that could be charged, and the permissible loan-to-value ratio of the various loan amounts, among other directives that were designed to insure that CAV lending was targeted towards lower and moderate-income borrowers.& 2.04 The return on CAV deposits was originally based on a three month moving average, for the months immediately preceding the calculation, of the combined consumer price indices of blue and white collar workers. Currently, the index is still changed daily with the quotations for the next month announced in advance. This method of indexation of the return on deposits of course means that the index is based on the past rate of inflation rather than a measure of inflation during the holding period for the deposit. It implies that an individual who deposits funds in a CAV knows with certainty the nominal rate of return but not the real rate of return. Consequently, the central feature of indexation is not that the financial contract has immunized real returns from the effects of inflation. Rather, the chief features have been to create a system of deposits on which the interest rates gradually adjust to changes in the rate of inflation and provide a competitive real return to savers. 2.05 Such a system is hardly the idealized method of indexation that is recommended by economists. See Fischer (1975). Nevertheless, these financial instruments have provided a means to avoid most of the inflation tax on short- term financial assets and transaction balances, and as Barro (1975) says they "have induced some increases in the nominal interest rates paid on other financial assets,.." p.5. They have, in other words, lowered the costs of relying on the formal financial sector to provide a service that a formal sector institution should have a comparative advantage in providing. 2.06 An approximation of how Colombian policy reduced the effects of inflation on the costs of holding monetary balances can be made by computing a measure of the aggregate tax rate on monetary balances. Prior to the introduction of indexation, this tax applied to all monetary balances because nominal interest rates on time deposit were both largely invariant with respect in three, when the decrease was negligible. In the 1972-86 period, in contrast, the informal market share contracted in half the years even though the indirect costs of formal sector employment increased sharply. A/ See Isaza (1987) for a complete listing of all the regulations governing CAVs since their creation, and Carrizosa et. al. (1982) for a discussion of broader financial market policies that have affected the functioning of the CAVs. - 6 - to changes in the inflation rate and lower than the inflation rate.21 As a consequence, increases in the inflation rate affected the cost of Ml, currency and demand deposits, as well as M2, which also includes time deposits. The tax on M1 is straightforward and in steady state is equal to 8(1+0), where 8 is the inflation rate. 2.07 For time deposits, prior to the introduction of CAVs, the tax is more complicated. Because longer term deposits yielded a negative real rate of return, the income to these assets was taxed at a 100 percent rate. But in addition, because the nominal return on these deposits, Rn, was always less than the inflation rate, these assets also lost value over time. Bringing all these effects together, the tax rate on what might be termed equivalent units of monetary balances can be described by 1)Ti- Ml (e - Rn) (M2 - Ml) (M2 - Ml) (1 + e) x-Y (1 + (6-Rn)) Y Y Rr is the real return on time deposits, and Y is GNP. The first and second terms on the right hand side express the tax on monetary balances as the share of income that would be needed to restore these balances to their prior level. In other words, they represent taxes on the stock of M1 and (M2-M1) balances, respectively. The tax on real return on the non-M1 portion of the monetary balances is represented by the third term on the right hand side. 2.08 Now consider how the introduction of indexed time and savings deposits affects this tax.!! If the return on time deposits competes with the return on CAV time deposits, and this real return becomes invariant with respect to changes in the inflation rate inflation would apply only to Ml, and not at all to M2 or M3, which includes M2 plus CAV deposits. In this case the tax rate on monetary balances like Bailey's (1956) stylized descriptions of the inflation tax is: (2) T2 - Mi (1 + e) Y This kind of regulatory change eliminates both the inflation tax and loss of real return on non-Mi monetary balances, and it results in the inflation tax being applied only to M1 balances. It amounts to assuming that the cost of the indexed balances is unaffected by changes in the inflation rate, so that non-Mi monetary balances become superneutral. 7./ See Carrizosa et al. (1982). 3/ Strictly speaking, the indexed time and savings deposits (CAV's) should be part of M2, but in our analysis, we separated the CAV deposits from M2 to isolate the effects of these deposits. The treatment, as far as taxes are concerned, of these two "monies" (M2-Ml) and (M3-M2) are identical from 1973 onwards. - 7 - 2.09 However, besides making the real rather than the nominal return on time deposits less variable with respect to changes in the inflation rate, the introduction of the CAVs also blurred the distinctions between the types of monetary balances. For example, Montenegro and Garcia (1986) found that after the introduction of indexation, the velocity of currency secularly increased. The continual decline in the share of Ml held in currency (from 31 percent in 1960 to less than 24 percent in 1974) was reversed. By 1984 the share of Ml held in currency had once again reached the level of 1960. They also found that the holdings of currency plus CAV savings deposits was without trend. They suggest that this latter result implies that CAV saving deposits became close substitutes for currency. In effect, CAV deposits became another vehicle through which the inflation tax could be avoided and the costs of holding monetary balances reduced. 2.10 Figure 1 plots out the tax rate on the monetary balances as a share of income described by the above equations. It also traces out the inflation rate. Prior to 1973, TI is used to measure the tax rate and after that T2 is the tax rate. It is quite clear that the inflation tax relative to inflation rate was very significantly reduced.21 The tax rate per percent of inflation is 0.166 percent in the former period and 0.116 percent in the latter period.11 Some evidence of how this reduction in the inflation tax rate and increase in the inflation rate affected the holdings of monetary balances is presented in the following table. 9/ The estimates are stylized for a number of reasons. Most importantly they use ex post measures of inflation rather than the ex ante rates that motivate the holdings of various types of balances. In addition, the assumption that real returns become completely invariant with respect to the inflation rate after indexation was introduced is an exaggeration. Complete insulation of real returns was not achieved so that assumption lowers the estimated tax rate. On the other hand, however, we make no attempt to account for the blurring of distinctions between types of monies. This assumption causes the estimates of tax in the post-1972 period to err in the other direction. Finally, we assume that the real rate of interest was constant and equal to 2.5 percent throughout the period. 10/ These numbers were obtained by calculating average inflation rates and average inflation tax over the two time periods; 1958-1972 and 1973-1984. For the time period 1958-1972, Ti was the inflation tax used and for 1973-84 period, T2 was the inflation tax used. The average inflation tax was divided by the average inflation rate to get these numbers. - 8 - Table 1: BEHAVIOR OF MONETARY AGGREGATES AND INFLATION OVER THE 1958-84 PERIOD 1958-72 1973-84 Ml/GDP > 0 < 0 M/GDP 0 > 0 M1/M .85 .57 M1/M > 0 < 0 E .110 .235 The . indicates a derivative with respect to time. In the latter period, the coefficients were of an opposite sign from the former period and the standard errors were greatly reduced. 2.11 In the pre-indexation period broadly-defined monetary balances, M, was a relatively constant share of GDP. In addition, Ml share of total monetary balances showed an increasing trend. In the latter period, behavior was very different: M1 declined in importance (as a share of both GDP and M), as firms and households avoided the tax of the latter period's higher inflation rate. At the same time, broadly-defined monetary balances increased, as the return on these balances were better insulated from changes in the inflation rate. 2.12 To summarize, with the introduction of indexation, the Colombian financial system became competitive on the resource mobilization side. This competition for funds provided a way for households and firms to avoid much of the increase in the inflation tax on transaction balances that would have occurred as a result of the sharp increase in the inflation rate. On the other hand, this system can hardly be described as a liberalized system that competitively allocates resources. As Correa (1986) documents, the assets of the system are still targeted to a wide range of below market interest rate loans in agriculture, industry, and low-income housing.11/ 2.13 A financial system that encourages more competition for deposits and simultaneously requires lenders to make below market rate loans ultimately imposes the costs of the loans on the institutions rather than the depositors. Ll/ Indeed, recent work by Dailami (1989) suggests that Colombian corporations are making use of below market interest rate credit to buy market rate financial assets. His work shows that in 1983 financial assets accounted for 20 percent of total assets of non-financial corporations in Colombia. This figure is double the rate observed in developed economies. - 9 - Hence the financial crisis that has affected the commercial banking system since the end of 1982 is not surprising.!1 But, this crisis is not the result of the increased competitiveness of the financial system. Rather, it is the incompleteness of the deregulation- -particularly the restrictions on lenders asset powers--that has created the problems. 12/ See World Bank (1987) and (1983) for discussions of the financial stress in Colombia. In 1982 this stress lead to a financial crisis and the creation of Fund to Guarantee Financial Institutions. The former study suggests that since 1985, after our estimation period, the structural weaknesses of the financial system became pronounced, p. 72. - 10 - III. THE MODEL AND THE DATA 3.01 A simple Cobb-Douglas production function with nonconstant returns to scale is assumed and estimated in log-linear form. Like Sinai and Stokes, we rely on single equation OLS estimation, corrected where necessary for autocorrelation. Our rationale for this single equation specification is twofold: first, the exploratory nature of our work; and second, the research subsequent to Sinai and Stokes' first article suggests that FIML, simultaneous equations or 2SLS approaches do not result in significant changes in the estimated coefficients in any of the countries for which the functions have been estimated. See, for example, Sinai and Stokes (1977), and (1981), as well as Short (1979), and Khan and Ahmad (1985). Cumulatively, the work that has followed the original article suggests that OLS estimation is a reasonable approach. While we acknowledge the potentially substantial problems that could arise from simultaneity concerns, they are not dealt with here.131 3.02 The following equation was estimated with annual data over the 1958- 84 period. (3) In GDP = In A + a In K + B In L + yln M + u where, GDP - total output, K - capital, L - labor, M - equivalent units of real money balances. A = an efficiency parameter, and the Greek letters are estimated parameters and u is a disturbance term. 3.03 Data for output, labor, and capital were taken from a number of recent World Bank studies of the Colombian economy. Data on real output and the real capital stock were obtained from an update of a Harberger (1969) study of the Colombian capital stock. Data on real monetary balances are from the Banco de la Republica as reported in various World Bank documents. Employment data are from a Presidential Employment Mission, as reported in the World Bank (1987). They measure the number of persons in the labor force. This measure is a poorer 11/ Romer (1987) raises doubts as to whether problems of simultaneity can be overcome by instrumental variables. He says "there is little hope that valid instruments exist." p. 186. - 11 - measure of actual labor input than is hours worked but, as Romer (1987) indicates, it is at least symmetric with the measure of capital input.-1 3.04 Our measure of equivalent units of monetary balances modifies the Sinai and Stokes' approach to account for the effects described in equations (1) and (2). To adjust for the more competitive yields on post-indexation time deposits, we assume that prior to indexation all monetary balances were taxed at the inflation rate, which is measured by the GDP deflator, and that after indexation was introduced in 1972, this tax applied only to Ml. That is, after indexation was introduced time deposits yielded the market rate of interest and hence did not bear any inflation tax; and prior to the introduction of indexation both the Ml and (M2-Ml) components of monetary balances were subject to the inflation tax as described in equation(1). 1 See the appendix for a complete description of all the variables. 3.05 Table 2 presents the results of the estimated equations with and without monetary balances. Equation (4) in the table indicates that a standard Cobb-Douglas production function without monetary balances describes the Colombian data fairly well. The returns to scale, 1.4, and the output elasticities -- labor 68 percent and capital 51 percent -- are similar to the results of Khan and Ahmad (1985) for Pakistan. They found returns to scale of 1.33 without money balances and elasticities of 75 and 58 percent, respectively. Sinai and Stokes (1972) also reported increasing returns to scale for the U.S., 1.78. Although their output elasticities, (1.36 and .43 respectively) were very different from ours, these kinds of differences between developed and developing countries--in particular a much higher relative elasticity for capital in 14/ We also estimated equations which adjusted the labor input for the effects that female participation rates and education would have in a manner suggested by Hanson et. al. (1985). Similarly, we also constructed measures of the utilized capital stock by relying on Cuddington's (1986) measures of permanent and cyclical measures of real GDP. We assumed that the capital stock was completely utilized in 1974, the year in which Cuddington estimates GDP was at the highest cyclical peak of our estimation period. In other years capital was assumed to be less than fully utilized by the same percent that cyclical output was less than output in the peak year. Equations estimated with these adjustments reduced the standard error of the equations and the regression coefficients. These results are not reported because of concern with ad hoc data transformations in an already highly aggregated equation. The results are available upon request. 1/ To give a concrete example of our adjustment for equivalent units of monetary balances, suppose that in real terms 100 units of M are observed in both periods 1 and 2, and that the inflation rate was 5 percent higher in period 2. In this case the holder of monetary balances in period 2 would have to allocate more of his income to such balances to derive the same level of services. Just as the Darby effect indicates that nominal interest rates must increase by 1/1-T to keep real returns constant with respect to a change in the rate of inflation, our approach implies that equivalent units of monetary balances are similarly constant if they are adjusted by 1/1-T where T=-. - 12 - developing economies--are consistent with Elias's (1978) findings for Latin America. 3.06 All but one of the coefficients in equations 4-7 are significant at the five percent level, (the labor coefficient in equation 5 is significant at the 10 percent level). The standard error of equation (4) without correction for autocorrelation, .047, is larger than the Sinai and Stokes estimate (.034) for a much longer period with superior input measures for the U.S. Equations 5-7 show that whether defined as Ml, M2, or M3, real monetary balances are of substantial importance when added to this standard production function. The standard error of the equation uncorrected for autocorrelation is reduced in every case; to .021 for the equation including Ml, .032 for the equation including M2, and .04 for the equation with M3. In addition, estimates of equations that were not corrected for autocorrelation indicate that there is much less of a problem in this regard in equations 5-7, than there is in equation 4, as would be expected if monetary balances were an omitted variable in equation 3.07 The coefficients on our measures of monetary balances ranged from .23 to .37. These results are somewhat higher than those of Sinai and Stoke's, .17 to .21, and somewhat lower than Khan and Ahmad's for Ml, .43 . Adding Ml to the equation did not significantly affect the returns to scale, whereas adding M2 or M3 did. The latter variables also reduced the contribution of labor by a much greater amount as is the case in previous research. Similarly, the pattern of change in coefficients when monetary balances are added to the estimated function is qualitatively similar to those of Sinai and Stokes. In particular: a5 < a4 and a6 Z a7 > a5; and B6 =7 5 =4 where the subscripts indicate the nun-'er of the equation. 3.08 Table 3 compares estimates of equation (3) without adjustment of monetary balances (M2) for equivalent units, i.e., like those of Sinai and Stokes with our adjusted measure of M2 from Table 2. A comparison of the results indicates that the adjustment to account for the inflation taxes on monetary balances improves the explanatory power of our estimation without having much effect on the coefficients of labor or capital. The SEE is lower in the equation 16/ Like Khan and Ahmad (1985), we also estimated equations including a time trend as a representation of neutral technological progress. Our results were similar to theirs. The coefficients of the other variables in the equation were not significantly different from zero. They suggest that this result seems to be caused by high collinearity. We also used a non-linear test for the appropriateness of the Cobb-Douglas specification as opposed to a CES functional form. Our results also provided strong support for the Cobb-Douglas specification. - 13 - where equivalent units of M2 are used and the coefficients are better confirmed.1U 3.09 To summarize, like previous studies our estimates suggest that monetary balances have played an important role in Colombian economic growth and should therefore be included in analyses of the sources of growth. We realize that our input data are clearly far from perfect, and even our measure of effect of the changes in the tax structure in the measurement of monetary balances will not achieve Jorgenson and Griliches' (1967) aspiration of eliminating the residual through better measurement of the inputs. Nevertheless, the robustness of our estimates under various input definitions is at least suggestive that our findings are not adventitious. Solow's (1988) recent comment on almost exactly this topic helps put our results in perspective: "Thus technology remains the dominant engine of growth, with human capital second. One does not have to believe in the accuracy of these numbers; the message they transmit is pretty clear anyway." "That is meant as a serious remark, every piece of empirical economics rests on a substructure of background assumptions that are probably not quite true. Under those circumstances, robustness should be the supreme economic virtue; ... so I would be happy if you were to accept the results I have been quoting to point to a qualitative truth and perhaps give some guide to orders of magnitude." Nobel address (1988) p. 314. 17/ For simplicity the only comparison presented in Table 2 is for equations that contain M2. This comparison is the most favorable for the unadjusted monetary balances. For example, using the unadjusted measure of M3 produces a statistically insignificant coefficient on M3 and a standard error that is trivially smaller, .045 versus .047, than that of the production function without monetary balances, i.e., equation (4). Similar results were obtained in the equation that used an unadjusted measure of M1. - 14 - IV. THE AUGMENTED PRODUCTION FUNCTION AND OTHER STUDIES OF COLOMBIAN ECONOMIC GROWTH 4.01 We focus on three of the many issues that have been raised in the extensive literature on Colombian growth: (1) Has the introduction of indexed mortgage instruments affected economic growth? (2) Can we draw any conclusions about the effect of financial policy on income distribution? and (3) Are there any additional potential "sources of growth" type problems that can be identified by the inclusion of monetary balances as a factor of production? A. Indexation and Economic Growth 4.02 Carrizosa et. al (1982) have argued that the introduction of indexation had little effect on the level of economic growth. They suggest that because of credit fungibility, the central effect of increasing formal sector mortgage financing was a substitution of financing from alternative sources of funds. This point of view has been contended by Currie and Rosas (1986) who argue that mortgage indexation played an important part in Colombia's economic growth by stimulating housing as a lead sector in the economy. 4.03 Whether mortgage indexation lead to an increased growth rate, particularly in the manner described by Currie (1974) is perhaps an intractable econometric question. Although the lower average level of GDP invested in housing after the introduction of indexation does provide some support to the credit fungibility argument raised by Carrizosa et. al. Our analysis suggests a different channel through which the introduction of mortgage indexation might have indirectly affected growth: by stimulating the competition for financial resources they helped reduce the burden of inflationary taxes on monetary balances. This effect, in turn, led to a reduction in the costs of an important factor of production. According to this perspective, this cost reduction facilitated investment rather than affected its composition, and thereby affected growth. 4.04 To get an approximation of the effects of financial technology on overall growth, it is convenient to assume that the production function is linearly homogeneous, and that the necessary conditions for producer equilibrium apply. With these assumptions output elasticities sum to one, and the effect of the estimated increasing returns to scale on total factor productivity is eliminated. Comparing the adjusted coefficients from linearized versions of equations (4) and (6), i.e., production functions with and without monetary balances, we find that in equation (4) technical change or, in Abramovitz's terms, the measure of our ignorance, accounts for 72 percent of growth in total factor productivity. In equation (6), in contrast, technical change accounts - 15 - for only 35 percent of the growth in total factor productivity.Il- The inclusion of monetary balances has cut the unexplained residual in half. Hence, even if our coefficients are off by a factor of two, it appears inescapable that the change in the structure of financial technology has made a very substantial contribution to economic growth in Colombia. B. Income Distribution Issues 4.05 Measuring the incidence of lower inflationary taxes or a more competitive financial system is, as Urrutia (1985) shows, a very difficult task, and our aggregate results shed little direct light on this important issue. Rather than trying to tease out the possible effects that financial policy may have had on income or wealth distribution, as Berry and Soligo (1980) have creatively done, it is perhaps of more interest to consider briefly in the words of Sherlock Holmes, "a dog that did not bark." The dog in this case is the observation that the share of income of the lowest income group did not deteriorate over the 1958-84 period. In fact, it improved.11 The improvement is surprising because the traditional view of the development process is that during development there is generally an initial deterioration in the earnings of lower income groups. Chenery and Syrquin's (1975) model allows for a rough quantification of how income level shares might be expected to behave.LY It indicates that based on Colombia's income level and population growth over this 1./ The growth in output per unit of labor is decomposed into growth in capital per unit of labor, growth in monetary balances per unit of labor and the remainder is attributed to "technical change." When monetary balances are not included, growth due to capital per labor is 28 percent and technical change, 72 percent. However, when monetary balances are included, growth due to capital is 21.5 percent, technical change, 35 percent and monetary balances, 43.5 percent. For more detail, see Solow (1957). 19/ See Reyes (1987) for the most recent data on income distribution. Urrutia (1985) provides the most comprehensive evidence for the 1970s. 20/ The Chenery and Syrquin work is a regression model of the behavior of 101 countries over the 1950-1970 period. It "explains" various characteristics of an economy, e.g. employment in different sectors, urbanization, saving, and income distribution measures as a function of the level of per capita income and population. The basic perspective of the work is that development processes are sufficiently uniform among countries to produce a consistent pattern of change. The analysis provides measures for the behavior of a representative developing country. For Colombia, the model's predictions for employment distribution among primary, manufacturing and service sectors were very close to the observed values; so too were its estimate of savings and investment rates and the distribution of income. - 16 - period, that a slight deterioration in the share of income in the lowest two quintals was to be expected.211 4.06 The interesting aspect of the somewhat surprising improvement in the relative position of the poor is that one of the chief reasons for proscribing market-rate housing finance systems in developing countries is the concern that these systems will not only not serve the poor, but they will also lead to a deterioration in the position of the poor. See, for example, Shelter, (1980), The World Bank. Indeed, in many countries the reliance on the housing finance system to provide "affordable," i.e., very low nominal interest rates, is a direct result of distributional considerations prompted by concerns about the presumed unaffordability of market-rate mortgage credit. Indeed, the ceiling imposed on the amount that mortgage payments can be adjusted for inflation in Colombia is a good example of such a policy. 4.07 We are not suggesting that mortgage indexation was a cause of observed distributional results. Factors other than housing finance policy or financial policy clearly have more to do with the observed trends in income distribution. Nevertheless, the Colombian case is interesting in that it suggests that the development of market-oriented housing finance systems can make a significant contribution to economic growth contemporaneously with an improvement in the position of the lowest income groups. Hence, it does not appear that greater access to mortgage credit by moderate and upper income households is antithetical to the interests of the poor. C. Financial Policy and the Sources of Growth 4.08 Perhaps the most appropriate standard against which to evaluate the usefulness of including monetary balances in the production function is whether it yields any insights about the sources of growth not suggested by the traditional growth accounting perspective. The augmented production function performs well on this score. The inclusion of monetary balances suggests an important channel through which macroeconomic financial policy can affect growth: the channel is the affect of the level of inflation on the competitiveness of the resource mobilization process. 4.09 Since 1984, the last year of our estimation period, the interest rate cap on the mortgage indexation adjustment has been below the rate of inflation. As a result, since that time the mortgages supplied--which now account for 25 percent of financial assets--provide lenders no protection against increases in the inflation rate. If inflation increases, lenders will be unable to increase borrowers' repayment by as much. Hence these instruments will not provide the CAVs a means of competing for deposits. As a result, the CAVs will either (1) be unable to compete for funds with commercial banks and suffer disintermediation; or (2) if the banks do not compete for funds with the CAVs 21/ It predicts that the share of income going to the lowest two quintals would decline slightly from 11.4 to 11.2 percent of income. By 1985, in the seven largest cities the households in the lowest two quintals received 12.8 percent. See Reyes (1987). - 17 - the overall competitiveness of the deposit system will be greatly reduced. In either case the cost of this factor of production will increase substantially. 4.10 For example, because of the current ceiling on indexation an increase in inflation would act like a tax on all monetary balances, not just Ml. As a consequence, a 10 percent increase in the rate of inflation (from 25 percent to about 35 percent) would result in pushing up the cost of M1, but, in addition, it would apply to all monetary balances. The tax base would more than double. Hence, the augmented production function permits the effects of increases in the inflation rate to be traced through to its effect on growth. Again, while this kind of quantification of the effects is stylized, it nevertheless is a clear channel through which the inflation and the current financial regulatory environment can very significantly affect growth. Moreover, it is a channel ignored by standard sources of growth analyses. - 18 - V. CONCLUSION 5.01 The role of financial policy in economic growth is always a difficult one to quantify. For an economy, such as Colombia, in which trade policy changes and illegal exports have played important roles, this comment carries even more weight. Nevertheless, the empirical approach developed by Sinai and Stokes is a helpful framework within which some of the more important financial development policy issues can be considered and broadly quantified. While caution should clearly be applied to interpretations of the coefficients, the results strongly suggest that the financial policy has played an important role in Colombia's record of sustained growth. 5.02 A central component of this policy has been the ability to finance investments in the "unproductive" and socially meretricious portion of the housing stock, i.e., the portion of housing production not allocated to the poor. However,importantly, our results indicate that it was not the effects of finance on the composition of investment patterns that mattered. Rather, growth was stimulated by not only permitting but by inducing the financial system to be able to minimize the effects of high and variable inflation rates on the cost of monetary balances. Household access to credit for "low priority" investments played an important part in the process of inducing a cost-reducing, more competitive financial technology. While it does not appear that the forced investment schemes that still litter the financial system have made the best use of the resources mobilized by the more competitive deposit system, one can only speculate about what would have occurred if the resources were not in the financial system at all. - 19 - APPENDICES, TABLES AND FIGURES - 20 - APPENDIX I EXPLANATION OF VARIABLES (1) GDP: Gross Domestic Product in 1980 Colombian billion Peso. (2) K: The capital series is from Harberger and is in 1980 Colombian billion pesos. (3) L: The number of persons in the labor force and is in 1000's. (4) NEWl: Equivalent units of monetary balances are defined as Ml in billions (Ml) of 1980 pesos, adjusted for inflation and indexation as follows: NEW1 = ml * 1 where ml is the real monetary balance (1-E) and E is the inflation rate. Hence, (1/1-8) acts as a measure of the change in the number of equivalent units of monetary monetary balances due to a change in the inflation rate. (5) NEW2: Equivalent units of monetary balances defined as M2 (M2) with the same (M2) adjustments made as Ml prior to 1973. From 1973 onwards, no adjustment is made for inflation and indexation, i.e., Pre 1973, NEW2 = 1/(l-9)* m2 where m2 is real monetary balances; 1973 and after: NEW2 = 1/(l-9)* ml+ (m2-ml). This means that the equivalent units of the non-Ml portion of monetary balances are unaffected by changes in the inflation rate. Indexation was introduced in the fourth quarter of 1972. (6) NEW3: Equivalent units of monetary balances defined as M2 and (M3) CAV deposits (M3) starting from 1973. The change in equivalent units of (M3-M2) is the same as that of (M2-Ml). (7) SOL1: Ml in real terms. (8) SOL2: M2 in real terms. (9) SOL3: M2+CAVS in real terms. Note: The inflation rate was derived from the GNP deflator. - 21 - APPENDIX II ADJUSTMENTS TO CAPITAL AND LABOR A measure of capital stock utilization was derived from Cuddington's (1986) decomposition of Colombian growth into permanent and cyclical components. We use his measures to derive an estimate of capital capacity utilization. In the year in which the cyclical component had the largest positive value, 1974, capital utilization was assumed to be 100 percent. In that year, Cuddington estimates that GDP was about 5 percent higher than what he terms the permanent GDP level. Consequently, in years in which output has a zero cyclical component, our measure implies that capacity utilization is about 95 percent. Adjustments to employment for education and the changing sex composition of the work force were made according to the estimates of Hanson et al (1987). The labor force was adjusted for changes in sex and education. Increases in female labor force participation reduces the equivalent units of labor inputs and increases in educational level has the opposite effect. A net increase of .5% cumulative growth rate was taken for the whole period and it was assumed that 4% of labor force is replaced. Hence, the new labor was given a higher weight. Hanson et al (1987) was used as a reference to adjust the labor force. The result of the regression with these adjustments are available on request. - 22 - TABLE 2. ESTIMATES OF THE PARAMETERS OF THE COBB-DOUGLAS PRODUCTION FUNCTION, WITH AND WITHOUT REAL MONEY BALANCES, CORRECTED FOR AUTOCORRELATION, FOR THE YEARS 1958-1984. LN GDP = LN A + ALPHA * LN K + BETA * LN L + GAMMA * LN M + u REGRESSION WITH:-- NO MOMEY NEW1 NEW2 NEW3 (4) (5) (6) (7) LN A -4.76 -1.78 -0.03 -0.78 (.694) (.613) (1.189) (1.543) A 0.0086 0.1686 0.9704 0.4584 ALPHA 0.51 0.16 0.32 0.43 (0.123) (.101) (.132) (.136) BETA 0.89 0.83 0.48 0.49 (.182) (.139) (.215) (.261) GAMMA ------- 0.37 0.36 0.23 (.036) (.065) (.066) SUMMATION 1.4 1.36 1.16 1.15 R-SQ (a) 0.9866 0.9975 0.9939 0.9914 S.E.E. (b) 0.047 0.021 0.032 0.04 D.W. (c) 1.742 1.673 1.506 1.648 STANDARD ERRORS OF REGRESSION COEFF. ARE IN PARENTHESES (a): ADJUSTED R-SQUARE FOR EQTN. NOT CORRECTED FOR AUTOCORRELATION (b): STANDARD ERROR OF ESTIMATION FOR EQUATION NOT CORRECTED FOR AUTOCORRELATION (c): DURBIN-WATSON STATISTIC FOR EQUATION CORRECTED FOR AUTOCORRELATION - 23 - TABLE 3. ESTIMATES OF THE PARAMETERS OF THE COBB-DOUGLAS PRODUCTION FUNCTION, WITH REAL MONEY BALANCES (WITH AND WITHOUT ADJUSTMENT FOR INDEXATION AND INFLATION) CORRECTED FOR AUTOCORRELATION, FOR THE YEARS 1958-1984. LN GDP = LN A + ALPHA *LN K + BETA * LN L + GAMMA * LN M + u SOL2 NEW2 (8) (9) LN A -0.61 -0.03 (1.506) (1.189) A 0.5434 0.9704 ALPHA 0.34 0.32 (.161) (.132) BETA 0.54 0.48 (.234) (.215) GAMMA 0.34 0.36 (.107) (.065) SUMMATION 1.22 1.16 R-SQ (a) 0.9918 0.9939 S.E.E. (b) 0.037 0.032 D.W. (c) 1.793 1.506 STANDARD ERRORS OF REGRESSION COEFF. ARE IN PARENTHESES (a): ADJUSTED R-SQUARE FOR EQTN. NOT CORRECTED FOR AUTOCORRELATION (b): STANDARD ERROR OF ESTIMATION FOR EQUATION NOT CORRECTED FOR AUTOCORRELATION (c): DURBIN-WATSON STATISTIC FOR EQUATION CORRECTED FOR AUTOCORRELATION - 24 - TABLE 4. ESTIMATES OF THE PARAMETERS OF THE COBB-DOUGLAS PRODUCTION FUNCTION, WITH AND WITHOUT REAL MONEY BALANCES, CORRECTED FOR AUTOCORRELATION, FOR THE YEARS 1958-1984. (CAPITAL IS ADJUSTED FOR CAPACITY UTILIZATION AND LABOR IS ADJUSTED FOR CHANGE IN SEX COMPOSITION AND EDUCATION.) LN Q = LN A + ALPHA * LN Kadj + BETA * LN Ladj + GAMMA *LN M + U NO M M1 M2 M3 LN A -3.99 -1.92 -0.33 -0.25 II (.588) (.470) (.935) (1.268) II A 0.0185 0.1466 0.7189 0.7788 11 ALPHA j 0.66 0.23 0.44 0.57 (0.102) (.088) (.101) (.103) BETA 0.68 0.79 0.42 0.31 II (.151) (.104) (.150) (.196) II GAMMA ------- 0.32 0.3 0.22 I (.039) (.060) (.060) SUMMATION 1.34 1.34 1.16 1.1 II R-SQ (a) 0.9921 0.9979 0.9959 0.9944 II S.E.E. (b) 0.036 0.019 0.026 0.031 II D.W. (c) 1.85 1.7 1.64 1.68 II STANDARD ERRORS OF REGRESSION COEFF. ARE IN PARENTHESES (a): ADJUSTED R-SQUARE FOR EQTN. NOT CORRECTED FOR AUTOCORRELATION (b): STANDARD ERROR OF ESTIMATION FOR EQUATION NOT CORRECTED FOR AUTOCORRELATION (c): DURBIN-WATSON STATISTIC FOR EQUATION CORRECTED FOR AUTOCORRELATION Kadj: ADJUSTED CAPITAL Ladj: ADJUSTED LABOR TABLE 5 DATA FOR COLOMBIA 1958-1984. GDP IN CAP. STOCK CAP. STOCK ADJ LAB. EXP. 1980 COL IN 1980 COL IN 1980 COL ADJ. LAB IN 1980 BIL ADJ INDXN ADJ INDXN ADJ INDXN SINAI SINAI SINAI YEAR PESO BIL. PESO BIL. BIL PESO LAB IN 1000 IN 1000 COL PESO BIL PESO BIL PESO BIL PESO BIL PESO BIL PESO BIL PESO YR GDP CSIM CADJ LSIM LADJ LEXP NEW1 NEW2 NEW3 SOL1 SOL2 SOL3 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 1958 490.05 1027.35 965.58 4417 4418 61.62 0.87 1.05 1.05 0.76 0.91 0.91 1959 525.56 1072.42 1016.54 4Š11 4513 61.50 0.85 1.03 1.03 0.81 0.98 0.98 1960 548.16 1069.87 1022.35 4617 4620 71.91 0.89 1.06 1.06 0.81 0.97 0.97 1961 576.14 1088.35 1037.73 4725 4729 78.58 1.02 1.21 1.21 0.94 1.11 1.11 1962 607.46 1166.54 1121.51 4834 4839 86.63 1.12 1.42 1.42 1.04 1.31 1,31 1963 627.23 1248.58 1191.05 4942 4948 91.30 1.24 1.52 1.52 0.96 1.17 1.17 1964 665.35 1186.28 1134.56 5094 5101 91.03 1.21 1.43 1.43 1.01 1.18 1.18 1965 690.12 1311.82 1256.84 5222 5231 96.38 1.18 1.45 1.45 1.08 1.33 1.33 1966 726.65 1413.51 1349.81 5361 5371 100.47 1.29 1.50 1.50 1.10 1.28 1.28 1967 753.22 1514.14 1452.06 5483 5494 105.88 1.35 1.56 1.56 1.23 1.42 1.42 1968 803.50 1597.78 1530.31 5662 5675 111.33 1.44 1.64 1.64 1.31 1.49 1.49 1969 854.78 1702.30 1648.88 5870 5884 122.79 1.61 1.84 1.84 1.48 1.69 1.69 1970 923.30 1755.23 1713.17 6062 6078 131.28 1.73 1.99 1.99 1.56 1.79 1.79 1971 980.44 1809.76 1781.13 6219 6237 141.65 1.76 2.05 2.05 1.58 1.84 1.84 1972 1054.56 1911.19 1894.57 6415 6435 150.85 2.04 2.41 2.41 1.77 2.10 2.10 1973 1125.74 1919.30 1916.27 6477 6499 155.02 2.41 2.84 3.04 1.93 2.36 2.56 1974 1189.59 2035.02 2035.02 6656 6680 161.19 2.43 2.97 3.28 1.81 2.35 2.66 1975 1216.91 2124.12 2104.83 6958 6984 167.69 2.29 2.88 3.29 1.77 2.36 2.76 1976 1273.98 2194.97 2146.44 7285 7314 172.28 2.55 3.17 3.64 1.90 2.52 2.99 1977 1327.21 2173.81 2110.06 7551 7583 179.33 2.70 3.39 3.84 1.92 2.61 3.06 1978 1439.98 2383.13 2325.89 7904 7939 208.36 2.54 3.29 3.84 2.10 2.85 3.40 1979 1516.35 2538.10 2514.07 8188 8226 226.27 2.79 3.49 4.17 2.12 2.82 3.50 1980 1579.13 2659.94 2619.83 8540 8582 239.43 2.93 4.01 4.84 2.12 3.20 4.04 1981 1614.63 2839.43 2762.91 8666 8710 251.82 2.70 4.16 5.15 2.09 3.54 4.54 1982 1630.09 2902.84 2749.35 8925 8972 256.21 2.79 4.12 5.24 2.10 3.43 4.55 1983 1655.36 3015.47 2798.98 9084 9134 261.38 2.70 4.13 5.45 2.15 3.58 4.90 1984 1708.42 3174.57 2923.55 9370 9424 268.67 2.81 4.25 5.59 2.19 3.63 4.97 TABLE 6 NATURAL LOGARITHMIC TRANSFORMATION OF THE VARIABLES GDP IN CAP. STOCK CAP. STOCK ADJ LAB. EXP. 1980 COL IN 1980 COL IN 1980 COL ADJ. LAB IN 1980 BIL ADJ INDXN ADJ INDXN ADJ INDXN SINAI SINAI SINAI YEAR PESO BIL. PESO BIL. BIL PESO LAB IN 1000 IN 1000 COL PESO BIL PESO BIL PESO BIL PESO BIL PESO BIL PESO BIL PESO YR GDP CSIM CADJ LSIM LADJ LEXP NEW1 NEW2 NEW3 SOL1 SOL2 SOL3 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) 1958 6.19451 6.93474 6.87273 8.39322 8.39342 4.12103 -0.13489 0.04600 0.04600 -0.27597 -0.09508 -0.09508 1959 6.26446 6.97767 6.92416 8.41427 8.41468 4.11902 -0.16639 0.02516 0.02516 -0.21402 -0.02247 -0.02247 1960 6.30657 6.97530 6.92986 8.43750 8.43810 4.27547 -0.11361 0.06200 0.06200 -0.20670 -0.03109 -0.03109 1961 6 35635 6.99242 6.94479 8.46062 8.46143 4.36414 0.01906 0.18901 0.18901 -0.06610 0.10385 0.10385 1962 6.40929 7.06180 7.02243 8.48343 8.48444 4.46163 0.11Z52 0.34890 0.34890 0.03905 0.27043 0.27043 1963 6.44131 7.12976 7.08259 8.50553 8.50674 4.51410 0.21401 0.41830 0.41830 -0.04485 0.15944 0.15944 1964 6.50031 7.07858 7.03400 8.53582 8.53724 4.51121 0.19365 0.35604 0.35604 0.00559 0.16799 0.16799 1965 6.53687 7.17917 7.13636 8.56064 8.56226 4.56830 0.16889 0.37382 0.37382 0.07966 0.28459 0.28459 1966 6.58844 7.25383 7.20772 8.58691 8.58874 4.60988 0.25473 0.40430 0.40430 0.09682 0.24640 0.24640 1967 6.62436 7.32260 7.28074 8.60941 8.61145 4.66231 0.30151 0.44481 0.44481 0.20914 0.35243 0.35243 1968 6.68898 7.37637 7.33323 8.64153 8.64379 4.71249 0.36488 0.49546 0.49546 0.27047 0.40105 0.40105 1969 6.75084 7.43973 7.40785 8.67761 8.68007 4.81049 0.47871 0.60877 0.60877 0.39245 0.52251 0.52251 1970 6.82795 7.47036 7.44610 8.70980 8.71247 4.87730 0.54621 0.68688 0.68688 0.44170 0.58237 0.58237 1971 6.88800 7.50095 7.48501 8.73536 8.73825 4.95339 0.56507 0.71751 0.71751 0.45507 0.60751 0.60751 1972 6.96088 7.55548 7.54674 8.76639 8.76950 5.01626 0.71244 0.88120 0.88120 0.57079 0.73955 0.73955 1973 7.02620 7.55972 7.55814 8.77601 8.77933 5.04353 0.87968 1.04328 1.11251 0.65654 0.85717 0.93999 1974 7.08136 7.61826 7.61826 8.80327 8.80681 5.08261 0.88753 1.08838 1.18681 0.59365 0.85481 0.97760 1975 7.10407 7.66111 7.65199 8.84765 8.85140 5.12213 0.83032 1.05845 1.19043 0.57054 0.85741 1.01656 1976 7.14990 7.69392 7.67157 8.89357 8.89754 5.14912 0.93610 1.15254 1.29217 0.64139 0.92240 1.09519 1977 7.19083 7.68424 7.65447 8.92944 8.93362 5.18922 0.99226 1.22113 1.34502 0.65051 0.95943 1.11758 1978 7.27238 7.77617 7.75186 8.97512 8,97953 5.33928 0.93291 1.18993 1.34531 0.74352 1.04671 1.22401 1979 .7.32406 7.83917 7.82966 9.01042 9.01505 5.42174 1.02466 1.24961 1.42677 0.74956 1.03634 1.25137 1980 7.36463 7.88606 7.87086 9.05252 9.05737 5.47827 1.07559 1.38939 1.57790 0.75330 1.16462 1.39551 1981 7.38686 7.95136 7.92404 9.06716 9.07224 5.52871 0.99484 1.42473 1.63937 0.73606 1.26417 1.51190 1982 7.39639 7.97344 7.91912 9.09661 9.10191 5.54598 1.02537 1.41618 1.65680 0.74094 1.23289 1.51563 1983 7.41177 8.01151 7.93701 9.11427 9.11979 5.56597 0.99390 1.41712 1.69591 0.76617 1.27397 1.58951 1984 7.44332 8.06293 7.98056 9.14527 9.15102 5.59347 1.03261 1.44656 1.72150 0.78184 1.28801 1.60342 - 27 - TABLE ?. GOP OF COLOMBIA 1958-1984. GOP IN 1980 COLOMBIAN PESO YEAR (IN BILLIONS) 1958 490.05 1959 525.56 1960 548.16 1961 576.14 1962 607.46 1963 627.23 1964 665.35 1965 690.12 1966 726.65 1967 753.22 1968 803.50 1969 854.78 1970 923.30 1971 980.44 1972 1054.56 1973 1125.74 1974 1189.59 1975 1216.91 1976 1273.98 1977 1327.21 1978 1439.98 1979 1516.35 1980 1579.13 1981 1614.63 1982 1630.09 1983 1655.36 1984 1708.42 - 28 - TABLE 8 CAPITAL STOCK FOR COLOMBIA 1958-1984 CAP. STOCK IN 1980 CUDDINGTON'S INDEX WITH CAPITAL STOCK ADJUSTED COL. PESO INDEX YEAR 1974=1 FOR CAPACITY UTILIZATION. YEAR (IN BILLIONS) 1980 COL. BIL. PESO 1958 1027.35 98.5676 0.93987 965.58 1959 1072.42 99.4091 0.94789 1016.54 1960 1069.87 100.2155 0.95558 1022.35 1961 1088.35 99.9957 0.95349 1037.73 1962 1166.54 100.8256 0.96140 1121.51 1963 1248.58 100.0418 0.95392 1191.05 1964 1186.28 100.3015 0.95640 1134.56 1965 1311.82 100.4785 0.95809 1256.84 1966 1413.51 100.1475 0.95493 1349.81 1967 1514.14 100.5741 0.95900 1452.06 1968 1597.78 100.4458 0.95778 1530.31 1969 1702.30 101.5829 0.96862 1648.88 1970 1755.23 102.3611 0.97604 1713.17 1971 1809.76 103.2149 0.98418 1781.13 1972 1911.19 103.9616 0.99130 1894.57 1973 1919.30 104.7085 0.99842 1916.27 1974 2035.02 104.8739 1.00000 2035.02 1975 2124.12 103.9215 0.99092 2104.83 1976 2194.97 102.5555 0.97789 2146.44 1977 2173.81 101.7983 0.97067 2110.06 1978 2383.13 102.3549 0.97598 2325.89 1979 2538.10 103.8810 0.99053 2514.07 1980 2659.94 103.2924 0.98492 2619.83 1981 2839.43 102.0476 0.97305 2762.91 1982 2902.84 99.3287 0.94712 2749.35 1983 3015.47 97.3444 0.92820 2798.98 1984 3174.57 96.5815 0.92093 2923.55 - 29 - TABLE 9. LABOR FORCE IN COLOMBIA 1958-1984. NUMBER OF SEX AND EDUC. FRACTION OF LAB IN 1000 LAB. EXP. PERSONS ADJ. (HANSEN) LABOR FORCE ADJ. FOR IN 1980 BIL YEAR (LAB IN 1000) 0.5% GROWTH WHICH IS NEW SEX & EDUC. COL PESO 1958 4417 0.00500 0.04000 4418 61.62 1959 4511 0.01003 0.04000 4513 61.50 1960 4617 0.01508 0.04000 4620 71.91 1961 4725 0.02015 0.04000 4729 78.58 1962 4834 0.02525 0.04000 4839 86.63 1963 4942 0.03038 0.04000 4948 91.30 1964 5094 0.03553 0.04000 5101 91.03 1965 5222 0.04071 0.04000 5231 96.38 1966 5361 0.04591 0.04000 5371 100.47 1967 5483 0.05114 0.04000 5494 105.88 1968 5662 0.05640 0.04000 5675 111.33 1969 5870 0.06168 0.04000 5884 122.79 1970 6062 0.06699 0.04000 6078 131.28 1971 6219 0.07232 0.04000 6237 141.65 1972 6415 0.07768 n.04000 6435 150.85 1973 6477 0.08307 0.04000 6499 155.02 1974 6656 0.08849 0.04000 6680 161.19 1975 6958 0.09393 0.04000 6984 167.69 1976 7285 0.09940 0.04000 7314 172.28 1977 .7551 0.10490 0.04000 7583 179.33 1978 7904 0.11042 0.04000 7939 208.36 1979 8188 0.11597 0.04000 8226 226.27 1980 8540 0.12155 0.04000 8582 239.43 1981 8666 0.12716 0.04000 8710 251.82 1982 8925 0.13280 0.04000 8972 256.21 1983 9084 0.13846 0.04000 9134 261.38 1984 9370 0.14415 0:04000 9424 268.67 - 30 - TABLE 10 MONETARY BALANCES IN COLOMBIA 1958-1984. MONEY + QUASI CAV M2 + CAVS. MONEY (MI) MONEY = M2 DEPOSITS = M3 YEAR BIL. PESO BIL. PESO BIL. PESO BIL. PESO 1958 3.26 3.91 0.00 3.91 1959 3.63 4.40 0.00 4.40 1960 3.99 4.75 0.00 4.75 1961 4.96 5.88 0.00 5.88 1962 5.93 7.47 0.00 7.47 1963 6.69 8.21 0.00 8.21 1964 8.25 9.70 0.00 9.70 1965 9.64 11.83 0.00 11.83 1966 11.24 13.05 0.00 13.05 1967 13.68 15.79 0.00 15.79 1968 15.86 18.07 0.00 18.07 1969 19.40 22.09 0.00 22.09 1970 22.40 25.78 0.00 25.78 1971 25.06 29.19 0.00 29.19 1972 31.85 . 37.71 0.00 37.71 1973 41.65 50.90 4.40 55.30 1974 49.07 63.71 8.32 72.03 1975 58.92 78.49 13.54 92.03 1976 79.38 105.14 19.83 124.97 1977 103.30 140.69 24.11 164.80 1978 132.93 180.01 34.92 214.93 1979 165.90 221.00 53.02 274.02 1980 212.40 320.47 83.23 403.70 1981 256.37 434.73 122.21 556.94 1982 321.40 525.65 171.76 697.41 1983 396.74 659.23 244.58 903.81 1984 492.39 816.84 302.90 1119.74 - 31 - TABLE 11 REAL MONETARY BALANCES FOR COLOMBIA 1958-1984. MONEY + QUASI CAV M2 + CAVS. INFLATION REAL MONEY REAL MONEY REAL MONEY MONEY (Ml) MONEY = M2 DEPOSITS = M3 GNP DEFLATOR BASED ON BALANCES BALANCES BALANCES YEAR BIL. PESO BIL. PESO BIL. PESO BIL. PESO (1980=100) GNP DEFLATOR SOLl SOL2 SOL3 1958 3.26 3.91 0.00 3.91 4.30 13.16% 0.76 0.91 0.91 1959 3.63 4.40 0.00 4.40 4.50 4.65% 0.81 0.98 0.98 1960 3.99 4.75 0.00 4.75 4.90 8.89% 0.81 0.97 0.97 1961 4.96 5.88 0.00 5.88 5.30 8.16% 0.94 1.11 1.11 1962 5.93 7.47 0.00 7.47 5.70 7.55% 1.04 1.31 1.31 1963 6.69 8.21 0.00 8.21 7.00 22.81% 0.96 1.17 1.17 1964 8.25 9.70 0.00 9.70 8.20 17.14% 1.01 1.18 1.18 1965 9.64 11.83 0.00 11.83 8.90 8.54% 1.08 1.33 1.33 1966 11.24 13.05 0.00 13.05 10.20 14.61% 1.10 1.28 1.28 1967 13.68 15.79 0.00 15.79 11.10 8.82% 1.23 1.42 1.42 1968 15.86 18.07 0.00 18.07 12.10 9.01% 1.31 1.49 1.49 1969 19.40 22.09 0.00 22.09 13.10 8.26% 1.48 1.69 1.69 1970 22.40 25.78 0.00 25.78 14.40 9.92% 1.56 1.79 1.79 1971 25.06 29.19 0.00 29.19 15.90 10.42% 1.58 1.84 1.84 1972 31.85 37.71 0.00 37.71 18.00 13.21% 1.77 2.10 2.10 1973 41.65 50.90 4.40 55.30 21.60 20.00% 1.93 2.36 2.56 1974 49.07 63.71 8.32 72.03 27.10 25.46% 1.81 2.35 2.66 1975 58.92 78.49 13.54 92.03 33.30 22.88% 1.77 2.36 2.76 1976 79.38 105.14 19.83 124.97 41.80 25.53% 1.90 2.52 2.99 1977 103.30 140.69 24.11 164.80 53.90 28.95% 1.92 2.61 3.06 1978 132.93 180.01 34.92 214.93 63.20 17.25% 2.10 2.85 3.40 1979 165.90 221.00 53.02 274.02 78.40 24.05% 2.12 2.82 3.50 1980 212.40 320.47 83.23 403.70 100.00 27.55% 2.12 3.20 4.04 1981 256.37 434.73 122.21 556.94 122.80 22.80% 2.09 3.54 4.54 1982 321.40 525.65 171.76 697.41 153.20 24.76% 2.10 3.43 4.55 1983 396.74 659.23 244.58 903.81 184.40 20.37% 2.15 3.58 4.90 1984 492.39 816.84 302.90 1119.74 225.30 22.18% 2.19 3.63 4.97 - 32 - TABLE 12 INDEXED REAL MONEY BALANCES FOR COLOMBIA 1958-1984. MONEY+QUASI CAV M2 + CAVS. GNP INFLATION PRICE OF PRICE ADJ. PRICE ADJ. PRICE ADJ. MONEY (Ml) MONEY = M2 DEPOSITS = M3 DEFLATOR BASED ON INFLATION REAL MONEY REAL MONEY REAL MONEY YR BIL. PESO BIL. PESO BIL. PESO BIL. PESO (1980=100) GNP DEFLATOR 1/1-INFL BAL (NEWI) BAL (NEW2) BAL (NEW3) 1958 3.26 3.91 0.00 3.91 4.30 13.16% 1.15 0.87 1.05 1.05 1959 3.63 4.40 0.00 4.40 4.50 4.65% 1.05 0.85 1.03 1.03 1960 3.99 4.75 0.00 4.75 4.90 8.89% 1.10 0.89 1.06 1.06 1961 4.96 5.88 0.00 5.88 5.30 8.16% 1.09 1.02 1.21 1.21 1962 5.93 7.47 0.00 7.47 5.70 7.55% 1.08 1.12 1.42 1.42 1963 6.69 8.21 0.00 8.21 7.00 22.81% 1.30 1.24 1.52 1.52 1964 8.25 9.70 0.00 9.70 8.20 17.14% 1.21 1.21 1.43 1.43 1965 9.64 11.83 0.00 11.83 8.90 8.54% 1.09 1.18 1.45 1.45 1966 11.24 13.05 0.00 13.05 10.20 14.61% 1.17 1.29 1.50 1.50 1967 13.68 15.79 0.00 15.79 11.10 8.82% 1.10 1.35 1.56 1.56 1968 15.86 18.07 0.00 18.07 12.10 9.01% 1.10 1.44 1.64 1.64 1969 19.40 22.09 0.00 22.09 13.10 8.26% 1.09 1.61 1.84 1.84 1970 22.40 25.78 0.00 25.78 14.40 9.92% 1.11 1.73 1.99 1.99 1971 25.06 29.19 0.00 29.19 15.90 10.42% 1.12 1.76 2.05 2.05 1972 31.85 37.71 0.00 37.71 18.00 13.21% 1.15 2.04 2.41 2.41 1973 41.65 50.90 4.40 55.30 21.60 20.00% 1.25 2.41 2.84 3.04 1974 49.07 63.71 8.32 72.03 27.10 . 25.46% 1.34 2.43 2.97 3.28 1975 58.92 78.49 13.54 92.03 33.30 22.88% 1.30 2.29 2.88 3.29 1976 79.38 105.14 19.83 124.97 41.80 25.53% 1.34 . 2.55 3.17 3.64 1977 103.30 140.69 24.11 164.80 53.90 28.95% 1.41 2.70 3.39 3.84 1978 132.93 180.01 34.92 214.93 63.20 17.25% 1.21 2.54 3.29 3.84 1979 165.90 221.00 53.02 274.02 78.40 24.05% 1.32 2.79 3.49 4.17 1980 212.40 320.47 83.23 403.70 100.00 27.55% 1.38 2.93 4.01 4.84 1981 256.37 434.73 122.21 556.94 122.80 22.80% 1.30 2.70 4.16 5.15 1982 321.40 525.65 171.76 697.41 153.20 24.76% 1.33 2.79 4.12 5.24 1983 396.74 659.23 244.58 903.81 184.40 20.37% 1.26 2.70 4.13 5.45 1984 492.39 816.84 302.90 1119.74 225.30 22.18% 1.29 2.81 4.25 5.59 - 33 - YEAR G0P CSIM LSIM TABLE 13 (REGRESSION WITH NO MONEY VARIABLE) 1958 490.050.000.000 1.027,355.000,000 4,417,000 1959 525.560,000,000 1,072.422.000.000 4,511.000 1960 548.160,000.000 1,069,874,000.000 4.617.000 1961 576,140.000.000 1,088,350,000,000 4.725.000 1962 607,460.000.000 1,166,541,000,000 4,834.000 1963 627.230,000.000 1,248,580,000,000 4.942.000 1964 665.350.000.000 1.186,283,000.000 5,094,000 1965 690.120,000.000 1,311,820,000,000 5,222,000 1966 726.650,000.000 1,413,510,000,000 5,361.000 1967 753,220.000.000 1,514,137.000,000 5,483.000 1968 803,500.000,000 1,597,778.000,000 5.662.000 1969 854,780.000.000 1,702,295.000.000 5.870.000 1970 923.300.000.000 1,755,230.000.000 6,062,000 1971 980.440.000.000 1.809,763.000.000 6.219.000 1972 1.054,560,000.000 1.911,191,000.000 6.415.000 1973 1.125,740,000.000 1.919.299.000.000 6,477.000 1974 1.189,590.000,000 2.035,018.000.000 6.656.000 1975 1.216,910,000,000 2.124.118.000.000 6.958.000 1976 1,273,980,000,000 2.194,967.000000 7.285.000 1977 1,327.210,000,000 2.173,814.000.000 7,551,000 1978 1,439.980,000,000 2.383.128,000.000 7.904,000 1979 1.516,350,000,000 2,538,102,000,000 8.188,000 1980 1,579.130.00,000 2.659,937,000,000 8,540,000 1981 1,614,630.000.000 2,839.431.000,000 8.666,000 1982 1,630,090,000.000 2,902,840,000.000 8.925.000 1983 1.655.360,000000 3.015,472,000.000 9.084,000 1984 1,708,420,000,000 3,174,569,000,000 9.370.000 CALCULATIONS FOR FINDING COMPONENTS OF GROWTH YEAR q = Q/L k KA q. k. q./q k/k wkk./k A./A A(t) 1958 110946.34 232591.13 1959 116506.32 237734.87 5559.974 5143.745 0.05011 0.02211 0.00806 0.04206 1.00000 1960 118726.45 231724.93 2220.128 -6009.941 0.01906 -0.02528 -0.00921 0.02827 1.04206 1961 121934.39 230338.62 3207.946 -1386.305 0.02702 -000598 -0.00218 0.02920 1.07151 1962 125664.05 241320.02 3729.655 10981.400 0.03059 0.04768 0.01737 0.01322 1.10280 1963 126918.25 252646.70 1254.205 11326.677 0.00998 0.04694 0.01710 -0.00712 1.11738 1964 130614.45 232878.48 3696.197 -19768.217 0.02912 -0.07824 -0.02850 0.05763 1.10942 1965 132156,26 251210.26 1541.814 18331.780 0.01180 0.07872 0.02868 -0.01687 1.17336 1966 135543.74 263665.36 3387.480 12455.097 0.02563 0.04958 0.01806 0.00757 1.15356 1967 137373.70 276151.19 1829.959 12485.834 0.01350 0.04735 0.01725 -0.00375 1.16229 1968 141910.99 282193.22 4537.285 6042.023 0,03303 0.02188 0.00797 0.02506 1.5794 1969 145618.40 289999.15 3707.413 7805.930 0.02612 0.02766 0.01008 0.01605 1.8695 1970 152309.47 289546.35 6691.070 -452.794 0.04595 -0.00156 -0.00057 0.04652 1.206C 1971 157652.36 291005.47 5342.887 1459.113 0.03508 0.00504 0.00184 0.03324 1 262: 1972 164389.71 297925.33 6737.356 6919.864 0.04274 0.02378 0.00866 0.03407 1.3C4^E 1973 173805.77 296325.30 9416.063 -1600.026 0.05728 -0.00537 -0.00196 0.05924 1.3484 1974 178724.46 305741.89 4918.685 9416.582 0.02830 0.03178 0.01158 0.01672 1.42837 1975 174893.65 305277.09 -3830.812 -464.796 -0.02143 -0.00152 -0.00055 -0.02088 1.452Z6 1976 174877.14 301299.52 -16.503 -3977.572 -0.00009 -0.01303 -0.00475 0.00465 1.42193 1977 175766.12 287884.25 888.979 -13415.266 0.00508 -0.04452 -0.01622 0.02130 1.42855 1978 182183.70 301509.11 6417.581 13624.856 0.03651 0.04733 0.01724 0.01927 1.45898 1979 185191.74 309978.26 3008.040 8469.152 0.01651 0.02809 0.01023 0.00628 1.48710 1980 184909.84 311468.03 -281.908 1489.772 -0.00152 0.00481 0.00175 -0.00327 1.49643 1981 186317.79 327651.86 1407.958 '6183.825 0.00761 0.05196 0.01893 -0.01131 1.49154 1982 182643.14 325248.18 -3674.656 -2403.679 -0.01972 -0.00734 -0.00267 -0.01705 1.47466 1983 182228.09 331954.21 -415.044 6706.026 -0.00227 0.02062 0.00751 -0.00978 1.44952 1984 182328.71 338801.39 100.615 6847.182 0.00055 0.02063 0.00751 -0.00696 1.43534 0.50654 0.14320 0.36334 GROWTH DUE TO: CAPITAL TECHNICAL CHG. 100.00% 28.27% 71.73% - 34 - TABLE 14 (REGRESSION WITH NEW2 AS INDEPENDENT VARIABLE) DATA USED FOR USING SOLOW'S APPROACH TO FIND COMPONENTS OF GROWTH UNADJUSTED NUMBER OF M2 WITH GOP CAPITAL (CSIM) PERSONS PRICES IN COL PESO YEAR COL 80 PESO COL 80 PESO EMPLOYED NEW2(INDEXATION) 1958 490,050,000,000 1,027,355,000,000 4,417,000 1,047,075,405 1959 525,560.000,000 1,072.422.000,000 4,511.000 1.025,474,255 1960 548.160,000,000 1,069,874.000,000 4.617,000 1.063,962,170 1961 576.140,000,000 1.088,350.000,000 4,725,000 1.208,050,314 1962 607,460,000,000 1,166.541,000,000 4,834,000 1,417,508,056 1963 627.230,000,000 1,248,580,000,000 4,942,000 1,519,383,117 1964 665,350,000,000 1,186,283,000,000 5,094,000 1.427.670,311 1965 690,120.000,000 1,311,820,000,000 5,222,000 1,453,273,408 1966 726,650,000,000 1,413,510,000.000 5,361,000 1,498.258,514 1967 753,220,000,000 1,514,137,000,000 5,483,000 1,560,185.992 1968 803,500,000,000 1,597,778,000,000 5,662,000 1,641.248.670 1969 854,780,000.000 1.702.295.000,000 5,870,000 1,838,174,816 1970 923,300,000.000 1,755,230.000,000 6,062,000 1,987,511,770 1971 980,440,000,000 1,809,763,000.000 6,219,000 2,049,319,877 1972 1,054,560,000,000 1,911.191,000,000 6,415,000 2,413,804,348 1973 1,125,740,000,000 1,919,299,000,000 6,477.000 2,838,506,944 1974 1,189,590,000,000 2.035,018.000,000 6,656.000 2,969,447,182 1975 1.216,910.000,000 2,124,118.000,000 6,958.000 2,881,897.208 1976 1,273.980.000,000 2,194,967,000,000 7.285.000 3.166.217,298 1977 1,327,210,000.000 2,173,814,000,000 7.551,000 3,391,005,291 1978 1.439,980.000,000 2,383,128,000,000 7,904,000 3,286,844,738 1979 1,516,350,000,000 2,538,102,000,000 8,188,000 3,488,966,837 1980 1,579.130,000,000 2.659.937,000,000 8,540,000 4,012.418,310 1981 1,614.630,000.000 2,839,431,000,000 8,666,000 4.156.722.249 1982 1,630,090,000,000 2,902,840,000,000 8.925,000 4,121,357.646 1983 1,655,360,000,000 3.015,472.000,000 9,084.000 4.125,224,387 1984 1,708,420,000,000 3.174,569,000,000 9,370,000 4,248,467,502 TABLE 14 (CONTD) CALCULATIONS FOR FINDING COMPONENTS OF GROWTH YEAR q = Q/L k = KI m = M/L q. k. m. q./q k./k m./m wk*k./k um*m./m A./A A(t) 1958 110946.34 232591.13 237.06 1959 116506.32 237734.87 227.33 5559.974 5143.745 -9.728 0.05011 0.02211 -0.04104 0.00610 -0.01274 0.05675 1.00000 1960 118726.45 231724.93 230.44 2220.128 -6009.941 3.117 0.01906 -0.02528 0.01371 -0.00697 0.00426 0.02177 1.05675 1961 121934.39 230338.62 255.67 3207.946 -1386.305 25.228 0.02702 -0.00598 0.10947 -0.00165 0.03397 -0.00530 1.07976 1962 125664.05 241320.02 293.24 3729.655 10981.400 31.565 0.03059 0.04768 0.14693 0.01315 0.04560 -0.02816 1.07403 1963 126918.25 252646.70 307.44 1254.205 11326.677 14.206 0.00998 0.04694 0.04845 0.01295 0.01503 -0.01800 1.04378 1964 130614.45 232878.48 280.27 3696.197 -19768.217 -27.178 0.02912 -0.07824 -0.08840 -0.02158 -0.02743 0.07814 1.02499 1965 132156.26 251210.26 278.30 1541.814 18331.780 -1.967 0.01180 0.07872 -0.00702 0.02172 -0.00218 -0.00773 1.10509 1966 135543.74 263665.36 279.47 3387.480 12455.097 1.175 0.02563 0.04958 0.00422 0.01368 0.00131 0.01064 1.09654 1967 137373.70 276151.19 284.55 1829.959 12485.834 5.076 0.01350 0.04735 0.01816 0.01306 0.00564 -0.00520 1.10822 1968 141910.99 282193.22 289.87 4537.285 6042.023 5.321 0.03303 0.02188 0.01870 0.00604 0.00580 0.02119 1.10245 t- 1969 145618.40 289999.15 313.15 3707.413 7805.930 23.276 0.02612 0.02766 0.08030 0.00763 0.02492 -0.00643 1.12581 1970 152309.47 289546.35 327.86 6691.070 -452.794 14.717 0.04595 -0.00156 0.04700 -0.00043 0.01458 0.03180 1.11858 1971 157652.36 291005.47 329.53 5342.887 1459.113 1.662 0.03508 0.00504 0.00507 0.00139 0.00157 0.03212 1.15414 1972 164389.71 297925.33 376.28 6737.356 6919.864 46.749 0.04274 0.02378 0.14187 0.00656 0.04403 -0.00785 1.19121 1973 173805.77 296325.30 438.24 9416.063 -1600.026 61.969 0.05728 -0.00537 0.16469 -0.00148 0.05111 0.00765 1.18186 1974 178724.46 305741.89 446.13 4918.685 9416.582 7.887 0.02830 0.03178 0.01800 0.00877 0.00559 0.01395 1.19090 1975 174893.65 305277.09 414.18 -3830.812 -464.796 -31.946 -0.02143 -0.00152 -0.07161 -0.00042 -0.02222 0.00121 1.20751 1976 174877.14 301299.52 434.62 -16.503 -3977.572 20.437 -0.00009 -0.01303 0.04934 -0.00359 0.01531 -0.01181 1.20897 1977 175766.12 287884.25 449.08 888.979 -13415.266 14.459 0.00508 -0.04452 0.03327 -0.01228 0.01032 0.00704 1.19469 1978 182183.70 301509.11 415.85 6417.581 13624.856 -33.235 0.03651 0.04733 -0.07401 0.01306 -0.02297 0.04642 1.20310 1979 185191.74 309978.26 426.11 3008.040 8469.152 10.262 0.01651 0.02809 0.02468 0.00775 0.00766 0.00110 1.25895 1980 184909.84 311468.03 469.84 -281.908 1489.772 43.731 -0.00152 0.00481 0.10263 0.00133 0.03185 -0.03470 1.26034 1981 186317.79 327651.86 479.66 1407.958 16183.825 9.820 0.00761 0.05196 0.02090 0.01433 0.00649 -0.01321 1.21661 1982 182643.14 325248.18 461.78 -3674.656 -2403.679 -17.882 -0.01972 -0.00734 -0.03728 -0.00202 -0.01157 -0.00613 1.20054 1983 182228.09 331954.21 454.12 -415.044 6706.026 -7.657 -0.00227 0.02062 -0.01658 0.00569 -0.00515 -0.00281 1.19318 1984 182328.71 338801.39 453.41 100.615 6847.182 -0.708 0.00055 0.02063 -0.00156 0.00569 -0.00048 -0.00465 1.18983 0.50654 0.10844 0.22031 0.17779 GROWTH DUE TO CAPITAL MONEY TECHNICAL CHANGE 100.00% 21.41% 43.49% 35.10% TABLE 13 DATA USED FOR PREDICTING THE VALUES YEAR 1958 1972 1984 LNY 5.5855724445 5.9410728 6.1828628 (LNY)SQ 31.19862 35.29635 38.22779 LNN 2.68354 3.09442 3.33508 (LNN)SQ 7.20140 9.57544 11.12274 PREDICTED VALUES FOR COLOMBIA FROM CHENERY & SYRQUIN MODEL ========================================= ===========PREDICTED VALUES====== COEFFICIENTS: CONSTANT LNY (LNY)SQ LNN (LNN)SQ 1958 1972 1984 SAVINGS -0.34 0.115 -0.006 0.051 -0.007 0.2016 0.2222 0.2339 INVESTMENT -0.161 0.085 -0.004 0.013 -0.002 0.2095 0.2239 0.2327 URBANIZAT -1.154 0.365 -0.016 0.019 -0.002 0.4221 0.4894 0.5322 o' PRIMARY 1.966 -0.449 0.027 -0.012 0.001 0.2754 0.2239 0.1931 INDUSTRY -0.522 0.154 -0.006 0.053 -0.007 0.2428 0.2781 0.2997 UTILITIES -0.002 0.006 0.001 0.01 -0.002 0.0751 0.0807 0.0844 SERVICES -0.442 0.288 -0.022 -0.051 0.008 0.4010 0.4113 0.4165 HIGH20 -0.228 0.292 -0.027 0 0 0.5606 0.5538 0.5452 LOW40 0.466 -0.119 0.01 0 0 0.1133 0.1120 0.1125 Y= PER CAPITA INCOME IN 1964 U.S. DOLLARS LNY= LN OF Y (LNY)SQ= SQUARE OF LNY N= POPULATION IN MILLIONS LNN= LN OF N (LNN)SQ= SQUARE OF LNN - 37 - TABLE 16 RATIO OF M2(BROAOLY DEFINED MONEY) OVER GOP YEAR ARG BRA CHL COL MEX PER TIME 1974 32.24% 17.66% 22.01% 22.34% NA 27.64% 1 1975 25.17% 17.92% 21.14% 22.72% NA 26.08% 2 1976 20.91% 15.38% 15.51% 23.'Q% NA 23.27% 3 1977 24.73% 14.60% 15.96% 23.../. 28.38% 21.00% 4 1978 27.99% 14.05% 17.98% 23.63% 29.91% 21.28% 5 1979 30.53% 14.46% 19.02% 23.05% 30.94% 22.00% 6 1980 29.03% 11.19% 21.48% 25.57% 30.32% 25.32% 7 1981 31.96% 11.16% 24.45% 28.09% 32.91% 24.91% 8 1982 31.12% 10.86% 31.67% 27.93% 32.44% 25.38% 9 1983 33.72% 10.75% 26.43% 29.59% 28.85% 27.83% 10 1984 31.02% 11.87% 29.43% 29.03% 28.98% 28.41% 11 LN OF THE ABOVE RATIOS AND TIME YEAR ARG BRA CHL COL MEX PER LNTIME 1974 -1.1318 -1.7341 -1.5136 -1.4986 NA -1.2858 0.0000 1975 -1.3793 -1.7192 -1.5539 -1.4820 NA -1.3439 0.6931 1976 -1.5650 -1.8718 -1.8634 -1.4490 NA -1.4580 1.0986 1977 -1.3972 -1.9244 -1.8349 -1.4690 -1.2595 -1.5605 1.3863 1978 -1.2734 -1.9622 -1.7157 -1.4425 -1.2071 -1.5473 1.6094 1979 -1.1864 -1.9335 -1.6595 -1.4675 -1.1732 -1.5142 1.7918 1980 -1.2370 -2.1902 -1.5378 -1.3639 -1.1933 -1.3735 1.9459 1981 -1.1407 -2.1927 -1.4087 -1.2698 -1.1115 -1.3900 2.0794 1982 -1.1674 -2.2197 -1.1497 -1.2756 -1.1257 -1.3712 2.1972 1983 -1.0870 -2.2301 -1.3306 -1.2176 -1.2432 -1.2790 2.3026 1984 -1.1706 -2.1315 -1.2232 -1.2367 -1.2385 -1.2586 2.3979 ARG=ARGENTINA COL=COLOMBIA BRA=BRAZIL MEX=MEXICO CHL=CHILE PER=PERU - 38 - TABLE 17 REGRESSION RESULTS OF FINANCIAL DEEPENING OVER TIME COLOMBIA ARGENTINA Regression Output: Regression Output: Constant -1.57070939 Constant -1.36728 Std Err of Y Est 0.065490196 Std Err of Y Est 0.140282 R Squared 0.675463875 R Squared 0.148275 No. of Observations 11 No. of Observations 11 Degrees of Freedom 9 Degrees of Freedom 9 X Coefficient(s) 0.120294716 X Coefficient(s) 0.074522 Std Err of Coef. 0.027794301 Std Err of Coef. 0.059536 BRAZIL MEXICO Regression Output: Regression Output: Constant -1.63614856 Constant -1.22529 Std Err of Y Est 0.082891446 Std Err of Y Est 0.056020 R Squared 0.832083677 R Squared 0.092869 No. of Observations 11 No. of Observations 8 Degrees of Freedom 9 Degrees of Freedom 6 X Coefficient(s) -0.23493487 X Coefficient(s) 0.023592 Std Err of Coef. 0.035179461 Std Err of Coef. 0.030102 CHILE PERU Regression Output: Regression Output: Constant -1.77551464 Constant -1.40860 Std Err of Y Est 0.214306234 Std Err of Y Est 0.113555 R Squared 0.247585125 R Squared 0.001979 No. of Observations 11 No. of Observations 11 Degrees of Freedom 9 Degrees of Freedom 9 X Coefficient(s) 0.156519737 X Coefficient(s) 0.006438 Std Err of Coef. 0.090952421 Std Err of Coef. 0.048193 (1)THE DEPENDENT VARIABLE IS BROADLY DEFINED MONETARY BALANCES AS A SHARE OF GROSS DOMESTIC PRODUC- (2)THE INDEPENDENT VARIABLE IS TIME. WITH 1974=1, 1975=2,....1984=11. - 39 - TABLE 18 INFLATION TAX ON MONEY BALANCES AS A SHARE OF INCOME MONEY (Ml) M1+QUASI=M2 M2+CAVS=M3. GNP IN INFLATION INFL. RATE- TAX DUE TO BIL. PESO BIL. PESO BIL. PESO BIL. PESO BASED ON NOMINAL INFLATION YR (NOMINAL) (NOMINAL) (NOMINAL) (NOMINAL) GNP DEFLATOR INTEREST RATE (T1,T2) 1958 3.26 3.91 3.91 20.30 13.16% 8.058% 2.206% 59 3.63 4.40 4.40 23.30 4.65% -0.449% 0.761% 60 3.99 4.75 4.75 26.40 8.89% 3.789% 1.414% 61 4.96 5.88 5.88 30.00 8.16% 3.063% 1.418% 62 5.93 7.47 7.47 33.70 7.55% 2.447% 1.461% 63 6.69 8.21 8.21 42.70 22.81% 17.707% 3.629% 64 8.25 9.70 9.70 53.00 17.14% 12.043% 2.676% 65 9.64 11.83 11.83 59.90 8.54% 3.437% 1.483% 66 11.24 13.05 13.05 72.40 14.61% 9.507% 2.279% 67 13.68 15.79 15.79 81.60 8.82% 3.724% 1.520% 68 15.86 18.07 18.07 94.40 9.01% 3.909% 1.539% 69 19.40 22.09 22.09 108.30 8.26% 1.164% 1.458% 70 22.40 25.78 25.78 129.90 9.92% 2.824% 1.695% 71 25.06 29.19 29.19 153.10 10.42% 3.317% 1.701% 72 31.85 37.71 37.71 186.00 13.21% 5.608% 2.253% 73 41.65 50.90 55.30 238.70 20.00% 2.908% 74 49.07 63.71 72.03 318.80 25.46% 3.124% 75 58.92 78.49 92.03 398.60 22.88% 2.752% 76 79.38 105.14 124.97 523.20 25.53% 3.085% 77 103.30 140.69 164.80 708.30 28.95% 3.274% 78 132.93 180.01 214.93 901.60 17.25% 2.170% 79 165.90 221.00 274.02 1181.60 24.05% 2.722% 80 212.40 320.47 403.70 1573.40 27.55% 2.916% 81 256.37 434.73 556.94 1972.30 22.80% 2.413% 82 321.40 525.65 697.41 2459.80 24.76% 2.593% 83 396.74 659.23 903.81 2982.70 20.37% 2.251% 84 492.39 816.84 1119.74 3757.50 22.18% 2.379% FIGURE 1 INFLATION TAX ON MONETARY BALANCES AS A SHARE OF INCOME (COLOMBIA:1958-1984) 30% 25%- +5% + + 20%- 15% - + INFLATION 10%_ 5% - +INFLATION TAX 10%0 1958 60 62 64 66 68 70 72 74 76 78 80 82 84 YEAR - INFLATION TAX - INFLATION - 41 - BIBLIOGRAPHY Bailey, M.J. 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