The Impact of Agricultural Credit on the Growth of the Agricultural Sector in Angola

1. Introduction

2. Contribution and potential of Agriculture to Angola’s GDP

3. Literature Review

4. Methodology

4.1. Econometric Model

The dynamics of the relationship between GDP and agricultural credit is analysed using Autoregressive distributed lag (ADL) model given the agricultural credit exogeneity assumption. That is, the ADL(p,p) can be written as:

$$Y_t={\alpha }_0+{\displaystyle \sum }_{i=1}^p{a}_i{Y}_{t-i}+{\displaystyle \sum }_{i=1}^p{b}_i{X}_{t-i}+{\epsilon }_{1t}$$

(1)

where,

$Y_t$ is the endogenous variable (GDP);

$Y_{t-i}$ represents the lagged values of the endogenous variable;

$X_t$ is the exogenous variable included in the model (agricultural credit)

$X_{t-i}$ represents the lagged values of the exogenous variable;

α and β are the parameters;

${\epsilon }_{1t}$ are the error terms of the model.

According to Borges and Parré (2022), it is necessary to verify the degree of stationarity of the series used in the ADL model. The Dickey and Fuller (1981) test is used to determine the level of integration of the series and to consider the possible differences that make the series stationary. …Introduce ADF test here….

Accoriding to Borges and Parré, if the series are stationary with respect to 0 (zero), they will be conducted to the point where they are estimated in equation (1). If the series are integrated into equation (1), the equation uses the variables according to the first difference.

Moreover, we use Granger test to investigate the causality between GDP and agricultural credit. Enders (2015) argues that the Granger test proposes testable definitions between the causality of two time series, based on the assumption that the cause precedes the effect. In this case, the test’s objectivity is restricted in the sense of observing how much of the variable Y is explained by the values of the variable X, that is, determining if the variable X can explain the observed value of Y, meaning that it determines whether the values of X are statistically significant.

To assess the stationarity of the time series in the present study, the augmented ADF test was used; whose purpose is to guide the level of integration between series by measuring the number of differences required for a series to be stationary.

4.1.1. Dickey-Fuller (ADF) Test

For the analysis of the stationarity accuracy of the estimation model, it is common to use the augmented Dickey-Fuller (ADF) test, since it is a single root test that allows identifying econometrically in time series the significant existence of variables with a behavior of stochastic trend through a hypothesis test; having with equation: $Y_t=\alpha + \delta Y_{t-1}+{\epsilon }_t$.

The augmented Dickey-Fuller test suggest three different forms, under three different null hypothesis. For each case, the null hypothesis is $\delta =0$, the series have a unit root and nonstationary (Forhad, Rahman, 2021):

1)

Y_t is Random Walk: ∆Y_t = δY_t−1 + ε_t

2)

Y_t is Random Walk with drift: ∆Y_t = β₁ + δY_t−1 + ε_t

3)

Y_t is Random Walk with drift and trend: ∆Y_t = β₁ + β₂t + δY_t−1 + ε_t

4.1.1.1. Dickey-Fuller Test for Unit Root Test

The tables below present the augmented ADF test of the time series. The results of augmented ADF test in first difference show that the TOTAL_AGR_CR series is I(0) stationary at the 5% level of significance. While, GDP_AGR was nonstationary at the same significance level. However, it was possible to make the GDP_AGR series stationary in first difference. Generating the first difference variable and running the unit root test one more tome.

Table 1. – nonconstant lags (1).

Table 1. – nonconstant lags (1).

Table 2. – trend lags (1).

Table 2. – trend lags (1).

Table 3. – drift lags (1).

Table 3. – drift lags (1).

Table 4. – generate (noconstant lags (1)).

Table 4. – generate (noconstant lags (1)).

Source: All prepared by the authors.

It is common to represent the null hypothesis for Augmented ADF test analysis as follows 2:

H₀: $\delta =1 \to$Stochastic trends in time series.

H₁: $<1\to$Absence of stochastic trends in time series.

According to Noami, (2023), in the Augmented ADF test, the null hypothesis reflects the possibility of nonstationary data, which implies the presence of a unit root in the variables of the estimated model, and alternative hypothesis, the data are stationary. However, the following rule exists: if the t-statistic is greater than critical 5% value, the null hypothesis is rejected. Therefore, the data is stationary. But, if the t-statistic is less than the critical value of 5%, the null hypothesis is accepted. Therefore, the data is nonstationary. In order to correcte the variables (of the model), generate the first difference variables and run the unit root test once more.

4.1.2. Autoregressive Distributed Lag (ADL) Model Estimation

Pereira, Gonçalves (2019), points out that, considering a linear model for time series:

$$Y_t = \mathsf{\alpha } + \varnothing Y_{t-1}+D\left(L\right)X_t +{\epsilon }_t$$

where, $D\left(L\right)={\delta }_0+{\delta }_{1}L+\dots +{\delta }_s{L}^s$, with L representing the lag operator, that is, $L{X}_t=X_{t-1};L^2{X}_t=X_{t-2};\dots +L^s=X_{t-s}$, $X_t$, represents the set of explanatory variables of the model, ${\epsilon }_t$, is the error term. This the most explicit version of an ADL model, for which the stability condition is assumed to be satisfied, |$\varnothing$| < 1, so there are unit root problems, although they are not very predictable in practice.

The same author says that among the strong points of this model is its generality, that is, because it has a more conservative perspective, in fact the articular cases that come from this model are very extensive, ranging from the static regressions themselves, without dynamics ($\varnothing =0 e {\delta }_1= {\delta }_2=\dots = {\delta }_s=0$, until we reach the Error Correction Models (MCE, acronym in Portuguese).

In the view of, Aparício, Azevedo (2018), “the Error Correction Model contains a variety of applicability in economic series given its components that make it a flexible model.” Much on account of being a model capable of incorporating both short-term and long-term mechanisms, as well as the speed of adjustment with which balance is reestablished. In general, the ECM is a particular case of the ADL model, in order to be more concise, an ADL (1,1) model with only a single explanatory variable is expressed, as is the case of present study.

$$Y_{1t}=\mu +{\mathsf{\alpha }}_1{Y}_{1t-1}+{\beta }_0{Y}_{2t}+{\beta }_1{Y}_{2t-1}+{\epsilon }_t$$

Which result in,

$$\Delta Y_{1t}=\left({\mathsf{\alpha }}_1-1\right)+\left[ Y_{1t-1}-\frac{\mu }{1-{ \mathsf{\alpha }}_1 }-\frac{{\beta }_0+{\beta }_1}{1-{ \mathsf{\alpha }}_1 }{Y}_{2t-1}\right]+{\beta }_0\Delta Y_{2t}+{\epsilon }_t$$

Looking at the previous equation, Aparício describes four characteristics of the ECM:

a)

It is a short-term dynamic model, since if there are no imbalances, $\Delta Y_{1t}$, driven only by $\Delta Y_{2t}$;

b)

The existing cointegration is incorporated in the model ($Y_{\mathit{1}t-1}-\frac{\mu }{1-{ \mathsf{\alpha }}_{\mathit{1}} } -\frac{{\beta }_0+ {\beta }_{\mathit{1}}}{1-{ \mathsf{\alpha }}_{\mathit{1}} }{Y}_{2t-\mathit{1}}$), and these quantities are specified in the model;

c)

Therefore, one can estimate the speed with which equilibrium is reestablished through (${\mathsf{\alpha }}_1-1$);

d)

Finally, the long-term multiplier is expressed by $\frac{{\beta }_0+ {\beta }_1}{1-{ \mathsf{\alpha }}_1 }$, and, on the other hand, the short-term multiplier is given by ${\beta }_0$, due to the fact that, quantities are specified in the model.

The issue of specification in the ECM model when estimating the regression parameters, that is, the coefficients of the explanatory variables is seen as a problem in the model, knowing that the OLS estimator is BLUE (Best Unbiased Linear Estimator), (Pereira 2019). On the other hand, to guarantee the satisfaction of this and other hypotheses necessary to validate the statistical inference and validity of the final chosen model, several tests are performed, such as BREUSCH-GODFREY and DURBIN-WATSON, etc. Therefore, for the present study, we chose to perform the DURBIN-WATSON test 3.

There is an autocorrelation problem in the estimated model, when the errors or residuals of the times series are correlated. Therefore, in order to diagnose autocorrelation problems in the time series studied, the Durbin-Watson (DW) t statistic was used, then analyzing the rule or decision diagram. In order to solve possible problems of autocorrelation in the model series, the PRAIS ESTIMATION was used, and with this, the consistency of the predictability of the estimated econometric model was maintained.

5. Results

In terms of presentation, Figure 5 demonstrates that the simple linear regression econometric model which has the following form: where the values in parentheses represent the standard deviations of the estimated econometric model parameters.

Table 6. – Estimated Model.

Table 6. – Estimated Model.

Table 7. – Prais Estimation (Error Correction of Model).

Table 7. – Prais Estimation (Error Correction of Model).

Source: All prepared by the authors based on research data.

Table 8. – Decision diagram for autocorrelation.

Table 8. – Decision diagram for autocorrelation.

6. Conclusions

7. Limitations

References

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