DEMAND FORECASTING Lecture-6.pptx, econometric model

The document talks about econometric demand forecasting method and input output model

1. ENERGY ECONOMICS – LECTURE 6 PRADIP CHANDA

2. ECONOMETRIC FORECASTING MODEL A  log - linear  model is a mathematical model that takes the form of a function whose  logarithm  equals a  linear  combination of the parameters of the model, which makes it possible to apply (possibly multivariate)  linear  regression. Let us draw some energy model on this Let E is energy consumption, Y is income (GDP), P is price, POP is population, EMP is employment of labour , a, b, c, d, e, f, - are coefficients to be determined through the estimation process, t is the Time period t while t-1 represents the time period before t. Then (a) Linear relation between energy and income (GDP) is E t = a + bY t (b) Log-linear specification of income and energy ln E t = ln a + b ln Y t (d) Log-linear specification of income, price and energy ln Et = ln a + b ln Yt + c ln Pt

3. ECONOMETRIC FORECASTING MODEL (e) Dynamic version of log-linear specification of energy with price and income variables lnE t = ln a + b ln Y t + c ln P t + d lnE t-1 (f) log-linear model of price and other demographic variables lnEt = ln a + b ln Pt + c ln EMPt + d lnPOPt (g) log-linear model of energy, price, income, fuel share and economic structure variables lnEt = ln a + b ln Pt + c ln Yt + d ln Ft + e ln St (h) dynamic version of the above model lnEt = ln a + b ln Pt + c ln Yt + d ln Ft + e ln St + f ln (Et-1)

4. ECONOMETRIC FORECASTING MODEL ( i ) linear relation between per capita energy and income Et/ POPt = a + b Yt / POPt (j) Log linear relation between per capita energy and income ln(Et/ POPt ) = ln a + b ln ( Yt / POPt ) (k) log-linear relation between energy intensity and other variables ln(Et/ Yt ) = ln a + b ln Pt + c ln Ft + d ln St (l) Dynamic version of log-linear energy intensity relation ln(Et/ Yt ) = ln a + b ln Pt + c ln Ft + d ln St + e ln (Et-1/Yt-1) b= short run income elastic, c= short run price elastic Long run income elastic = b/(1-d), Long run price elastic = c/(1-d) The error in forecasting can be given by root mean square error = forecast, = actual, T = number of periods  

5. EXAMPLE Table 3.9 presents the annual per person gasoline consumption, per person GDP and gasoline prices for Iran between 1980 and 2005. Using a simple specification, analyze the gasoline demand econometrically.

6. EXAMPLE We use the demand model shown below.

7. EXAMPLE Result is tabulated below.

8. ENERGY DEMAND ANALYSIS- DISAGGREGATED LEVEL PRADIP CHANDA

9. Disaggregation of demand When energy demand is split into a number of sector like industry, transport, residential, commercial, agricultural etc. then it is said to be disaggregated. Within each sector further disaggregation may be done to enhance homogeneity in demand behaviour

10. Disaggregation of demand The level of disaggregation is decided based on the availability of data required for the analysis, importance of the activities of a sector and subsector and the purpose of the study. A separate set of accounts called sectoral energy accounts are created for this

11. Sectoral Energy Accounting Sectoral energy accounts attempts for an overall picture of the energy balance by finer details of the consumption and demand pattern.

12. Disaggregation in Energy intensity The level of disaggregation affects the results of decomposition. The more disaggregated the group, the more relevant and reliable is the measurement. In such a case, the extension of the basic energy intensity equation takes the following form: where eij = energy consumption in subsector j of sector i ; Qij = activity of subsector j in sector i ; SEIij = sub sectoral energy intensity in subsector j of sector i ; SSij = sub sectoral share of subsector j in sector i . Other variables have same meaning as before.

13. Disaggregation in Energy intensity Differentiating the Equation we get where Si = sectoral share at the overall level; sij = subs ectoral share of sub-sector j in sector I; Wi = weight at the sectoral level; wij = weight at the sub sectoral level; EIij = energy intensity of sub-sector j in sector i . Equation can be rearranged as Integration of the Eq. between 2 years in discrete form results: The first term measures the structural effect at the upper level (i.e. sectoral level), the second term measures the intra-sectoral structural effect and the third term measures the intensity effect (which is also called the real intensity effect).

14. Energy Demand forecasting – Input Output model Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 = Industry 2 = ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n = Total output Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 Industry 2 ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n Total output Assumptions Each industry produces only one homogeneous commodity Each industry uses a fixed input ratio for production of its output Production in every industry is subjected to constant return ( if input increases, output also increases) Output for each industry is worth of a rupee

15. Energy Demand forecasting – Input Output model Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 = Industry 2 = ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n = Total output Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 Industry 2 ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n Total output Now production of each unit of jth [the first subscript refers to input and the 2 nd out put] commodity will require a 1j amount from first industry, a 2j from 2 nd industry …… a nj from nth industry known as input coefficient. For n-industry economy, the input coefficient can be arranged into a matrix A = [ aij ] in which each column specify the input requirement for the production of one unit (say equivalent to one rupee) of the out put of a particular industry. If no industry uses its own product as an input, then the element in the principal diagonal of matrix A will be zero.

16. Energy Demand forecasting – Input Output model Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 = Industry 2 = ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n = Total output Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 Industry 2 ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n Total output The model also contains an open sector (say house hold or government) which exogenously asks for a final demand (non-input demand) for the product of each industry/ which supplies a primary input not produced by the ‘n’ industry themselves, then the model is known as open model. If industry 1 is to produce an output just sufficient to meet the input requirement of the ‘n’ industries as well as final demand of the open sector, its output x1 must satisfy

17. Energy Demand forecasting – Input Output model Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 = Industry 2 = ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n = Total output Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 Industry 2 ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n Total output X 1 = a 11 x 1 + a 12 x 2 + ……………a 1n x n + d 1 . The equation can be re-arranged to (1-a 11 )x 1 – a 12 x 2 – a 13 x 3 ……..- a 1n x n = d 1 . Similarly -a21x1 – (1-a22)x2 …………….-a2nxn = d2 ------------------------------------------------------ -an1x1 – an2x2 ………………….(1-ann) xn = dn In matrix notation

18. Energy Demand forecasting – Input Output model Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 = Industry 2 = ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n = Total output Input output Industry 1 Industry 2 ----Industry n Consumer demand Total input Industry 1 Industry 2 ------------------- --------------- --------------- --------------- ------------------ -------------------- Industry n Total output Let 1’s in the diagonal matrix ignored. The new matrix will be -A = [- aij ] Therefore the above matrix is sum of a identity matrix I and the matrix –A. Thus the above matrix can be written as (I-A)x = d or x = (I-A )-1 d  

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