Journal Issue

Mali: Selected Issues

International Monetary Fund
Published Date:
March 2006
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III. Economic Growth and Total Factor Productivity in Mali14

This paper assesses the impact of structural reforms on Mali’s aggregate output growth. It uses the growth accounting framework, which disaggregates output growth into that resulting from the accumulation of factors of production and the efficiency with which these factors are used separately and jointly. The paper employs econometric estimates of the Cobb-Douglass functions for Mali’s aggregate output, taking into account the relevant issues for empirically modeling production functions: economic theory, data measurement, returns to scale, parameter constancy, cointegration, exogeneity, and policy implications. The empirical methodology explores cointegrating relationships among output, physical and human capital stocks, and labor force over the period 1968–2004. The estimated parameters are used to derive overall total factor productivity (TFP) growth over the sample period. Single-equation models are used to estimate the determinants of overall TFP growth.

A. Analytical Framework

19. There is a large literature on the sources of economic growth following the work of Krugman (1994) and Young (1995). Krugman in particular argued that the growth in the East Asian economies was unsustainable because it was largely driven by capital and labor accumulation, rather than gains in productivity. In this perspective, identifying the sources of growth is crucial to assessing a country’s long-term economic prospects.

20. The point of departure is the standard Cobb-Douglas aggregate production function linking output to factor inputs (capital and labor) and productivity (along the lines of the neoclassical growth model; see, for instance, Barro and Sala-i-Martin, 1995):

Where t is a time index, Y is real gross domestic product, K is real capital stock, L is total employment, α is the contribution of capital to output, and the expression A ebt is total factor productivity (TFP)—the fixed component of TFP (A) is assumed to grow at a rate b. The TFP measures the shift in the production function at given levels of capital and labor. Dividing by L and taking the natural logarithms of the left and right hand sides of equation (1) yields:

Where the lowercase variables y and k denote respectively the natural logarithms of output and physical capital, measured in per capita terms. For the purpose of estimation, the variable a (or natural logarithm of A) is unobservable and will be captured through the residuals of equation (2). This production function is widely used and has many convenient properties such as perfect competition, constant returns to scale (CRTS), and constant factor income shares.

21. Data used in this exercise are from the Malian authorities, and the IMF World Economic Outlook database. Estimates of the capital stock are computed using the perpetual inventory method, and assuming a depreciation rate of 5 percent and a capital-output ratio of 1.5 in the base year. Given the severe data limitations, the population aged 15-60 is used as a proxy for the labor force. We also use a literate labor force variable to give insights of the impact the quality of labor on growth.

22. Unit root tests (ADF) are ran to assess the series statistical properties. If the series are not stationary, a long-run relationship between output per capita and physical stock per capita will exist only if they are cointegrated. The finding of cointegration will imply the existence of a stable, long-run equilibrium relationship among the two series in the sense that they tend to move together in the long run rather than move independently. To estimate the long-run production function, we apply the Johansen (1988, 1991) and Johansen and Juselius (1990) multivariate cointegration procedure to the output per capita and physical capital stock per capita series over the sample period. In addition to taking into account the nonstationarity of the data, the Johansen cointegration test does not assume a priori that the physical capital stock is exogenous. The potential endogeneity of factor inputs (capital and labor) has been often advanced in the growth literature as an argument against the estimation of production functions for determining the share of physical capital.

B. Empirical Findings

Statistical properties of the data

23. The main statistical properties of the data are shown in Table 1 and Figure 1:

Table 1.Mali: Descriptive statistics on Solow model variables
Real outputPhysical

Labor forceLiterate labor

Std. Dev.
  • GDP growth is very volatile, averaging 3.5 percent over the period or ½ percentage point per year, on a per capita basis.

  • Physical capital is also very volatile, but increases more rapidly than GDP growth, the labor force, and population. The elasticity of output growth to capital is less than one supporting a hypothesis of decreasing returns to scale.

  • Owing to a scarcity of data, the labor force is equated to the population aged 15-60 years. The literate labor force is the product of literacy rate and population aged 15–60 years. Overall, efforts to cut illiteracy have outpaced labor force growth during the period, albeit with relatively high volatility.

Figure 1.Mali: Growth Patterns of Solow Variables

24. The Augmented Dickey-Fuller (ADF) test statistic shows that output growth, growth of physical capital and growth of literate labor force are stationary variables. Labor force growth and growth of the literate labor force display a drift, and contain a unit root. Regressions of output growth on variables with the same order of integration capture the long-run relationship between these variables (Table 2).

Table 2;Mali: Results of Solow model regression
Dependent Variable: Output growth
Method: Least Squares
Sample: 1968 2004
VariableCoefficientStd. Errort-StatisticProb.
Growth of physical capital0.4510.1702.6480.012
Growth of labor force4.3964.0491.0860.285
R-squared0.232Mean depend. var.0.036
Adjusted R-squared0.187S.D. depend. var0.060
S.E. of regression0.054Akaike info criterion-2.905
Sum squared resid0.101Schwarz criterion-2.775
Log likelihood56.749F-statistic5.132
Durbin-Watson stat2.163Prob(F-statistic)0.011

Sources of growth

25. Labor and investment growth explain only about one quarter of fluctuations of GDP growth. The remainder stems from technology innovations and shocks. Investment is positively and significantly related to growth. The elasticity of output growth to physical capital is estimated at 0.451 slightly higher than typically assumed in the literature (0.4). The null hypothesis of constant returns of scale (βkl = 1) could not be rejected. Although the sign of the coefficient on labor is consistent with the literature, this variable is not significant in explaining output growth. This could stem from quality of data on the labor force and also because of the nonstationarity of the series. When the regression is run using the first difference of this series (a stationary variable), the series affect growth significantly and with a positive sign. However, results that use first differences of growth variables are difficult to interpret in the context of the Solow model.

26. Two methodologies can be used to account for growth changes. The first one sets by assumption the elasticity of output to capital. The estimate used in the literature is an elasticity of 0.4. Once the elasticity is known and under the assumption of constant returns to scale, all Solow series can be retrieved by difference. We prefer an alternative approach in which we use our estimate of the elasticity of output to capital obtained in Table 2. Total factor productivity growth is then computed on the basis of the following Solow model regression:.

Where: gkt and ght represent growth rates of physical capital and labor force, respectively. The parameters α (constant of the regression), and β and γ (output elasticities of capital and labor, respectively) are estimated. With the estimates for β and γ the series of unobserved residuals ε can be derived. The series ε is filtered using the Hodrick-Prescott Filter method, that decomposes the original series into the sum of two series.15 The smoothed series represent the permanent component of ε and is interpreted as TFP growth. Differences between the smoothed series and the original series represent exogenous shocks.

27. The growth accounting analysis is divided into sub-periods to illustrate changes over time in factor accumulation and productivity (Table 3). In the early sub-periods, central planning of the economy was dominant. During the 1980’s Mali embarked on a process of adjustment and reform. Post-1994, following CFA franc devaluation, economic reforms have been pursued further, including in the areas of domestic and international trade policies and regulations, financial sector, and privatization. However, structural reform implementation has been mixed and uneven across time.

Table 3.Mali: Growth Accounting Results
Real GDP growth3.
Factor accumulation2.
Solow residual0.70.7-3.8-1.1-0.23.0
Total factor productivity2.60.1-2.2-
Exogenous shocks-1.90.6-1.60.5-0.71.5
Memorandum items
Investment-GDP ratio5.710.116.717.819.217.5
Real investment growth11.513.
Initial capital stock ratio (K/Y)0.72
Capital depreciation rate0.05
Output elasticity to capital0.45
Output elasticity to labor0.55

28. The results consistently point to the predominance of factor accumulation over total factor productivity growth in explaining output growth, particularly before 1994. Total factor productivity is estimated to have been nil over the period 1968-2004, although productivity tended to improve during and after periods of intensive economic reforms. Such reforms began in the mid-1980’s with a series of economic adjustment and refrom programs.

29. Economic shocks have also hit Mali with a 10-year cycle pattern, with droughts and terms of trade shocks being the main driving factors of these shocks. Figure 2 shows that shocks obtained from the accounting exercise display broadly the same patterns as changes in terms of trade: both have a sizable magnitude and are difficult to predict. The difference of magnitude between both series could be partially explained by natural shocks such as drought, bird or locust infestation. This underscores the need to broad Mali’s economic base through diversification to absorb exogenous shocks.

Figure 2.Mali: Solow Shocks and Changes in Terms of Trade

Determinants of TFP growth

30. The possible determinants of TFP growth (are selected on the basis of the most frequently proposed explanatory variables in empirical studies as determinants of economic growth.16 The variables selected are: (i) the ratio of credit to the government to GDP as an indicator of the fiscal stance; (ii) the ratio of domestic credit to the private sector to GDP to represent financial sector role in allocating efficiently savings between competing uses; (iii) the ratio of merchandise trade to GDP to assess Mali’s integration into the global economy; (iv) aid per capita to analyze the impact of resources transfers on Mali’s economy; (v) the overall quality of institutions (using a Maryland worldwide data base on institutions quality); and (vi) a dummy variable to capture the effect of the devaluation. These variables are used to identify factors contributing to TFP growth calculated using the Solow regression approach (Table 4).

Table 4.Mali: Explaining Total Factor Productivity Growth
Dependent Variable: Total Factor Productivity Growth
Method: Least Squares
Sample (adjusted): 1969 2001
VariableCoefficientStd. Errort-StatisticProb.
Credit to the government-0.0660.022-2.9750.007
Consumer price inflation0.0030.0040.7950.434
Credit to the private sector0.0500.0202.4700.021
Trade as a share of GDP0.0110.0111.0700.295
Aid per capita-0.0030.002-1.2490.224
Overall quality of institutions0.0010.0002.3490.027
Devaluation dummy0.0080.0033.1440.004
R-squared0.986Mean dependent var-0.003
Adjusted R-squared0.981S.D. dependent var0.016
S.E. of regression0.002Akaike info criterion-9.144
Sum squared resid0.000Schwarz criterion-8.736
Log likelihood159.884F-statistic203.941
Durbin-Watson stat1.234Prob(F-statistic)0.000
Inverted AR Roots0.88

31. The results are broadly in line with the literature and show that prudent fiscal polices, sound financial institutions, and strong institutions that foster stability and promote the private sector are key to boosting TFP growth. Thus high government deficits are found to be an impediment to growth, particularly when the deficit is financed through domestic banks. Such policies may increase inefficiencies in resource allocation, and are facilitated where government is heavily involved in the banking sector. We also find that openness to financial flows and financial development, proxied by the private sector credit-to-GDP has a positive and significant effect on TFP growth. The results point to the importance of the economic, political, and legal environment in fostering investment and TFP growth. Political instability has a negative impact on economic growth by disrupting the business environment and economic activity. A well-functioning, dynamic market economy requires a set of “good” institutions that secure property rights and political stability, by promoting the rule of law, guaranteeing low-cost enforcement of contracts, creating an effective and predictable judiciary, and limiting the power of rulers.

32. However the results could not confirm the role of inflation and aid predicted generally in the literature. The literature conjectures that high inflation has a negative effect on growth by reducing long-term investment and the productivity of capital. However, in Mali a significant and negative impact of inflation on TFP growth could not be confirmed. This may result from the relatively low and stable level of inflation achieved in Mali. A credible monetary policy conducted by the BCEAO has led to low inflation expectations by investors and consumers. Our results also show a negative and marginally significant effect of aid on TFP growth. This could result from an endogenity problem (aid pours into the country when shocks reduce growth) or inefficiencies in aid delivery.

33. The variables used to predict TFP growth capture an important part of TFP growth volatility (Figure 3). Using the above results, and historical data on factor accumulation since 2000 (3.5 percent on average), TFP growth would need to be boosted to an average 3.2 percent (from its 1 percent average during 1994-2004) to achieve the Poverty Reduction Strategy growth targets of 6.7 percent per year. Moreover, this assumes that Mali’s economy is shielded from exogenous shocks (Table 5). The increase in productivity and investment needed to attain PRGF annual growth objectives of 5½ percent appear more attainable, albeit still optimistic given Mali’s track record. In brief, this shows the extent to which Mali’s PRSP growth objectives are ambitious, and the urgency of advancing the structural reform agenda and stay the course on macroeconomic management and promotion of diversification to increase Mali’s resilience to shocks. Under both scenarios, investment would also need to be boosted substantially to raise the contribution of factor accumulation to growth, notably through improving the investment climate. Improving labor skills and human capital would help achieve the growth objective under more plausible target for investment growth.

Figure 3.Mali: Total Factor Productivity Growth: Actual against Fitted

Table 5.Mali: TFP growth required to achieve selected output growth objectives
2 percent negative shockNo shocks2 percent positive shock
Real GDP growth5.
Factor accumulation2.
Total factor productivity5.
Average investment growth21.426.721.426.721.426.7

C. Conclusions and Implications for Future Growth

34. The growth accounting exercise produced results consistent with the economic literature on the sources of growth. On the basis of historical data, the elasticity of output to physical capital has been estimated for Mali at 0.45 in line with estimates used in similar analyses (0.4). A test for constant returns to scale could not be rejected. The results also show that the bulk of Mali’s growth results from factor accumulation rather than TFP growth. Mali’s TFP growth declined during period of economic centralization, and increased with the liberalization of the economy, peaking after the devaluation. This result pointing to the impact of economic policies on TFP growth is confirmed by the analysis of determinants of TFP growth. Sound economic policies underpinned by strong institutions promote economic growth through improvements in factor productivity. However we find a puzzling negative impact of aid per capita on growth, which could possibly be explained by aid endogeneity and/or inefficiencies in aid delivery and usage.


This paper was prepared by Abdoul Aziz Wane and Jean-Claude Nachega.

The Hodrick-Prescott Filter is a series decomposition method aimed at obtaining a smooth estimate of the long-term trend component of a series.

Early empirical work exploring the impact of policy, institutional, or exogenous variables on a number of African countries includes Easterly (1996), Ghura and Hadjimichael (1996), and Elbadawi and Ndulu (1996), Sachs and Warner (1997), Collier and Gunning (1999). Recent developments in growth theory have stressed the importance of good institutions (North, 1990) and sound policies in creating an environment that fosters economic development through the accumulation of factors of production and the efficient use of resources.

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