Interest Spreads in Banking: Costs, Financial Taxation, Market Power, and Loan Quality in the Colombian Case 1974–96

Adolfo Barajas; Natalia Salazar; Roberto Steiner

doi:10.5089/9781451853315.001.A001

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Interest Spreads in Banking: Costs, Financial Taxation, Market Power, and Loan Quality in the Colombian Case 1974–96

Author: Mr. Adolfo Barajas, Ms. Natalia Salazar¹, and Mr. Roberto Steiner²

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
| ² 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Authors’ E-Mail Addresses: abarajas@imf.org; rsteiner@fedesarrollo.org.co; nsalazar@fedesarrollo.org.co

Publication Date:: 01 Aug 1998

eISBN:: 9781451853315

Language:: English

Keywords:: WP; banking system; market power; bank behavior; bank intermediation; quality variability; bank variability; bank intermediation spread

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This paper examines the determinants of the high intermediation spread observed in the Colombian banking sector for over two decades. A reduced-form equation is estimated on the basis of a bank profit maximization model that permits a decomposition into operational costs, financial taxation, market power, and loan quality. Although the average spread did not change between the pre liberalization (1974-88) and post liberalization (1991-96) periods, its composition did, with market power being significantly reduced and the responsiveness to loan quality increased. Colombia’s progress in reducing operational costs and financial taxation and improving loan quality, will determine whether it can narrow the spread.

Abstract

I. Introduction

A key variable in the financial system is the spread between lending and deposit interest rates. When it is too large, it is generally regarded as a considerable impediment to the expansion and development of financial intermediation, as it discourages potential savers with low returns on deposits and limits financing for potential borrowers, thus reducing feasible investment opportunities and therefore the growth potential of the economy.

Financial systems in developing countries have been shown to exhibit significantly and persistently larger intermediation spreads on average than those in developed countries (Hanson & de Rezende Rocha, 1986). These high spreads have frequently been attributed to such factors as high operating costs, financial taxation or repression, lack of competition, and high inflation rates. However, with some notable exceptions², there has been a scarcity of direct tests of the relevance of these factors, and a lack of a consistent theoretical banking model on which to base the statistical analysis. In this paper we adopt a “New Empirical Industrial Organization” (Bresnahan, 1989) approach which has been used to examine competitiveness in banking³, and we apply it specifically to the determination of the intermediation spread, allowing for certain peculiar characteristics of banking systems in developing countries.

Colombia provides an interesting case study. During the seventies and eighties intermediation spreads traditionally were high, both compared to world levels (Clavijo, 1991) and to those in Latin America (Morris, 1990). The financial system appeared to be highly repressed, inefficient, and non-competitive, as banks were subject to high rates of financial taxation and exhibited high operating costs and a high degree of concentration and state ownership (Barajas, 1996). Starting in the early nineties, however, Colombian policymakers embarked on an ambitious and far-reaching economic reform program, and took several actions aimed at redefining the structure and operation of the financial system⁴. They eased entry restrictions, relaxed the specialization of intermediaries by moving towards a multi-banking scheme, reduced financial taxation by eliminating mandatory investments and simplifying reserve requirements, phased out directed credit programs, undertook substantial privatization of financial institutions, and strengthened prudential norms. These measures sought to increase financial intermediation and facilitate efficiency, competitiveness, and stability of the domestic financial system, and to increase private participation, both domestic and foreign.

However, as has occurred in previous instances of financial reform in Colombia, these measures were reversed to some degree as a result of changes in the direction of macroeconomic policy. In particular, policymakers decided to attempt to sterilize the buildup of international reserves between 1989 and 1995 with restrictive monetary policy and exchange controls, at times increasing reserve requirements, imposing direct controls on credit expansion and taxes on foreign borrowing. Therefore, a tradeoff emerged between the longer-term goals of the financial reform program and the short-term objectives of the macroeconomic stabilization policy.

Consequently, bank intermediation spreads, overhead costs, and financial taxation have remained high during the nineties. As a percentage of total assets, the interest spread averaged 6-8 percent over the 1988-1995 period, compared to 2-3 percent in industrialized countries, while overhead expenses in relation to total assets averaged 7-8 percent, compared to 2-3 percent in industrialized countries and 6 percent on average in Latin America (Table 1)⁵. With regard to financial taxation, policymakers were able to reduce reserve requirements and forced investments from their late-seventies peak levels of around 50 percent of total bank deposits to about 20 percent by the end of the eighties, but the early nineties saw a renewed increase, to 32 percent, and in recent years this ratio remains around 20 percent (Table 2).

Table 1.

Bank Intermediation Spreads and Overhead Costs in Colombia as Compared to Latin American and Industrialized Countries: Average 1988-1995

Claessens, et.al. (1997)

Table 1.

Bank Intermediation Spreads and Overhead Costs in Colombia as Compared to Latin American and Industrialized Countries: Average 1988-1995

		Net Interest Margin/ Total Assets	Overhead/ Total Assets
		(percentage)
Colombia
	Domestic banks	6.2	8.0
	Foreign-owned banks	7.6	6.9
Latin America
	Domestic banks	5.8	6.1
	Foreign-owned banks	7.4	6.3
Industrial Economies
	Domestic banks	2.8	2.6
	Foreign-owned banks	2.3	2.3

Claessens, et.al. (1997)

Table 1.

Bank Intermediation Spreads and Overhead Costs in Colombia as Compared to Latin American and Industrialized Countries: Average 1988-1995

		Net Interest Margin/ Total Assets	Overhead/ Total Assets
		(percentage)
Colombia
	Domestic banks	6.2	8.0
	Foreign-owned banks	7.6	6.9
Latin America
	Domestic banks	5.8	6.1
	Foreign-owned banks	7.4	6.3
Industrial Economies
	Domestic banks	2.8	2.6
	Foreign-owned banks	2.3	2.3

Claessens, et.al. (1997)

Table 2.

Indicators of Financial Taxation, Selected Periods

(end-of-quarter percentages)

^{^1/}Defined as the additional cost of deposits from reserve requirements and forced investments. In the post-liberalization period, in which forced investments and remunerated reserves are close to zero, the tax rate is equal to 1/(1-e)-1, where e is the average reserve ratio. In the pre-liberalization period, the measure includes forced investments as well, and is adjusted by the rate of remuneration of both required reserves and forced investments. A detailed description of this measure is contained in Barajas (1996).

Table 2.

Indicators of Financial Taxation, Selected Periods

(end-of-quarter percentages)

Quarter	Reserve Requirements & Forced Investments/ Total Deposits	Average Tax Rate on Deposits ^1/
	Pre-liberalization period
1974:1	43.4	41.7
1979:3	49.5	74.9
1984:4	29.9	20.9
1988:4	26.5	20.6
	Post-liberalization period
1991:1	25.8	34.8
1992:2	32.4	47.9
1994:2	28.6	40.0
1996:3	19.0	23.4

Table 2.

Indicators of Financial Taxation, Selected Periods

(end-of-quarter percentages)

Quarter	Reserve Requirements & Forced Investments/ Total Deposits	Average Tax Rate on Deposits ^1/
	Pre-liberalization period
1974:1	43.4	41.7
1979:3	49.5	74.9
1984:4	29.9	20.9
1988:4	26.5	20.6
	Post-liberalization period
1991:1	25.8	34.8
1992:2	32.4	47.9
1994:2	28.6	40.0
1996:3	19.0	23.4

It is evident that considerable financial deepening has taken place in Colombia, as shown by the growth of broad money in relation to GDP, particularly between 1992 and 1996, when this ratio increased from 30 to almost 40 percent (Figure 1). Substantial privatization has also taken place during the nineties, with the share of private banks in total assets increasing from 45 to 79 percent, and their share in capital rising from 62 to 81 percent (Table 3). However, what is not directly apparent is how much progress has been made in increasing efficiency and competitiveness of financial institutions. Since these factors are expected to be reflected in the banking intermediation spread, the study of spreads will allow us to assess the progress made in these areas.

Table 3.

Private and State-Owned Banks in Colombia Distribution of Assets and Capital, 1991-1996

Source. Colombian Bankers’ Association and estimates by the authors.

Table 3.

Private and State-Owned Banks in Colombia Distribution of Assets and Capital, 1991-1996

		1991		1994		1996
		June		December		June
		Assets	Capital	Assets	Capital	Assets	Capital
1. State-Owned Banks		55.0	38.6	22.1	20.6	20.6	19.3
2. Private banks		45.0	61.5	77.9	79.4	79.4	80.7
	of which: Foreign	7.6	9.7	8.6	10.0	9.7	10.7

Source. Colombian Bankers’ Association and estimates by the authors.

Table 3.

Private and State-Owned Banks in Colombia Distribution of Assets and Capital, 1991-1996

		1991		1994		1996
		June		December		June
		Assets	Capital	Assets	Capital	Assets	Capital
1. State-Owned Banks		55.0	38.6	22.1	20.6	20.6	19.3
2. Private banks		45.0	61.5	77.9	79.4	79.4	80.7
	of which: Foreign	7.6	9.7	8.6	10.0	9.7	10.7

Source. Colombian Bankers’ Association and estimates by the authors.

As we will show, intermediation spreads can be broken down into different components relating to bank costs, market power, and loan quality. In order to assess the relative importance of each factor and to evaluate whether the (incomplete) financial liberalization policies have been successful in reducing intermediation spreads, we will use a theoretical framework based on profit-maximizing bank behavior, which will then serve as the basis for the econometric analysis.

One must note that there is a possible tradeoff involved when analyzing spreads. While a high level is generally indicative of inefficiency, excessive risk-taking, or lack of competition within the banking sector, it is also true that high spreads can contribute to high bank earnings which, if channeled into the capital base of the system, may promote safety and stability in the system. This is particularly relevant in the case of developing countries, where the existence of an implicit government bailout commitment has frequently led to a moral hazard situation in the financial system. It is not entirely clear which is preferable from a social standpoint; a banking system with low spreads and (consequently) low capital which may require a government-funded bailout, or a system with high spreads and a high capital base that may not require a bailout⁶. Section IV presents evidence that sheds light on the probable uses of high spreads in the Colombian case, and will confirm that the above tradeoff clearly applies here; while high spreads indicate certain shortcomings of the liberalization policies, they also appear to have facilitated a well-needed capitalization process during the present decade.

The paper is divided into five sections. The first is descriptive and presents the stylized facts, based on measurements of the spread and related indicators and their evolution by groups of banks. Section II examines a few key statistical relationships and offers a motivation for the theoretical model developed in Section III and for the econometric analysis shown in Section I. Section V summarizes the findings and discusses the principal conclusions and policy implications.

II. Interest Rate Spreads in Colombia, 1974-1996

Based on the available balance sheet and profit-loss information, we constructed two separate databases, a quarterly series of the aggregate banking system for the pre-liberalization 1974-1988 period, and a monthly series with individual bank data covering the post-liberalization 1991-1996 period. The break in the data corresponds to a transition period during which financial intermediaries adapted to a new accounting standard. The intermediation spread (m) is defined as the difference between the average rate charged on loans⁷ (i_l) minus the average rate paid on deposits (i_d), and is shown in Figures 2a and 2b⁸. In the pre-liberalization period the spread ranged between 16 and 32 percentage points, increasing steadily from 1974 up to its peak level in late 1979 and then falling again gradually until 1988, where it reached just under 19 percentage points. In the post-liberalization period, the spread declined steadily from an initial level of about 25 in 1991 to 19 percentage points in 1996.

A. A Closer Look at Intermediation Spreads and Related Banking Indicators in 1991-1996

The average intermediation spread m may be compared to a spread obtained from survey lending and deposit rates reported by banks weekly to the Colombian Banking Superintendency, a measure we define as m_s, equal to the difference between the average rate charged on loans on the last week of each month (i_ls) and the average rate paid on three-month time deposits during the last week of each month (i_ds). While the average spread (m) fell by about 6 percentage points between 1991 and 1996, with most of the fall occurring before 1994, the survey spread (m_s) remained relatively constant at around 10 percentage points throughout the period (Figure 2b).

In order to observe in greater detail the differences between these two measures, we analyzed the time series properties of both spreads using the Hodrick & Prescott method of decomposition into trend and seasonal components⁹. Using the Hodrick & Prescott suggested β value for monthly time series, we decomposed interest rates and spreads into trend and seasonal components. As expected, the trend component is clearly declining for the average spread m, but is relatively flat for the survey spread m_s. The decline in the average spread reflects a clear upward trend in the average deposit rate and a possible slight downward trend in the implicit lending rate, while both survey interest rates exhibit very similar U-shaped behavior in their trend components.

Throughout the 1991-1996 period Colombian interest rates were high in real terms and, once accounting for observed devaluation, high relative to the U.S.. On average, the deposit rate i_d was 14 percent, the lending rate was around 36 percent, and the rate on 3-month time deposits (i_ds) was 28 percent, compared to an average inflation rate of 23 percent and an average rate of nominal devaluation of 13 percent.

Figure 4 shows several indicators that may be related to interest spreads: the nonperforming loan ratio, the average reserve ratio, the ratio of administrative costs to assets, and the ratio of demand deposits to total deposits. It should be noted that the average reserve ratio is not strictly a policy variable; since it is an average of different reserve requirements over all types of deposits, it also depends on the composition of the public’s demand for different deposits. The observed decline in the average reserve ratio, from 33 percent in 1992 to less than 20 percent in 1996, was the result of both a reduction in reserve requirements and a shift in deposits away from demand deposits and toward savings and time deposits. The average percentage of nonperforming loans was relatively constant at 5-7 percent, with the exception of a brief upsurge in 1992¹⁰, and administrative costs did not show a clear upward or downward trend, fluctuating between 4 and 6.5 percent of total bank assets.

Figure 4 also sheds some light on the differing behavior between average and survey interest spreads. Although interest rates on time deposits did not increase substantially throughout the period, the share of demand deposits declined from 45 to 30 percent, thus increasing the average interest cost of bank deposits. This recomposition in deposits reflects significant changes in the money demand and the possible presence of financial innovations undertaken by the banking system as well as competition from non-bank financial intermediaries.

B. Private Versus State-Owned Banks in 1991-1996

From Figure 5, one can see that average spreads exhibit a downward trend for both state and private banks. State banks had a consistently higher spread throughout the period, as a result of charging slightly more on loans and paying significantly less on deposits, which in turn may reflect the state banks’ relatively higher percentage of nonperforming loans and higher ratio of demand deposits to total deposits, as seen in Figure 6. The higher observed percentage of demand deposits for state banks stems from the fact that these banks tend to manage the funds used by the government to carry out spending. Therefore, the recomposition toward interest-bearing deposits has been slower for these institutions. State banks also tended to maintain a greater amount of reserves relative to total deposits, and had higher labor costs in relation to their total assets. Although overall bank productivity increased throughout the nineties, as measured by the real value of loans per employee or per number of branches, it was consistently lower for state banks than for private banks.

III. Intermediation Spreads in 1991-1996: Some Simple Statistics

In this section we present two simple statistical tests, one showing the degree of cross-section versus time variability, and another showing a positive correlation between the percentage of nonperforming loans and the size of the intermediation spread. These, along with the descriptive statistics presented in the previous section, will help motivate the derivation and estimation of a simple model of bank behavior in which the intermediation spread is a function of costs (including financial taxation), credit risk, and, possibly, market power.

A. Cross-section versus Time Variability

Table 4 presents variation coefficients for the implicit lending and deposit interest rates (used to calculate m), the percentage of nonperforming loans, and the ratio of administrative costs to total assets. The cross-bank coefficient is obtained by computing a single average observation over time for each bank, and the time variation coefficient is obtained by computing an aggregate banking sector average for each time period. It appears that cross-bank variability is larger than time variability in general for all four variables shown. Variability in interest rates appears to be relatively small--and greater for deposit rates than for lending rates, reflecting the differences in deposit composition between private and state-owned banks-while loan quality variability is quite large across banks. This result suggests that a panel data approach to the empirical modeling would be useful in capturing this type of cross-section variability.

Table 4.

Variation Over Time and Across Individual Banks

Source: Estimates by the authors based on Colombian Bankers’ Association data.

Table 4.

Variation Over Time and Across Individual Banks

	Over Time	Across Banks
Implicit average deposit rate id variation coefficient	0.17	0.30
Implicit lending rate il variation coefficient	0.07	0.20
Percentage of nonperforming loans NPL variation coefficient	0.16	0.57
Administrative costs/Total assets variation coefficient	0.07	0.22

Source: Estimates by the authors based on Colombian Bankers’ Association data.

Table 4.

Variation Over Time and Across Individual Banks

	Over Time	Across Banks
Implicit average deposit rate id variation coefficient	0.17	0.30
Implicit lending rate il variation coefficient	0.07	0.20
Percentage of nonperforming loans NPL variation coefficient	0.16	0.57
Administrative costs/Total assets variation coefficient	0.07	0.22

Source: Estimates by the authors based on Colombian Bankers’ Association data.

B. Correlation between Loan Quality and the Intermediation Spread

We conducted a simple exercise to examine the possible relation between bank spreads and loan quality. First, we computed the average percentage of non-performing loans for the banking system and plotted it against the intermediation spread in Figure 7, where there is evidence of a positive correlation between the two. This suggests that banks may be transferring to their customers (either borrowers or depositors) a portion of the additional costs of a deterioration in loan quality.

This result was reinforced by Granger-causality tests on these two variables. The upper panel of Table 5 shows that the null hypothesis of a unit root cannot be rejected at a 5% level for the percentage of nonperforming loans (NPL) and the spread (m)¹¹. Therefore, the Granger causality tests were conducted on the first differences of the variables. The lower panel of Table 5 shows that the null hypothesis of lack of causality going from the percentage of nonperforming loans to the spread was rejected at a 1 percent level. On the other hand, lack of causality in the opposite direction was not rejected, thus suggesting that loan quality is an important determinant of the intermediation spread in Colombia, and since two-way causality was ruled out, loan quality also appears to be exogenous to the spread¹².

Table 5.

Statistical Tests on Loan Quality and the Intermediation Spread, 1992:05-1996:08

Table 5.

Statistical Tests on Loan Quality and the Intermediation Spread, 1992:05-1996:08

	Augmented Dickey-Fuller Test
Variable	Definition	Statistic	Critical value at a 5% level of significance	Constant (C) and/or Trend (T)	No. of lags
NPL	Percentage of nonperforming loans	-2.65	-2.92	C	1
dNPL		-4.58	-2.60		3
m	Intermediation spread	-2.52	-3.50	C,T	2
dm		-4.44	-1.95		3
	Granger Causality Test
	Null Hypothesis	No. of obs	No. of lags	F-statistic	Prob.
a.	d(m) does not cause d(NPL)	52	4	0.17	0.95
	d(npl) does not cause d(m)	52	4	4.49	0.00
b.	d(m) does not cause d(NPL)	52	1	2.06	0.16
	d(NPL) does not cause d(m)	52	1	14.56	0.00

Table 5.

Statistical Tests on Loan Quality and the Intermediation Spread, 1992:05-1996:08

	Augmented Dickey-Fuller Test
Variable	Definition	Statistic	Critical value at a 5% level of significance	Constant (C) and/or Trend (T)	No. of lags
NPL	Percentage of nonperforming loans	-2.65	-2.92	C	1
dNPL		-4.58	-2.60		3
m	Intermediation spread	-2.52	-3.50	C,T	2
dm		-4.44	-1.95		3
	Granger Causality Test
	Null Hypothesis	No. of obs	No. of lags	F-statistic	Prob.
a.	d(m) does not cause d(NPL)	52	4	0.17	0.95
	d(npl) does not cause d(m)	52	4	4.49	0.00
b.	d(m) does not cause d(NPL)	52	1	2.06	0.16
	d(NPL) does not cause d(m)	52	1	14.56	0.00

To summarize the results of this section, we found that intermediation spreads in Colombia tended to vary considerably across banks, that deteriorations in loan quality were positively correlated with spreads, and that causality appeared to go from loan quality to the spread. These results suggest that spreads in Colombia should be analyzed with a model that incorporates the effect of loan quality, and that panel data techniques would be useful to account for cross-section heterogeneity.

IV. A Simple Bank Intermediation Model

We begin with an intermediation model to represent bank behavior, based on the Shaffer (1989, 1993) analysis of market power in the Canadian and U.S. banking systems, but which incorporates a specific balance sheet relationship between deposits and loans and explicitly derives a condition for the bank intermediation spread¹³. Each bank j produces an output, namely loans (L_j) and uses two inputs, labor and deposits (D_j). In addition to loans, on the asset side the bank is also required to hold a certain amount of reserves (R_j) with the central bank. Liabilities are made up of deposits plus an exogenous residual, “other net liabilities” (ONL_j). Therefore, for a given required reserve ratio (ε_j)¹⁴, the balance sheet condition for each bank is:

\begin{matrix} L_{j} + R_{j} = D_{j} + {ONL}_{j} \Rightarrow L_{j} - D_{j} (1 - ε_{j}) - {ONL}_{j} = 0 & (1) \end{matrix}

Banks receive revenues from the interest on loans and must pay the interest costs of deposits as well as the real resource costs--mostly wages--of engaging in financial intermediation. They maximize profits (U_j) which are defined as the difference between financial revenues and (financial and nonfinancial) costs:

\begin{matrix} U_{j} = i_{j} L_{j} - i_{d} D_{j} - C (L_{j}, w, x) & (2) \end{matrix}

where i_land i_d are the lending and deposit interest rates, respectively, w is the wage rate, and x is a vector of other variables that affect marginal nonfinancial costs. In this simple formulation there is no uncertainty and the banks choose their level of output in order to maximize profits. The first-order condition for profit maximization is¹⁵:

\begin{matrix} \frac{\partial U_{j}}{\partial L_{j}} = i_{l} + L_{j} (\frac{\partial i_{l}}{\partial L_{j}}) - i_{d} \frac{\partial D_{j}}{\partial L_{j}} - D_{j} \frac{\partial i_{d}}{\partial L_{j}} - C_{l} = o & (3) \end{matrix}

where C_l is the marginal nonfinancial cost of producing loans. From the balance sheet condition we obtain a relationship between loans and deposits which shows how credit growth is constrained by the amount of reserves banks must hold: $\frac{\partial D_{j}}{\partial L_{j}} = \frac{1}{1 - ε_{j}}$ . Therefore, the first order condition can be written as:

\begin{matrix} i_{l} - \frac{i_{d}}{1 - ε_{j}} = - L_{j} (\frac{\partial i_{l}}{\partial L_{j}}) + [D_{j} \frac{\partial i_{d}}{\partial D_{j}})] \frac{1}{(1 - ε_{j})} + C_{l} & (4) \end{matrix}

The term on the left-hand side may be called the “net spread”, equal to the difference between the lending rate and the deposit rate adjusted by the level of financial taxation. Therefore, the right-hand side of the equation contains factors additional to financial taxation which drive a wedge between deposit and lending rates, in particular, market power and nonfinancial costs of intermediation. In this framework a bank possesses market power to the extent that its output decisions affect interest rates, as indicated by the terms δi_l/δL_j and δi_d/δD_j. Market power will be affected by the industry-wide price elasticity of demand, the market share of bank j, and the response of other banks to changes in bank j output. If industry demand is infinitely elastic, or the bank is very small, or if reactions by other banks offset its output decisions, then the bank will not possess market power. Equation (4) can be rewritten to reflect these different effects:

\begin{array}{l} i_{j} - \frac{i_{d}}{1 - ε_{j}} = - L \frac{L_{j}}{L} (\frac{\partial i_{l}}{\partial L} \frac{\partial L}{\partial L_{j}}) + D \frac{D_{j}}{D} (\frac{\partial i_{d}}{\partial D} \frac{\partial D}{\partial D_{j}}) \frac{1}{(1 - ε_{j})} + C_{l} \\ i_{j} - \frac{i_{d}}{1 - ε_{j}} = - L ({sl}_{j} {rl}_{j}) (\frac{\partial i_{l}}{\partial L}) + D ({sd}_{j} {rd}_{j}) (\frac{\partial i_{d}}{\partial D}) + C_{l} & (5) \end{array}

where sl_j and sd_j represent the market shares of bank j in loans and deposits, respectively, and rl_j and rd_j represent the response of total banking system loans and deposits to changes in output by bank j.

A. Shaffer Estimation Approach

In the Shaffer approach, banks are assumed to be price takers in the input markets, so the estimation of (5) involves only the market power on bank output, and is estimated jointly with a demand equation that provides the relevant slope parameters. Shaffer specifies demand for bank output (in our case, loans) as a linear function of its price (i_l), income (Y), and the price of substitutes (z_l), with certain interaction terms:

\begin{matrix} L = a_{0} + a_{1} i_{l} + a_{2} Y + a_{3} z_{l} + a_{4} i_{l} Y + a_{5} i_{l} z_{l} & (6) \end{matrix}

Marginal costs are assumed to be a linear function of output, the wage rate (w), and other variables (x) that may shift the marginal cost curve:

\begin{matrix} C_{l} = b_{0} + b_{1} L + b_{2} w + b_{3} x & (7) \end{matrix}

When we substitute the demand and marginal cost function parameters in (6) and (7) into the spread equation (5), and assuming that banks are price takers in the deposit market, we may rewrite the profit-maximizing spread condition as the following regression equation:

\begin{matrix} i_{l} - \frac{i_{d}}{1 - ε_{j}} = - L λ (\frac{1}{a_{1} + a_{4} Y + a_{5} z_{1}}) + b_{0} + b_{1} L + b_{2} w + b_{3} x & (5a) \end{matrix}

Equations (6) and (5a) may then be estimated jointly for the aggregate banking system, yielding estimates of all demand and marginal cost parameters, and of average market power in the banking system (λ). Note that λ is equal to the market share times the response indicator $λ = {sl}_{j} {rl}_{j} = \frac{L_{j}}{L} \frac{\partial L}{\partial L_{j}}$ , and is equal to zero in the case of perfect competition, to the inverse of the number of banks (1/N) in the case of a Cournot oligopoly, and is equal to unity in the case of collusion. In order to identify λ, either a₄ or a₅ must be nonzero, and in order to obtain a downward sloping demand curve for loans, the estimated values of a₁+a₄Y+a₅z_l must be positive.

It can be shown how one can relax the Shaffer assumption¹⁶ that banks are price takers in the deposit market, thus requiring the estimation of a demand function for deposits. Suominen (1994)¹⁷, followed this type of approach, by modeling a demand function analogous to that of loans, as a function of income, the deposit interest rate (i_d), the price of substitutes (z_d), and several interaction terms. For simplicity, we will maintain the assumption of a perfectly competitive market for bank deposits.

B. An Alternative Specification

We derive a second, slightly more restrictive specification but which does not require joint estimation with the demand function. Equation (4) may be rewritten in terms of the lending interest rate:

\begin{array}{l} i_{l} (1 + \frac{L_{j}}{i_{l}} \frac{\partial i_{l}}{\partial L_{j}}) = \frac{i_{d}}{1 - ε_{j}} (1 + \frac{D_{j}}{i_{j}} \frac{\partial i_{d}}{\partial D_{j}}) + C_{l} \\ i_{l} (1 + \frac{θ_{l}}{η_{l}}) = \frac{i_{d}}{1 - ε} (1 + \frac{θ_{d}}{n_{d}}) + C_{l} \\ i_{l} = \frac{i_{d} (\frac{ϕ_{d}}{ϕ_{l}})}{1 - ε} + \frac{C_{l}}{ϕ_{l}} & (4a) \end{array}

where we define θ_l = ml_jrl_j, θ_d = md_jrd_j and $η_{l} = \frac{\partial L}{\partial i_{l}} \frac{i_{l}}{L}, η_{d} = \frac{\partial D}{\partial i_{d}} \frac{i_{d}}{D}$ are the interest elasticities of demand for deposits and loans, and we define $ϕ = 1 + \frac{θ}{η}$ . Therefore, equation (4a) defines a profit-maximizing relationship between the lending interest rate, the deposit rate (adjusted by the rate of financial taxation), and marginal costs. This then becomes the following regression equation for the lending rate:

\begin{array}{l} i_{l} = d_{0} + d_{1} \frac{i_{d}}{1 - ε} + d_{2} w + d_{3} x \\ d_{0} = \frac{b_{0}}{ϕ_{t}}, d_{1} \frac{ϕ_{d}}{ϕ_{l}}, d_{2} = \frac{b_{2}}{ϕ_{l}}, d_{3} = \frac{b_{3}}{ϕ_{l}} & (5b) \end{array}

In this single-equation specification it is no longer possible to separate the effects of market power from the loan and deposit markets; d₁ summarizes the effect of both, and will be equal to unity unless market power exists in at least one of the two markets. If both markets for deposits and loans are perfectly competitive, then θ_l = θ_d = 0→ϕ_l = ϕ_d = 1 and the interest rate charged on loans will be equal to the marginal cost of producing loans and deposits, i.e., $i_{l} = C_{l} + \frac{i_{d}}{(1 - ε_{j})}$ . If, on the contrary, we assume that one of the markets is perfectly competitive, then the above regression equation will estimate the degree of market power in the remaining market. Hannan & Liang (1993) use a similar to approach to U.S. banks, and assume the loan side to be perfectly competitive and therefore set out to estimate market power on the deposit side.

V. Estimation Results

For the econometric analysis, we used banking system data for the 1974-1988 (quarterly) and 1992:05 - 1996:08 (monthly) periods for the aggregate system, and a panel of 22 banks for the 1991:03 - 1996:08 period¹⁸. We estimated the single-equation specification described in equation (5b) and, in the later period, we estimated the system equation specification described in (5a)¹⁹. The wage variable was constructed as the ratio of total labor costs to employment²⁰, the scale variable L was the average monthly stock of loans, and the income variable used Y was the monthly index of industrial production. Wages, loans and deposits were taken in real terms, by deflating the nominal values by the CPI. The price of substitutes of bank output z_l was the interest rate on 90-day Central Bank bills²¹.

Finally, in order to incorporate the possible effects of changes in loan quality, the percentage of nonperforming loans was included in the spread equation, reflecting two possible responses by banks. First, as a shift variable x, nonperforming loans would reflect the extent to which bank managers increase operational expenses in response to deteriorations in loan quality²². Second, in the spread equation the effect of nonperforming loans may express a risk premium charged by banks in response to the financial costs of foregone interest revenue. Thus, if at least one of these responses is present in the Colombian case, we would expect increases in the percentage of nonperforming loans to widen the interest spread.

A. Aggregate Estimation

The aggregate single equation results are shown in Table 6. The first column shows the results for the pre-liberalization period, and the remaining columns display the results for the post-liberalization period, for the banking system as a whole and for private and state-owned banks separately. The fit of all regressions is relatively close, serial correlation of the error term up to lag 4 is ruled out at a 5 percent level, and all coefficients have the expected sign. Real wages, due to their relatively high correlation with the scale variable (real loans), appear not to be significant--when the scale variable is excluded, wages become significant.

Table 6.

Aggregate Estimation of the Spread Equation Single Equation Specification: il=d0+d1(id/1−e)+d2L+d3w+d4NPL

^{^1/}Contains AR terms to eliminate autocorrelation of order 1,3, and 4.

*(**) significant at a 95%(99%) level.

Table 6.

Aggregate Estimation of the Spread Equation Single Equation Specification: il=d0+d1(id/1−e)+d2L+d3w+d4NPL

	(1)	(2)	(3)	(4)	(5)
	Banking System			Private	State-owned
	TSLS	TSLS		TSLS	TSLS
	1974-1988 ^1/	1992-1996		1992-1996	1992-1996
Constant term: d0	0.23 (15.93)**	10.94 (7.04)**	8.94 (4.36)**	11.85 (5.62)**	3.91 (1.61)
Market power: d1	1.29 (22.51)**	1.12 (13.01)**	1.09 (12.67)**	1.23 (15.63)**	0.86 (7.15)**
Real loans: d2	-0.01 (9.59)**	-0.17 (2.99)**	-0.22 (3.37)**	-0.46 (5.55)**	1.15 (2.61)*
Real wage rate: d3			1.14 (1.45)	0.58 (0.62)	0.53 (1.28)
Nonperforming loans: d4	0.16 (3.06)**	1.00 (5.48)**	0.99 (5.58)**	0.86 (3.43)**	1.15 (8.49)**
Dumny variable for 1980.2: d5	0.04 (6.26)**
R2	0.94	0.88	0.89	0.90	0.81
Durbin-Watson	2.10	1.96	1.82	2.15	1.54
*Tests*
Wald test for market power
Ho: Perfect competition, d1=1
X²	25.35	1.90	1.11	8.60	1.32
Probability	0.00	0.17	0.30	0.00	0.25
IM test for serial correlation up to lag 4
Ho: white noise error term
F	1.84	2.48	2.51	1.32	0.21
Probability	0.17	0.058	0.055	0.86	0.93
Observations	60	52	52	52	52

^{^1/}Contains AR terms to eliminate autocorrelation of order 1,3, and 4.

*(**) significant at a 95%(99%) level.

Table 6.

Aggregate Estimation of the Spread Equation Single Equation Specification: il=d0+d1(id/1−e)+d2L+d3w+d4NPL

	(1)	(2)	(3)	(4)	(5)
	Banking System			Private	State-owned
	TSLS	TSLS		TSLS	TSLS
	1974-1988 ^1/	1992-1996		1992-1996	1992-1996
Constant term: d0	0.23 (15.93)**	10.94 (7.04)**	8.94 (4.36)**	11.85 (5.62)**	3.91 (1.61)
Market power: d1	1.29 (22.51)**	1.12 (13.01)**	1.09 (12.67)**	1.23 (15.63)**	0.86 (7.15)**
Real loans: d2	-0.01 (9.59)**	-0.17 (2.99)**	-0.22 (3.37)**	-0.46 (5.55)**	1.15 (2.61)*
Real wage rate: d3			1.14 (1.45)	0.58 (0.62)	0.53 (1.28)
Nonperforming loans: d4	0.16 (3.06)**	1.00 (5.48)**	0.99 (5.58)**	0.86 (3.43)**	1.15 (8.49)**
Dumny variable for 1980.2: d5	0.04 (6.26)**
R2	0.94	0.88	0.89	0.90	0.81
Durbin-Watson	2.10	1.96	1.82	2.15	1.54
*Tests*
Wald test for market power
Ho: Perfect competition, d1=1
X²	25.35	1.90	1.11	8.60	1.32
Probability	0.00	0.17	0.30	0.00	0.25
IM test for serial correlation up to lag 4
Ho: white noise error term
F	1.84	2.48	2.51	1.32	0.21
Probability	0.17	0.058	0.055	0.86	0.93
Observations	60	52	52	52	52

^{^1/}Contains AR terms to eliminate autocorrelation of order 1,3, and 4.

*(**) significant at a 95%(99%) level.

One salient result is that market power appears to have declined between the two periods. The estimated market power parameter, d₁ is 1.29 in the pre-liberalization sample and is significantly greater than unity with almost complete certainty²³. In the post-liberalization period, on the other hand, the estimated parameter declines to 1.12, and is not significantly different from unity, thus indicating competitive behavior overall²⁴. However, when we disaggregate private and state banks, we find that market power is still significant for private banks, who tend to charge a 23 percent markup over marginal financial costs, while state banks behave as price takers in the loan market in the sense that their intermediation spread just covers marginal costs.

The results also show a prevalence of economies of scale in both periods, with the exception of state banks in the post-liberalization period. The general result is consistent with the findings of studies adopting a cost function approach to economies of scale and efficiency in the Colombian banking sector (Bernai & Herrera, 1983; Suescún, 1987; Acosta & Villegas, 1989; Ferrufino, 1991; and Suescún & Misas, 1996).

Nonperforming loans are a significant factor contributing to the widening of interest spreads in both periods, as an indication of additional resources that banks must commit to deal with bad loan problems. Furthermore, banks’ sensitivity to changes in nonperforming loans appears to have increased considerably from the pre to the post-liberalization period; the estimated coefficient increases from 0.16 to about 1.0²⁵. This change could signal a heightened awareness on the part of bank managers regarding credit risk, and/or it could reflect an improved reporting of nonperforming loans. Since the earlier period included the mid-1980s financial crisis, prior to which banking behavior most likely contained a significant element of moral hazard, the change in the second period may also reflect a decline in moral hazard, itself an indication of success in the manner in which policymakers dealt with the crisis²⁶ and in the measures undertaken in the early nineties to tighten prudential regulation and strengthen bank supervision.

Finally, liberalization of interest rates appears to have increased the spread through its effect on intermediation costs. Prior to 1980, all bank deposit interest rates were subject to policy-imposed ceilings, often at very low real levels. The estimation results show a significant widening of the spread (by approximately 4 percentage points) following the liberalization of the interest rate on time deposits in the first quarter of 1980. As banks were now able to compete for deposits with other financial intermediaries, the subsequent rapid increase in these deposits appears to have led to increases in banks’ marginal costs.

B. System and Panel Data Estimation in the Post-Liberalization Period

The single equation results for the aggregate banking system are confirmed when estimating the spread using a system approach. We estimated the spread equation (5a) jointly with a demand function for loans (6), using a Full Information Maximum Likelihood (FIML) procedure, providing initial values from preliminary 3SLS estimations. As discussed earlier, in this specification the net spread becomes the dependent variable and market power arises if the λ coefficient is significantly greater than zero. As the top panel of Table 7 shows, competitive behavior again cannot be ruled out for the banking system as a whole. The other coefficient estimates are similar to their single-equation values, although the coefficient on real wages is larger (1.47 versus 1.14) and is now significant at a 1 percent level.

Table 7.

Post-liberalization Period: System and Panel Data Estimation of the Spread Equation

^{^1/}Chi-squared statistic reported above, probability reported below.

*(**) significant at a 95% (99%) level.

Table 7.

Post-liberalization Period: System and Panel Data Estimation of the Spread Equation

System Estimation (FIML)		il-id/(1 - ε) =d0 -λL(dil/dL)+d2L+d3w+d4NPL
		Period: 1992:05 - 1996:08	Intercept d0	Market Power: λ	Real loans: d2	Real wages: d3	Nonperforming loans: d4		R²	dw
		8.48 (3.65)**	0.00 (0.01)	-0.11 (4.80)**	1.47 (3.18)**	1.09 (4.61)**		0.89	1.72
Panel Data Estimations		il=d0+d1(id/1-ε)+d2L+d3w+d4NPL
		d0	d1	d2	d3	d4	State bank dummy
Pooled OLS, Fixed Coefficients, with State Bank dummy		24.87 (31.49)**	0.47 (12.13)**	-0.08 (4.47)**	-0.23 (1.49)	0.46 (9.57)**	1.27 (2.53)*	0.21	0.29
	Period: 1992:05 - 1996:08
Random Coefficients									Tests ^1/
									H₀: d1=1	H₀: Constant
	22 private and state banks								coefficients across banks
	1991:03 - 1996:08 (1438 observations)	18.54 (6.47)**	0.88 (14.54)**	-1.62 (2.35)*	0.30 (0.97)	0.77 (5.46)**		3.94 0.05	5497.0 0.00
	19 private banks
	1991:03 - 1996:08 (1254 observations)	19.38 (6.62)**	0.94 (20.53)**	-1.88 (2.45)*	0.32 (0.90)	0.70 (4.51)**		1.77 0.18	5087.1 0.00

^{^1/}Chi-squared statistic reported above, probability reported below.

*(**) significant at a 95% (99%) level.

Table 7.

Post-liberalization Period: System and Panel Data Estimation of the Spread Equation

System Estimation (FIML)		il-id/(1 - ε) =d0 -λL(dil/dL)+d2L+d3w+d4NPL
		Period: 1992:05 - 1996:08	Intercept d0	Market Power: λ	Real loans: d2	Real wages: d3	Nonperforming loans: d4		R²	dw
		8.48 (3.65)**	0.00 (0.01)	-0.11 (4.80)**	1.47 (3.18)**	1.09 (4.61)**		0.89	1.72
Panel Data Estimations		il=d0+d1(id/1-ε)+d2L+d3w+d4NPL
		d0	d1	d2	d3	d4	State bank dummy
Pooled OLS, Fixed Coefficients, with State Bank dummy		24.87 (31.49)**	0.47 (12.13)**	-0.08 (4.47)**	-0.23 (1.49)	0.46 (9.57)**	1.27 (2.53)*	0.21	0.29
	Period: 1992:05 - 1996:08
Random Coefficients									Tests ^1/
									H₀: d1=1	H₀: Constant
	22 private and state banks								coefficients across banks
	1991:03 - 1996:08 (1438 observations)	18.54 (6.47)**	0.88 (14.54)**	-1.62 (2.35)*	0.30 (0.97)	0.77 (5.46)**		3.94 0.05	5497.0 0.00
	19 private banks
	1991:03 - 1996:08 (1254 observations)	19.38 (6.62)**	0.94 (20.53)**	-1.88 (2.45)*	0.32 (0.90)	0.70 (4.51)**		1.77 0.18	5087.1 0.00

^{^1/}Chi-squared statistic reported above, probability reported below.

*(**) significant at a 95% (99%) level.

The results of single-equation panel data regressions provided additional insight into the heterogeneity of behavior across banks. When we ran a simple pooled OLS regression which restricted all coefficients to be equal across banks, but which allowed for a change in intercept between private and state banks, the coefficients on total loans, the nonperforming loan ratio, and on the state bank dummy variable were significant and had the expected sign, but the fit of the regression was relatively poor and showed considerable evidence of autocorrelation (see Table 7, second panel). Indeed, we used a χ² test on the equality of coefficients across banks and overwhelmingly rejected the null hypothesis both for the banking system as a whole and for private banks separately. Therefore, we estimated the spread equation using a Random Coefficients Model (RCM), a GLS method which allows for changes in all coefficients across banks, and treats each coefficient as a random drawing from the same probability distribution (see Judge, et. al., 1985).

The final two panels of Table 7 report the average coefficient values for the RCM on the banking system as a whole, and for private banks, respectively. All coefficients have the expected sign, and again all but the wage rate are significant at least at a 95 percent level. The estimated values of both the intercept and the coefficient of the scale variable (real loans) are considerably larger than in the aggregate case, reflecting the much smaller values for the scale variable at the individual bank level²⁷. The estimated effect of nonperforming loans on interest spreads appears to be smaller than in the aggregate case (0.77 versus 0.99), and the results tend to give greater support to the finding of competition; the estimated values of the market power parameter are smaller than in the aggregate estimation, and now competitive behavior cannot be rejected in the case of private banks²⁸.

To summarize, the aggregate regression results show evidence of two crucial changes in the behavior of interest spreads between the pre and post-liberalization periods in Colombia: an increase in competition and a greater responsiveness of spreads to changes in loan quality. The estimates of marginal nonfinancial costs of intermediation exhibit some degree of scale economies in both periods, and the first period shows a significant cost effect brought on by the increased competition for deposits following the liberalization of time deposit rates in early 1980. Finally, panel data analysis in the post-liberalization period revealed significant heterogeneity in the spread equation parameters across banks, and tended to give greater support to the hypothesis of competitive behavior and to the relative importance of operational costs versus loan quality.

C. Decomposition of the Spread

In order to measure the main determinants of interest spreads in the two periods, we used the regressions reported in columns (1) and (4) of Table 6 and modified versions of the equations in columns (3) and (5)²⁹ to break down the estimated interest spreads into their different components: financial taxation, nonfinancial costs, nonperforming loans, and market power. As Table 8a shows, although both periods exhibited similar interest spreads on average--about 21 percentage points--the pre--liberalization period is characterized by a much higher variability. Between 1974 and 1980 the estimated spread nearly doubled (from 17 to 31 percentage points) as a result of increased financial and nonfinancial costs brought on to some degree by the interest rate liberalization of 1980, and by a sharp increase in financial taxation. The spread then declined gradually to 16 percentage points by the end of the period, as marginal costs and financial taxation fell to their levels of the early seventies. On average during the pre-liberalization period operating costs made up about 38 percent of the spread, financial taxation represented about 22 percent and market power accounted for 36 percent of the spread. Changes in loan quality had very little effect on marginal costs and therefore on the spread--they accounted for less than 4 percent of the spread.

Table 8a.

Decomposition of Estimated Interest Spreads in Colombia

(Percentages)