Cobb Douglas production function

A Cobb Douglas production function is expressed in a non-linear form as 2:

Where EC is the consumption of industry and construction sectors in the year t; G, I, X, and P are represented for the GDP of industry and construction sectors, income per person (US$/person), proportion of industry and construction sectors’ electricity consumption in total, and electric tariff in the year t, respectively. The technological parameter is indicated by φ; β are returns to scale linked with the four variables.

A logarithmic transformation is applied for two sides of the equation (1) to linearize it to become a linear form as:

Testing

In other to evaluate the accuracy of econometric model, many testing methods have been recorded. Testing methods are computed with aims to maximize the accuracy and reliability of forecasting equation. For those researches proving the causality between variables, the date in time series should be tested the stationary (Augmented Dickey Fuller (ADF) or Phillips-Perron (P-P)) to avoid the spurious regression. After stationary test, the causality between variables is proven by using Granger causality test. For forecasting purpose, stationary test only is enough.

Stationary test

In order to ensure the sustainability of this study, two unit root test namely ADF and P-P are employed to test the stationary of prediction function. They are employed to avoid the spurious regression or non-sense regression when applying regression algorithm onto a non-stationary time series data. If there are some non-stationary series, to solve the problem, the first difference (Δ) of the series is done, then eliminating inappropriate variables. If all series are non-stationary, it leads to take the first difference of all variables, then removes the primary features of the series. However, it leads to the low R in regressing. The low R means the low accuracy of the prediction. To avoid the low of R, co-integration test is conducted.

Cointegration test

Engle and Granger (1987) 8 supposed the linear combination between non-stationary time series can be a stationary series and these non-stationary time series are co-integrated. The non-stationary linear combination is called co-integration equation and can be explained as the balance relationship between variables in long-term. Therefore, if variables co-integrate, the regression can be conducted. In this article, Johansen trace test is utilized to test the co-integration. In the Trace test (T-test), there are some hypotheses H listed as follow: “None”, means there is no co-integration; “At most 1; 2; 3…”, means there is 1, or 2, or 3 co-integrations. To decide if we should reject or accept hypothesis H, Trace Statistic value and Critical Value of 5% are compared. If Trace Statistic < Critical Value, accept H; if Trace Statistic > Critical Value, reject H.

R test (R square) and p-test

R plays an important role to evaluate the impact of dependent variables to independent variables. The condition to choose the impact factors of function is that R is approximately 1. For example, if the value of R is 0.997953, then it means that 99.8% dependent variables have impact on independent ones. However, in order to decide if any independent variable is needed to function, then a p-value test must be conducted. The condition to choose the value of p-value is p-value ≤ 0.05. If any independent variable has its p-value bigger than 0.05 (p > 0.05), then that variable must be eliminated and testing process must be iterated to get higher accurate forecasted results.

MAPE test

Beside the stationary and co-integration test, a feasibility test based on historical time-series data of prediction function will be conducted by employing a Mean Absolute Percentage Error (MAPE) method to measure the accuracy of prediction. It has a fact that a relative error of a forecast can be measured by a MAPE, which could be expressed as:

Where A is recorded consumption of the year n; F is forecasted consumption of the year n. It is noted that MAPE has an opposite principle with R as a lower computed MAPE will lead to higher reliable prediction, while a higher R could act the same meaning. MAPE is launched in this paper to evaluate the accuracy of forecast function and to compare with tolerance indicator values.

Forecasting

After building a standard function for predicting the electricity consumption of Vietnam industry and construction sectors, variable data and its corresponding historical data will then be obtained to import to the function. The consumption demand of Vietnam industry and construction sectors in the year 2020, 2025, and 2030 will be forecasted correspondingly afterward.

Data

GDP of industry and construction sectors

Vietnam is remarked as one of the most rapid growing countries in the world with the GDP growth rate at about 6.5%/year in recent years; in which industry and construction sectors is the biggest contributor with the GDP growth rate is still maintained at a higher rate than the GDP of the entire economics. In 2011, the GDP growth rate of industry and construction sectors reached 6.68% while the value of the national economics is recorded at 6.24%; corresponding values in 2012 are 5.75% and 5.25%, 5.5% and 5.4% in 2013. The average values of the last three years are 6% and 5.4%, correspondingly. There are three growing scenarios for Vietnam’s GDP to 2035 have been released; in which the GDP growth rates in the low scenario are forecasted to reach 6.5%/year in 2016-2025 and 6%/year from 2026 to 2035 9. These results are closely similar to forecasted growth rate of electricity consumption demands which are released by the Revised version of Master Plan N0. VII for Power System in Vietnam (PDP.VII rev.) 9. This similarity can be used to demonstrated that GDP and electricity consumption demand could have a somehow correlation. The GDP data of industry and construction sectors will be cited from the PDP.VII rev.

Income

Income per person and person’s electricity demand are confidentially believed to have a linear relation as the increase of person’s incomes will lead to the higher needs of electric appliances and corresponding consumptions to improve the living conditions. For example at a low income condition, air conditioner and electric water heater could be dispensable. However, when the income is improved on enough to cover a high-cost electric bill, then they might be purchased to meet the demand of the house owners. It definitely leads to the more pressure on electric supply conditions. Therefore, the person’s income is launched as an essential variable of forecasting model in this paper to quantify its relation with electricity demand 10. The income per capita data will be collected from World Bank data source 11.

Proportion of industry and construction sectors’s electricity consumption in total

The 2017 report of EVN highlighted a rapid increase of proportion in total of electricity consumption needed for the industry, and construction sectors. It has been recorded to increase from 46.7% in 2005 to 51.9% in 2010, and to 54.77% in 2015. Also, it is remarked that the growth rate in the duration of 2010-2015 is lower than the ones recorded in the previous duration (2005-2010). However, the industry and construction sectors are still acting as the leading sector and contribute at a highest level in comparison with other sectors in economics. Data relevant to proportion of electricity consumption of industry and construction sectors are be referred from the PDP.VII rev.

Electric tariff

Electric tariff is an essential condition which impacts directly on every production in economics. In other words, electric tariff plays as a major input manufacturing cost of all sectors in economics. A number of studies on the impacts of electric tariff onto consumption behaviors have already been deployed in the last decades. However, it is really difficult to get an unanimity between those studies as the tariff policy is differed from countries to countries. Vietnam’s electric tariff is identified as the lowest fare level in region and worldwide. Data involving national electric tariff will be obtained from EVN’s database 9.

Collecting data in time series of 1990 to 2015

After analyzing factors which could make influence on the electricity consumption of industry and construction sectors in Vietnam, then the historical records of those factors are assembled from various database sources. The more sufficient, reliable and long enough data, the more accurate forecasted results are. With a given time series data and k represents for an independent variable of prediction model, then (n – k) > 2012, 13.

In this paper, GDP of industry and construction sectors, the proportion of industry and construction sectors in entire economics, income of person, and electric tariff will be brought into forecasting model as independent variables. Four independent variables will lead to n > 20 + 4.

In this paper, historical data from 1990 to 2015 are assembled and constructed as a time series order. This selected 26 values (equivalent to 26 years) time series is relatively long enough to be tested. The collected data are shown in Table 1.

Converting variables into natural logarithms

The input time series data will be converted into natural logarithm forms. Converted results are shown in Table 2.

Testing

Stationary test

A stationary test is conducted to test the stationary characteristics of data. Results shown in Table 3 indicate that all variables are non-stationary. As shown in Table 3, the p-value of almost variables are higher than α (α = 0.05). The only variable has the p-value of lower than 0.05 is the GDP of industry and construction sectors [ln(G)]. As all variables are non-stationary, a co-integration test will be employed to be conducted instead of computing a first difference calculation.

Co-integration test

Results of co-integration test are performed in Table 4. The T-test results indicate that there are only four co-integration variables at the value of 0.05. It is corresponding to the four mentioned non-stationary time series data.

R and p-value testing

After conducting co-integration test, the coefficients of equation (2) are computed. Calculated results are performed in Table 5. The condition for choosing the coefficients of equation is that the R value is approximately 1 and p-value of all variables are less than 0.05. Table 5 shows the value of R testing of 0.992581. It means that 99.3% of dependent variables have impacts on independent ones. However, as p-value of lnP is above 0.05, lnP is eliminated. Then all coefficients of equation will be recalculated in second time. Recalculated results are shown in Table 6; in which p-value of all variables are less than 0.05.

Eliminating inappropriate variables

As lnP is eliminated, the equation (2) become:

With β, β, β, and β are -5.05, 0.372, 0.623, and 1.864, respectively. Then the equation (4) becomes:

That equation (5) is the qualified equation for forecasting.

Comparison to historical data and evaluating MAPE

The equation (5) is launched to recalculate the electricity consumption in the past. Results are brought into a comparison with historical data to evaluate the accuracy of forecasting. Then a MAPE testing is applied with results are shown in Table 7. It is realized that the MAPE has a value of 7.66%. This value is noticeable as it is much lower than usual MAPE errors for long-term forecasting 14. Therefore, if there is no significant fluctuation in economics and society, then the equation (5) could be a feasible forecasting tool for national power system.

Forecast on electricity consumption of industry and construction sectors to 2030

Forecasted value of GDP of industry and construction sectors, proportion of industry and construction sectors in entire economics, and income per capita of Vietnam to 2030 are collected and listed in Table 89. As mentioned processing, those data will be converted into its corresponding natural logarithms.

Then the equation (5) is applied to forecast the electricity consumption of Vietnam’s industry and construction sectors in the future. Forecasted results are shown in Table 9.

The results show that: (1) in the low scenario, the electricity demand of the industry and construction sectors will reach 111,039 GWh, 167,945 GWh, and 227,634 GWh in 2020, 2025, and 2030, respectively; (2) the forecasted values of the base scenario are 112,853 GWh in 2020, 172,691 GWh in 2025, and 242,027 GWh in 2030; and (3) the corresponding predictions for high scenario in 2020, 2025, and 2030 are 115,947 GWh, 181,591 GWh, and 257,272 GWh, respectively. The vaules in high scenario in this study are less than from 9.0% to 15.8 % of that of the based of in the Revised version of master plan N0. VII 9.