Econometric Modelling of Solid Waste Generation in Jordan

The objective of this study is to develop an econometric model that might help decision-makers to imply better policies based on the information about key factors influencing the amount of waste generation in Jordan. We found out that the most informative factor is the level of consumption which is correlated with the number of population and gross national income. Consumption culture itself rather than the population growth stimulates waste production. In order to reduce the level of waste generation, it is necessary to move from an unreasonable culture of unrestrained consumption to a reasonable and responsible attitude to the resources of the country and the environment as a whole. It is also necessary to introduce modern waste management methods, develop technologies for waste recycling and reuse.


Introduction
To plan the proper solid waste management (SWM) system, it is essential to know the amount of waste produced in the country. Knowing the amount of waste allows authorities to understand the scale of the problem and put forward appropriate plans. It also provides SWM organizations with the opportunity to optimize their investments to buy new machinery for recycling facilities, equip transition stations, evaluate disposal capacities of landfills and plan other sanitarian measures for the future. The objective of this study is to develop an econometric model that might help decision-makers to imply better policies based on the information about key factors influencing the amount of waste generation in the country. We try to find out the most significant variables explaining the current situation in Jordan and to develop an econometric tool for prediction the amount of waste produced.

Literature review
Increasing income and economic growth influence the rate of solid waste generation. Hockett et al. (1995) discovered that income is an important factor in solid waste generation. Chung (2010a) also found out that the level of income of individual waste generators is a variable that usually has no reliable source of data. To obtain the permission to collect these data is generally complicated. Thus, other approaches should be utilized instead. Joutz (1996) used the ratio of two economic indices computed at the national level so as to approximate the real incomes. Bach et al. (2004) and Gay et al. (1993) found that the level of employment can be a good factor to predict commercial waste. Samson et al. (2017) suggest that GDP and population are the two compelling factors affecting municipal solid waste generation. They conclude that without an in-depth understanding of the variables affection waste generation waste reduction policies may be ineffective and unsuccessful. Afroz et al. (2010) found out that the waste generation of the households is significantly affected by the concern about the environment, income, household size and willingness to separate the waste.
Alongside with economic factors, changes in social variables may influence waste generation levels. For example, change in population numbers and household size. In the article of Abdoli & Falahnehzad (2011), similar to the study of Dennison et al. (1996b) and Beigl et al. (2004Beigl et al. ( , 2008, the average household size and the municipal solid waste have a reverse relationship. Population and household size are highly correlated. Thus, for preventing multicollinearity, Abdoli & Falahnehzad (2011) select population for the model estimation. McBean & Fortin (1993) has also considered population as one of the most important variables affecting total waste generation rate.
Some authors analyzed the impact of consumption factors on the generation of municipal solid waste (Liu et al. (2019); Lu et al. (2017); Mahees et al. 2011;Hage et al. 2018). The results showed that developing regions generate more waste than developed regions. Thus, different regions have to control waste levels by optimizing consumption pattern, as well as to implement best experience of developed regions. Many scholars also use socioeconomic and demographic data to model solid waste generation (Trang et al. 2017;Bosire et al. (2019); Prades et al. 2015;Chhay et al. 2018;Khan et al. 2016).

Variables
The data set for this study is an annual time series for the period 1991-2018. It consists of the following variables (World Bank data):  popurb -urban population (Note 1);  poprur -rural population (Note 2);  pop -total population computed as aggregation of urban and rural population;  gni -gross national income (current US $) (Note 3);  gnicap -gross national income per capita (current US $) (GNI per capita, Atlas method, current US$);  cons -final consumption expenditure (current US $) (Note 4);  conscap -household consumption expenditure per capita (constant 2010 US$);  empagr -employment in agriculture (% of total employment);  empind -employment in industry (% of total employment);  empserv -employment in services (% of total employment);  wasteurb -waste produced in urban areas (tone/year) computed as follows (Note 5): = • 0.99 * 365/1000  wasterur -waste produced in rural areas (tone/year) computed as follows: = • 0.87 * 365/1000  waste -total waste computed as aggregation of waste in urban and waste in rural areas (tone/year).

Research plan
First, in this study a panel data set with selected socio-economic indicators for Jordan is created. The importance of the input variable depends on the linear correlation coefficient (r). Thus, second, we compute linear correlation coefficients and create visualizations of the relationship between selected economic variables: scatter plots and bubble charts. Third, regression analysis is conducted. Several econometric models for solid waste generation are estimated with the help of the ordinary least-squares (OLS) method. Then, based on statistical criteria, the best fitted model is chosen, and every input variable is given an interpretation. Tests for multi-collinearity, heteroscedasticity and autocorrelation are fulfilled. Forth, time series analysis is conducted. We detect whether our time series is a stationary process, then conduct auto simulation in R/R-Studio. Projections for waste generation until 2043 are made. Finally, conclusions are made.

Descriptive statistics
There are numerical characteristics of selected variables represented in Table 1. Source: Author's computation in R-Studio (R-script is in Appendix).
The Table 1 shows that minimum waste value corresponds with minimum values of population, GNI and consumption, as well as maximum value of waste corresponds with maximum values of population, GNI and consumption. This is also approved by high values of linear correlation coefficients between waste and population (0.99) (Figure 1   The visualizations show that relationships between mentioned variables are strictly deterministic.
There are bubble charts for two numeric variables evaluated by the third numeric variable representing the size of the bubble. Figure 4 shows the relationship between waste in urban and rural areas evaluated by population. The visualization shows that for 14 years, since 1991 to 2004, the relationship between volumes of waste in urban and rural areas was positive: both variables rose. For the next 11 years, since 2004 to 2014, the relationship was negative showing that the amounts of waste produced shifted to urban areas alongside with the population growth. Since 2014 we observe slow increase in volumes of waste both in urban and rural areas.  Visualization in Figure 5 matches visualization in Figure 4 which is explained by high value of a linear correlation coefficient between population and consumption. The visualization shows that for 14 years the relationship between volumes of waste in urban and rural areas was positive: both variables rose. For the next 11 years the relationship was negative showing that the amounts of waste produced shifted to urban areas alongside with the high consumption growth. Since 2014 we observe slow increase in volumes of waste both in urban and rural areas. The further in time the higher values of consumption which we consider the cause of high volumes of waste generation.

Model selection
While selecting a better model we base upon the following features of a "good" model: out of two models, reflecting the reality approximately similarly, a simpler model, with a fewer number of variables, is chosen; beta-Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855 (Online) Vol.11, No.16, 2020 estimators must be unique, i.e. have a single meaning; model is admitted to be better if it may explain more variance of a dependent variable (in comparison with other models), and the model with a higher value of R-squaredadjusted is selected; model is qualitative if it is acknowledged by real data, i.e. it has good prognostic qualities.

Econometric tests
First, we test a hypothesis for some linear restrictions simultaneously. The null hypothesis (H0) implies that the whole regression is insignificant. The alternative hypothesis (Ha) implies that at least one of β-coefficients is significant (non-zero) so the whole regression is considered to be significant. The null hypothesis is verified with the help of the Wald test based on the algorithm of the F-test (Table 4). The Wald test shows that even though some coefficients significant and some are not (Table 2), regression models 3 and 4 are significant. At 5 % level of significance null hypothesis is rejected (p-values are close to zero for all regressions). Thus, at least one of the β-coefficients is not equal to zero, and omission of coefficients is not reasonable (Note 7).
If we have observations, then, in order to verify whether significant variables were omitted or not, we use F-test Thus, second, we verify whether we have omitted regressors in the model, for which we don't have observations. The null hypothesis (H0) implies that the model is correct: we included exactly those variables that must have been included. There are not any omitted regressors. The alternative hypothesis (Ha) implies that there are unknown omitted regressors. The null hypothesis is verified with the help of Ramsey (RESET) test (Table 4). The results of computations show that for four alternative models p-values are much higher than the 5 % level of significance. Thus, null hypothesis is not rejected. Regression models don't contain omitted informative variables.
Third, also a possible problem of multi-collinearity (linear relationship between explanatory variables) has to be taken into account. Even though it does not affect the standard set of OLS-assumptions, in particular the Gauss-Markov theorem (beta-coefficients are still unbiased and asymptotically normal, we can test hypothesis and construct confidence intervals), standard errors of beta-estimators become very large. Thus, we may get an over fitted model which is not statistically robust, i,e, it does not predict reliably across numerous samples. In order to check the presence of multi-collinearity variance inflation factors (VIF) are computed for every estimated model (Table 5). When > 10 there is potentially an indication of multi-collinearity in the model. Source: Author's computation in R-Studio (R-script is in Appendix).
We don't consider multi-collinearity in the Model 1 because it is a simple linear regression. The Model 2 shows high multi-collinearity: values of population, consumption and GNI are highly linearly correlated. The results of calculations for the Model 3, presented in exponential format, also indicate high multi-collinearity. The Model 4 also demonstrates high multi-collinearity. In such cases it is recommended to drop one of the correlated explanatory variables out of the model keeping in mind that we miss some information and beta-estimators for remained correlated variables become biased. In terms of multi-collinearity the Model 1 is the best. Additionally, it has high values of coefficient of determination (Table 3) and satisfactory results in Wald-and RESET tests. At this stage the Model 1 is considered to be the first-best.
Forth, the presence of heteroscedasticity (variance of residuals is not constant for every observation) in the model has been verified ( Table 4). The null hypothesis (H0) in the Breusch-Pagan test implies that there is no heteroscedasticity in a model. Since p-values for the Model 1 and the Model 2 are high (more than = 10%), then null hypothesis is not rejected. These models do not have a problem of heteroscedasticity of residuals. Betacoefficients are unbiased, consistent and efficient. The Model 3 and the Model 4 have a problem of heteroscedasticity (p-values are less than the 5 % level of significance, usual for economic studies). Betacoefficients are still linear and unbiased but not efficient, even asymptotically. As a consequence, all statistical inferences based on t-and F-statistics above, as well as confidence intervals, are unreliable. Therefore, they are not applicable for construction of adequate models. At this stage we may exclude the Model 3 and the Model 4 from consideration.
Fifth, the presence of autocorrelation (whether residuals are correlated between observations) in the models has Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855 (Online) Vol.11, No.16, 2020 been checked. For this purpose, Durbin-Watson test for the autocorrelation of the first order has been fulfilled ( Table 4). The Durbin-Watson test showed that there is autocorrelation of the first order in every alternative model (p-values are less than the level of significance, so null hypothesis on absence of autocorrelation is rejected). This outcome is quite logical because we deal with time series.
All conducted econometric tests show that the regression Model 1 is the most adequate to the data. The volume of waste produced is the most explained by the level of consumption. Consumption culture itself rather than the population growth stimulates waste production. In order to reduce the level of waste generation, it is necessary to move from an unreasonable culture of unrestrained consumption to a reasonable and responsible attitude to the resources of the country and the environment as a whole (Alhanaqtah 2020a(Alhanaqtah , 2020b. It is also necessary to introduce modern waste management methods, develop technologies for waste recycling and reuse.

Time series analysis
In this section we will try to predict waste generation for the next 25 years since 2018. First, we test a time series for the variable "waste" for stationarity. Visualization of a time series in the Figure 6. We see that our series takes a compromised position between stationary and non-stationary processes. Autocovariance function (ACF) is decreasing but no that quick as it takes place in an ideal stationary processes. The first PACF is non-zero, other PACFs are equal to zero (Note 8). In other words, PACF plot has a significant spike only at lag 1, meaning that all the higher-order autocorrelations are effectively explained by the lag-1 autocorrelation. This is the graph of a typical random walk with drift. In order to be certain of that, let's take differences, i.e. build the same parameters for ∆ . The outcome of the command ndiffs() in R shows that 2 differences is required to make this process stationary.
In the Figure 7 we see that the autocorrelation falls to zero fairly quickly which is typical for a stationary time series.
Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855 (Online) Vol.11, No.16, 2020 213 It means that our initial series is a non-stationary process with drift.
In order not to simulate at random we may request R-Studio to choose the model with minimum AIC out of the models with a few lags. In other words, we can choose the better model on ACAICE criteria automatically via auto-simulation command auto.arima(). The outcome of the command shows that our process is ARIMA(2, 2, 0). The time series for "waste" is non-stationary.
Additionally, in accordance with the Model 1 we compute cross correlation between two time series: waste and consumption ( Figure 8). We may conclude that levels of waste and consumption change together in one direction with no shift in time.
Journal of Economics and Sustainable Development www.iiste.org ISSN 2222-1700 (Paper) ISSN 2222-2855 (Online) Vol.11, No.16, 2020 214 The forecast by the auto-simulation is in the Figure 9, where grey line is actual numbers, blue line is forecasts, grey interval is 95 % limits. The model predicts that the level of waste in Jordan will increase in the nearest 25 years (Table 6). The forecasts for the model show a linear upward trend projected into the future. The trend in the long-term forecasts is due to fact that the model includes two non-seasonal differences: this model is basically a random walk with growth fine-tuned by the addition of two autoregressive terms, i.e. two lags of the differenced series.

Conclusion
All conducted econometric tests show that the volume of waste produced in Jordan is the most explained by the level of consumption. Consumption culture itself rather than the population growth stimulates waste production. In order to reduce the level of waste generation, it is necessary to move from an unreasonable culture of unrestrained consumption to a reasonable and responsible attitude to the resources of the country and the environment as a whole. It is also necessary to introduce modern waste management methods, develop technologies for waste recycling and reuse.
Projections for waste generation until 2043 are given with the help of ARIMA (2, 2, 0). The forecasts show a linear upward trend projected into the future.