The Impact of Rapid Population Growth on Economic Growth: Evidence From Ethiopia

Rapid population growth is increasing from time to time as a result of high fertility and migration rate. This has a greater impact on the quality life of the society, in case of increasing number of unemployed peoples, lack of job opportunity, decrease in land share, infrastructure and so on. The objective of this study aimed to examine the impact of rapid population on economic growth of Ethiopia country by employing Autoregressive distributed lag model for the time period spanning from 1975 to 2019. The variables used in model were, population, consumer price index, gross investment proxied by gross capital formation and trade openness as explanatory variables and RGDP proxy for economic growth used as dependent variable. To check stationarity properties of the data augmented dickey fuller unit root test was used and the result indicates all the variables are non-stationary at level and become stationary at first difference. Regarding cointegration test, ARDL bound test used to test the existence of long-run association among the variables and the result confirmed that there is long run relationship among RGDP and explanatory variables. The empirical result obtained from ARDL Model revealed that gross capital formation and consumer price index have found to be positive and statistical significant impact on RGDP in both short run and long run where as our variable of interest meaning population growth is negatively affecting real GDP in the short run but, in the long run it is found to be positive and statistical significantly affecting economic growth.

living. Population have a major barrier to alleviate poverty cycle, inequality and under growth of economic absorbing capacities of economy increases unemployment and migration of labor force. Population growth dampens economic growth and social transformation through capital shadowing effect that is reduction in capital per worker ratio, age dependence of young resulting in high consumption of food production, depleting saving and investment activity in the country (EEA, 2000).
Rapid population growth in developing countries especially in Ethiopia in the context of low technological advancement is exerting heavy pressure on natural resource and environment condition. The rising demand for food supply result from rapid population growth had led to the expansion of cultivation in to land, generally, unsuitable for crop production and animal husbandry. The traditional means of exploiting natural resource have to be environmentally harmed full and economically unproductive. Ethiopians cultivating system is mostly by traditional which leads to shortening of fallow periods and crop rotation that helped maintain soil fertility. This traditional means of cultivation have led to increase rate of erosion, but decrease agricultural production. High demand for new farm lands, for age for livestock and fuel wood and charcoal for cooking have contributed significantly to the massive reduction and destruction of forest and woodland resources (Befekadu.D and Birhanu, N, 2000).
The empirical analysis by Robert Barro (1991), shows that the increased resources devoted to child rearing instead of production contribute to the negative relationship between population growth rate and income per capita.
He used cross-country empirical study of virtually 100 countries. According to the finding population growth is likely to hamper growth in the first few decades of the 21 st century in Africa and parts of South Asia unless economic, population, and environmental policies adjusted. In contrary, Birdsall, Kelley, and Sinding (2003) found a positive relationship between population growth and per capita output growth among DCs.
Moreover, Klasen and Lawson (2007) identified a positive impact of population growth on economic growth.
They conducted the link between population, per capita growth and poverty in Uganda using both cross-section and panel data. Yet, Dao (2012) found the negative impact of population growth on output growth. This study was conduct in developing Countries by using the least-squares estimation technique in a multivariate linear regression. Afzal et.al (2009) also investigated the link between population growth and economic growth in Pakistan by employing simple linear regression model. The result show that population growth negatively impulse economic growth. From aforesaid empirical and theoretical literature one can comprehend that, the relation between population growth and economic growth might be negative or positive depending on countries economic status and demographic structure.

Types of data and source of data
Regarding data type, the study used secondary time series data for about 45 years obtained from internal and external sources. The selection of this sample size is made based on the availability of data for each of the variable included in the model for the entire time horizon while its sufficiency is taken into consideration as well. The major sources of data for the problem under investigation were Ministry of Finance and Economic Cooperation (MoFEC), publications of National Bank of Ethiopia (NBE), Central Statistics Authority (CSA) of Ethiopia, Ministry of Education and Ethiopian Revenue and customs authority (ERCA). In addition to these domestic Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855 (Online) Vol.11, No.15, 2020 5 sources, some variables for which there are no sufficient data from the domestic sources are collected from external sources, especially from IMF and WB databases.

Model specification
According to the third neo-classical growth model, output growth results from effective allocation of one or more of three factors: labor in terms of quantity and quality through population growth and education, increase in capital through saving and investment, and improvement in technology (Todaro, 1994: 86). The assumption of this model is that poor economies with lower values of capital and output tend to catch up with the initial rich ones. This model also assumes that population and technology as exogenously determined and production functions are assumed to satisfy the law of diminishing returns. Although the neo-classical growth model has its limitations in some aspects, it can be applied by some modification of population exogenous assumptions and is better for this study.
The standard neoclassical model of economic growth concerns rates on the Cobb-Douglas production function in the form of: Where: Y is total output, K denotes capital, L represents labor, A is total factor of productivity, is elasticity of output with respect to capital and β is elasticity of output with respect to labour But, according to the objective of the study, labor can be considered as part of population (not as special productive force). Therefore, labor is replaced by total population and equation (1) can be written as: Rather than taking the entire unexplained variable in the technology which is exogenously determined, including additional combination variables in the model that should be a proxy for technology is important because it makes the model more predictable and appropriate to know the accurate effects these variables on economic growth (Imoughele et al., 2013). Therefore, = + , the above equation can be rewritten as below when control variables are included; Where K is total capital stock proxied by gross investment as % of GDP and Pt is Total population proxy for population growth whereas Xt is a vector of control variables namely inflation and trade openness.

GDP = F (population, investment, inflation, trade openness)
Sinceall the variables under study were transformed into Log data so as avoid heteroscedasticity (Gujarati., 2004) and to show elasticity of the variables; the growth function of equation can be re-written as:- Where, GDP= real Gross Domestic Product POP= Total population

GCF= capital stock accumulation proxied by Gross capital formation
INF=Inflation proved by consumer price index Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855 (Online) Vol.11, No.15, 2020 6 TO= Trade openness which is the summation of Export + Import dived by GDP.
U= Disturbance term (factors that are not explained) t= time period

Unit Root Test
The necessary condition to be addressed for testing unit root test is to check whether the variables enter in the regression are not order two (I.e. I(2)). Therefore, running any sort of regression analysis is impossible without testing for time series variables. So, the first step in this study is testing unit root before running regression analysis.
The testing procedure for the ADF unit root test is specified as follows: Where is a time series variables which are mentioned above in this model at time t, t is a time trend variable; Δ denotes the first difference operator; is the error term; is the optimal lag length of each variable chosen such that first-differenced terms make a white noise. Thus, the ADF test the null hypothesis of no unit root (stationary) which is expressed as follows Regarding decision of unit root test, if the t value or t-statistic is more negative than the critical values, the null hypothesis (I.e. H0) is rejected and the conclusion is that the series is stationary. Conversely, if the t-statistic is less negative than the critical values, the null hypothesis is accepted and the conclusion is that the series is nonstationary. Failure to reject the null hypothesis of unit root test leads to take the test on the difference of the time series to come up out with stationary variable for analysis.

The Autoregressive distributed lag Model (ARDL)
There are numbers of advantages of using ARDL model also called 'Bound Testing Approach' instead of the conventional Engle-Granger two-step procedure (1987), Maximum likelihood methods of cointegration (Johansen, 1988) and Johansen and Juselius (1990).
First, the ARDL model is the more statistically significant approach to determine the cointegration relation in small samples as the case in this study (Pesaran et al., 2001;Narayan, 2004 Hence, ARDL model can be specified as: o Where the symbol  is the first difference operator; p, q, r, s, and v are the lag length with their Accordingly, with the existence of cointegration, the short run elasticities can also be manipulated through building the error correction of the series as stated the follows. Here all variables are as previously defined. The order of the lags in the ARDL Model is selected by either the Akaike Information criterion (AIC) or the Schwarz Bayesian criterion (SBC) automatically, before the selected model is estimated by ARDL model.    Vol.11, No.15, 2020

Test of Parameter Stability
The stability of the model for long run and short run relationship is detected by usingthe cumulative sum of recursive residuals (CUSUM) which helps as to show if coefficient of the parameters is changing systematically and the cumulative sum of squares ofrecursive residuals (CUSUMSQ) tests which is useful to indicate if the coefficient of regression is changing suddenly. Accordingly, if the blue line cross redline which is critical line and never returns back between two critical line, we accept the null hypothesis of the parameter instability whereas thecumulative sum goes inside the area (can returns back) between the two critical lines, then there is parameter stability in the short run and long run.

Long Run ARDL Bounds Tests for Co-integration
Since we determined the stationary nature of the variables, the next task in the bounds test approach of cointegration is estimating the ARDL model specified in equation (chapter 3) using the appropriate lag-length selection criterion. According to Pesaran and Shine (1999), as cited in Narayan (2004) for the annual data are recommended to choose a maximum of two lag lengths for small data because when the lag length increases the observation fail to show the appropriate long run relationship among variables because to show the long run relationship the number observation must be greater than 30.
As we discussed so far, the F-test through the Wald-test (bound test) is performed to check the joint significance of the coefficients specified in equation (ARDL equation chapter 3). The Wald test is conducted by Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855 (Online) Vol.11, No.15, 2020 10 imposing restrictions on the estimated long-run coefficients of POP, GCF, CPI, and TO. The computed F-statistic value is compared with the lower bound and bound critical values provided by Pesaran et al. (2001) and Narayan (2004)  Source; own computation from EViews 9.5 result, 2020 From the above table calculated F statistics (6.044841) is higher than both the Pesaran et al. (2001) and Narayan (2004) upper bound critical values at 1% level of significance. This implies that the null hypothesis of no long -run relationship is rejected; rather accept the alternative hypothesis (there is long-run relationship) based on critical values at 1% level of significance. Therefore, there is cointegration relationship among the variables in long run.

Long Run ARDL Model Estimation
After confirming the existence of long-run co-integration relationship among the variables, the next step is running the appropriate ARDL model to find out the long run coefficients, which is reported in table below. Source; own computation from EViews 9.5, 2020 Note: the sign *, ** and *** indicate that the variables are significant at the level of 1%, 5% and 10% respectively. The responsiveness of GDP toward the change growth capital formation (investment) is 0.49016 which is Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855(Online) Vol.11, No.15, 2020 11 statistical significant to affect the economic growth. The coefficient reveals 1% increase in growth capital formation leads increase GDP by 0.49016 in the country economy. The positive responsiveness of this relationship leads high employment creation, higher income level which followed to higher aggregate demand of goods and services. Aggregate demand automatically increases because of expanded investment and employment. Therefore finally, the economy experienced by increased GDP.
The other significant determinant of GDP is inflation (consumer price index). The responsiveness of GDP to the change in inflation is 0.77914. Meaning that 1% increase in inflation leads GDP to increase by 0.77914. A rise in the inflation since it have a positive response to the increases in Real GDP, in turn lead to increase in the country money supply, investment, national income and aggregate demand. However, the long run responsiveness of GDP to the change in trade openness (export + import) has positive relationship but insignificantly affect Ethiopia's GDP.

Short Run Error Correction Model
After the acceptance of long-run coefficients of the GDP equation, the short-run ECM model is estimated. The error correction term (ECM), as we discussed in chapter three, indicates the speed of adjustment to restore equilibrium in the dynamic model. It is one lagged period residual obtained from the estimated dynamic long run model. The coefficient of the error correction term indicates how quickly variables converge to equilibrium.
Moreover, it should have a negative sign and statistically significant at a standard significant level (i.e. p -value should be less than 0.05) This is because at this stage they do not produce anything to add up to GDP growth but rather consume what already exist. The empirical result is consistent with Razin and Sadka (1995) who reported a negative relationship between population growth and economic growth. The empirical result again corroborates with Dao (2012) who revealed that population has negative impact on economic growth.
If the variables are cointegrated, their dynamic relationship can be specified by an error correction representation in which an error correction term (ECT) computed from the long-run equation must be incorporated in order to capture both the short-run and long-run relationships (Engle and Granger, 1991). The error correction coefficient, estimated at -0.22 is highly significant, has the correct negative sign, and implies a very high speed of adjustment to equilibrium. Moreover, the coefficient of the error term implies that the deviation from long run equilibrium level of GDP in the current period is corrected by 22% in the next period to bring back equilibrium when there is a shock to a steady state relationship.

Conclusion and policy implication
The general objective of the paper was stressed to assess the determinant and over all issues of rapid population growth and its impact on economic growth in Ethiopia. The variables used in model were, population, consumer price index, gross investment proxied by gross capital formation and trade openness as explanatory variables and real GDP proxy for economic growth used as dependent variable. To check stationarity properties of the data augmented duller unit root test was used and the result indicates all the variables are non-stationary at level and become stationary at first difference. Regarding to cointegration test, ARDL bound test used to test the existence of long-run association among the variables and the result confirmed that there is long run relationship among real GDP and explanatory variables. The empirical result obtained from ARDL Model revealed that population issue is very controversial because although it has negative impact in the short run, implication is positive in the long run as we have seen. The short run implication explains that large number of economically inactive people with high growth rate of population depresses the GDP growth of the country whereas economy can adjust in the long run and absorb existing people as labor force and that the burden of population can be avoided so that people can play as active actor of economic development of the country.
As obtained from the result, high rate of population growth has held per capita GDP of the country at low level in the short run. Therefore, government should reduce rapid population growth in the country through well conducted population policy that can address the main population growth impact through successfully accomplish of plans such as; expanding job opportunity, social service distribution, infrastructure facilities, proper utilization or mobilization of resource, protection of environment and reduction of rural-urban migration.
Moreover, Government should motivate participation of private and NGOs investment by creating better conducive environment for investment to expand more job opportunity, to increase production of good and services, to reduce dependence ratio and unemployment, increase per capital income and improving living standard of the society.