Time Series Analysis on the Effect of Organic and Inorganic Fertilizer in Production of Teff ( Eragrostis tef ) in Ethiopia

Ethiopia is the only country that produces teff ( Eragrostis tef ) in the world, but the production of teff is still low compared to other cereal crops. The main purpose of this study was to evaluate the impacts of organic and inorganic fertilizers on teff yield between 1995 and 2017 using an autoregressive distributed lag with co-integration approach. The Phillips Peron test and the Augmented Dickey-Fuller test for time series stationary checking and capturing serial correlation were used, whereas the Breusch Godfrey Lagrange multiplier and the cumulative sum test were used for determining the autocorrelation of residuals and the stability of coefficients. The result showed that the average yield of teff was 11.25 quintals per hectare, and the bounded F-test for co-integration among the variables does not show evidence of a long-run relationship between fertilizers applied and teff yield per hectare. The quantity of urea applied had a positive and significant impact on the yield of teff, and the quantity of di-ammonium phosphate (DAP) application had a negative impact in the short run. In conclusion, there was no co-integration between the yield of teff crops and fertilizer types such as urea and di-ammonium phosphate, which indicates that the quantity of urea fertilizer used for the production of teff has a positive relationship while the quantity of DAP fertilizer had an indirect relationship. Hence inorganic fertilizer like DAP is negatively correlated with the production of teff while organic fertilizer (urea) is positively correlated.


Introduction
Cereals are the most important agricultural commodities for meeting the food requirements of the world's population (Asgari et al., 2017;Slama et al., 2005).It provides a privileged source for animal feed and multiple industrial applications (Belaid, 2000;Zargar et al., 2017).Cereal crops like teff (Eragrostis tef) have the potential to gain the interest of the western world due to the health benefits (Roussis et al., 2019).
Cereals are the principal class of crops in Ethiopia, with 10.22 million hectares area covered, a volume of 25.38 million metric tons of grain production, and 16.24 million smallholders are engaged in it.However, the production of teff in Ethiopia has been low as compared to other cereal crops (Evangelista, Young and Burnett, 2013).Teff productivity is being affected by low soil fertility as well as organic matter depletion.Regardless of its wider adaptation, the productivity of teff is low in Ethiopia, with the national average grain yield of 1.379 tons per hectare (Zhao et al., 2016).
Soil fertility depletion in small farms is the basic biophysical root that is a cause of declining per capita food production (Quansah, 2010).Farmers are using high levels of inorganic fertilizer, which is causing declining soil organic matter levels in Ethiopia (Werede, Smith and Boke, 2018).In addition, organic fertilizer is also important as an alternative to chemical fertilizers for teff production (Roussis et al., 2019).Therefore, fertilizers are important for enhancing soil nutrient availability, microbial biomass, enzymatic activity, and crop yields (Zhao et al., 2016).Teff is a small-grained cereal crop grown as a food crop in Ethiopia.Most teff grains are used to make injera, the most popular food in the national diet (Haileselassie, Stomph and Hoffland, 2011).The main reasons for the decline in teff production in Ethiopia are poor soil fertility and irregular fertilizer rate (Bezabeh, 2016).
Several studies on teff production have focused on the effects of organic and inorganic fertilizers on the production of cereal crops.For instance, a study was conducted by Weldegebriel (2015, pp.1 & 36) revealed the determinants of the technical efficiency of farmers in the production of teff.Similarly, another investigation confirmed the determinants of market participation and the intensity of the market surplus of teff production (Tura et al., 2016).Moreover, yet another study claimed the determinants of smallholder farmers in teff market supply (Habtewold, Challa and Latha, 2017).
As one can observe, most studies have been done on the ways of improving teff production.However, none of them considered the constancy of means and variances in analyzing time series variables.Moreover, those studies did not identify the multiple co-integrating vectors.Similarly, the previous studies did not throw light on the long-run relationship between series with different orders of integration.In light of that, this study was carried out to test the presence of a long-run relationship between the variables.Therefore, to fill the gap, this study uses time series analysis with the autoregressive distributed lag co-integration technique.The autoregressive distributed lag co-integration technique helps avoid the pretesting problems associated with standard co-integration analysis, which requires the classification of the variables into I(0) and I(1).In addition, this study inquires whether a long-run equilibrium relationship exists between the production of teff and the associated determinants of teff production.The bound co-integration testing procedure does not require the pre-testing of the variables included in the model for unit roots, and it is robust when there is a single long-run relationship between the underlying variables.A dynamic error correction model (ECM)1 is normally used for I(0) variables, which could also be the first differences of I(1) or co-integrating combinations of I(1).However, autoregressive distributed lag (ARDL)2 can handle both I (non-integrated) and I (integrated) variables at the same time.It is used to assess the effect of organic and inorganic fertilizers on the production of teff in Ethiopia.Further, ARDL is used to test the presence of the long-run relationship between the variables.

Methods and Materials
The Source of Data The data was obtained from the Ethiopian National Bank and compiled by the Central Statistical Agency between 1995 and 2017.In this study, secondary sources of data were used.The data is a time-series data set.

Study Variables
The production of teff was considered a dependent variable.On the other hand, the independent variables were the quantity of urea fertilizer, the quantity of DAP fertilizer, time, and the lagged value of the production of teff.

The Method of Data Analysis
This data was analyzed by Eviews (6.4) statistical software.Descriptive statistics such as mean, standard deviation, minimum, maximum, etc. were used.In order to determine whether the series was stationary or not, a non-parametric test like Phillips-Peron3 (PP) tests and Augmented Dickey-Fuller (ADF)4 tests were used.The Phillips-Peron (PP) tests were used to estimate the long-run variance of the differences, while the Augmented Dickey-Fuller (ADF) tests were used for the parametric autoregressive structure to capture serial correlation.Thus, the study used the ADF and PP tests, including trend and intercepts, to check the stationary of each variable at a 5% level of significance.A time plot was used to check stationary before one could attempt to fit a suitable model.This study also uses a unit root test as a starting point of analysis for the time series variables.The study used a method of transformation from non-stationary to stationary by subtracting each time-series data point from its proceeds or it's lagging values.
The autoregressive distributed lag (ARDL) bound test was used based on the assumption that the variables are I(0), I(1), or mixed order, but not I(2).Therefore, before applying the ARDL bound test, the orders of integration of all variables using the unit root tests were determined.The unit root tests used to ensure the variables are either (1) true or (2) spurious (Pesaran, Shin and Smith, 2001).
The Akaike Information Criterion (AIC)5 , Schwarz Information Criterion (SC)6 , Bayesian Information Criteria (BIC)7 and Hannan-Quin (HQ) Information Criteria8 were used to determine the appropriate lag length for the vector autoregressive (VAR) model9 and model selection.A model that has a minimum AIC and a minimum BIC was selected as appropriate to describe the data well.The lag length for the VAR model was determined using model selection criteria.The Wald lag exclusion test10 was used to check whether the chosen lag is optimal or not (Box, Jenkins and Reinsel, 2008).Maximum likelihood estimation is employed to estimate the parameters of the VAR model in this study.Breusch-Godfrey Lagrange Multiplier (LM) test11 and Portmanteau test12 were also used to test the autocorrelation of residuals in the VAR (p) process.The study used the CUSUM13 and CUSUMSQ14 tests to check the stability of the coefficients in the model based on the recursive regression residuals as suggested by Brown, Durbin and Evans (1975).In addition to the graphical technique, the model fitness was checked by the coefficient of determination.Time series analysis depends on the lag order selected critically.

Results
Table 1 below shows that the average yield of teff production was 11.25 quintals per hectare in Ethiopia from 1995 to 2017.In addition, the average use of urea and DAP fertilizers for the production of teff was 0.56 quintals per hectare and 0.64 quintals per hectare, respectively, over the specified period of time.In Ethiopia, farmers used more di-ammonium phosphate (DAP) fertilizer than urea during the reference period.Additionally, table 1 shows the p-value of the teff production, the quantity of urea, and the quantity of DAP fertilizer used for production.But the p-value for the quantity of urea fertilizer used for the production of teff is greater than the significance level of 0.05.It implies that the quantity of urea fertilizer used for production does not satisfy the normality assumption.However, the quantity of DAP fertilizer used for production satisfied the normality assumption.
Figure 1 indicates that the parameters are stable, and the estimated residuals lie inside the 95% confidence region.In addition, the figure 2 shows the estimated residuals satisfied the normality assumption.The standard deviation of teff production, the quantity of urea, and the quantity of DAP, respectively, was 3.50 quintals per hectare, 0.15 quintals per hectare, and 0.19 quintals per hectare.The minimum yield of teff production, the quantity of urea, and the DAP fertilizer used for production were 17.9, 0.9, and 0.9 quintals per hectare, respectively.

Unit Root Test
Table 2 indicates that the production of teff and the quantity of DAP fertilizer used for the production of teff are not stationary at the original data level.But the production of teff and the quantity of DAP fertilizer used for the production of teff became stationary after the first difference.So this study used integrated order one, I(1), but the quantity of urea fertilizer used for teff production is stationary at the original data level, so it has integrated order zero, I(0).Therefore, the study variables were mixed orders of integration, i.e., I(0) and I(1).Since no variables were integrated into orders of two in this study, it used the ARDL bound test co-integration technique for both long-run and short-run relationships, which is more appropriate than other co-integration techniques.

Lag Order Selection
Table 3 shows that the appropriate lag order is 2, and it is selected by the entire criterion.

ARDL bound test for co-integration
Table 4 shows that the F-statistic value is equal to 0.6369, which is lower than the critical values of I(0) and I(1) at 10%, 5%, and 1% levels.It indicates that there is no co-integration among those associated variables.The result implies that there is no long-run relationship between variables.

Model Selection
As a result of there being no long-run relationship between the production of teff and the quantity of urea and DAP fertilizer, the study used a short-run dynamic regression model, or ARDL (refer to Table 4).The ARDL model was an appropriate model to determine the impact of the quantity of urea and the quantity of DAP fertilizer on the production of teff.Therefore, this study evaluated 20 models.Among these, the selected model was ARDL (2, 0, 2,) due to its minimum AIC and BIC.It implies the production of teff is lag two, the quantity of urea fertilizer used for the production of teff is lag zero, and the quantity of DAP fertilizer used for the production of teff is lag two.

Parameter Estimation and Interpretation
Table 6 shows that the quantity of urea and the quantity of DAP used for the production of teff have a significant impact on the yield of production of teff at a level of significance equal to 0.05.The yield of teff increased by 5.14 quintals per hectare when the quantity of urea fertilizer changed by one quintal per hectare.
But when the quantity of DAP was increased by 1 quintal per hectare, the yield of teff decreased by 2.86 quintals per hectare.

Model Evaluation and Stability Test
This study evaluated the estimated residual properties to be performed.The study checked the stability of the coefficients in the model.The parameters are stable because the estimated residuals lie inside the 95% confidence region.

A Specification Error Test
This study considered another potential problem that may have omitted variables due to bias, like fertilizerrelated variables (NPK, NPS, natural fertilizers, etc.).It affects the cereal yield that has been left out of the ARDL model.Additionally, this study used the Ramsey Regression Specification Error Test (RESET) 15 for omitted variables.The Ramsey regression specification error test checks the existence or non-existence of structural breaks.H0: the model is specified correctly vs. H1: the model is not correctly specified.Table 7 shows that the model is specified correctly with a p-value equal to 0.8316.Table 8 indicates that there is no serial correlation in the residual (P-value equal to 0.6137).Additionally, the variance of the error term is constant (p-value equal to 0.4888).The p-value equal to 0.9252 is greater than the alpha equal to 0.05.It shows that the residual satisfied the normality assumption.

Discussion
Cereals like teff are sources of dietary protein and energy throughout the world.But teff is the major cereal crop that is produced only in Ethiopia.Teff's productivity is being affected by low soil fertility and organic matter depletion.This paper has attempted to determine the effect of organic and inorganic fertilizers on the production of teff in Ethiopia.ARDL models were used to assess the effects of organic and inorganic fertilizers.ARDL was also used to test the long-run relationship between the associated variables.
From 1995 to 2017, the average yield of teff production was 11.25 quintals per hectare in Ethiopia.In addition, the average use of urea and DAP fertilizers for the production of teff was 0.56 quintals per hectare and 0.64 quintals per hectare, respectively, in the specified period of time.In Ethiopia, farmers used more DAP fertilizer than urea for the production of teff during the specified years.The standard deviation, or the variation of teff production, the quantity of urea, and DAP were 3.50 quintals per hectare, 0.15 quintals per hectare, and 0.19 quintals per hectare, respectively.Similarly, the standard deviation indicates that the variation of production between consecutive years was high when farmers used DAP fertilizers.This finding is confirmed by another study by Habtewold, Challa and Latha (2017, pp.133 & 140).
The production of teff and the quantity of DAP fertilizer used for the production of teff are not stationary at the original data level.But the production of teff and the quantity of DAP fertilizer used for the production of teff became stationary after the first difference.The bound test of co-integration was implemented for analyzing the long-run relationship between variables.It indicates that there is no co-integration among variables.Therefore, the study variables were mixed orders of integration, i.e., I(0) and I(1).It used the ARDL bound test co-integration technique for both long-run and short-run relationships, which is more appropriate than other co-integration techniques.This study evaluated 20 models.Among these, the selected model was ARDL (2, 0, 2). Figure 1 shows parameters are stable, and the estimated residuals lie inside the 95% confidence region.Further, the figure 2 shows the estimated residuals satisfied the normality assumption.
According to the findings of this study, the quantity of urea fertilizer was an important predictor of the production of teff.This implies that if the quantity of urea fertilizer increases by 1 quintal per hectare, then the mean production of teff will increase by 5.14 quintals per hectare.This result was confirmed by a few studies done in Ethiopia (Ayalew, Kena and Dejene., 2011;Mesfin and Ledin, 2004;Werede et al., 2018).In addition, the study done in Ethiopia by Chala and Gurmu (2016) showed the application of different organic fertilizers like urea to improve the organic matter, total N, available P, and pH of the soil in the study area.It implies that inorganic fertilizer (urea) is positively correlated.The study done in Pakistan by Muhammad et al. (2020) reported that inorganic fertilizers like urea can improve the fertility of soil and crop yield.So, the grain yield of teff is high when the quantity of inorganic fertilizer is high.The yield of teff decreased by 2.86 quintals per hectare when the quantity of inorganic fertilizer like DAP increased by 1 quintal per hectare.This result was confirmed by several studies done in Ethiopia (Ayalew, Kena and Dejene., 2011;Aragow, 2017;Abera, 2019;Abewa et al., 2019;Werede et al., 2018).Other study in Ethiopia (Habte, Smith and Boke., 2018) confirmed that the lowest yield of teff was recorded from 50% recommended inorganic fertilizer plus 50% recommended organic fertilizer.Therefore, the number of inorganic fertilizers like DAP had negative effects on the yield of Teff.

Conclusion
Cereal crops like teff have the potential to offer health benefits.Ethiopia is the only country that produces teff in the world.The main purpose of this study was to evaluate the impacts of organic and inorganic fertilizers on teff production from 1995 to 2017 using an autoregressive distributed lag with co-integration approach.Moreover, the study employed the bound test co-integration technique.From this study, fertilizers such as urea and di-ammonium phosphate (DAP) were found statistically significant at a 5% level of significance for the production of teff in Ethiopia.In this study, relationships between the production of teff and the associated variables such as the quantity of urea and DAP were examined in Ethiopia from 1995 to 2017.Its result indicates that there is no co-integration between the yield of teff, the quantity of urea, and the quantity of DAP.Therefore, this study focused in the short run due to no co-integration between the yield of teff, quantity of urea, and quantity of DAP.It shows that urea and DAP have positive and negative significant impacts on the yield of teff, respectively.The yield of teff increased by 5.14 quintals per hectare when the quantity of urea fertilizer increased by 1 quintal per hectare.But when the quantity of DAP fertilizer used was increased by 1 quintal per hectare, the yield of teff decreased by 2.86 quintals per hectare.Hence, the concerned government agencies should focus on creating awareness about the DAP fertilizer's appropriate rate of usage.Furthermore, researchers should also give attention to investigate the effect of fertilizer rate being applied.A farmer also needs to be aware about the precise quantity of a fertilizer for production of teff.

Table 2 :
Unit Root Test for Study Variables , *** denotes the level of significance of trend and intercepts of stationary for each variable at 5% *

Table 3 :
Select Appropriate Lag Order based on Production of Teff *denotes the level of significance of lag order at 5%

Table 4 :
Selection appropriate Lag Order based on production of Teff (Eragrostis tef)