An Empirical Reassessment of the Relationship Between Finance and Growth

Contributor Notes

Author’s E-Mail Address: giovanni.favara@iies.su.se

This paper reexamines the empirical relationship between financial development and economic growth. It presents evidence based on cross-section and panel data using an updated dataset, a variety of econometric methods, and two standard measures of financial development: the level of liquid liabilities of the banking system and the amount of credit issued to the private sector by banks and other financial institutions. The paper identifies two sets of findings. First, in contrast with the recent evidence of Levine, Loayza, and Beck (2001), cross-section and panel-data-instrumental-variables regressions reveal that the relationship between financial development and economic growth is, at best, weak. Second, there is evidence of nonlinearities in the data, suggesting that finance matters for growth only at intermediate levels of financial development. Moreover, using a procedure appropriately designed to estimate long-run relationships in a panel with heterogeneous slope coefficients, there is no clear indication that finance spurs economic growth. Instead, for some specifications, the relationship is, puzzlingly, negative.

Abstract

This paper reexamines the empirical relationship between financial development and economic growth. It presents evidence based on cross-section and panel data using an updated dataset, a variety of econometric methods, and two standard measures of financial development: the level of liquid liabilities of the banking system and the amount of credit issued to the private sector by banks and other financial institutions. The paper identifies two sets of findings. First, in contrast with the recent evidence of Levine, Loayza, and Beck (2001), cross-section and panel-data-instrumental-variables regressions reveal that the relationship between financial development and economic growth is, at best, weak. Second, there is evidence of nonlinearities in the data, suggesting that finance matters for growth only at intermediate levels of financial development. Moreover, using a procedure appropriately designed to estimate long-run relationships in a panel with heterogeneous slope coefficients, there is no clear indication that finance spurs economic growth. Instead, for some specifications, the relationship is, puzzlingly, negative.

I. Introduction

There is a fair amount of consensus in the growth literature that financial development promotes economic growth. The main theoretical explanation is that financial intermediaries encourage the mobilization of saving, ameliorate asymmetric information, and provide greater opportunity for risk spreading and risk pooling. At the aggregate level, this translates into higher saving and more efficient allocation of resources with positive effects for the rate of capital accumulation and technological innovation.2

Several empirical studies have confirmed these theoretical predictions. In an influential paper, King and Levine (1993) use ordinary-least-squares (OLS) estimates on a large cross-section of countries and find that indicators of banking development are good predictors of future economic growth. Similarly, Levine and Zervos (1996, 1998) find that other measures of financial development, such as stock market development, are associated with higher income per capita. Using extreme-bound analysis, these authors even conclude that banks and stock markets are robust determinants of long-run economic growth.

Despite the well-known econometric problems associated with OLS cross-country regressions, similar findings are reported in a series of more elaborated analyses by Levine, Loayza, and Beck (2001); Beck, Loayza, and Levine (2001); and Beck and Levine (2002). These authors use a general-method-of-moments (GMM) estimator for dynamic panel data to answer the question whether financial development causes economic growth. The GMM panel estimator improves upon cross-section estimators because it directly controls for the potential bias induced by the omission of country-specific effects and the endogeneity of all regressors. The overall conclusion of this research agenda is that the positive correlation between bank development and growth is not due to simultaneity bias and that financial development exerts a first-order effect on long-run economic growth.

This paper re-examines and extends the analysis of Levine, Loayza and Beck (2001) (hereinafter referred to as LLB). In line with their work, it presents evidence based on cross-section and panel data, using a larger and updated dataset of countries, a variety of econometric methods, and two standard measures of financial development: the level of liquid liabilities of the banking system and the amount of credit issued to the private sector by banks and other financial institutions.

In the first part of the paper, the analysis is conducted on a cross-section of countries. OLS estimates suggest that the relationship between finance and growth is positive, sizeable, and robust to outlier and functional form specification, corroborating and reinforcing the findings of King and Levine (1993). However, when the likely endogeneity of financial development is addressed by instrumental-variables regression, the OLS results are upset and the statistical significance of financial development becomes tenuous. This result stands in sharp contrast with LLB’s paper and the reason presumably lies in our use of a dataset comprising different countries and time periods.

The second part of the paper exploits the time-series dimension of the data and, following LLB, presents GMM panel data estimates. Unlike those obtained from LLB’s analysis, though, the estimates are not based on the two-step GMM estimator, which is asymptotically efficient in the presence of heteroskedastic errors. As is well known (see Arellano and Bond, 1991, and Blundell and Bond, 1998), this estimator can be highly inaccurate, with standard errors downward biased in finite samples. Estimates based on the more appropriate one-step GMM estimator reveal that the relationship between finance and growth is, at best, weak. For most of the specifications considered, the contribution of financial development to growth is statistically insignificant and the magnitudes of the estimated effects are not economically large. Moreover, the finance-growth relationship is sensitive to different combinations of control variables and sample periods.

The third part of the paper extends the panel-data analysis in one particular direction. It relaxes the assumption that countries obey a common linear specification and investigates the effects of permitting parameter heterogeneity across countries. The findings are twofold. First, using a nonparametric approach, the data support the presence of a nonlinear relationship between the level of the credit in the economy and GDP growth, suggesting that the financial sector exerts positive effects on growth only at intermediate levels of financial development. This result is in line with the predictions of some theoretical models where threshold effects and multiple equilibria arise as economies progress through different stages of financial development (see Acemoglu and Zilibotti 1997, 1999). Second, using a procedure specifically designed to estimate panel data with varying slope coefficients, our study finds that the effects of financial development differ considerably across countries and display no obvious pattern related to geographic location, the level of economic development, or institutional characteristics. As a consequence, standard growth regressions estimated by previous authors, which tend to mask these properties of the data, may be misspecified. The central finding of this analysis is that the level of financial development has ambiguous effects on economic growth. The effects are positive for some specifications and, surprisingly, negative for others. Since the main requirement for implementing this empirical strategy is to use panel data with observations kept in annual format, it may be argued that business cycles and measurement errors are the driving forces of these findings. Yet the conflicting results are puzzlingly confined to the indicators of financial development while standard growth determinants maintain their expected contribution to GDP growth.

The outline of the paper is as follows. Section II describes the data and presents some descriptive statistics. Section III discusses the empirical framework used for the cross-section analysis of Section IV and the panel data estimates of Section V. Section VI introduces the empirical strategy that allows slope parameters to vary across countries and discusses the empirical findings. Section VII concludes.

II. Preliminaries

A. The Data

The dataset refers to an unbalanced panel of roughly 85 countries observed from 1960 to 1998. A detailed list of countries is presented in Table 1. In contrast to the LLB paper, the dataset includes a larger number of countries, mainly African, observed for a longer time period. However, the indicators of financial development and the set of control variables, which I now discuss, are similar to those used by LLB.

Table 1.

Country Coverage

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Notes: 1 countries missing in the cross-section analysis; 2 in the 5 years panel data; 3 for the PMG estimator

Financial Variables

Following the vast literature on this topic, the focus will be on two indicators of financial development. The first, LLY, measures the amount of liquid liabilities of the financial system, including liabilities of banks, central banks and other financial intermediaries. This indicator is meant to capture the overall size of the financial sector and its ability to provide broad transaction services. The second measure, PCY, is defined as the value of loans made by deposit money banks and other financial institutions to the private sector. PCY is a better proxy of financial development since it only accounts for credit granted to the private sector, as opposed to credit issued to government and other non-private institutions. It also excludes credit issued by the central bank and is thus a more accurate measure of the savings that financial intermediaries channel to the private sector. Both indicators are appropriately deflated and expressed in percentage of real GDP.3 The source for this data is the International Financial Statistics of the IMF.

Control Variables

The choice of control variables is crucial since a central concern of the cross-country empirical literature is that the results may be sensitive to the set of variables held constant in the regressions. In order to make the analysis comparable to LLB, the set of controls includes, as in their paper, proxies for initial conditions, measures of macroeconomic stability and indicators of trade openness. Initial conditions are proxied by the level of real per capita GDP (Y0) and the average years of attainment in secondary and higher education (SEC). Indicators of external openness are the ratio of export plus import over GDP (OPEN) and the black market premium on foreign exchange transactions (BMP). Measures of macroeconomic instability are the ratio of government consumption to GDP (GOV) and the level of inflation rate (INF). Previous studies have shown that these variables correlate significantly with GDP growth (Barro and Sala-i-Martin, 1995, and Barro, 1999).

Differently from LLB, however, I also control for the ratio of gross domestic investment to GDP (1NV), since the effects of finance on growth could be channeled through higher physical capital or through increasing the efficiency of investment. After controlling for INV, the estimated coefficients on LLY and PCY should capture the effects of financial development on the efficiency of investment. Including INV can therefore reduce the effects of finance on growth if these effects are operative through factor accumulation. On the other hand, omitting INV from the set of controls can inappropriately attribute too large an effect to PCY or LLY.

The data for real GDP, investment, government expenditure and export plus imports is obtained from the Penn World Table 6.1. Data for human capital is from Barro and Lee (2000) and the index for black market premium is taken from Easterly and Sewadeh (2002). A more detailed description of the data is given in Table 2.

Table 2.

Definition of Variables and Sources

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B. Summary Statistics and Some Stylized Facts

Before embarking on the estimation of the effects of financial development on economic growth it is worth presenting some properties of the data. Summary statistics for all variables used in this paper are given in Table 3. These statistics refer to a panel with observations kept in yearly format. The table suggests that most of the variability in the data occurs between country, yet some variables—including the two indicators of financial development—also have large within-country variations. In a typical OECD country (i.e., France), the level of PCY varies, for example, from 44 percent to 102 percent over the 1960-1998 period; for a typical African economy (i.e., Chad), PCY oscillates between 6 percent and 48 percent.

Table 3.

Summary Statistics - Panel Data (yearly data)

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To further highlight the time series and cross-sectional properties of the two indicators of financial development, Figures la and lb plot the distribution of PCY and LLY for different groups of countries. The scattered dots refer to the dispersion of PCY and LLY over the whole sample, the upward sloping curves are group-specific time averages, and the horizontal line is the overall mean across time and units. The interesting feature of Figure 1 is that the two ratios vary a great deal across countries and also over time. In all cases the distributions drift upward, reflecting an increase in the financial sector’s size, though the trend is less pronounced for the poorest countries, those in Africa and Latin America. On average, the poorest countries are also the least financially developed, having a group mean below the cross-sectional average. The size of the financial sector is the largest for the OECD countries; for the Asian economies, both indicators exhibit a spectacular trend dominated to a large extent by countries such as Thailand, Singapore, Malaysia and Korea, while the time pattern for the Middle Eastern countries is predominantly flat.

Figure 1:
Figure 1:

Distribution of PCY and LLY

(a) Distribution of pcy

(b) Distribution of lly

Citation: IMF Working Papers 2003, 123; 10.5089/9781451854633.001.A001

Some insights into the correlations between the two measures of financial deepening and the level of economic development can be gained by looking at Figure 2. In the attempt to isolate similar levels of economic and financial development, countries are again divided by geographical area; the series reported are also standardized, to facilitate the comparison. Figure 2 relates the level of financial development with the level of real per capita GDP. The graph indicates the existence of a clear long-run equilibrium relation among the series. Over the long-run, both financial variables, and PCY in particular, appear to share the same trend of real per capita GDP, indicating that as the economy develops the size of the financial sector gets larger. This evidence is striking when compared with a similar exercise (figure not reported) that relates PCY and LLY to the level of real investment INV—taken as an alternative measure of economic development. The time series properties of PCY, LLY and INV are significantly different from those of Figure 2, indicating that no clear-cut long-run relationship seems to hold for these series over the entire sample period.

Figure 2.
Figure 2.

Time series plot for PCY, LLY and GDP

Citation: IMF Working Papers 2003, 123; 10.5089/9781451854633.001.A001

The pairwise correlations matrix for the variables of interest is reported in Table 4, using both cross-section and panel data. All signs are as expected: the growth rate of GDP per capita correlates positively with the level of human and physical capital, the degree of openness and both indicators of financial development. In addition, the level of investment is on average positively correlated with the level of financial development, whereas a high level of inflation appears to correlate negatively with the size of the financial sector. Based on the graphical evidence presented above, the high correlation between LLY and PCY is also expected.

Table 4.

Pairwise Correlation Matrices

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III. A Framework for Empirical Analysis

The empirical framework adopted in the remainder of the paper to evaluate the independent effect of financial development on economic growth is the one based on conditional convergence, as used extensively in the empirical growth literature. Specifically, the effects of financial development on economic growth are evaluated by estimating the following convergence regression:

yityi,t1=λyi,t1+βxit+vit(1)
vit=μi+vt+εit(2)

which is based on a linear approximation around the steady state of the standard neoclassical growth model. In equation (1), yit is the logarithm of income per capita in country i in period t,xit. is a vector of “fundamental” determinants of growth, FINit is an indicator of financial development and vit is a general disturbance, including a country specific unobservable effect, μi, a time specific factor vt, and an idiosyncratic disturbance εit. The fixed effects μi act as proxy for other determinants of a country’s steady state not already included in xit and the time specific factor vt controls for shocks common to all countries. In the neoclassical growth model, diminishing returns to factor accumulation imply that the economy’s growth rate yit - yit-1 decreases with the level of income, represented by yi,t-1. For a given xit permanent increase in xit or FINit initially raises the growth rate and over time the level of income per capita. Therefore, in the long-run an increase, say, in the amount of bank credit has an impact on the level of per capita output, not its growth rate.

Equation (1) is usually estimated by OLS on a single cross-section of countries, under the assumption that the fixed effects μi, are the same across countries (and thus relegated to the error term) and the error vit, is uncorrelated with the set of control variables. In the empirical literature on finance and growth, this approach is used, among others, by King and Levine (1993) and Levine and Zervos (1996, 1998). Cross-section estimates, with data averaged over the entire sample period, are meant to uncover low-frequency properties of the data and, for the purpose of this paper, to provide information about the long-run effects of financial development on GDP growth. The major problem of this estimation strategy, however, is that parameter estimates are inconsistent if the regressors are endogenous or correlated with the unobserved individual effects, a point made familiar by Caselli et al. (1996).

In the absence of good instruments and suitable proxies for country specific effects, a solution is to use panel data methods. Panel data allow to control for individual effects and to use lags of the regressors as instruments for the endogenous variables. The additional advantage is that the time series variation of the data expands the sample information. This information is valuable for the measures of financial development that, as documented in Section II, vary a great deal over time. Application of panel data methods to study the link between financial development and long-run growth are in Levine, Loayza and Beck (2001); Beck, Levine and Loayza (2002); and Beck and Levine (2002). These authors, in particular, use a GMM estimator to simultaneously address the issue of unobserved intercept heterogeneity and regressor endogeneity. Their empirical method is thus more suitable for drawing conclusions about the casual effects of financial development on economic growth.

One potential limitation of the GMM approach is that not much heterogeneity is allowed across countries. Heterogeneity is restricted to the intercept but is not permitted in the slope coefficients. Yet, if the slope coefficients vary across units lagged, values of serially correlated regressors cannot be used as valid instruments. Pesaran and Smith (1995) show that if in a dynamic panel model, such as equation (1), slope coefficients are assumed constant but in fact vary across units, traditional panel estimators (i.e., fixed effects or GMM estimators) yield inconsistent estimates, even in a panel with a sufficiently large number of cross-sections and time series. In our context, estimates of the long-run effects of FINit on yit will be upward biased if the regressor FINit is positively serially correlated and the slope parameter y is heterogeneous across units.

Throughout this paper I estimate variants of equation (1). In Sections IV and V, 1 use OLS cross-section and GMM panel estimators, mainly to compare the results with previous work. In section VI, I estimate a generalized version of (1) that allows for slope coefficients to vary across units.

IV. Cross-Sectional Evidence

1 start the analysis by exploiting the cross-sectional variation in the data and estimating equation (1) by OLS on a single cross-section. The dependent variable is the log difference of GDP between 1960 and 1998 and the independent variables are period averages, except for lagged per capita GDP and educational attainment, measured at the beginning of the period.

A. Cross-Section Results

Table 5 shows the results. Column 1 refers to the benchmark specification used in LLB. In line with their findings, the level of financial development is positively and significantly related to economic growth. The overall effect on growth is also economically large. According to the coefficient on PCY, Argentina, whose average PCY is 16 percent, had a growth disadvantage relative to the mean country (for which PCY is 34 percent) of around 0.75 percent per year, during the period 1960-1998.4 This is a sizable number given that, over the same period, the average growth rate for the cross-section was only 1.6 percent. When multiplied by 2.5 (=1/0.404) to measure the effect on long-run income, the coefficient on PCY also implies that GDP per capita is 1 percentage point higher for every 1 percentage point increase in the amount of bank credit to the private sector.

Table 5.

Cross-Section Data — OLS Estimates Dependent Variable Log-difference GDP per capita. Sample 1960-1998

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Note: Estimation by OLS Robust t–statistics in small fonts below the corresponding coefficients

In column 2, the investment ratio is included as additional regressor. The major effect is that the point estimates for PCY and LLY are reduced by roughly one half, indicating that half of the effect of PCY or LLY on growth goes through an increase in the efficiency of investment, and half through an increase in the volume of investment. Both PCY and LLY remain, however, significantly correlated to GDP growth.

To control for unobserved regional effects, columns 3 and 4 augment the previous specifications with two continent dummies, AFRICA for sub-Saharan countries and LAC for Latin American and Caribbean countries. This modification does not alter the positive and significant correlation of PCY and LLY with GDP growth, although the size of the estimated coefficients is further reduced. Since the two dummies are significantly different from zero, and their inclusion increases the goodness of the fit substantially, some regularity appears to be missing from the empirical model. This is an indication that there exists some degree of heterogeneity among the countries in the sample and that the cross-section estimates may be biased due to the omission of unobserved fixed effects. This problem is addressed in Sections V and VI using panel data methods.

As a final remark, it is worth noticing that, although in some specifications some regressors are not significant, the majority of control variables has the expected sign. The only exception is the positive (yet always insignificant) coefficient for inflation. This contrasts with the conventional wisdom, but supports the findings—discussed among others in Fisher (1993) and Bruno and Easterly (1998)—that the negative correlation between inflation and growth is hard to detect with cross-sectional data.

B. Robustness Tests

Although the OLS estimates are in line with the results reported in previous studies, it remains useful to assess their robustness. To this aim, I perform a series of experiments. Namely, I control for outliers, question the assumption of a common linear specification for all countries, and confront the issue of endogeneity for the two measures of financial development.

Outliers

Outliers may occur for several reasons: measurement errors, omitted variables or parameter heterogeneity—each of which is likely to arise in a cross-section of heterogeneous countries. Following Temple (1998), the influence of outliers is evaluated by running a re-weighted least squares (RWLS) regression. This is a standard OLS regression after dropping observations identified as outliers through the residuals of the least trimmed squares (LTS) estimator. As discussed in Rousseeuw and Leroy (1987), this method disregards bad leverage points (i.e., values of the explanatory variables which lie far away from the bulk of the data) and is far less sensitive than OLS to deviant observations.

The results are shown in Table 6 using specifications similar to those in Table 5. The list of outliers (not reported) reveals that the majority of countries receiving zero weight in the RWLS regression belong to the African group; depending on the specification, however, some OECD and Asian countries were also dropped. A comparison with the estimates of Table 5 indicates that the exclusion of these outliers has no material effect on the estimated coefficients for PCY and LLY. Indeed, the point estimates are larger and more precise, though the magnitude remains smaller if the level of investment rate is included among the control variables.

Table 6.

Cross-Section Data - RWLS Estimates Dependent Variable Log-difference GDP per capita. Sample 1960-1998

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Note: Asymptotic t–statistics in small fonts below the corresponding coefficients Estimation by Reweighted Least Squares using residuals from Least Trimmed Squares Regression

Threshold Effects

The results presented so far are based on the assumption that all countries obey a common linear specification. Since this assumption may not be valid in a panel of heterogeneous countries, I investigate the possibility of threshold effects. Specifically, regressions of the following form are estimated:

yityi,t1=λyi,t1+βxit+γFINitdi(τ)+vit

where di(τ) = {FINiτ} is an indicator function and τ is the unknown threshold level of FINi. In this model, the regression parameter γ is allowed to differ depending on the value of FINi, and the sample is split into two groups based on the estimated values of τ. A Lagrange multiplier test (LM) suggested by Hansen (2000) is used to test the existence of a threshold effect, under the assumptions that the error term is normally distributed and the regressors are strictly exogenous.

Table 7 reports p-values for the null of no threshold, the least square estimates of τ with the associated 95 percent asymptotic confidence intervals, and the estimated coefficients of PCY and LLY across sub-samples. The evidence regarding the absence of threshold effects is mixed. It largely depends on the set of controls and, for each specification, on the indicator of financial development considered. The estimated thresholds, however, are very similar across specifications and approximately correspond to the cross-sectional median level of PCY (24 percent) and LLY (31 percent). In most cases, however, the number of countries that fall in the 95 percent confidence interval is so large, that any attempt to classify countries into the first or the second regime must be made with caution. Overall, the evidence suggests that there is some indication of a sample split based on PCY or LLY. The coefficients on PCY and LLY remain positive across sub-samples, despite not being significative when INV and/or the two regional dummies are used as control variables. In these cases, however, inference must be taken with care given the reduced number of observations in each sub-sample. On balance, the results do not differ substantially from the overall picture that emerges from the baseline regressions in Table 5.

Table 7.

Cross–Section Data– Threshold Regression Model Dependent Variable Log–difference GDP per captia. Sample 1960–1996.

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Notes: Estimation by OLS. Robust t-statistic in small fonts below the corresponding coefficientsINV test reports p-value for the null of a threshold effect 95% C.I. is the conifidence interval associated to the estimated thresholdX1 incluldes: ln(YO),ln(GOV), ln(OPEN), ln(1+INF), ln(1+BMP)Dummies are for AfFRICA and LAC

Experiments were also conducted to check the possibility of additional regimes. In particular, the initial level of GDP per capita was used as threshold variable, to check if the coefficients on the financial variables could vary depending on the level of economic development. In this case, however, the LM test could not find evidence of such a threshold effect.

Reverse Causality

As mentioned earlier, OLS estimates may be plagued by problems of reverse causality. If economic development leads to a larger financial sector, the error term in the growth regression is positively correlated with PCY and LLY and the estimated coefficients biased upward. A way to address this problem is to use initial values of PCY and LLY. This approach is taken by King and Levine (1993) to check if the predetermined components of financial development are good predictors of long-run growth. My results (not reported) indicate that the initial values of PCY and LLY are significant predictors of subsequent growth, regardless of the set of controls used and the sample of countries considered.

A more appropriate way to address the same problem is to estimate the linear regression (1) via an instrumental variables (IV) estimator. This approach is pursued by LLB. I follow their analysis and use national legal origins as instrumental variables for the two indicators of financial development. In choosing these instruments, LLB rely on the evidence of La Porta et al. (1998), which show that the origin of a country’s legal system significantly affects the structure and development of its financial system. The instruments (indicators of legal origins) are dummy variables for countries whose legal system has roots in the French, German or English legal tradition.

Table 8 summarizes the IV estimates and reports p-values for the Hansen test of instruments validity. To compare the results with the corresponding OLS estimates, I use the same specifications of Table 5. Consider first the estimates of column 1, which reports the baseline regressions. Compared with the OLS estimates, the coefficients on PCY and LLY decrease by one half, with the t-statistics indicating that these variables are no longer significantly related to GDP growth. The drop in the magnitude of the coefficients is even more dramatic in column 2, where investment is added as additional control. For this specification the magnitude of the coefficients for PCY and LLY falls to 0.041 and 0.051, respectively. The drop in these coefficients means that the contribution to growth for Argentina, if it had increased its average level of PCY towards the mean country, is now of only 0.07 percent per year.

Table 8.

Cross Section Data-IV Estimates Dependent Variable Log-difference GDP per capita. Sample 1960-1998

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Note: Estimation by IV. Robust t-statistic in small fonts below the coressponding coefficientsJ-Test refers to the Hansen test for the null that instrilments are not correlated with the reslidualsInstruments are: French, German and British legal origins

Further indications that the OLS estimates may be biased, due to reverse causality but also because of unobserved omitted variables, arise in the regressions of column 3 and 4. After controlling for the two continent dummies, the size of the coefficients for PCY and LLY becomes larger, though their statistical significance remains fragile. Interestingly, for all specifications the J-statistic does not detect any problem with instrument validity. Moreover, the contribution to growth of LY0, INV, SEC and GOV is of the same size and has the same statistical significance as the OLS estimates.

C. Summary of the Cross-Section Results

The central message of the cross-sectional evidence is that the correlation between financial development and economic growth is positive, statistically significant and robust to outliers and functional form misspecifications. These results corroborate and reinforce the findings of King and Levine (1993). However, if the problem of reverse causality is addressed using IV regressions, the contribution of financial development to economic growth seems to become negligible. This result stands in contrast with that recently reported by LLB, despite the fact that the same set of instrumental variables is used. Differently from LLB’s conclusion, there is no indication that the exogenous component of financial development encourages economic growth. For some specifications, there is also evidence that country-specific characteristics have been omitted from the growth regression. The size and the t-statistics for the coefficients of the two continental dummies are taken as evidence of misspecification in this direction. In an attempt to control for this additional potential bias and to correct for the endogeneity of all regressors, and not just of financial development, I now turn to the evidence from panel data methods.

V. Panel Data Evidence

Most of the analysis conducted by LLB is based on a GMM estimator for panel data. As mentioned above, this technique improves upon cross-sectional estimates because it directly controls for the potential bias induced by the omission of country-specific effects and the endogeneity of all regressors. Furthermore, it has the advantage of accounting for variation of financial development over time within a country, which is neglected by the cross-section analysis.

A. The System GMM Estimator

The GMM estimator used in LLB’s paper is the system GMM estimator (SYS-GMM) of Arellano and Bower (1995) and Blundell and Bond (1998). The basic idea behind this estimator is as follows. First, the unobserved fixed effects μi, are removed by taking first difference of equation (1):

Δ(yityi,t1)=λ(yi,t1yi,t2)+β(xitxit1)+γ(FINitFINit1)+Δvt+Δεit(3)

Second, the right hand side variables are instrumented using lagged values of the regressors, and the equations in first differences (3) and in levels (1) are jointly estimated in a system of equations. Under the assumption that the error εit is serially uncorrelated, and the regressors Xit = (xit, FINit) are endogenous, valid instruments for the equation in first difference are levels of the series lagged two periods. In addition, assuming that Δ(yityi,t−1) and ΔXit are uncorrelated with μi, valid instruments for the equation in levels are lagged first differences of the series.5

Third, the validity of the instruments is tested using a standard Sargan test of over-identifying restrictions and a test for the absence of serial correlation of the residuals, since the moment conditions are valid if the error term is not serially correlated.

A final point worth stressing is that the system GMM estimates can be based on either a one-step or a two-step estimator. 6 Although the two-step estimator is asymptotically more efficient in presence of heteroskedasticity of the error term εit, Monte Carlo simulation in Arellano and Bond (1991) and Blundell and Bond (1998) shows that standard errors associated with the two-step estimates are downward biased in small samples. Inference based on the two-step estimator can thus be highly inaccurate and a one-step GMM estimator with standard errors corrected for heteroskedasticity is to be preferred. It is worth stressing this point because the results of LLB appear to be based on the two-step GMM estimator. However, as will be shown below, the statistical significance of the financial variables may become rather weak in the growth regression, if the more appropriate one-step estimator is employed.

B. The GMM Results

To replicate the results of LLB, the SYS-GMM estimator is applied to a panel with annual observations divided into intervals of five years. The dependent variable is the growth rate of GDP per capita for each five-year period and the independent variables are averages over the same five-year intervals, except for the initial level of GDP and the level of school attainment, which are measured at the beginning of each sub-period. All variables are also expressed in deviations from cross-sectional means, which eliminates the need for time dummies vt.

The results are shown in Table 9. Columns 1 and 3 refer to the two-step estimates; columns 2 and 4 report the one-step estimates. The bottom part of the table includes p-values for the Sargan test and the m2 test for the absence of a second order serial correlation of the residuals in the differenced regression, Δεit, implying that the error term in the level regression, εit, is not serially correlated. High ρ values give support to the validity of the instruments and hence the consistency of the GMM estimates.

Table 9.

Panel Data – SYS-GMM Estimates Dependent Variable Log-difference GDP per capita

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Note: SYS-GMM Estimates: Robust t-statistic are in small fonts below the corresponding coefficients.Sargan test and m2 test atr p-values for the null of instruments validityInstruments: Y0 and SEC are considered predetermined. The remaining variables endogenousData is in deviation from cross-section mean

The results for the two-step estimator of column 1 are, by and large, similar to those of LLB. The estimates associated with the financial variables are positive and highly significant, suggesting that the exogenous component of financial development accelerates economic growth.7 The remaining control variables also have the expected sign and are very tightly estimated. Moreover, the Sargan test and the m2 test do not detect any problem with instrument validity.

In column 2, however, the more reliable one-step estimator reveals that the statistical significance of some regressors is rather weak, including PCY. Although the point estimates are similar to those of column 1, the t-statistics suggest that PCY, the preferred indicator of financial development, is no longer significantly related to economic growth. LLY, instead, remains significant at the 5 percent level. The estimated impact on GDP growth coming from PCY is also smaller than the corresponding cross-section effect: if bank credit in Argentina had been at the level of the mean country during the period 1996-98 (48 percent), instead of its actual level (21 percent), Argentina would have grown at 0.35 percent faster per year; the long-run effect on GDP per capita would have been 0.7 percent.

The results for PCY change more sharply in column 4, where the level of investment is also included as control variable in the regression. Its coefficient is now insignificant and essentially zero, while the point estimates for the remaining covariates hardly change. Similar results emerge when the regression includes LLY. Notice that, in column 3, where the two-step estimates are displayed, all regressors continue to be highly significant.

Overall, in accord with the IV cross-section estimates of the previous section, the one-step GMM estimator indicates that PCY is not significantly related to GDP growth. Also, in line with the cross-section results, INV and GOV (and SEC for the specification including PCY) remain important determinants of long-run economic growth. Worth noticing is the sign of the estimated coefficients on INF: higher levels of inflation, now, have harmful effects on economic growth, in agreement with the panel evidence in the growth literature.

C. Robustness Checks

This section compares the SYS-GMM estimates with alternative panel data estimates and checks whether the results change across sub-samples or for different combinations of control variables.

Alternative Panel Estimators

Table 10 displays the estimated coefficients for PCY and LLY using the OLS level estimator (OLS), Within Group estimator (WG) and GMM first-difference estimator (DIF-GMM). Although it is well known that in a large N small T panel these estimators give a biased estimate of the autoregressive coefficient, precise biases results have not yet been extended to the remaining parameters (i.e., β and γ in equation (1)) when the regressors are endogenous. For this reason, it is instructive to compare the results across different estimators. For each estimator, the first column refers to the baseline regression of Table 9, while the second column also controls for the level of investment.8 The SYS-GMM estimates of Table 9 are reproduced in the last two columns, for the sake of comparison.

Table 10.

Panel Data Estimates Dependent Variable Log-difference GDP per capita

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Note: Estimations are, Pooled OLS(OLS), within Groups (WG), First Difference GMM(DIF-GMM) and system GMM (SYS-GMM) estimates. Robust t-statistic are in small fonts below the corresponding coefficients.Sargan test and m2 test are p-values for the null of instruments validityInstruments: Y0 and SEC are considered predetermined. The remaining variables endogenousX1 include: ln(Y0), ln(SEC), ln(GOV), ln(OPEN), ln(1+NF), ln(1+BMP)Data is in deviation from cross-section means

There are minor variations in the coefficients for PCY and LLY. The estimated parameters for both variables are marginally significant only with the OLS and WG estimators and if INV is excluded from the set of controls. In the remaining cases the coefficients are always poorly estimated. Overall, the statistical performance of PCY and LLY does not appear to change substantially across different panel estimators. It remains in line with the indications from the one-step SYS-GMM estimator: financial development is a not a good predictor of economic growth.

Subsample Stability

Table 11 assesses the stability of the GMM estimates across sub-samples. It considers the 1960-85 and 1970-98 sub-periods, to account for the fact that in recent years financial innovation has mainly occurred outside the banking system. Given that the two indicators of financial development refer solely to the banking sector, a smaller effect of PCY and LLY on growth is expected in the 1970-98 sample. When the T size of the panel is reduced, however, the properties of some panel estimators are also affected. The biases for the WG and DIF-GMM are expected to worsen whereas the SYS-GMM should provide more reliable estimates. For this reason, I also compare the results across estimators. Tables 11a-11b show that the preferred panel estimator, the SYS-GMM, does not indicate any substantial differences in the finance-growth link, over different intervals. The point estimates for PCY and LLY are very similar across samples, and in all cases are not significantly different from zero, apart from the OLS estimates in the sample 1960-85. In some cases, the coefficients are all insignificant or, surprisingly, negative.

Table 11.

Panel Data Estimates Dependent Variable Log-difference GDP per capita.

Note: See notes to Table 8
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Note: See notes to Table 8

Tables 12a and 12b report the results of two additional experiments. Table 12a uses the same sample of countries as LLB. As can be seen, the SYS-GMM estimates do not differ much from the baseline regressions. In Table 12b the data is divided in sub-periods of 10-year intervals. The puzzling effect is that PCY is now significantly related to GDP growth, whereas LLY is not. Also, the estimated coefficients for LLY become negative if INV is held constant.

Table 12.

Panel Data Estimates Dependent Variable Log-difference GDP per capita.

Note: See notes to Table 8
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Note: See notes to Table 8

Control Variables

As a final check, Table 13 presents estimates using a smaller set of covariates. In each case, I control for initial conditions and include INV, INF and GOV in different combinations. BMP and OPEN are dropped because they were invariably insignificant. The one step SYS-GMM results suggest that, with the exception of the parsimonious specification of column 1, PCY is never significantly related to growth. By contrast, LLY becomes insignificant when I jointly control for the level of INF and INV.

Table 13.

Panel Data: One–Step GMM Estimates Dependent Variable: Log-difference GDP per capita. Sample: 1960-1998

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Notes: see notes to Table 7

D. Summary of the Panel Data Results

Altogether, the conclusion of these experiments is that financial development, as measured by PCY, is not significantly related to long-run economic growth. The results are slightly different for LLY—which is found to be significant in some regressions—although they are not robust to different specifications and across sub-samples. Clearly, this conclusion contrasts with the evidence reported in LLB. The robustness checks reported above suggest that the main reason is not due to differences in the set of countries or sample period used. Rather, it appears to be the use of the more appropriate one-step GMM estimator.

VI. Nonlinearities and Heterogeneity

This section extends the analysis presented so far by relaxing the assumption that the slope coefficients in equation (1) are constant across units. There are several reasons that motivate the desire to move away from the standard framework.

First, although linearity is a convenient assumption, it is not tenable in a panel where countries differ along several dimensions. In principle, financial deepening may have growth-promoting effects at all stages of economic development. In practice, a variety of non-linear relationships may arise. One may conjecture that at early stages of economic development countries have no capital to invest and factors other than financial development are crucial for economic growth. Similarly, as the economy develops, but the quality of institutions supporting credit markets remain poor, it may be the case that only a few productive investments are undertaken while the effects of a larger banking sector for output performance remain of secondary importance. Finally, it can be conjectured that as the system of financial intermediation becomes more sophisticated, other forms of financing become available outside the banking system; in this case indicators of banking development are not very informative for evaluating the effects of financial development on economic growth. Models of economic development emphasizing thresholds effects (Azariadis and Drazen, 1990) are fully consistent with these non-linearities, as argued by Acemoglu and Zilibotti (1997, 1999) in the finance-growth context.

Second, in a multi-country panel setup, forcing parameters to be exactly equal in all units may create systematic distortions. In the empirical growth literature this objection has been raised by Durlauf and Johnson (1996), Lee et al. (1997) and Canova and Marcet (1998), who document widespread heterogeneity in the context of convergence of per capita income across countries; and by Liu and Stengos (1999), Kalaitzidakis et al. (2001) and Durlauf et al. (2001), who present evidence that standard growth determinants affect the growth rate of GDP in a non-linear way.

Third, the assumption of slope homogeneity in equation (1) has statistical shortcomings. If parameters are heterogeneous but held constant across units, traditional dynamic panel estimators are inconsistent. The source of inconsistency is that slope heterogeneity causes the disturbances to be serially correlated as well as contemporaneously correlated with the included regressors. Consequently, the presence of a lagged dependent variable renders the estimates of λ, β and γ inconsistent, even in a panel with uncorreclated regressors and with a sufficiently large number of countries and time series. The problems are aggravated if the regressors display serial correlation—as is likely for most of the variables of this paper. In these cases, estimation by GMM is no longer valid, since lagged values of serially correlated regressors cannot be used as instruments. (see Pesaran and Smith, 1995 and Pesaran, Smith and Im, 1999).

In what follows, the issue of parameter heterogeneity is addressed in two steps. First, I document the existence of widespread heterogeneity in the parameter y of equation (1) by using a semiparametric model, where no functional form assumption is imposed on the relationship between finance and growth. Second, the average long-run effect of finance on GDP per capita is re-examined using the Pooled Mean Group (PMG) estimator of Pesaran, Shin and Smith (1999), which is specifically designed to consistently estimate a dynamic panel in the presence of slope heterogeneity.

A. Nonlinearities: Empirical Specification and the Evidence

A straightforward way to question the linearity assumption for the relationship between financial development and economic growth, is to rewrite equation (1) as follows:

yityi,t1=λyi,t1+βxit+θ(FINit)+vit(4)

where θ(FINit) is a smooth function of unknown form, and the vector of point-wise derivatives γit(FINit) = ∂θ(FINit)/∂FINt contains varying response coefficients (both across countries and time).

Following Li and Wooldridge (2002), the functions θ(FINit) and γit(FINit) are estimated by a local linear kernel method, after “partialling out” the linear part of the model using a non parametric kernel method, as in Robinson (1988) or Stock (1989).9 I use the same panel of the previous section with data averaged over 5-year periods. The vector of controls xit includes the baseline regressors and the two regional dummies, AFRICA and LAC. All variables are also expressed in deviation from the cross-sectional mean to eliminate common time period effects.

Figure 3 plots the estimates of θ(FINit) (dotted curve) and the corresponding pooled OLS regression line (solid curve) to highlight the difference between the semiparametric and the linear model. On the horizontal axis, both graphs have the logarithm of PCY or LLY in deviation from the cross-sectional mean.

Figure 3:
Figure 3:

θ (.) Function for PCY and LLY

Citation: IMF Working Papers 2003, 123; 10.5089/9781451854633.001.A001

The first interesting result is that for both indicators of financial development, the relationship between finance and growth is non-linear. The graphical impression is also confirmed by the functional form test of Li and Wang (1998). Under the null of a linear model (equation (1)) against a semiparameteric alternative (equation (4)), the test has an asymp