PAPELES DE TRABAJO · 2018. 3. 22. · AMINO PAPELES DE TRABAJO 1/2018 Determining macroeconomic indicators to implement a short-term forecasting model for VAT revenue C G ONZÁLEZ

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PAPELES DE TRABAJO 1/2018

Determining macroeconomic indicators to implement a short-term forecasting model for VAT revenue

CAMINO GONZÁLEZ VASCO (*)

CÉSAR PÉREZ LÓPEZ (*)

Institute for Fiscal Studies Spain

(*) We are grateful to all the “12th IFO Dresden Workshop on Macroeconomics and the Business Cycle” panelists for comments and suggestions which have greatly improved this paper. We also thank our colleague RAQUEL PAJARES

ROJO at the Spanish Institute for Fiscal Studies who has provided us with valuable feedback.

© Instituto de Estudios Fiscales I.S.S.N.: 1578-0252

Avda. Cardenal Herrera Oria, 378, 28035 Madrid N.I.P.O.: 173-18-002-6

The views expressed in this paper are those of the authors and do not necessarily reflect those of the Spanish Institute of Fiscal Studies

INDEX

Abstract

1. INTRODUCTION

2. ESTIMATION STRATEGY

3. THE DATA SET

4. ESTIMATION RESULTS

4.1. Finding the orthogonal regressors

4.2. Determining the transfer function

4.3. Out of sample forecasts

5. Conclusions

References

Papeles de Trabajo del Instituto de Estudios Fiscales 1/2018

Abstract

Macroeconomic indicators are a good source of information for short-term forecasting due to several rea

sons: they cover different areas of the economy and provide faster modes of dissemination. In this study we

use a set of indicators to obtain a valid forecast for VAT revenue using a blend of statistical methods such

as transfer functions and principal component analysis. The objective is to enforce parsimony and avoid

multicollinearity problems with minimum information loss.

In a previous paper we combine several macroeconomic indicators obtaining good predictive performance in

terms of prediction error and RMSE for VAT revenue. In this study we add some leading indicators related to

consumption for maximizing prediction accuracy. The evaluations involved splitting the data into a training

sample and a validation sample using one-step ahead forecast during the validation period and comparing

results with the observed values of VAT revenue. The results in the validation sample account for the im

provement in model prediction.

We apply the proposed method to quarterly data beginning in 1995 and ending in the last quarter of 2017.

Keywords: Principal Components Regression, VAT forecasting, forecast combination, generated regressors.

JEL classification numbers: E62, C51, H68, C22.


4 CAMINO GONZÁLEZ VASCO y CÉSAR PÉREZ LÓPEZ


1. INTRODUCTION

Forecasting of revenues is an issue of crucial relevance to governments in ensuring stability in tax and expenditure policies. Just as demand analysis and forecasting in the private sector is of criti

cal importance because sales sustain the financial health of business, adequate and predictable

tax and non-tax revenues underpin the financial sustainability and stability of the government.

The importance of revenue forecasting in public budgeting has increased with governments shif

ting from annual cash-based budgets to medium-term budgeting as fiscal policy design and im

plementation have paid more attention to medium term constraints and the importance of budgeting for multiyear financial commitments. To address these goals, many countries have built a

Medium-Term Budgetary Framework (MTBF)1, a system of projections tailored to obtain values of

revenues and expenditures in future periods.

These MTBF also serve as meaningful tools that provide a starting point in addressing compliance

problems and supporting evasion deters. The main drawback of these prediction systems is that

their construction involves the use of techniques related to time series theory, transfer function models and multivariate analysis.

In particular, regarding to Value-Added Tax models, there are several approaches in the literature

that either calculate or forecast the VAT revenue.

Most of the models that compute tax revenue of VAT are focused on estimating the VAT base.

Prominent examples of such strategy are the models based on the National Accounts approach,

used by the U.S. Department of the Treasury and by the International Monetary Fund2 for numerous countries, the models based on the Sectoral Approach, and the Input-Output Models ap

proach that is also used for simulation3.

If we focus on VAT revenue forecasting, we often find in the literature methodologies grounded on the GDP based tax forecasting models. As a first step, the models require the construction of data

series for tax revenues and their bases for each tax. All these tax bases are assumed to be prede

termined and are obtained from macroeconomic variables derived from National Accounts and balance of payments aggregates. These historical data series of tax revenues have embedded in

them the effects of increases in national income or expenditure, as well as discretionary changes

made in the tax system over time. For the VAT revenue model we present in this paper, these changes brought about by discretionary changes are introduced by dummy variables.

The next step for setting up the GDP based forecasting models is to establish an exact relation

ship between the tax revenue and the economic variables (ie proxy base). In order to do this, it is

1 See the IMF working paper “Medium-Term Budgetary Frameworks-Lessons for Austria from International Experience” by ERIK J. LUNDBACK

2 See e. g. H. H. ZEE and J. P. BODING “Aspects of introducing a Value-Added Tax in Sri Lanka“ paper prepared for the International Monetary Fund, Fiscal Affairs Department, (August 1992).

3 See “Tax Analysis and Revenue Forecasting-Issues and Techniques”, by GLENN P. JENKINS , CHU-YAN KUO and GANGADHAR

P. SHUKLA, Harvard Institute for International Development, Harvard University, for a detailed description of these models.




necessary to determine the correct base for each tax using the National Accounts. Subsequently,

it is necessary to find out which component of the National Account corresponds most closely to the base for a particular tax.

In the case of Value-Added Tax, tax revenues are linked with Total Consumption Expenditure on Goods and Services4. This could be written as a transfer function and a regression analysis is carried out to forecast future revenue collections.

Obviously the predictive ability of this type of models is limited and error margins are large. This is partly because tax revenues are highly sensitive to a wide variety of economic variables and specifically to the economic cycle, and our ability to forecast the path of the economy using only one explanatory variable in a transfer function is restricted.

In order to address this problem, we could explore the possibility of introducing additional variables covering different areas of the economy (Domestic Demand, Labour Market and Activity Indicators, among others), but the high degree of linear dependency among these indicators would cause multicollinearity in the model.

Therefore, we propose principal component analysis applied to the entire set of numerical independent variables, to provide orthogonal regressors for the transfer function, ensuring the lack of multicollinearity with little information loss and increasing the forecasting accuracy.

This approach has the advantage of considering the behavioral responses of certain economic sectors (such as Tourism Industry or Construction) to the introduction of changes in the existing tax laws, and reciprocally, it is able to capture the influence of a decrease in one specific sector on the VAT revenue.

This paper is organized as follows. Section I outlines the derivation of the model employed and describes the estimation technique and the empirical framework. Section II presents the data set. Section III shows the estimation results and the forecast evaluation for the validation sample. The last section provides the main conclusions of this study.

2. ESTIMATION STRATEGY

Starting from a set of indicators relative to different areas of the economy (Construction and Services Activity Indicators, Private Consumption variables, Labour Market Indicators and External Trade Indicators) we propose a principal component analysis as a dimension reduction technique for the set of independent variables. The next step is to use the first three principal components as inputs to the transfer function to estimate the VAT revenue.

The ultimate goal in principal components analysis is to find the minimum number of dimensions that are able to explain the largest variance contained in the initial set of indicators. We intend to simplify the information which gives us the correlation matrix to make it easier to interpret.

The Institute for Fiscal Studies’s public finance forecasting model, which was used to produce forecasts in Britain in each Green Budget up to 2013, was based on the assumption that VAT revenues grew in line with nominal consumer spending. For further information see “Forecasting the PSBR Outside Government: The IFS Perspective” by CHRISTOPHER

GILES and JOHN HALL, Fiscal Studies, Volume 19, Issue 1 (February, 1998).


4



Principal component analysis was originated by Pearson (1901) and later developed by Hotelling

(1933). The application of principal components is discussed by Rao (1964), Cooley and Lohnes (1971), and Gnanadesikan (1977). Exceptional statistical treatments of principal components are

found in Kshirsagar (1972), Morrison (1976), and Mardia, Kent, and Bibby (1979).

Given a data set with p numeric variables, we can compute up to p principal components. Each principal component is a linear combination of the original variables, with coefficients equal to

the eigenvectors of the correlation or covariance matrix. The eigenvectors are customarily taken

with unit length. The principal components are sorted by descending order of the eigenvalues, which are equal to the variances of the components.

The principal components meet the following properties (Rao 1964; Kshirsagar 1972):

— The eigenvectors are orthogonal, so the principal components represent jointly perpendicular directions through the space of the original variables.

— The principal component scores are jointly uncorrelated. This property ensures the lack of

multicollinearity when we use then as input variables in a regression model.

— The first principal component has the largest variance of any unit-length linear combination of

the observed variables. The jth principal component has the largest variance of any unit

length linear combination orthogonal to the first j-1 principal components. The last principal component has the smallest variance of any linear combination of the original variables.

— The scores on the first j principal components have the highest possible generalized Variance

of any set of unit-length linear combinations of the original variables.

— The first j principal components provide a least squares solution to the model:

Y=XB+E

Where:

Y is an nxp matrix of the centered observed variables;

X is the nxj matrix of scores on the first j principal components;

B is the jxp matrix of eigenvectors;

E is an nxp matrix of residuals.

Our goal is to minimize the trace of E’E. That means that the first j principal components are the best linear predictors of the original variables among all possible sets of j variables, although any

nonsingular linear transformation of the first j principal components would provide an equally

good prediction.

In geometric terms, the j-dimensional linear subspace spanned by the first j principal components

provides the best possible fit to the data points as measured by the sum of squared perpendicu

lar distances from each data point to the subspace. This is in contrast to the geometric interpretation of least squares regression, which minimizes the sum of squared vertical distances.




3. THE DATA SET

Our starting point was an extensive collection of time series data comprised of quarterly indica

tors on a wide range of economic areas valued at current prices (raw data) covering the period

starting in 1995 onwards.

We next selected a subset of indicators, taking into account various attributes: high correlation to

the VAT revenue at current prices and quarterly variation rate, speed of publication, operability

(easy access), coverage, cyclical sensitivity and frequency.

The selected indicators according to these criteria were: Industry Production Index in consumer

goods, Goods and services imports, Passenger car registrations, Large firms sales in consump

tion, Housing investment, Foreign tourists arrivals, Retail trade index, Large Firms Sales index,

Compensation of employees, Employment (Registered contracts), Electric power consumption,

Industry capacity utilization %, Business tendency surveys: production future tendency in con

sumer goods, and order books in consumer goods.

Figure 1

PEARSON CORRELATION COEFFICIENTS AND ASSOCIATED P-VALUES FOR VAT TAX REVENUE AND

THE RESULTING TEN PARTIAL INDICATORS5

The correlation coefficients of some variables are low compared to the rest of the indicators. We considered this

reference series as useful indicators because of their cycle pattern (Figures 2-4), their relatively short publication lags,

and because they belong to economic areas which are sensitive to policy changes.


5



The next step in the process was to identify the underlying cyclical pattern of the indicators. This

goal required the removal of two factors: long term trends and high frequency noise. We decided

to remove these factors in a single step using a Fixed length Symmetric Band-Pass Filter (Baxter-

King) with 12 lags (k=12) and limits for the cycle periods between 6 and 32 quarters. These limits

are defined according to the National Bureau of Economic Research economic cycle definition, as

periodic fluctuations between 6 and 32 quarters.

Figure 2

CYCLICAL PATTERNS OF VAT REVENUE AND SELECTED PARTIAL INDICATORS OBTAINED BY A

BAXTER-KING FILTER

If the cyclical profiles are highly correlated6, the indicator would provide a signal, not only to ap

proaching turning points, but also to developments over the whole cycle. The cross correlation

function between the cyclical component of the partial indicators and the cyclical component of

the VAT revenue, provides valuable information on cyclical conformity. The location of the peak of

the cross-correlation function is a good indicator of average lead time.

The methodology guideline “OECD System of Composite Leading Indicators” prepared by GYORGY GYOMAI and EMMA-

NUELLE GUIDETTI in April 2012, specifies this approach to select the reference series based on cyclical profiles.


6



Figure 3.a

COINCIDENT PARTIAL INDICATORS:

CROSS CORRELOGRAMS OF THE CYCLICAL COMPONENT OF VAT REVENUE AND THE CYCLICAL

COMPONENTS OF COINCIDENT PARTIAL INDICATORS (BAXTER-KING)

Figure 3.b

LEADING PARTIAL INDICATORS


COMPONENTS OF LEADING PARTIAL INDICATORS (BAXTER-KING)




Figure 3.c

INDUSTRY CAPACITY UTILIZATION:


COMPONENTS OF ICU (BAXTER-KING)

The cross-correlation analysis of the two cyclical components shows that the cyclical component

of Electric Power Consumption is highly correlated to the cyclical component of VAT revenue at

lag=0 (Rho=0.6577).

Figures 3.b feature similar results for the cyclical component of Passenger Car Registrations; the

cross-correlation analysis of the two cyclical components shows that the cyclical component of

Passenger Car Registrations is highly correlated to the cyclical component of VAT revenue at

lag=0 (Rho=0.5262) but the maximum occurs at lag=2 (Rho=0.7643). That result reveals a lea

ding relationship between these two variables.

Similar cyclical pattern analysis of the rest of the candidate reference series are shown in Figures

3.a, 3.b and 3.c. Specifically, for selected partial indicators, Business tendency survey: Production

future tendency, Large Firms Sales Index and Passenger car registrations provide leading infor

mation about the VAT revenue. The rest of the indicators, including Industry capacity utilization7

are more significant in providing contemporaneous information.

Note that whereas the correlation value of the peak provides a measure of how well the cyclical

profiles of the indicators match, the size of the correlations cannot be the only indicators used for

component selection.

We fitted the model using a training data set from t=1 (first quarter of 1995) to t=T (last quarter

of 2012) and then we tested its performance computing one-step ahead forecasts on a validation

data set (first quarter of 2013 to third quarter of 2017). Once we have checked the predictive

ability of the model, and since the latest update of the VAT revenue released by the Spanish Tax

Agency corresponds to the third quarter of 2017, we provide forecasts for the last quarter of

As shown in Figure 3.c based on the available cyclical information, the Industry Capacity Utilization indicator could

be interpreted as a coincident indicator with the VAT revenue (correlation coefficient of 0.58).


7

Camino González Vasco y César Pérez López 11Determining macroeconomic indicators to implement a short-term forecasting model for VAT revenue

2017. Predictions with a longer time horizon will be performed by extending the partial indicators

using seasonal ARIMA models.

The following sections provide a more detailed description of the various steps highlighted

above.

4. ESTIMATION RESULTS

4.1. Finding the orthogonal regressors

As indicated before, the purpose of the principal component analysis is to compute three va

riables that best summarize all fourteen partial indicators.

Table 1

EIGENVALUES OF THE CORRELATION MATRIX

The SAS System

T h e FA C TO R P rocedure In itia l F a c to r M eth o d : P rin c ip a l C om p o n en ts

P rio r C o m m u n a lity Estim ates: O N E

E ig e n v a lu e s o f th e C o rre la tio n M atrix : T o ta l = 14 A v e ra g e = 1

E ig e n v a lu e D iffe re n c e Proportion C u m u la tiv e

1 6 59987851 2 81601284 0 4 7 1 4 0 4714

2 3 78386567 2 01450864 0 2 7 0 3 0 7417

3 1 76935703 1 16715045 0 1264 0 8681

4 0 60220658 0 09954469 0 0430 0 9111

5 0 50266188 0 18962683 0.0359 0 9470

6 0 31303505 0 19404867 0 0224 0 9694

7 0 11898638 0 01161523 0.0085 0 9779

8 0 10737115 0 02882967 0 0077 0 9 8 5 5

9 0 07854148 0 02018283 0 0056 0 9911

10 0 05835865 0 02591266 0 0042 0 9953

11 0 03244599 0 01639305 0 0023 0 9976

12 0 01605294 0 00620463 0 0011 0 9988

13 0 00984831 0 00245794 0 0007 0 9995

14 0 00739037 0 0005 1 0000

Results of the principal component analysis are displayed on Table 1. We compute principal com

ponents from the correlation matrix. The set of partial indicators shows a high correlation bet

ween the variables, validating the relevance of prior principal component analysis to avoid pro

blems of multicollinearity. Following the Kaiser Rule to select the number of principal components

we keep the first three principal components.

Papeles de Trabajo del Instituto de Estudios Fiscales 1 /2 018


Figure 4

SCREE PLOT AND VARIANCE EXPLAINED PLOT

The Scree Plot on the left in Figure 4 shows that the eigenvalue of the first component is appro

ximately 6.6 and the eigenvalue of the second and third components are largely decreased to 3.8

and 1.8. The Variance Explained Plot on the right in Figure 4 shows that the first three principal

components account for nearly 87% of the total standardized variance, which indicates that two

components provide a good summary of the data.

Table 2

FACTOR PATTERN OF THE THREE PRINCIPAL COMPONENTS

F u c io r P in a m

iv a f iic to r l i v i l a t t o r i i v a l a a o r }

IV C S Large Firm SaJea In de « 0 33315 0 J3750 -0 3J133

V Û ftO tl U r g e F irm s & ^les in C onsum ption 0 37543 ■0 09113 0 0^733

HATPIC P o s s e n p e r C s* R egislrgdnn 0 37795 0 $ 1 4 0 9 0 02030

IM POR

R A

G o a d s end Services im parts

C o m p e n sa tio n o fE m p lo y s e s

o a j? s5

f l a n «

■0 36663

4 )5 2 9 9 4

0 29502

0 12297

FB C Fviv iend a H o using Invastm enl 0 35932 0 23479 -0 33540

CE E le c tr ic 3 ovwer C onsum ption 0 a « 4 2 -0 42206 0 03230

Cfi P e r p i le n r i i t i m l n f k a a i? n a 41 n?9?J A 4 S 7 M

7 U R IS R S

U C P

F a m in g Td uiis I Arrivals

l i i d e > l i y C^p^oity U l J l i i J l L H i

0,37419

0IÏ33O9

■0 24776

0 71307

0 62905

C 30430

ECI_CP0C B u s in e s s T e n d e ru y S u rv iy_p r« iL ie tion Hjltire ten d en c y m c e n s u m p u n goods -0 01404 0 73799 0 66261

E C L P P B C B u s in e s s T e n d e n c y S urvty_cnder books in consum er good s ■0 3190S 0 79392 0 3-397

ICM R e ta il Trade Indes 0 31976 0.37336 41.36302

IP1_BC In d u stry P ro d u c in g Index In C o n su m er G oads 0 43312 0 74392 ■0.3:765




The factor pattern (Table 2) shows that the first component (labeled “Ivafactor1”) has large positive

loadings for all coincident indicators: Large Firm Sales Index, Large Firms Sales in Consumption,

Goods and Services Imports, Compensation of Employees, Housing Investment, Electric Power Con

sumption, Registered Contracts, and Retail Trade Index. The second component (labeled “ivafactor2”)

has large positive loadings for all leading indicators: Industry Production Index In Consumer Goods,

Industry Capacity Utilization, Passenger Car Registration, Business Tendency Survey_production fu

ture tendency in consumption goods, Business Tendency Survey_order books in consumer goods.

The last component (labeled “ivafactor3” has large positive loadings for Foreign Tourist Arrivals.

The results of the Graphical Plot of the factor loadings are shown in Figure 5.

Figure 5

GRAPHICAL PLOT OF FACTOR LOADINGS

The graphical plot of factor loadings clearly features that coincident indicators cluster together on

Factor 1 axis, while leading indicators and Foreign Tourist Arrivals cluster together on Factor 2 axis.

4.2. Determining the transfer function

The second part of the methodology makes use of these factors as input variables for a transfer function:



Figure 6

CORRELATION ANALYSIS PANEL FOR VAT REVENUE.SAMPLE AUTOCORRELATION FUNCTION PLOT (ACF), PARTIAL AUTOCORRELATION FUNCTION PLOT (PACF)

AND SAMPLE INVERSE AUTOCORRELATION FUNCTION PLOT (IACF) OF VAT REVENUE

We introduce in the model two level shifts corresponding to the second quarter of 2010 and the

third quarter of 2012 (VAT reform). The parameter estimates table and goodness-of-fit statistics for this model are shown in the conditional Least Squares Estimation table (Table 3).

Table 3

TABLE OF PARAMETER ESTIMATES. METHOD: CONDITIONAL LEAST SQUARES

Conditional Least Squares Estimation

Approx Parameter Estimate Standard Error t Value Pr > |t| Lag Variable Shift

MU 8961 7 572 85313 15 64 < 0001 0 IVA 0

MA1.1 0 27422 0.11139 2 4 6 0 01 59 1 IVA 0

AR1.1 0 91475 0 05134 17 82 < 0001 4 IVA 0

NUM1 866 06089 379 97096 2 2 8 0 0252 0 ivafactorl 0

NUM2 2305 1 363 46813 6 3 4 < 0001 0 ivafactor2 0

NUM3 540 97856 162 10413 3.34 0 0013 0 ivafactor3 0

NUM4 4531 8 55843659 8 12 < 0001 0 Is2010q2 0

NUM5 2688 6 509 95067 5 2 7 < 0001 0 Is2012q3 0



As shown in table 3, all parameters are statistically significant.

Table 4

CHECK FOR WHITE NOISE RESIDUALS

Autoco frei a lion Check of Residuals

To Lag Chi Square DF Pr > ChiSq Autocorrelations

6 4.25 4 0 3T37 0.036 -0 165 0.075 0.062 -0 057 0.078

12 12 15 10 02749 0.177 -0 069 -0.037 -0.157 ■0.002 -0 091

IB 14 32 16 0 .5T47 -0.013 0 010 -0 026 -0.053 -0 051 - o . n o

24 20.94 22 0.5244 -0.126 0 094 0.049 0 095 ■0.117 -0.069

The autocorrelations checks of residuals (Table 4) features there is no autocorrelation of residuals at any lag. Test statistics fail to reject the no-autocorrelation hypothesis at a high level of

significance (p = 0.3790 for the first six lags). This result seems fairly robust to changes in the number of lags.

The probability of white noise is clearly high (Figure 9).

Figure 7

CORRELATION ANALYSIS PANEL FOR RESIDUALS. ACF, PACF AND IACF PLOTS OF THE RESIDUALS.WHITE NOISE PROBABILITY PLOT

Residual Correlation Diagnostics for IVA




Figure 8

RESIDUAL NORMALITY DIAGNOSTICS

We use the Q-Q plot in Figure 8 as a test to verify that the residuals follow a Normal Distribution.

Roughly speaking, the Q-Q plot take the sample data, sort it in ascending order, and then plot

them versus quantiles calculated from a theoretical distribution known as the standard normal

distribution with mean 0 and standard deviation 1. If both sets of quantiles come from the same

distribution, we should see the points converge to the straight line.

Figure 8 shows the Normality can be assumed, and we have stability in the model error.

As showed in Figure 8 residuals of the model follow a Normal distribution.

4.3. Out of sample forecasts

In this subsection we present the results of some backtesting exercises. In all cases the model

has proved its usefulness as a tool for short-term VAT revenue forecasting.

The forecast for the last quarter of 2017 according to this model is

In order to perform forecast evaluation and to avoid overfitting, we have divided the sample into a

training sample (from the first quarter of 1995 to the last quarter of 2012) and a validation sam

ple (from the first quarter of 2013 to the third quarter of 2017) with the following results.



Table 5FORECAST EVALUATION FOR VAT REVENUE IN VALIDATION SAMPLE. BACKTESTING DURING THE

SPAM 2003Q1-2017Q3. RECURSIVE ONE STEP AHEAD FORECAST

Forecasts,Std Error, 95% Confidence Limits and Residuals for variable VAT

Obs yeartrim FORECAST STD L95 U95 VAT RESIDUAL

1 2013Q1 15762 15 1139 22 13529 32 17994 98 13946 46 -1815 69

2 2013Q2 12033 40 1143 44 9792 30 14274 49 11522 37 -511 02

3 2013Q3 11814 81 1135 95 9588 38 14041 23 13004 41 118961

4 2013Q4 14225 10 1136 26 11998 06 16452 14 13457 55 -767 55

5 2014Q1 14854 61 1131 38 12637 13 17072 08 15792.49 937 88

6 201402 12457 77 1128 44 10246 07 14669 47 12292 14 -165 63

7 201403 13843 09 1120.51 11646 94 16039 24 1384347 0 38

8 2014Q4 14538 31 1112 59 12357 68 16718 94 14245 84 -292 46

9 2015Q1 16292 02 1105 35 14125 58 18458 45 16997 66 705 64

10 2015Q2 13057 67 1100 70 10900 33 15215 00 13032 93 -24 74

11 2015Q3 14886 54 1093 24 12743 82 17029 25 14976 82 90 29

12 2015Q4 15239 76 1085 98 13111 28 17368.23 15297 48 57 72

13 201601 17770 81 1078 8 3 15656 34 19885 27 17618 11 -152 69

14 2016Q2 14227 90 1071 94 12126 95 16328 86 13702.74 -525.16

15 2016Q3 15789 94 1066 66 13699 32 17880 55 15860 15 70.21

16 2016Q4 16168 17 1059 91 14090 78 18245 57 15664 37 -503 80

17 2017Q1 17824 64 1054 73 15757 40 19891 88 19100.62 1275 98

18 2017Q2 14141 09 1 0 5 7 1 0 12069 22 16212 97 14815.67 674 58

19 2017Q3 16333 07 1053 05 14269 12 18397 02 13135 96 -3197 11

20 2017Q4 16297 45 1099 92 14141.64 18453 25 ■

Figure 9GRAPH OF FORECAST EVALUATION IN THE VALIDATION SAMPLE. VAT REVENUE WITH SII EFFECT.

BACKTESTING DURING THE SPAM 2003Q1-2017Q3. RECURSIVE ONE STEP AHEAD FORECAST20000

I BUÛ0

16000

1 4 0 0 0

12000

10000

J a r Jan Jan Jan Jan Jan2013 2U1 6 2017 2018

yeartnm

□ 9 5 % Confidence Limite REALVAT REVENUE — — VAT FORECAST




Figures 9 and 11 show the predictive performance of the model in both, the validation sample and the whole sample. Although there is an anomalous fall in the third quarter of 2017 (the real value of VAT is outside the confidence limits), the model follows with enough accuracy the dynamics of the stochastic process that generates the serie, as it is shown in figure 12.

As mentioned before, there is an unexpected fall in the third quarter of 2017 which does not follow the time series pattern. This is due to the fact that August revenues were affected by the introduction of the new supply system “The immediate supply of information system (SII)” in the VAT returns. Since July, companies under this new system can submit their VAT returns until the 30th of the following month, instead of until the 20th day (due date that, in general, applies to monthly filing statements).

The Immediate Supply of Information System (SII) is a new system of keeping the VAT Register Books updated through the almost immediate supply of the billing records to the AEAT Electronic Tax Office.

For cash collection purposes this means that the revenues corresponding to July from the companies covered by the SII are accounted for in September rather than in August, as it used to be until July. It is estimated that, for this reason, in August, the VAT revenue has been biased downwards in 3,839 million.

Figure 10

BAR CHART OF THE DIFFERENCE IN REVENUE BETWEEN VAT AND THE VAT WITHOUT SII EFFECTS

This issue necessarily require an intervention to be introduced in the model at the last point of the validation period. Instead, for the assessment of the predictive ability of the model we use the variable “VAT revenue without the effects of the introduction of the SII” published by the Spanish Tax Agency8.

According to this correction, the forecast for the last quarter of 2017 is:

http://www.agenciatributaria.es/static_files/AEAT/Estudios/Estadisticas/Informes_Estadisticos/Informes_mensuales_ recaudacion_tributaria/2017/IMR_17_08.pdf.


8

http://www.agenciatributaria.es/static_files/AEAT/Estudios/Estadisticas/Informes_Estadisticos/Informes_mensuales



And the forecast evaluation graph without the effects of the introduction of the SII is shown in figure 11.

Figure 11

VAT REVENUE FORECAST, REAL VAT REVENUE WI THOUT THE EFFECTS OF SII, AND CONFIDENCE

LIMITS IN THE VALIDATION SAMPLE. BACKTESTING DURING THE SPAM 2003Q1-2017Q3.

RECURSIVE ONE STEP AHEAD FORECAST

Figure 12

VAT REVENUE AND FORECASTS DURING THE WHOLE PERIOD AND WITH THE

CORRECTION OF THE SII EFFECTS




5. CONCLUSIONS

As mentioned in the introduction, the final aim of this paper is to propose a methodology that successfully combines principal components analysis and transfer function theory to forecast VAT

revenue. This approach offers advantages to Value-Added Tax forecasting models based on the

National Accounts approach, and specifically, to those using Total Consumption Expenditure on

Goods and Services as the only input explanatory variable. The pre-selection of the reference se

ries and the dimension reduction technique enables to incorporate in advance changes in speci

fic fields of the economy that may affect tax revenues.

The analysis of which partial indicators contain useful leading or coincident information about the

dependent variable and the filtering process aimed to identify underlying cyclical pattern of the can

didate component series was not simple. The approach taken does not in any sense attempt to construct an optimal set of partial indicators, but has the more limited aim of assessing which indi

cators contain information that is useful for VAT revenue short-term forecasting. Among other crite

ria, we selected those variables that exhibited a cyclical profile highly correlated to the cyclical pattern of VAT revenue. Industry Production Index In Consumer Goods, Industry Capacity Utilization,

Passenger Car Registration, Business Tendency Survey (production future tendency in consumption

goods) and Business Tendency Survey (order books in consumer goods) were found to add significant leading information to the model. The usefulness of the rest of indicators arises from the con

temporaneous relationships between the variables, and their inclusion in the model found some

support in less sophisticated methods such as correlation analysis. Consumption indicators selected also have the advantage of having shorter publications lags than the National Accounts.

The output factors obtained from the dimension reduction technique were highly significant as

explanatory variables in the transfer function. Thus, their influence has been crucial for achieving such high predictive power of the model.

The forecast evaluation during the validation period provides evidence of the predictive ability of the

model. Despite the fact that there is an anomalous fall in the third quarter of 2017 (caused by the introduction of a new electronic supply system, SII), using the estimation of the effect published by

the Spanish Tax Agency, it is clearly shown the robustness of the forecast provided by the model.

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PAPELES DE TRABAJO · 2018. 3. 22. · AMINO PAPELES DE TRABAJO 1/2018 Determining macroeconomic indicators to implement a short-term forecasting model for VAT revenue C G ONZÁLEZ