metadata: authors: 0: author: Buckley, Robert
1: author: Dokeniya, Anupam
2: author: INU
3: author: PRE
count: Colombia
docna: 0: docna: Inflation, monetary balances and the
            aggregate production function : the case of Colombia
docty: Policy Research Working Paper
subtopic: Economic Theory & Research,Industrial Economics,Labor Markets,Housing Finance,Capital Markets and Capital Flows,Non Bank Financial Institutions,Capital Flows,Economic Growth,Inflation,Financial Sector Policy
teratopic: Finance and Financial Sector Development
abstracts: cdata!: The role of monetary balances in
            economic growth has long been a topic of macroeconomic
            research. This paper examines the role of real money
            balances in an aggregate production function of a developing
            economy, Colombia. Colombia is an interesting case to
            analyze for several 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. Second, data
            is readily available, since Colombia has been studied
            extensively. Therefore, Colombia is one of the few
            developing countries for which an empirical study can be
            made of the effects of financial policy on economic growth.
            Finally, the role that monetary balances may have played in
            economic growth is of interest because indexed mortgages
            played a major role in this change in financial policy.
            These indexed mortgages were similar to introducing a
            competitive "Trojan Horse" into the Colombian
            financial system. Other depository institutions were forced
            to compete with indexed mortgage lenders for deposits.
            Growth was stimulated by inducing the financial system to
            minimize the effects of high and variable inflation rates on
            the cost of monetary balances.
geo_reg_key: 119228,517191
repnme: repnme: Inflation, monetary balances and the
            aggregate production function : the case of Colombia
display_title: Inflation, monetary balances and the
            aggregate production function : the case of Colombia
listing_relative_url: /research/1989/10/700431/inflation-monetary-balances-aggregate-production-function-case-colombia
topicv3: Economic Growth m1326241 471,Informal Sector m1326258 1168,Inflation m1326709 0870F4727ACED1CF8525815C00471347,Housing Finance m1327222 612,Financial Sector Development m1327681 1920
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Finance and Financial Sector Development
origu: Policy, Research & Ect Affairs
no_of_pages: 49
model_extractions: Copyright 1989 **0** The Worle Bank 1818 H Street, N.W.

Alt 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 accordanc2 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 Sank 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 presentatiorn 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
# MSETRACT

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 4n 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 monetazy 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.
li

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# INFLATION. MONETARY BALANCES AND THE AGGREGATE PRODUCTION FUNCTION

# THE CASE OE COLOMBIA

# Table of Contents

||Paze No.|
|---|---|
|I.|INTRODUCTION. . . .<br>. . . . .<br>. . . . . . . . . . . . . . .|
|II.|<br>INDEXED MONETARY BALANCES IN COLOMBIA . . . . . . . . . . . .<br>4|
|III.|THE MODEL AND THEDATA............<br>.<br>.<br>.<br>.....<br>10|
|IV.|THE AUGMENTED PRODUCTION FUNCTION<br>AND OTHER STUDIES OF COLOMBIAN ECONOMIC GROWTH . . . . . . . .<br>14|
||A.<br>Indexation and Economic Growth . . . . . . . . . . . . .<br>14|
||B.<br>Income Distribution Issues . . . . . . . . . . . . . . .<br>15|
||C.<br>Financial Policy andl he Sources of Growth .<br>.<br>.<br>.<br>.<br>.<br>.<br>16|
|V.|CONCLUSION<br>.... . . . . . .<br>.... . . . . . . . . . .<br>.<br>18|
||APPENDIX I<br>.................................................<br>20|
||APPENDIX II<br>.... . . . . . . . . . . . . . . . . . . . .<br>.<br>21|
||TABLES|
||Table 1- Behavior of Monetary Aggregates and Inflation<br>over the 1958-84 Period<br>.<br>. . . .<br>8<br>Table 2- Estimates of the Parameters of the Cobb-Douglas<br>Production Function, with and without Real Money<br>Balances, Corrected for Autocorrelation, for the<br>years 1958-1984 . . . . . . . . . . . . i. . . .<br>22<br>Table 3- Estimates of the Parameters of the Cobb-Douglas<br>Production Function, with Real Money Balances<br>(with and without Adjustment for Indexation and<br>Inflation) Corrected for Autocorrelation, for<br>the Years 1958-1984 . . . . . . . . . . . . . . .<br>23|
* iii -

Page No.

# JULES (continued)

|Table 4- Estimates of the Parameters of the Cobb-Douglas<br>Production Function, with the without Real Money||
|---|---|
|Balances, Corrected for Autocorrelation, for the||
|Years 1958-1984. (Capital is Adjusted for Capacity<br>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<br>of the Variables .|26|
|Table 7- GDP of Colombia 1958-1984 . . . i. . . . . . . . . .|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|
|Table11- Real Monetary Balances for Colombia 1958-1984 . .<br>.<br>.|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<br>. .<br>.<br>.|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. ITRMQD-UCTION_

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. Nore 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 bulances 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.<sup>11</sup> 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.

I/ 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-Aeut, 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 R<sup>2</sup> 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 Employmon- Study as reported in World Bank (1987) were developed, and in the former cas i updated. In this respect, Colombia is one of the few developing countries **LoL** 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 196G-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. _LI_

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.

1.0 Coherent with the preliminary nature of our research, the econometric spec.fication 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.
Indeed, the approach taken is very much in the spirit 3f the original Solow (1957) article on aggregate production functions and t:e 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 w'th inflation, indexation, and increased financial competition is described. T.he 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.
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# 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 heve 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 implement&tion were placed under the direction of Laughlin Currie.A1 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.21 i/ 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.

A/ 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.

5/ The informal sector generally has three important dimensions: finance, employment and housing production. In contrastt to many other Latin American economies, each of these aspects of the inform.al 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.<sup>19</sup> -<sup>23</sup> 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 grei. 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 bacause 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 UPACE,, 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 w. designed to insure that CAV lending was targeted towards lower and moderate ome borrowers.h1 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 st _Il_ changed daily with the quotations for the next month announced in advanc... 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 featare cf' 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 shortterm 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 indexatic-. this tax applied to all monetary balances because nominal interest rates ox. -ime 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.

j/ 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 MI, currency and demand eseposits, as well as M2, which also includes time deposits. The tax on MI is .traightforfard and in steady state is ecqtal to e(14+), where e is the inflation rate.

2.07 For time deposits, prior to the introduction of CAVs, the tax is more complicated. Becauie 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, Tas always less than the inflation rate, these asst.cs also lost value over time. Bringing all these effects together, the tax rate on what might be termed equivalent units of monetary balane.es can be described by 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 Ml and (M2-Ml) balances, respectively. The tax on real return on the non-Ml 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.1' If the return on time deposits competes with the return on CAV time deposits, and this **iea1** return becomes invariant with respect to changes in the inflation rate inflation would apply only to Ml, and not at all to K2 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: This kind of regulatory change eliminates both the inflation tax and loss of real return on non-Ml monetary balances, and it results in the inflation tax being applied only to Ml balances. It amounts to assuming that the cost of the indexed balances is unaffected by changes in the inflation rate, so that non-Ml monetary balances become superneutral.

Z/ See Carrizosa et al. (1982).

A/ Strictly speaking, the indexed time and savings deposits (GAV's) shou2d be part of K2, 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 "monie3" (M2-M1) and (M3-M2) are identical from 1973 onwards.
-7-

2.09 However, besides making the rMea 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.91 The tax rate per percent of inflation is 0.166 percent in the former period and 0.116 percent in the latter period.J&' 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.

i/ The estimates are stylized for a number of reasons. Most importantly tbey 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.

J,Q/ 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

||12958-72|1973-84|
|---|---|---|
|M1/GDP|> 0|< 0|
|M/GDP|0|><br>0|
|Mi/M|.85|.57|
|Mi/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, MH share of total monetary balances showed an increasing trend. In the latter period, behavior was very different: Ml 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. V/ 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.
Hence the financial crisis that has affected the comercial banking system since the end of 1982 is not surprising.la' 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 retutas 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.U' 3.02 The following equation was estimated with annual data over the 195884 period.

(3) In GDP = ln A + a ln K + 8 In L + yln M + u where, GDP - total output, K - capital, L - labor, H - 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 2J/ 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.
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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.l'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 MI. 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(l).211 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, the3e 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.

1L/ 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 l/l-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/l-T where T-G.
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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 perceant 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 _Al,_ 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 MI, .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 4.* L 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: 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 16J 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.
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where equivalent units of M2 are used and the coefficients are better confirmed. 1 Z 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.

12/ 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 Ml.
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# IV. THE AUGMENTED PRODUCTION FUNCTION AND ER 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
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for only 35 per,nt of the growth in total factor productivity.1t / 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.12 1 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.<sup>221</sup> It indicates that based on Colombia's income level and population growth over this 1E/ 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).

IV/ See Reyes (1987) for the most recent data on income distribution. Urrutia (1985) provides the most comprehensive evidence for the 1970s.

ZQ/ 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.
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period, that a slight deterioration in the share of income in the lowest two quintals was to be expected.2Ui 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. Financia 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 _Iv_ 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).
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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 A11 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.
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# 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 -4-Ality to finance investments in the "unproductive" and socially meretricio" p-.rtion of the housing stock, i.e., the portion of housing production not Lliocated 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