Government Revenue Forecasting in Nepal


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1 Governmen Revenue Forecasing in Nepal T. P. Koirala, Ph.D.* Absrac This paper aemps o idenify appropriae mehods for governmen revenues forecasing based on ime series forecasing. I have uilized level daa of monhly revenue series including 92 observaions saring from 997 o 202 for he analysis. Among he five compeiive mehods under scruiny, Winer mehod and Seasonal ARIMA mehod are found in racking he acual Daa Generaing Process (DGP) of monhly revenue series of he governmen of Nepal. Ou of wo seleced mehods, seasonal ARIMA mehod albei superior in erms of minimum MPE and MAPE crieria. However, he resuls of forecased revenues in his paper may vary depending on he applicaion of more sophisicaed mehods of forecasing which capure cyclical componens of he revenue series. The prevailing forecasing mehod based paricularly on growh rae mehod exended wih discreionary adjusmen of a number of updaed assumpions and personal judgmen can creae uncerainy in revenue forecasing pracice. Therefore, he mehods recommended here in his paper help in reducing forecasing error of he governmen revenue in Nepal. Key words: Daa generaing process, forecas bias, seasonal paern, underorover esimaion, governmen revenue, seasonaliy JEL Classificaion: H2, O23 * Assisan Direcor, Research Deparmen, Nepal Rasra Bank. Acknowledgemen: I would like o hank Ediorial Board of NRB Economic Review and anonymous referees for heir consrucive commens on he paper.
2 48 NRB ECONOMIC REVIEW I. INTRODUCTION The revenue forecass by he naional governmen are carried ou in course of budge preparaion. An accuracy of revenue forecass is one key issue in he design and execuion of fiscal policies (IMF, 200). Under or overpredicion of revenue forecas creaes budge planning vulnerable. Revenue forecas provides necessary discipline for negoiaions beween he execuive and legislaive branches of he governmen. I helps in seing up performance arges for revenue deparmens and agencies (Auerbach, 999, Danninger, 2005). One of he major sources of error (or bias) in revenue forecasing is he mehods adoped in forecasing revenue in addiion o variey of poliical and insiuional facors deermining such bias (Golosov and Kind, 2002, Kyobe and Danninger, 2005). In Nepal, revenue forecass is an imporan ask of Minisry of Finance (MOF) in he course of budge preparaion and specifying performance arges of revenue collecion offices. Major insiuions involved in forecasing revenue in he counry are MOF and Nepal Rasra Bank (NRB) as heir work of forecasing is an essenial par of he budgeary process. The IMF, especially is Fiscal Affairs Deparmen (FAD) ofen gives advice for a sysemaic analysis of forecasing in lowincome counries in he conex of reforms on he budge planning process (Kyobe and Danninger, 2005). However, forecasing echniques are generally no pu down in formal documens, and counry pracices are ofen a mix of idiosyncraic budge pracices and influences from legacy sysems. Too much reliance on few mehods in forecasing revenue of he governmen of Nepal is considered o be less efficien in capuring rue DGP of revenue sequence. No a remarkable exercise has been carried ou in idenifying appropriae mehodology of revenue forecasing from hose insiuions involved in revenue forecasing a presen and here is a lack of privae insiuional forecaser of revenue in he economy. As a resul, here is an overesimaion or underesimaion of he revenue of he governmen. The forecas error as percenage of GDP shows downward rend wih erraic movemen as represened by forecas error or bias as shown in Diagram. Revenue forecas shows upward biased before FY 200/02 and downward biased hereafer in Nepal. Realizing he facs ha any misspecificaion of appropriae forecasing echniques ha leads o much error in revenue forecasing as moivaing facor of his sudy. In ligh of his fac, he objecives of his paper is o ideniy appropriae mehods for revenue forecasing using monhly oal revenue sequence and rank he mehods under scruiny based on some saisical crieria. Following five imporan mehods of forecasing under consideraion, his sudy found wo mehods namely SARIMA and Winer as he represenaive mehods of revenue forecasing in Nepal. The res of he paper is organized as follows. Nex secion presens
3 Governmen Revenue Forecasing in Nepal 49 explanaion of each of he five mehods under he heading mehodology. Secion III provides resuls and analysis. Finally, he las secion draws he conclusion. II. METHODOLOGY In caegorizing forecasing mehodologies, wo broad approaches can be disinguished. Time series forecasing aemps in predicing he values of a variable from he pas values of he same variable. In conras o he ime series approach economeric forecasing is based on a regression model ha relaes one or more dependen variables o a number of independen variables. The ime series approach has generally been found o be superior o he economeric approach when shorrun predicions are made (Ramanahan, 2002). In his paper, use is made of ime series forecasing approach uilizing level daa of monhly oal revenue series saring from 997 o 202. Las 24 ou of oal 92 observaions are aken o check he accuracy of he forecasing mehods employed in his paper. An exane forecass of 24 observaions are presened in he Appendix. Boh he cumulaive as well as ne monhly forecass are presened uilizing each of he mehods of forecasing employed. The iniial period of sample in FY 997/98 has been chosen based on he year when he governmen of Nepal adoped Value Added Tax as a landmark reform in revenue srucure in Nepal. Followings are he explanaion of basic characerisics of each of he seleced se of mehods ha are used for forecasing in his paper. Hol Mehod : The forecasing mehod developed by Hol (957) is one popular smoohing echnique of forecasing. The woparameer exponenial smoohing echnique developed by Hol is a modified mehod of simple exponenial smoohing formula of ~ y ( ) ~ = α y + α y ; where > α > 0 incorporaing average changes in he longrun rend (increase or decline) of he sequence y }. Here, ~ y } is smoohed sequence. Hol { mehods is superior o exponenial smoohing echnique ha former mehod incorporaes rend in he smoohing series. The smoohed or esimaed series is derived by using wo recursive equaions as given in equaion () and (2). The smoohness of he series depends on wo smoohing parameers, α and β boh of which mus lie beween 0 and, ha is, he smaller are α and β he heavier is he smoohing (Makridikis, Wheelwrigh and Hyndman, 998). ~ y = + ( )( ~ + α y α y r ) ;where, > α > 0 () r ~ ~ = β ( y y ) + ( β ) r ; where, > β > 0 (2) y ˆ = ~ y + lr (3) + l T T Here, y~ denoes an esimae of he level of he series a ime and r denoes an esimae of he slope of he series a ime. Equaion (2) adjuss y~ direcly for he rend of he previous period, r by adding i o he las smoohed value ~ y. Equaion (3) is used o forecas l. {
4 50 NRB ECONOMIC REVIEW Winer Mehod: Winer (960) exended Hol mehod by reaing seasonal effec in he forecasing equaion. Winer mehod is based on hree smoohing equaions one for he level, one for rend, and one for seasonaliy as. ~ y y ( )( ~ = α + α y + r ) ; where, > α > 0 (4) s s r ~ ~ = β ( y y ) + ( β ) r ; where, > β > 0 (5) y s = γ ~ + ( γ ) s s where, > γ > 0 (6) y ˆ = ( ~ y r ) s (7) y + m T + Tm s+ m Where, s is he lengh of seasonaliy, y~ represens he level of he series, r denoes he rend, s is he seasonal componen, and y ˆ + m is he forecas for m periods ahead. Decomposiion Mehod: Classical decomposiion is one of he oldes commonly used forecasing mehods. This mehod is used o decompose a ime series ino rend, cyclical and seasonal componens presened in a ime series. An essenial par of his mehod includes he concep of seasonal index. The srong seasonaliy of some series makes i difficul o measure heir rend and cyclical movemens (Gujarai, 2004). In he regression decomposiion mehod, dummy (dichoomous) variables are uilized o measure seasonal influences on high frequency daa. The seasonal influence can be modeled using eiher an addiive model, or a muliplicaive model. The selecion of eiher model depends on he magniudes of he seasonal peaks and roughs of he level of he series. The formulas for addiive and muliplicaive models are represened in equaions (8) and (9) respecively. y = α + β T + β2 X 2 + β3x β n Xnn (8) ln( y ) = α + β T + β2 X 2 + β3x β n Xnn (9) Where, y is level of he series, T ime value in period, X 2, X Xnn are dummy variables for each period (i.e. monhly), ln( y ) is he logarihm of he series o he base of he naural number e. The anilog form of he muliplicaive model of equaion (9) is used o ransform logarihmic values o level values using formula represened in equaion (0). yˆ α β = e + e + e + e e T β2x 2 β3x 3 βn Xnn (0) Seasonal Auoregressive Inegraed Moving Average (SARIMA) Mehod: Popularly known as BoxJenkin (994) mehodology, he ARIMA model building mehod consiss of four seps: idenificaion, esimaion, diagnosic checking and forecasing (Gujarai, 2004). ARIMA model conains he use of simple and versaile model noaion designaed by he level of Auoregressive (AR), Inegraion (I), and Moving Averages (MA)
5 Governmen Revenue Forecasing in Nepal 5 (DeLurgio, 998). The sandard noaion idenifies he order of AR by p, I by d and MA by q. An exension of seasonal influence in ARIMA model is represened by SARIMA specificaion. A mixure of AR, I and MA formulaion is known as ARMA (p,d,q) where difference (d) is done before ARMA is specified. The general form of ARIMA model is: y = β y + β2 y β p y p + ε φε φε 2... φqε q () Seasonaliy in a ime series is a regular paern of changes ha repeas over S ime periods, where S defines he number of ime periods unil he paern repeas again. The ARIMA noaion can be exended readily o handle seasonal aspecs, and he general shorhand noaion is ARIMA (p,d,q) (P,D.Q)s (Pindyck and Rubinfeld (997). In a seasonal ARIMA model, seasonal AR and MA erms predic y using daa values and errors a imes wih lags ha are muliples of S (he span of he seasonaliy). Wih monhly daa (S=2), and seasonal firs order auoregressive model would use y 2 o predic y. Variance nonsainary in he ime series is handled by logarihmic ransformaion before SARIMA mehod is adoped. Growh Rae Mehod: Revenue forecasing based on yearonyear growh rae is supposed o capure seasonal influence. The forecas of period +s is calculaed based on average of pas five years (yearonyear) growh raes from period. The increase/decrease of he forecased revenue deermines increase/decrease of forecas revenue from period, ha is, condiional forecass. The formulas for growh mehod are presened in equaion () and (2). r = n n y y ( y i= yˆ = y + ( y * n )*00 (2) + r) /00 (3) Measures of accuracy for forecasing which are free of scale of he daa are adoped in his paper. Two popular relaive measures as frequenly used in measuring accuracy of forecas are Mean Percenage Error (MPE) and Mean Absolue Percenage Error (MAPE) where Percenage Error (PE) is calculaed using he formula Y F PE = *00 (4) Y n MPE = PE (5) n = n MAPE = PE (6) n = The mehods explained above are considered appropriae o capure daa generaing process of oal hisorical revenue series in his paper. While selecing appropriae mehods, due emphasis will be given o hose mehods ha incorporae rend and seasonal
6 52 NRB ECONOMIC REVIEW componen in a ime series analysis. The cyclical componen has no been decomposed from rend componen in his analysis. III. RESULTS AND ANALYSIS In he presen paper, I have conduced shorerm revenue forecas of he governmen of Nepal for 24 monhs saring from Augus 202 o Augus 204 (i.e. wo years) based on 92 hisorical monhly revenue series beginning from Augus 997 o July 202. A visual inspecion of revenue series in Figure 2 reveals some sylized facs ha he daa generaing process of monhly revenue series clearly shows upward rend accompanied wih monhly seasonal paern. Revenue series shows also ime varying variance over he period. The seasonal paern is no clearly visible in he Diagram 2 as he diagram covers whole sample period. In order o be more specific, he seasonal paern is displayed by he monhly daa for he FY 20/2 reveals clear seasonal paern in he monh of January (six monh), April (nine monh) and July (welve monh). Such seasonal paern can be applicable for he inference of monhly seasonal paern for oher FYs as depiced in Figure 3. The reason for such seasonal influence of revenue mobilizaion in hose monhs is ha he corporae eniies in Nepal are direced o pay declared ax ino hreeinsallmen each year including 40% ill midjanuary (six monh), 70% ill midapril (nine monh) and 00% ill midjuly (Twelve monh). I have uilized five equally compeiive mehods ha are applicable for forecasing in case of a ime series daa characerizing periodoperiod upward rend, seasonal paern and imevarying variance. Those mehods include (a) Hol mehod, (b) Winer mehod, (c) decomposiion mehod (d) SARIMA mehod, and (e) growh rae mehod. Among hose mehods, Hol and Winer are he smoohing mehods of forecasing ime series. The esimaed values of he smoohing parameers of α, β and γ deermine he forecas values in hese mehods. As α, β and γ represen smoohing, rend and seasonal parameers respecively, he esimaed values of hose parameers uilizing whole sample daa of presen analysis are presened in Table. The crierion for he selecion of hose parameers is he minimum mean sum of squared error.
7 Governmen Revenue Forecasing in Nepal 53 Table : Esimaed Smoohing and Seasonal Parameers (996 Augus o 202 July) Smoohing and Seasonal Hol's wo parameer Winer's Three Parameer Parameers (no seasonal) (Seasonal) α β γ Subsiuing he values of smoohing parameers in he corresponding equaions of Hol and Winer mehods for revenue forecasing looks like: Hol Mehod: ~ y 0.04 ( 0.04)( ~ = y + y + r ) ; where, > α > 0 (7) r.5( ~ ~ = 0 y y ) + ( 0.5) r ; where, > β > 0 (8) Forecasing for l period ahead as: y ˆ l = ~ + yt + lrt (9) Winer Mehod: ~ y y 0.8 ( 0.8)( ~ = + y + r ) ; where, > α > 0 (20) s s r.8( ~ ~ = 0 y y ) + ( 0.8) r ; where, > β > 0 (2) y s 0 s where, > γ > 0 (22) =.65 ~ + ( 0.65) y s Forecasing for m period ahead as: ˆ ( ~ (23) y + m = yt + rtm ) s s+ m The monhly revenue forecass using Hol and Winer mehods for he FY 202/3 and he FY 203/4 are presened in Table of Appendix I. As shown in Diagram of Appendix II, Hol mehod could no capure rue daa generaing process of governmen of Nepal as revenue series of he governmen characerizes seasonal effec. Winer mehod includes seasonal parameer γ, he noable seasonal picks are found in he monhs of January, April and July as shown in Diagram 4. The exane revenue forecass under his mehod are found more accurae han ha of Hol mehod as displayed in Diagram 2 of Appendix II. Under decomposiion mehod, regression mehod of decomposiion has been used o decompose revenue series ino rend and seasonal componen in his paper. The varian of muliple decomposiion formula is considered plausible here because he revenue series under review characerizes variance nonsaionariy. Twelve monhly dummies are inroduced o capure seasonal influence. Excep he dummy for he second monh, all
8 54 NRB ECONOMIC REVIEW oher coefficiens of monhly dummies including consan erm and rend componen are found saisically significanly differen from zero. Subsiuing he values of esimaed parameers in he corresponding regression equaon looks like: ln(rev ) = T + 0.0D S2 + 0.D D D D7 = (45.9) (47.38) (0.7) (.54) (4.8) (2.80) (9.6) (2.) 0.3D D D D+ 0.89D2 (24) (.98) (6.26) (3.63) (5.30) (3.8) As shown in Diagram 3 of Appendix II, expos forecass of revenue are racking well o he acual revenues from his mehod oo. The revenue forecasing under his mehod are presened in Table of Appendix I. The ARIMA mehod exended wih seasonal componens represened by SARIMA has been uilized in his paper by assuming ha he revenue series under review characerizes seasonal influence. While using SARIMA mehod, revenue series has been convered ino logarihm o he base e before is use in he analysis o capure variance nonsaionary. The SARIMA (0,0,0)(,0,0) 2 is he final specificaion based on idenificaion and diagnosic checking of he mehod. As such he logarihmic 2 h order difference wihou consan erm is he robus represenaion of he model as: ln(rev ) =.02*ln(Rev) 2 (25) = (688.55) Above specificaion yields very good racking of revenue forecass o acual revenue as shown in Diagram 4 of Appendix II. Applying he growh rae mehod, revenue forecasing is deermined by he increase/decrease of five years average of yearonyear growh raes of monhly revenue. The exane forecas for consecuive monhs in he fuure dae are considered condiional forecas based on he forecased revenue a he same monh las year, ha is, i is he ieraive process. Based on his mehod, he forecased revenue during he insample period is found saisfacory as depiced by he forecas revenues ha are well racking he acual revenues as shown in he Diagram 5 of Appendix II. The basis for he selecion of appropriae mehods of revenue forecasing in his paper, as quaniaive measure, is he minimum values of MPE and MAPE saisics for each mehod. For his purpose, MPE and MAPE have been calculaed based on laes 24 observaions of forecas errors derived from he difference of acual and esimaed values. The mehod ha obains values of MPE and MAPE close o zero is considered he bes mehod. The MPE and MAPE for each mehod are presened in Table 2.
9 Governmen Revenue Forecasing in Nepal 55 Table 2: Saisical Measures of Model Accuracy (996 Augus o 202 July) S. No. Saisical mehods Mean Percenage Error (MPE) Mean Absolue Percenage Error (MAPE). Hol Mehod Winer Mehod Regression Decomposiion Mehod 4. SARIMA Mehod Growh Rae Mehod Ou of five compeing mehods, wo mehods including Hol mehod, Decomposiion mehod are found less saisfacory mehods in erms of minimum MPE and MAPE crieria. On he remaining hree mehods, growh rae mehod is ranked hird. SARIMA mehod and Winer mehods rank firs and second posiion respecively. The MPE and MAPE for SARIMA mehod are and 6.22 respecively whereas for Winer mehod hey are .27 and 6.24 respecively. As boh he Winer and SARIMA mehods have builin characer o capure he seasonal influence in forecasing, hese mehods can be he represenaive mehods of forecasing governmen revenue in Nepal. Boh he monhly ne and monhly cumulaive forecass for he FY 202/3 and FY 203/4 are presened in Table and 2 of Appendix I. The cumulaive forecas revenues for he FY 202/3 and FY203/4 incorporaing all he five mehods are dragged in Table 3 from Table 2 of Appendix I o inerpree some ineresing conclusions. As SARIMA mehod is ranked firs among he five alernaive mehods under rial, he cumulaive revenue forecass accouns o Rs billion and Rs billion respecively in he FY202/3 and FY203/4. I yields yearonyear growh raes of 4.8 percen and 5.7 percen respecively in FY 202/3 and FY203/4. Table 3: Cumulaive Revenue Foecass and Growh Raes FY Cumulaive Forecas (Rs in Million Percenage Change Decomposiion Growh Decomp Growh Hol Winer ARIMA Rae Hol Winer osiion ARIMA Rae 20/ / / Similarly, he cumulaive forecas revenues using Winer mehod, as i is found second bes mehod in his paper, are Rs billion and billion for he FY202/3 and FY203/4 respecively. The growh rae is projeced o be increased by 4.8 percen in FY 202/3 and 5.7 percen in FY203/4 according o his mehod. Las bu no he leas, wha i can be concluded in his paper is ha Growh rae mehod is found overly opimisic whereas Decomposiion mehod underesimaes he forecass. Hol mehod is ruledou because i does no capure seasonal influence. Therefore, among he five compeiive mehods under scruiny in his paper, Winer and ARIMA are found suiable for revenue projecion based on saisical crieria specified in his paper.
10 56 NRB ECONOMIC REVIEW However, he conclusion drawn in his paper depends on he use of five mehods of forecasing only. Complex forecasing mehods which capure cyclical influence in revenue mobiliaion are ou of perview in his paper. Since he moivaion of he sudy is o use ime series analysis in revenue forecsing as agains he condiional foecass mehod, laer mehod may obain differen resuls. IV. CONCLUSION Governmen revenue forecasing is an imporan aspec in he design and execuion of sound fiscal policies. The forecas error as percen of GDP over he sudy period is downward rending. As a consequence, here is an overesimaion of revenue followed by underesimaion. Furher, here is an erraic movemen of forecas error oo. As he exising mehods of revenue forecasing in Nepal is limied o growh rae basis and hence miss he arge, he objecive of he paper is o idenify appropriae mehodology of revenue forecasing. This paper uilizes monhly revenue series including 92 observaions saring from 997 o 202 or he analysis. Ou of he five popular echniques scruinized in his paper, wo compeing mehods including Winer and SARIMA mehods are found o be appropriae for he revenue forecasing in Nepal. However, SARIMA mehod is found albei superior han Winer mehod in erm of minimum MPE and MAPE crierion. Using SARIMA mehod, oal revenue is forecased o be increase by 5.7 in FY 202/3 and 4.8 percen in FY 203/4. The resuls of revenue forecasing in his paper may vary depending on he use of mehods ha capure cyclical componen of revenue series. Furher, he mehods of condiional forecasing are no applied here and hence may give differen resuls. Therefore, in ligh of hese limiaions, he forecasing aemps in his paper have opened an avenue for he sysemaic analysis of revenue forecasing using several mehods raher han depending on exising growh rae mehod. REFERENCES Auerbach, A J "On he Performance and Use of Governmen Revenue Forecass." Universiy of California, Berkeley and NBER, USA. Box, G.P.E. and G. M. Jenkins Time Series Analysis, Forecasing and Conrol. 3 rd ed. Englewood Cliffs, NJ: PreniceHall. Danninger, S "Revenue Forecass as Performance Targes." IMF Working Paper No. WP/05/4, IMF, Washingon, D.C. DeLurgio, S.A Forecasing Principles and Applicaions. Irwin McGrawHill Book Co., Singapore. Gujarai, D.N Basic Economerics 4 h ediion, Taa McGrawHill Publishing Company Ld., New Delhi. Hol, C.C "Forecasing Seasonal and Trends by Exponenially Weighed Moving Averages, Office of Naval Research, Research Memorandum No.52.
11 Governmen Revenue Forecasing in Nepal 57 Golosov, M. and J. King "The Revenue Forecass in IMFSuppored Programs." IMF Working Paper No.WP/02/236, Washingon D.C., USA. Inernaional Moneary Fund Revised Manual of Fiscal Transparency. Washingon D.C. USA. Kyobe A, and S. Danninger "Revenue ForecasingHow is i Done? Resuls from a Survey of LowIncome Counries." IMF working paper No.WP/05/24, IMF, Washingon D.C., USA Makridikis, S., Wheelwrigh, S.C., and R.J. Hyndman Forecasing Mehods and Applicaions. John Wiley and Sons (Asia) Pe.Ld. Singapore. Pindyck, R.S. and D.L. Rubinfeld. 997., Economeric Models and Economic Forecasings. 4 h Ediion, McGrawHill, Inernaional Ediion, Singapore. Ramanahan R Inroducory Economerics wih Applicaions. 5 h Ediion, Thomson Asia Pe Ld., Singapore. Winers, P.R "Forecasing sales by exponenially weighed moving averages. Managemen Science 6, p.p
12 58 NRB ECONOMIC REVIEW Appendix I: Tables Table : Monhly Revenue Forecass for 202/3 and 203/4 MidMonhs Hol Mehod Winer Mehod Decomposiion Mehod ARIMA Mehod (Rs in million) Growh Rae Mehod Ne Forecased Revenue for he FY 202/3 Augus Sepember Ocober November December January February March April May June July Ne Forecased Revenue for he FY 203/4 Augus Sepember Ocober November December January February March April May June July
13 Governmen Revenue Forecasing in Nepal 59 Table 2: Monhly Revenue Forecas (Cumulaive) for 202/3 and 203/4 Rs in million MidMonhs Hol Mehod Winer Mehod Decomposiion Mehod ARIMA Mehod Growh Rae Mehod Monhly Revenue Forecas (Cumulaive) for 202/3 Augus Sepember Ocober November December January February March April May June July Monhly Revenue Forecas (Cumulaive) for 203/4 Augus Sepember Ocober November December January February March April May June July
14 60 NRB ECONOMIC REVIEW Appendix II: Diagrams
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