Brazilian Electricity Demand Estimation: What Has Changed After - - PowerPoint PPT Presentation

Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001?

An Application of Time Varying Parameter Error Correction Model Amanda Pimenta Carlos Hilton Notini Luiz Maciel

Getulio Vargas Foundation Graduate School of Economics

June, 2009.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 1 / 32

Introduction

First of all, it is necessary to de…ne the equilibrium in this market and why we are justi…ed in estimate only the demand side. Hydroelectricity accounted for 19% of total electricity consumed around the world in 2005. Speci…c situation: Brazil is the third country (only behind China and Canada) in hydro power installed capacity and a share of 85% of electricity in Brazil come from dams. The annual demand do not reach 50% of installed capacity. Construction of a Hydroeletric power plant of medium size requires not less than …ve years. So, analysts say that the estimate of Brazilian electricity demand drives the future investments in the sector and the supply growth.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 2 / 32

Introduction

Stylized Fact: Installed capacity expansion after reestructuring in 1994. An important issue of the electricity sector planning is understanding electricity demand, its main determinants and its answer to speci…c shocks on its exogenous variables. There are some estimates for Brazilian electricity demand parameters, using the Cointegration and Vector Error Correction Model (VECM) approach that became the standard method for electricity applied research in demand topic since the seminal works of Engle and Granger (1987 and 1989)...

...but all of them are for a period that exclude the severe power rationing crisis,

• ccurred in 2001.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 3 / 32

Contribution to Literature

With the present paper we search to …ll some blanks in the Brazilian energy economics literature:

1

To our knowledge, there isn’t a paper, applied to Brazilian data, that tests structural break in an estimated electricity demand, with a period including the 2001 power rationing.

2

Besides, there is no work that evaluates the demand equation coe¢cients dynamics. Maybe there is a variation in the elasticities in the analyzed period.

3

Inclusion of determinants (explanatory variables) commonly used in international electricty demand estimation - like temperature, in residential demand (seasonality).

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 4 / 32

Motivation

Castro & Rosental (2008) say that a change in the level of Brazilian electricity elasticity is in process, due to a more rational and e¢cient use of the input, specially by industrial consumers, that has been utilizing methods and energy saving equipments, after the 2001 rationing. Last year we saw in Brazilian data: GDP growing 3.7%, but electricity demand increasing less than expected, only 3.4%. Why? Residential - There isn’t an obvious trend to residential consumption. On the one hand, consumers are buying energy-e¢cient appliances, but on the other hand - according to EPE - more and more houses have refrigerator and television. Furthermore, an increasing share of consumers are living alone and we see population aging. Both counteract the e¢ciency gains.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 5 / 32

Motivation

Industrial - Eletrobras data shows that industrial consumption has been in‡uenced by self production growth. In the siderurgical sector, self production has increased more than 40% from 2005 to 2007; the self production represented 28% of total consumption in 2005 and 37% in 2007. Energy-intensive sectors: Steel, aluminium, cement, petrochemical, paper &

• cellulose. From 2008 to 2017, EPE estimates that self production will increase 11%

each year. From 1991 to 2007, self production have had a 8% rate of increase. Industries invest in their own plant to avoid power and prices instabilities. According to Abiape, the installed capacity from associate self producers is of 7 GW, or 7% of total Brazilian installed capacity.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 6 / 32

Update of Brazilian Demand Equation Estimation

Results update; su…ciently relevant period after Rationing Crisis. Inclusion of variables like temperature and credit (important in the Brazilian recent economic context); Methodology never used; allows to test the dynamics in the short-run elasticities. Structural Break Test - not yet applied to Brazilian electricity demand.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 7 / 32

Data

Monthly data from January 1999 to December 2007. Sample size at least the double of others Brazilian applications. In table 1, we see our variables.

Variable Name Source Residential Demand (MWh) Lres ANEEL Residential Tari¤ (R$/MWh) Ltres ANEEL GDP (R$) Lpib Notini & Issler (2008) PPI - Appliances Lipaelm Ipeadata LPG gas (Thousands of barrels) Lglp Banco Central Consumer Loan Operations (R$) Lcred…s Ipeadata Median Temperature (o C) Ltemp INMET Industrial Demand (MWh) Lind ANEEL Industrial Tari¤ (R$/MWh) Ltind ANEEL Industrial Production (R$) Lproind IBGE PPI - Machines and Equipments Lipaq Ipeadata PPI - Oil Lipaq Ipeadata Corporate Loan Operations (R$) Lipac Ipeadata Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 8 / 32

Data

Residential Demand (GWh in logs) Industrial Demand (GWh in logs)

8.5 8.6 8.7 8.8 8.9 9.0 99 00 01 02 03 04 05 06 07 9.1 9.2 9.3 9.4 9.5 9.6 9.7 99 00 01 02 03 04 05 06 07 Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 9 / 32

Data - Income Variables

Residential Demand X GDP Industrial Demand X Production

8.5 8.6 8.7 8.8 8.9 9.0 4.4 4.5 4.6 4.7 4.8 1999 2000 2001 2002 2003 2004 2005 2006 2007 Tendência até Racionamento Tendência após Racionamento LRES LPIB 9.1 9.2 9.3 9.4 9.5 9.6 9.7 4.4 4.5 4.6 4.7 4.8 4.9 1999 2000 2001 2002 2003 2004 2005 2006 2007 Tendência até Racionamento Tendência após o Racionamento LIND LPROINDSA

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 10 / 32

Data - Price Variables

Since 2003, Federal government starts to apply a tari¤ realignment in the annual adjusts, whose objective is to …nish with the cross-subsidy. Residential Tari¤ Industrial Tari¤

3.8 4.0 4.2 4.4 4.6 4.8 99 00 01 02 03 04 05 06 07 LTRES 3.6 4.0 4.4 4.8 5.2 99 00 01 02 03 04 05 06 07 LTIND Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 11 / 32

Data - Unit Root Test

ADF test indicates that all the variables can be characterized as non-stationary variables, except the temperature.

Variable Terms Included T Stats p-value Residential Demand (MWh) Constant

• 2.08 (-2.89)

0.250 Residential Tari¤ (R$/MWh) Constant and Trend 1.10 (-3.45) 0.999 GDP (R$) Constant and Trend

• 2.09 (-3.45)

0.543 PPI - Appliances Constant

• 1.15 (-2.89)

0.690 LPG gas (Thousands of barrels) Constant

• 1.10 (-2.89)

0.711 Consumer Loan Operations (R$) Constant and Trend

• 1.65 (-3.45)

0.765 Median Temperature (o C) Constant

• 7.64 (-2.89)

0.000 Industrial Demand (MWh) Constant and Trend

• 2.73 (-3.45)

0.226 Industrial Tari¤ (R$/MWh) Constant

• 1.16 (-2.89)

0.685 Industrial Production (R$) Constant

• 0.86 (-2.89)

0.806 PPI - Machines and Equipments Constant and Trend

• 1.02 (-3.45)

0.934 PPI - Oil Constant and Trend

• 2.50 (-3.45)

0.325 Corporate Loan Operations (R$) Constant

• 1.58 (-2.89)

0.999 Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 12 / 32

TVP-ECM Model

In this paper, the econometric setting we use to deal with the relationship between the electricity demand and its determinants is a Time Varying Parameter Error Correction Model, TVP-ECM. The model chosen is adequate to capture the long-run relationship between the variables and allows a ‡exible way to model their short-run dynamics. We de…ne the TVP-ECM for each demand - residential and industrial - using three equations. The …rst one deals with the long-run relationship, that is, the cointegration between the variables and it is stated as follow:

dt = α0+ α1zt +ǫt, ǫt NID (0, σ2

ǫ)

(1) where dt and zt are respectively electricity demand and its determinants, t (t = 1, ..., n, ) , α0 are α1 …xed scalars and ǫt is an error term.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 13 / 32

TVP-ECM Model

The second step deals with the short-run dynamics of the relationship between

demand and its determinants. Replacing the error term ǫt1 by its estimate, ˆ

ǫt1,

we run the second equation, the TVP-ECM measurement equation, which is given by

∆dt= β1tǫt1+

p

∑

i=1

γit∆dti+

p

∑

i=1

λit∆zti+et, et NID (0, σ2

e)

(2) where ∆dt = dt dt1 (j = 1, 2), ǫt1 is the error term from equation (1), β1t, γ1,t, ..., γp,t, λ1,t, ..., λp,t are the time varying coe¢cients.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 14 / 32

TVP-ECM Model

Evolution of second equation over time is given by the third equation of the model, the state equation. Measurement and state equations are estimated in a State Space Model simultaneously, with the Kalman Filter algorithm.

βt= φ + Φβt1+ ut, ut NID (0, Σ) (3)

where βt = (β1t, γ1,t, ..., γp,t, λ1,t, ..., λp,t)0 is the 2p + 1 1 state vector in time t φ is a 2p 1 vector, Φ is a diagonal 2p + 1 2p + 1 matrix, ut is a

2p + 1 1 vector of error terms with a 2p + 1 2p + 1 covariance matrix, Σ.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 15 / 32

Estimation

Step-by-step for estimation, once series are non-stationary:

• 1. Johansen VECM-Cointegration approach:

(a) With the variables for each model (residential demand and industrial demand) we run a VAR and, with the information criteria, select the optimal number of lags; (b) Using these lags, we test cointegration; (c) If there is a cointegration relationship between the I(1) variables, we already have the long-run elasticities. Besides, we can identify the short-run elasticities with the Error Correction Model. (d) The VECM give us the short-run …xed over time coe¢cients.

2.

We get the ECM equation relative to electricity demand and test structural break.

3.

If we …nd a break, we get started with the analysis of short-run elasticities dynamics, the ECM equation as the observable equation of a Kalman Filter.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 16 / 32

Results - Johansen Cointegration Test - Residential

Optimal number of lags selected by Information Criteria: 3 lags for the estimated residential VAR. Johansen Cointegration Test - Residential Possibles CE’s Eigenvalue Trace Stats 5% Critical Value

• Prob. **

None* 0.401391 125.3693 76.97277 0.0000 At most 1* 0.299604 72.00204 54.07904 0.0006 At most 2 0.193875 34.96663 35.19275 0.0529 At most 3 0.088648 12.55290 20.26184 0.4006 Tests indicates 2 cointegrating vectors at 5% of signi…cance.

lrest = 0.94 0.96 ltrest + 1.76 lpibt + 0.92 lipaelm + ǫt

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 17 / 32

Results - VECM - Residential Demand

Inclusion of exogenous variable I(0) - temperature - doesn’t change test statistics distribution. Error Correction Model for Residential Demand Variables Coe¢cients Standard-Errors T-Stats CointEq1

• 0.098

(0.04307) [-2.28099] CointEq2 0.400 (0.06807) [ 5.87778] D(Lres(-2)) 0.206 (0.09952) [ 2.07067] D(Lipaelm(-2))

• 0.245

(0.19979) [-1.22924] D(Lpib(-1)) 1.068 (0.45802) [ 2.33226] D(Lpib(-2))

• 0.970

(0.47686) [-2.03594] D(Ltres(-2))

• 0.461

(0.27751) [-1.66156] Ltemp 0.147 (0.02425) [ 6.08996] Adj R-squared 0.352707 Log Likelihood 1448.23

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 18 / 32

Results - Structural Break Test - Residential Demand

"If QLR statistic rejects the null hypothesis of no break, it can mean that there is a single discrete break or that there is slow evolution of the parameters." Chow Structural Break Test - Residential H0: there’s no break /at speci…c breakpoints Statistics Value Prob. P-value F-Statistic (2001 M08) 2.6611

• Prob. F(11,82)

0.0057 Log Likelihood ratio 31.7470

• Prob. Chi-Square (11)

0.0008 Wald Statistic 29.2721

• Prob. Chi-square (11)

0.0021 We can reject the null hyphoteses there’s no break to August, 2001.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 19 / 32

Results - Kalman Filter - Residential Demand

State equations may not contain signal equation dependent variables, or leads or lags of these variables; may contain exogenous variables and unknown coe¢cients, and may be nonlinear in these elements. Each state equation must be linear in the

• ne-period lag of the states.

We have four state equations (SV1 to SV4) because we only tested stability for the two long-run components of the ECM equation and for short run income and price elasticities =

) high number of parameters to be estimated. Short-Run Dynamics of Estimation - Residential Final State Root MSE z-Statistic Prob. SV1 0.90809 1.09E-05 83657.8 0.000 SV2

• 0.33184

1.91E-05

• 17381.5

0.000 SV3 0.00046 0.162845 0.00287 0.9977 SV4 0.00044 0.389678 0.00114 0.9991 Log Likelihood 202.0321 BIC

• 3.12

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 20 / 32

Results - Short-Run Elasticities Dynamics - Residential Demand

These graphs show the dynamics of short-run elasticities.

= ) Short-run income elasticity stay above zero (positive) most of time and many times

bellow unity (inelastic);

= ) Short-run price elasticity stay bellow zero most of time.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 21 / 32

Results - Johansen Cointegration Test - Industrial

Optimal number of lags selected by Information Criteria: 3 lags for the estimated industrial VAR. Johansen Cointegration Test - Industrial

Possible CE’s

Eigenvalue Trace Stats 5% Critical Value

• Prob. **

None* 0.228542 81.17640 76.97277 0.0230 At most 1* 0.191144 54.19117 54.07904 0.0489 At most 2 0.140716 32.12924 35.19275 0.1032 At most 3 0.089141 16.35707 20.26184 0.1584 Tests indicates 2 cointegrating vectors at 5% of signi…cance.

lindt = 1.93 0.24 ltindt + 1.31 lproindsat + 0.50 lipaq + ǫt

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 22 / 32

Results - VECM - Industrial Demand

Error Correction Model for Industrial Demand Variables Coe¢cients Standard-Errors T-Stats CointEq1

• 0.061213

(0.05786) [-1.05786] CointEq2

• 0.016252

(0.01609) [-1.01032] D(Lipac(-2))

• 0.128715

(0.12526) [-1.02757] D(Lipaq(-1))

• 0.816395

(0.41002) [-1.99112] D(Lipaq(-2)) 0.399629 (0.37395) [ 1.06868] D(Lproindsa(-1)) 0.193423 (0.14112) [ 1.37065] D(Ltind(-2))

• 0.184482

(0.09156) [-2.01494] Adj R-squared 0.059238 Log Likelihood 1313.103

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 23 / 32

Results -Structural Break Test - Industrial Demand

In the industrial case, we can also reject the null hyphoteses there’s no break to August, 2001. Chow Structural Break Test - Industrial H0: there’s no break /at speci…c breakpoints Statistics Value Prob. P-value F-Statistic (2001 M08) 1.8773

• Prob. F(11,82)

0.0661 Log Likelihood ratio 18.6551

• Prob. Chi-Square (11)

0.0283 Wald Statistic 16.8964

• Prob. Chi-square (11)

0.0504

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 24 / 32

Results - Kalman Filter - Industrial Demand

The dynamics for short-run income and price elasticities are signi…cative. The …nal estimated value for income elasticity was 0.40 and for price elasticity,

• 0.68.

Short-Run Dynamics of Estimation - Industrial Final State Root MSE z-Statistic Prob.

SV2

• 0.68150

8.67e-05

• 7857.373

0.000

SV1

0.40554 3.73E-06 108828.5 0.000

SV3

• 0.00002

0.201752

• 0.001416

0.9989

SV4

2.00E-10 6.61E-05 3.02E-06 1.000 Log Likelihood 199.3253 BIC

• 3.30

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 25 / 32

Results - Short-Run Elasticities Dynamics - Industrial Demand

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 26 / 32

Results - Short-Run Elasticities Dynamics

The p-value (between parentheses) shows that we can not reject the hypothesis that persistence a¤ects the dynamics of price-elasticities in residential and industrial

• demand. And is bigger in industrial case.

Besides, the consumers credit seems to smooth the e¤ect of tari¤ (price-elasticity) in the electricity demand. We didn’t …nd signi…cative dynamics determinants for income-elasticities. We don’t have yet a way to capture the self production increase in data. This could explain something in the dynamics. Results - Residential Income Price Persistence

• 0.19
• 0.48

(0.36) (0.02) Credit

• 51.61
• 30.47

(0.12) (0.00) Industrial Income Price Persistence

• 0.0027

0.85 (0.99) (0.02) Credit 0.75

• 8.52

(0.95) (0.24) Volatility

• 205.49
• 8.52

(0.82) (0.64)

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 27 / 32

Results Comparisons

Elasticities Estimates and Comparisons Y-LongRun Y-ShortRun P-LongRun P-ShortRun Residential (Fixed) 1.76 1.06

• 0.96
• 0.46

Industrial (Fixed) 1.31 0.19

• 0.24
• 0.18

Residential (Final) 0.90

• 0.33

Industrial (Final) 0.40

• 0.68

Chang (2003) Residential 1.95

• 0.44

Industrial 1.29

• 0.25

Porter (2004) Residential

• 0.94

Industrial

• 0.55

Modiano (1984) Residential 1.13 0.33

• 0.40
• 0.11

Industrial 1.36 0.50

• 0.45
• 0.22

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 28 / 32

Results

Using monthly data, from 1999.1 to 2007.12, we found consistent long-run and short-run estimates for residential and industrial elasticities of electricity demand. Our long and short-run residential price-elasticity was 0.96 and 0.46; and the industrial price-elasticities of long and short-run was 0.24 and 0.18. The long and short-run income-elasticities was 1.76 and 1.06 for residential consumers and 1.31 and 0.19 for industrial consumers. Using a structural break test we found one structural break at 2001, what gives some evidence that rationing crisis changed the pattern of the electricity demand in Brazil. Finally, the time-varying analysis showed that income elasticities for residential and industrial consumers stay beyond unity for many times. And persistence of the shocks is the double in industrial price-elasticity than in residential one.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 29 / 32

Conclusions

This paper update the modelling of Brazilian electricity demand, with a spam of time that includes the power rationing crisis from 2001. Due to a possible break, that we con…rm to be signi…cative, the estimates from other authors may be desaligned with the current scenario. The present paper suggests that Brazilian residential consumers are more sensible to price and income than industrial ones. This result is compatible with conclusions

• f Chang and Martinez-Chombo (2004) for long-run estimates of Mexican

price-elasticities and with Kamerschen and Porter (2004), whose residential price-elasticity stayed in the range 0.85 and 0.94, and industrial between

0.34 and 0.55.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 30 / 32

Conclusions

The power rationing crisis appears like a structural break to Brazilian data. This emphasizes that elasticities (the answer of electricity demand to shocks in its determinants) can vary over time and we test this for short-run elasticities. With the State Space model, we obtain that income elasticities may stay beyond the unity during sometimes. The implication of our results are important, once policymakers need to consider the varying responses of elasticities to its determinants. For example, income elasticities correctly estimate are essential to planning investment needs in power generation, while price elasticities are very important to regulation of electricity sector, where incentives are made with tari¤ on the basis.

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 31 / 32

Some References

CHANG, Yoosoon & MARTINEZ-CHOMBO, Eduardo. (2003). Electricity Demand Analysis Using Cointegrating and Error-Correction Models with Time Varying Parameters: The Mexican Case. Working paper. ENGLE, R. & GRANGER, C. (1987). Cointegration and Error-correction: Representation, Estimation and Testing, Econometrica, vol 55, p. 251-276. ENGLE, R. ; GRANGER, C. & HALLMAN, J. (1989). Merging Short and Long run Forecasts: An Application of Seasonal Cointegration to Monthly Electricity Sales Forecasting, Journal of Econometrics, vol 43, p. 45-62. HALL, S. (1993). Modelling Structural change using the Kalman Filter, Economics

• f Planning, 26, 243-60.

JOHANSEN, S. (1991). Estimation and Hypothesis of Cointegration Vectors in Gaussian Vector Autoregressive Models, Econometrica vol 59, p. 1551-80. KAMERSCHEN & PORTER (2004), The demand for residential, industrial and total electricity, 1973–1998 .Energy Economics 26 (2004) 87–100

Amanda Pimenta Carlos, Hilton Notini, Luiz Maciel (Institute) Brazilian Electricity Demand Estimation: What Has Changed After Rationing in 2001? June, 2009. 32 / 32