1. Introduction

2. Contribution and Potential of Agriculture to Contribute to Angola’s GDP

Figure 1. Credit provided to real economy and agriculture.

Figure 1. Credit provided to real economy and agriculture.

Figure 2. Share of agri-credit in total credit provided to the economy (%).

Figure 2. Share of agri-credit in total credit provided to the economy (%).

Figure 3. GDP and agricultural GDP growth rates (%).

Figure 3. GDP and agricultural GDP growth rates (%).

Figure 4. Contribution of agriculture to Angola’s GDP (%).

Figure 4. Contribution of agriculture to Angola’s GDP (%).

3. Literature Review

4. Methodology

4.2. Econometric Model

The ARDL model has become an important tool for detecting the cointegration relationship based on the work of Pesaran and Shin (1999). The authors demonstrate that with an ARDL representation, it is possible to identify cointegration relationships in a system formed by variables that are all I(1), all I(0), or a mixture of stationary variables and variables I(1). This constitutes a great advantage compared to the Johansen cointegration method and even the FMOLS estimator, as both assume that all variables in the system are I(1).

For this reason, in the case of long-term time series for an economy with large probabilities of lag, we believe the choice to be better suited, that is, to test the model’s estimators/regressors using the ARDL test.

The dynamics of the relationship between GDP and agricultural credit are analyzed using the ARDL model given the agricultural credit exogeneity assumption. That is, ARDL(p,k) can be written as:

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

(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 ARDL 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.

According 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 the 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 variable Y is explained by the values of variable X, that is, determining if 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.

4.2.1. 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 econometrical identification in time series of the significant existence of variables showing a stochastic trend through a hypothesis test; this is assessed using the following equation: $Y_t={\alpha +\delta Y}_{t-1}+{\epsilon }_t$.

The augmented Dickey–Fuller test suggests 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: ${∆Y}_t={\delta Y}_{t-1}+{\epsilon }_t$

2) $Y_t$ is Random Walk with drift: ${∆Y}_t={\beta }_1{+\delta Y}_{t-1}+{\epsilon }_t$

3) $Y_t$ is Random Walk with drift and trend: ${∆Y}_t={\beta }_1{+{\beta }_{2}t+\delta Y}_{t-1}+{\epsilon }_t$

4.2.1.1. 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 a 5% level of significance. GDP_AGR was nonstationary at the same significance level. However, it was possible to make the GDP_AGR series stationary in first difference. This was achieved by generating the first difference variable and running the unit root test one more time.

Table 1. Nonconstant lags (1).

Table 1. Nonconstant lags (1).

Variable	ADF (1)	Critical Value
	nonconstant lags	1%	5%	10%
GDP_AGR.	-0.065	-2.660	-1.950	-1.600
TOTAL_AGR_CR	2.798	-2.660	-1.950	-1.600

Table 2. Trend lags (1).

Table 2. Trend lags (1).

Variable	ADF (1)	Critical Value
	trend lags	1%	5%	10%
GDP_AGR.	-3,855	-4,380	-3,600	-3,240
TOTAL_AGR_CR	-1,279	-4,380	-3,600	-3,240

Table 3. Drift lags (1).

Table 3. Drift lags (1).

Variable	ADF (1)	Critical Value
	drift lags	1%	5%	10%
GDP_AGR.	-1,463	-2,602	-1,753	-1,341
TOTAL_AGR_CR	1,821	-2,602	-1,753	-1,341

Table 4. Generate (nonconstant lags (1)).

Table 4. Generate (nonconstant lags (1)).

Variable	ADF (1)	Critical Value
	generate (noconstant lags)	1%	5%	10%
GDP_AGR.	-5,145	-2,660	-1,950	-1,600
TOTAL_AGR_CR	-0,511	-2,660	-1,950	-1,600

Source: All prepared by the authors.

It is common to represent the null hypothesis for the augmented ADF test analysis as follows1:

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 the alternative hypothesis is that the data are stationary. However, the following rule exists: if the t-statistic is greater than the critical 5% value, the null hypothesis is rejected. Therefore, the data are stationary. However, if the t-statistic is less than the critical value of 5%, the null hypothesis is accepted. Therefore, the data are nonstationary. In order to correct the variables (of the model), the first difference variables are generated and the unit root test is run once more.

4.2.2. Autoregressive Distributed Lag Model Estimation

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

$$Y_t=\alpha +{\varnothing Y}_{t-1}+{D\left(L\right)X}_t+{\epsilon }_t$$

where $D\left(L\right)={\delta }_0+{\delta }_{1}L+\dots +{\delta }_s{L}^s$, with L representing the lag operator, that is, ${LX}_t=X_{t-1};L^2{X}_t=X_{t-2};\dots +L^s=X_{t-s}$, where $X_t$ represents the set of explanatory variables of the model and ${\epsilon }_t$ is the error term. This the most explicit version of an ARDL 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 outlines that among the strong points of this model is its generality, that is, because it has a more conservative perspective, the articular cases that come from this model are very extensive, ranging from the static regressions themselves, without dynamics ($\varnothing =0e{\delta }_1={\delta }_2=\dots ={\delta }_s=0$), until we reach the Error Correction Model (ECM).

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

$$Y_{1t}=\mu +{\alpha }_1{Y}_{1t-1}+{{\beta }_{0}Y}_{2t}+{\beta }_1{Y}_{2t-1}+{\epsilon }_t$$

which results in,

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

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, ${∆Y}_{1t}$ is driven only by ${∆Y}_{2t}$;

b)

The existing cointegration is incorporated in the model ($Y_{1t-1}-\frac{\mu }{1-{\alpha }_1}-\frac{{\beta }_0+{\beta }_1}{1-{\alpha }_1}{Y}_{2t-1}$), and these quantities are specified in the model;

c)

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

d)

Finally, the long-term multiplier is expressed by $\frac{{\beta }_0+{\beta }_1}{1-{\alpha }_1}$, 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.

There is the issue of specification in the VECM model when estimating the regression parameters, that is, the coefficients of the explanatory variables are 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 the Breusch–Godfrey test, Durbin–Watson test, etc. Therefore, for the present study, we chose to perform the Durbin–Watson test2.

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, Prais estimation was used, and with this, the consistency of the predictability of the estimated econometric model was maintained.

5. Results

Figure 5. The evolution of GDP and agricultural credit.

Figure 5. The evolution of GDP and agricultural credit.

Table 6. Estimated Model.

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

6. Conclusions

7. Limitations

References

1. (Akram et al. 2008) Akram, Waqar, Zakir Hussain, Hazoor Sabir, and Ijaz Hussain. 2008. Impact of agriculture credit on growth and poverty in Pakistan. European Journal of Scientific Research 23: 243–51.
2. (Borges and Parré 2022) Borges, Murilo José, and José Luiz Parré. 2022. O impacto do crédito rural no produto agropecuário brasileiro. Revista de Economia e Sociologia Rural 60: e230521. https://doi.org/10.1590/1806-9479.2021.230521. [CrossRef]
3. (Carroll et al. 2012) Carroll, Tom, Andrew Stern, Dan Zook, Rocio Funes, Angela Rastegar, and Yuting Lien. 2012. Catalyzing Smallholder Agricultural Finance. New York: Dalberg Global Development Advisors.
4. (Castro and Teixeira 2004) Castro, Eduardo Rodrigues, and Erly Cardoso Teixeira. 2004. Retorno dos gastos com a equalização das taxas de juros do crédito rural na economia brasileira. Revista de Política Agrícola 3: 52–57.
5. (Castro and Teixeira 2010) Castro, Eduardo Rodrigues, and Erly Cardoso Teixeira. 2010. Crédito rural e oferta agrícola no Brasil. Revista de Política Agrícola XIX: 9–16.
6. (Dickey and Fuller 1981) Dickey, David A., and Wayne A. Fuller. 1981. The Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica 49: 1057–72.
7. (Enders 2015) Enders, Walter. 2015. Applied Econometric Time Series, 4th ed. New York: John Wiley & Sons.
8. (FitzGerald 2006) FitzGerald, Valpy. 2006. Financial Development and Economic Growth: A Critical View, Background Paper for World Economic and Social Survey. Oxford University. Available online: http://www.un.org/en/development/desa/policy/wess/wess_bg_papers/bp_wess2006_fitzgerald.pdf (accessed on 4 June 2022).
9. (Gasques et al. 2017) Gasques, José Garcia, Mirian Rumenos P. Bacchi, and Eliana Teles Bastos. 2017. Impactos do crédito rural sobre as variáveis do agronegócio. Revista de Política Agrícola 26: 132–40.
10. (Kaleemuddin and Masih 2017) Kaleemuddin, Mohammed and Mansur Masih. 2017. Does financial development drive economic growth? an ARDL approach. MPRA Paper 110716, University Library of Munich, Germany: 1-23. Available online: https://mpra.ub.uni-muenchen.de/110716/.
11. (King and Levine 1993) King, Robert G., and Ross Levine. 1993. Finance, entrepreneurship, and growth. Theory and evidence. Journal of Monetary Economics 32: 513–42.
12. (Koivu 2002) Koivu, Tuuli. 2002. Do Efficient Banking Sectors Accelerate Economic Growth in Transition Countries? BOFIT Discussion Papers, No. 14/2002. Helsinki: Bank of Finland, Institute for Economies in Transition (BOFIT), pp. 1–29, ISBN 951-686-842-8. Available online: https://nbn-resolving.de/urn:NBN:fi:bof-201408071978 (accessed on 04 April 2022).
13. (Leitão 2012) Leitão, Nuno Carlos. 2012. Bank, credit, and economic growth. A dynamic panel analysis. The Economic Research Guardian 2: 256–67. Available online: https://repositorio.ipsantarem.pt/bitstream/10400.15/761/1/NunoLeitao_ERG_2012.pdf (accessed on 22 July 2022).
14. (Lucas 1988) Lucas, Robert E., Jr. 1988. On the mechanics of economic development. Journal of Monetary Economics 22: 3–42.
15. (Melo et al. 2013) Melo, Marcelo Miranda, Émerson Lemos Marinho, and Almir Bittencourt Silva. 2013. O impulso do crédito rural no produto do seto primário brasileiro. Nexos Econômicos 7: 9–35.
16. (Moura 2016) Moura, Fábio Rodrigues. 2016. O nexo causal entre crédito rural e crescimento do produto agro-pecuário na economia brasileira. PhD thesis, Escola Superior de Agricultura Luiz Queiroz, Piracicaba, Brazil. Available online: http://www.teses.usp.br/teses/disponiveis/11/11132/tde22062016-163722/en.php (accessed on 03 October 2022).
17. (Pesaran and Shin 1999) Pesaran, Mohammad Hashem and Yongcheol Shin. 1999. An Autoregressive Distributed Lag Modelling Approach to Cointegration Analysis. Strom, S., Ed., Chapter 11 in Econometrics and Economic Theory in the 20th Century the Ragnar Frisch Centennial Symposium. Cambridge University Press, Cambridge: 371-413.
18. (Pham and Nguyen 2020) Pham, Hung, and Phuong Minh Nguyen. 2020. Empirical research on the impact of credit on economic growth in Vietnam. Management Science Letters 10: 2897–2904.
19. (Pistoresi and Venturelli 2012) Pistoresi, Barbara, and Valeria Venturelli. 2012. Credit, Venture Capital and Regional Economic Growth. Journal of Economics and Finance 39: 742–61. https://doi.org/10.1007/s12197-013-9277-8. [CrossRef]
20. (Stern 1989) Stern, Nicholas. 1989. The Economics of Development: A Survey. The Economic Journal 99: 597–685.
21. (Schumpeter 2021) Schumpeter, Joseph A. 2021, The Theory of Economic Development. London: Routledge.
22. (Wheeler and Pélissier 2009) Wheeler, Douglas L., and René Pélissier. 2009. História de Angola. Lisboa: Tinta da China.