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PAPELES DE TRABAJO

9/2019

Exploring the predictive capacity of real estate sector indicators in

forecasting regional tax revenues on Real Property Transfers

(RPTT) and Stamped Legal Documents (STD)

JOSÉ Mª PIÑERO CAMPOS

[email protected]

CAMINO GONZÁLEZ VASCO

[email protected]

Institute for Fiscal Studies, Spain

December, 2019

.

mailto:[email protected]

Papeles de Trabajo del Instituto de Estudios Fiscales 9/2019

ÍNDICE

Abstract

1. INTRODUCTION

2. ESTIMATION STRATEGY

2.1. Auto-Regressive with eXogenous input models (ARX)

2.2. Principal component analysis as a dimension reduction technique

3. ESTIMATION RESULTS AND FORECAST EVALUATION FOR THE VALIDATION SAMPLE. ANNUAL MODEL

3.1. Out of sample forecast: backtesting exercises

4. ESTIMATION RESULTS AND FORECAST EVALUATION FOR THE VALIDATION SAMPLE. MONTHLY MODEL

5. CONCLUSION

References

Annex 1: results obtained by the annual forecasting models for the RPTT and SLD Tax revenue by autono-

mous communities

Annex 2: annual model’s equations by autonomous community


Abstract

This paper contributes to the empirical literature on the development and estimation of a forecasting model

for Real Property Transfers (RPTT) and Stamped Legal Documents (SLD) tax base at regional level focusing

on the study of real estate sector indicators. We propose two kinds of ARX models to estimate this tax base.

Firstly, we test whether the number of annual approvals for new residential constructions is a good predic-

tor or the annual RPTT and SLD tax base for each Spanish autonomous community over the period 1992–

2018. Secondly, we extend the number of real estate indicators considering monthly data from Mortgage

Statistics and the Statistics on Transfer of Property Rights provided by the Spanish National Statistics Insti-

tute. These indicators are found to be significant determinants of the tax base for every region. Applying the

corresponding tax rate to the estimated tax base, we obtain the prediction for the tax revenue.

Results of the backtesting exercises show that both annual and monthly models successfully predicts the

evolution of the actual RPTT and SLD tax revenues for every region and illustrate its usefulness as a tool for

regional revenue forecasting.

Keywords: normative tax collection, fiscal capacity, fiscal federalism, revenue forecasting, ARX models.

JEL classification numbers: : H71 ,C53, H68, C22.

JOSÉ Mª PIÑERO CAMPOS y CAMINO GONZÁLEZ VASCO

Exploring the predictive capacity of real estate sector indicators in forecasting regional tax revenues on Real Property

Transfers (RPTT) and Stamped Legal Documents (STD)


4

1. INTRODUCTION

Spain is one of the countries in Europe with the most visible splits on territorial issues. Regional

inequalities as well as language policy have been given increasing salience on the political agen-

da during the last few decades. The Spanish state is now one of the most decentralized in Eu-

rope. The current vertical organization of government includes, besides the central government,

17 autonomous communities (regional governments) and 2 Autonomous Cities. The Spanish

Constitution establishes two basic different systems for financing the regional governments: the

common and the foral regime. The common regime applies to all autonomous communities (AC)

with the exception of two: the Basque Country and Navarre. These two AC operate under the foral

(special) regime. Our research work focuses on those regions operating under the common re-

gime.

When analyzing the financing of the ACs in Spain, the control over taxes assigned to the AC (so-

called “ceded taxes”) acquire special relevance, since these are the ones that best represent the

ACs' autonomy and those that reflect in a more effective way the principle of co-responsibility. The

Spanish AC have almost complete autonomy over these taxes and can act in a very effective way

on them, both from the point of view of tax management, and from the point of view of tax rates

and tax bases. Ultimately, over the tax collection.

It is true that, if it were not for the fact that, unfortunately, these taxes are not quantitatively very

important, it could be said that the financing system of the AC is based on the ceded taxes, since

the rest of the financing system’s resources would be the necessary complement to be able to

reach the necessary financing so that the provision of the transferred services can be covered.

It is precisely due to this aspect of the financing system that is fundamental that this base is equi-

table for all the ACs, in the sense that it provides the same equality of opportunities for all of them

to be able to provide the services that they have assigned (decentralized). The definition of this

equitable starting point is one of the fundamental problems presented by the current funding

system of the ACs, since the current definition, the so-called regulatory collection, is based on the

starting revenue of an evolved year projected by an annual index, the same for all the ACs.

This definition has meant that, even under similar conditions of application of ceded taxes, differ-

ences between actual and regulatory collections have been observed ranging from one third to

more than twice that regulatory value. This result is deeply unfair, because if the actual collection

is one third of what was assumed when calculating the financing complement that the other re-

sources of the financing system should provide, the corresponding AC will not be able to provide

the services in conditions of equality with respect to the rest of the ACs.

If, on the other hand, the actual collection is more than double that the one used to calculate the

rest of the resources that complement the financing of a specific AC, this AC will have enough

resources which will probably be used to provide additional services not previously foreseen,

when this resources could have been assigned to those under-financed AC and thus contribute to

the cost optimization of the financing system as a whole.





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The use of the actual real revenue collection of ceded taxes for the purpose of calculating the

financing system is discarded since it would make the AC to lose the incentive they have for exer-

cising their regulation capacity over tax rates and tax bases adjusting their taxes to the services

demanded by their inhabitants, ie, implementing the healthy use of the “co-responsibility” con-

cept. Thus, a fairer calculation of what would be the regulatory value of the collection of ceded

taxes is crucial to be able to move towards a more equitable financing system of the Spanish ACs.

The normative or regulatory collection of a tax should try to approximate the revenues that the

different regions would have obtained if a common tax scale had been applied throughout the

whole country and the efficiency on collection of taxes had been similar across the different re-

gions. After more than 30 years of regional managing of taxes, differences related to inefficiency

would have faded in comparison with differences due to tax scale. Then, the magnitude that we

would like to use in regional financing is the collection that each AC would have obtained if they

have not made use of its normative competences in tax matters.

In this regard there are numerous studies that illustrates the problem related to the normative

collection for the traditional ceded taxes, as it is highlighted in the applied studies of López-

Laborda (2015) and De La Fuente (2012, 2014 and 2016). Among the ceded taxes, the Real

Property Transfers (RPTT) and Stamped Legal Documents (STD) tax stands out, which accounts

for more than half of the total set of ceded taxes and that has come to represent, in the years of

the real estate boom, more than 20% of the resources of the financing system of the Spanish

ACs.

Then, as a first approach to the problem of a more fair calculation of the normative value of the

ceded taxes, the main goal of this paper is to approximate the actual and future revenue collec-

tion of Real Property Transfers (RPTT) and Stamped Legal Documents (STD) tax that will be ob-

tained in each AC applying the actual tax rates to a forecasted tax base. This tax base is the result

of an ARX model using as an exogenous regressor one of the leading indicators of activity in the

contruction sector: the number of annual approvals for new residential constructions.

The use of a different model for each AC does not allow regional comparisons in terms of efficien-

cy in tax management but, as stated before, these differences should not be significant at pre-

sent and, on the contrary, it is considered that different relationships between regional indicators

and revenue collection from each region should exist due to socioeconomic differences.

Another key aspect of the use of the proposed ARX model is that the existence of lags in the input

exogenous regressor allows us to provide regional revenue forecastings obtained from observed

values of the regional real estate indicators. These forecastings can be used in the calculation of

“credit into account” made by the Central Govermment to the ACs’ budgets every year.

Thus, the real estate indicators observed data, for the purpose of calculating the final settlement

in terms of AC financing system, are known with a maximum delay of just months, much earlier

than with the current system, where the value of the update rates is known more than two years

late.





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This paper is organized as follows. Section 1 illustrates the design of the regional financing sys-

tem in Spain and the importance within the system of the RPTT and STD tax collection. Section 2

outlines the derivation of the model employed and describes the estimation technique and the

empirical framework. Section 3 presents the estimation results and the forecast evaluation for

the validation sample in the annual model. Section 4 presents the estimation results and the

forecast evaluation for the validation sample in the monthly model. The last section provides the

main conclusions of this study.

2. ESTIMATION STRATEGY

The main goal of this paper is to approximate the actual and future revenue collection of Real

Property Transfers (RPTT) and Stamped Legal Documents (STD) tax that will be obtained in each

AC applying the actual tax rates to a forecasted tax base. This tax base is the result of an ARX

model using as an exogenous regressor one of the leading indicators of activity in the construc-

tion sector: the number of annual approvals for new residential constructions.

The estimation strategy is divided into two steps. In a first step we propose two kinds of alterna-

tive ARX models to predict the tax base. The second step consists on applying the actual tax rates

of each region to the forecasted tax base to obtain the projected revenue collected.

We propose two alternatives to estimate the tax base for each AC for the year 2019: an annual

model and a monthly model.

The annual model has the advantage of managing the time interval we need to obtain forecasts,

in addition to decreasing the prediction bias by using "one step ahead" forecasts. Its main disad-

vantage lies in the minimum history length needed for the ARX approach, which limits us the

available indicators related to the real estate sector with annual frequency, regional disaggrega-

tion and history length needed. Thus, taking into account the available data, the exogenous vari-

able that will guide the prediction in the annual model will be, for each AC, the number of

approvals for new residential construction. This indicator is published by the Spanish Ministry of

Public Works.

Although we understand that new constructions are subject to VAT and not Real Property Transfer

tax, what we intend is to use a leading indicator able to track the investment in construction and

foresee its short/medium-term evolution, in the Spanish case. The number of approvals for new

residential construction is used as a leading indicator concerning the construction sector from the

supply side, able to predict the adjustment in the residential sector (Gómez, A. L., et al. (2017)).

The monthly model has the advantage of having longer time series, and therefore there are more

indicators related to the construction sector available to guide the prediction. A principal

component analysis prior to the transfer function model eliminates the possible multicollinearity

problems that could be caused by working with several highly correlated indicators. The main

disadvantage of the model is related to the forecast horizon: the bias in the prediction increases

as the forecast horizon lengthens. Since our interest is to obtain an annual prediction, despite





7

having monthly data, we expect the data corresponding to the year (twelve steps ahead in the

monthly model) to be less accurate than the one obtained in the annual model with the same

number of indicators. However, when using the monthly model we can use several construction

indicators (since there are more indicators with sufficient historical data available) the predictive

capacity of this monthly model may exceed that of the annual model. For this monthly model we

use, in addition to the number of monthly approvals for new residential constructions, monthly

data from Mortgage Statistics and the Statistics on Transfer of Property Rights provided by the

Spanish National Statistics Institute.

All data referring to tax on Property Transfers and Stamp Duty by AC have been provided by The

General Inspectorate of the Ministry of Finance and Civil Service.

We will now outline the techniques applied.

2.1. Auto-Regressive with eXogenous input models (ARX)

Suppose that the l-dimensional time series consists of p-dimensional output variables:

and q-dimensional input variables:

So that l=p+q and =

The autoregressive exogenous model (ARX model) with inputs and outputs is given by:

Where and are (p×p) and (p×q) matrices, and is a p-dimensional white noise covariance

matrix .

Note that this ARX model is a part of the AR model for l-dimensional time series

With the relation

,

The symbol indicates that this part of the matrix is not used in the ARX model. This means that

the parameters of the ARX model are obtained as part of the multivariate AR model for the time





8

series . Therefore, the Yule-Walker estimates of and ,j = 1,..., m can be obtained from

those of Aj , j = 1,..., m.

However, the best order for this ARX model is not necessarily the same as that of the multivariate

AR model for .

The AIC for the ARX model is given by

AICm = N log |Wr,m| + 2p(p + q)m + p(p + 1),

where N is the data length, and | Wr,m | is the determinant of the estimate of the variance covar-

iance matrix of the innovation of the ARX model of order m.

Moreover, the sum of the second and third terms on the right-hand side is equal to twice the

number of parameters of this model. According to the minimum AIC procedure, the order that

attains the minimum of AICm is considered to be the best model (Akaike, H. (1974), Konishi, S.

and Kitagawa, G. (2008)).

2.2. Principal component analysis as a dimension reduction technique

The ultimate goal in principal components analysis (PCA) is to find the minimum number of di-

mensions 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 inter-

pret.

PCA was originated by Pearson, K. (1901) and later developed by Hotelling, H. (1933). The appli-

cation of principal components is discussed by Rao, C.R. (1964), Cooley, W.W. et al. (1971), and

Gnanadesikan, R. (1977). Exceptional statistical treatments of principal components are found in

Kshirsagar, A. (1972), Morrison, D.G. (1976), and Mardia,K.V. et al.(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, C.R. (1964), Kshirsagar, A. (1972)):

The eigenvectors are orthogonal, so the principal components represent jointly perpen-

dicular 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 combina-

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





9

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 orig-

inal variables.

The scores on the first j principal components have the highest possible generalized Var-

iance 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 interpreta-

tion of least squares regression, which minimizes the sum of squared vertical distances.

3. ESTIMATION RESULTS AND FORECAST EVALUATION FOR THE VALIDATION SAMPLE. ANNUAL

MODEL

We present the results of the ARX model using annual approvals for new residential constructions

as a predictor of the tax base for each of the AC of the common system. The estimated tax base

will be multiplied by the tax rate to obtain the projected revenue collection.

Next figure show the results of the conditional least square estimation for the regional RPTT and

STD tax base using the annual ARX model.





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Figure 1

CONDITIONAL LEAST SQUARE ESTIMATION FOR THE RPTT AND STD TAX BASE. THE INPUT REGRESSOR

LVISADOS STANDS FOR NATURAL LOGARITHM OF THE NUMBER OF ANNUAL APPROVALS FOR NEW RES-

IDENTIAL CONSTRUCTIONS BY AC





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The ARX model uses the natural logarithm of the number of annual approvals for new residential

constructions by region as an exogenous regressor in the model. Although it is true that the pur-

chase of newly built constructions is subject to VAT and not to Real Property Transfer Tax, the

correlation of this variable with the purchase of existing homes is clearly high: in terms of

interannual growth rate variations the coefficient of correlation during the time spam 2007-2017

for the whole country is 0,87893743.





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Figure 1 bis

EVOLUTION IN TERMS OF INTERANNUAL VARIATION RATES FOR THE WHOLE COUNTRY OF “NUMBER OF

PROPERTY TRANSFERS” AND “ANNUAL APPROVALS FOR NEW RESIDENTIAL CONSTRUCTION”

Due to the historical data of annual approvals for new residential construction for all ACs, we will

consider this variable as an exogenous regressor for the annual model.

In most of the regions there is a significant structural break in the taxable base after the 2008

crisis, which is introduced into the model with the dicotomic indicator LS2008.

Annex 2 displays for every AC the equation derived from this conditional least squared estimation.

In all models, all coefficients are significantly different from zero considering the p-value for the

test of individual significance (t-test).

The autocorrelation check of the residuals is shown in Figure 2.





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Figure 2

AUTOCORRELATION CHECK OF THE RESIDUALS. NULL HYPOTHESIS: THERE IS NO AUTOCORRELATION IN

RESIDUALS UP TO LAGS 6, 12, 18 OR 24





14

For all regions, the autocorrelations check of the residuals 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. These results seem fairly robust to changes in the number of lags.

Next figure shows the correlation analysis panel for residuals in the annual ARX model for the

fifteen ACs:

Figure 3

CORRELATION ANALYSIS PANEL FOR RESIDUALS IN THE ARX ANNUAL MODEL FOR EVERY REGION. SAM-

PLE AUTOCORRELATION FUNCTION PLOT (ACF), PARTIAL AUTOCORRELATION FUNCTION PLOT (PACF)

AND SAMPLE INVERSE AUTOCORRELATION FUNCTION PLOT (IACF)





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16

Autocorrelation function and Partial Autocorrelation Function of residuals show no peaks that

exceed the confidence limits (95%). The probability of residuals being a white noise is clearly high

for all the Spain’s ACs over the period 1992-2018.

We use the Q-Q plot in next figure as a test to verify that the residuals in all the ARX annual mod-

els follow a Normal Distribution.





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Figure 4

RESIDUAL NORMALITY DIAGNOSIS FOR THE ARX ANNUAL MODEL. SPAIN’S AUTONOMOUS COMMUNITIES





18

In those regions where the graphical Q-Q plot is not conclusive (Andalucía and La Rioja) we pre-

sent the skewness and kurtosis values of the residual distribution which are in the (-2, 2) interval.

The values for skewness and kurtosis between -2 and +2 are considered acceptable in order to

prove Normal univariate distribution (George, D. et al. (2010)).





19

Figure 5

SKEWNESS AND KURTOSIS VALUES OF THE RESIDUALS DISTRIBUTION IN THE ARX ANNUAL MODEL FOR

THE REGIONS OF ANDALUCIA AND LA RIOJA

3.1. Out of sample forecast: backtesting exercises

In order to perform forecast evaluation, we have conducted several backtesting exercises to

compare the forecasted revenue with the actual revenue collected. In all ACs the model has

proved its usefulness as a tool for RPTT and STD tax revenue forecasting.

Figures 6 to 9 show the predictive performance of the ARX annual model in a recursive one-step

ahead forecast during the whole period. For each region, we test the ARX model forecast for the

regional tax base. We then obtain the projected revenue collected as the product of the tax rate

and the predicted tax base.





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Figure 6

FORECAST EVALUATION FOR THE REGIONS OF ANDALUCÍA, ARAGÓN, ASTURIAS Y

BALEARES.BACKTESTING DURING THE TIME SPAN 1992-2019





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Figure 7

FORECAST EVALUATION FOR THE REGIONS OF CANARIAS, CANTABRIA, CASTILLA LA MANCHA Y CASTILLA

Y LEON. BACKTESTING DURING THE TIME SPAN 1992-2019





22

Figure 8

FORECAST EVALUATION FOR THE REGIONS OF CATALUÑA, EXTREMADURA, GALICIA Y MADRID.

BACKTESTING DURING THE TIME SPAN 1992-2019





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Figure 9

FORECAST EVALUATION FOR THE REGIONS OF MURCIA, LA RIOJA AND COMUNIDAD VALENCIANA.

BACKTESTING DURING THE TIME SPAN 1992-2019

Figures 6 to 9 show the good tracking properties of the annual ARX model during the whole peri-

od. The red line in the graphs stands for the real revenue collected. The blue dashed line repre-

sents the forecasts of the ARX annual model using the number of annual approvals for new

residential constructions as an exogenous predictor. The blue shaded area shows the confidence

limits. Annex 1 shows the figures for this exercises obtained with the annual model.





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4. ESTIMATION RESULTS AND FORECAST EVALUATION FOR THE VALIDATION SAMPLE.

MONTHLY MODEL

As we have specified in section 2, the monthly model has the advantage of offering a greater

number of indicators related to the construction sector with sufficient historical data to guide the

prediction. For this monthly model we have chosen four main regressors from January 2007 on-

wards: the number of monthly approvals for new residential constructions published by the Span-

ish Ministry of Public Works, monthly data from Mortgage Statistics and the Statistics on Transfer

of Property Rights provided by the Spanish National Statistics Institute. These indicators are high-

ly correlated, so we will use a dimension reduction technique such as PCA to avoid

multicollinearity problems in the model. The two resulting principal components which are orthog-

onal will be used as inputs of the ARX model.

We will now outline the results of the Comunidad de Madrid region. The model can easily be ex-

tended to the rest of the ACs with the same indicators and similar results.

Next figure shows the eigenvalues of the correlation matrix in the PCA. The set of three indicators

show high correlation between the variables, validating the relevance of applying a dimension

reduction technique prior of the ARX model.

Figure 10

EIGENVALUES OF THE CORRELATION MATRIX

Despite the fact that if we followed the Kaiser rule we should select only the first principal com-

ponent (eigenvalue 3.27 is greater than one) choosing the two first principal components we are

able to explain almost the 95% of the total variance of the set of indicators, as shown in the vari-

ance explained plot. Both components are significant regressors in the ARX model.





25

Figure 11

SCREE PLOT AND VARIANCE EXPLAINED PLOT

The Scree Plot on the left of figure 11 shows that the eigenvalue of the first component is well

over three and the eigenvalue of the second component is largely decreased to 0.49. The vari-

ance explained plot on the right shows that the first two principal components account for nearly

95% of the total variance.

Ideally, we would like to review the correlations between the variables and the components and

use this information to interpret the components. Unfortunately, when more than one component

has been retained in an analysis, the interpretation of an unrotated factor pattern is usually quite

difficult. To make interpretation easier, we perform a VARIMAX rotation, that is a linear transfor-

mation performed on the factor solution for the purpose of making the solution easier to interpret.

A VARIMAX rotation is an orthogonal rotation, meaning that it results in uncorrelated components.

Compared to some other types of rotations, a varimax rotation tends to maximize the variance of

a column of the factor pattern matrix (as opposed to a row of the matrix). This rotation is probably

the most commonly used orthogonal rotation in the social sciences.

Next figure shows the Varimax rotated factor Pattern Plot of Component 2 by Component 1





26

Figure 12

VARIMAX ROTATED FACTOR LOADINGS

Interpreting a rotated solution means determining just what is measured by each of the retained

components. Briefly, this involves identifying the variables that demonstrate high loadings for a

PCA given component, and determining what these variables have in common. The two indicators

relative to monthly data from mortgage statistics (number and amount) cluster together on factor

one axis. The indicators related to the number of monthly approvals for new residential construc-

tions and the number of Transfer of Property Rights provided by the Spanish National Statistics

Institute cluster together on factor 2 axis.

Once we have two orthogonal regressors (two principal components) that summarize the infor-

mation of the initial four indicators, we can use these regressors as inputs in the ARX model to

guide the prediction of the tax base in the Comunidad de Madrid region.





27

Figure 13

CONDITIONAL LEAST SQUARES ESTIMATION FOR THE RPTT AND SLD TAX BASE

The ARX model uses the two principal components obtained in the previous section itpfactor1,

itpfactor2 as exogenous regressors in the model. Regarding the first factor, the one in which the

highest scores correspond to “monthly approvals for new residential constructions” and the

“number of transfers of property rights”, there is a delay of three months with respect to the value

of the RPTT and SLD tax base. The ARX model also includes a seasonal moving average parame-

ter. According to figure 13 all the parameters are statistically significant.

+ 385747 I

Where:

is the RPTT and SLD tax base.

is the innovation

are the two first principal components.

B is the lag operator.

= 1 if t>=2007m09

=0 if t< 2007m09

The autocorrelation check of the residuals is shown in Figure 14.

Figure 14

AUTOCORRELATION CHECK OF RESIDUALS





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The autocorrelations checks of residuals feature there is no autocorrelation of residuals at any

lag. Test statistics fail to reject the no-autocorrelation hypothesis at a high level of significance.

This result seems fairly robust to changes in the number of lags.

Figure15

CORRELATION ANALYSIS PANEL FOR RESIDUALS. SAMPLE AUTOCORRELATION FUNCTION PLOT (ACF),

PARTIAL AUTOCORRELATION FUNCTION PLOT (PACF) AND SAMPLE INVERSE AUTOCORRELATION FUNC-

TION PLOT (IACF)

Autocorrelation Function and Parcial Autocorrelation Function of residuals show no peaks that

exceed the confidence limits (95%). The probability of residuals being a white noise is clearly

high.

Figure 16

RESIDUAL NORMALITY DIAGNOSTICS FOR THE ARX MODEL





29

The histogram confirms the Normality of the distribution (bell-shaped) as it shows the highest

frequency in the center of the distribution. In the Q-Q plot the deviations from the straight line are

minimal and focused on the extreme values of the residual distribution.

The following figure shows the recursive forecast (one step ahead) for the RPTT and SLD tax base

during the whole period:

Figure 17

RECURSIVE FORECAST ONE STEP AHEAD FOR THE RPTT AND SLD TAX BASE USING THE ARX MODEL

As shown in Figure 17, the model forecast successfully follow the real tax base and stays within

the 95% confidence limits. Indicators related to mortages and transfer of property rights seem to

sucessfully follow the evolution of the tax base during the entire period.

The last step in the model is to apply the tax rate to the forecasted tax base to obtain the fore-

casted tax revenue. The result of the backtesting exercise for the whole period is shown in figure

18.





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Figure 18

RECURSIVE ONE STEP AHEAD FORECAST FOR THE RPTT AND SLD TAX REVENUES USING THE ARX MODEL

In the previous figure, the red line represents the amount of revenue actually collected per

month, while the blue dashed line represents the collection predicted by the model. The blue

shaded area represents the confidence limits.

This backtesting exercise shows that the overall forecasts of the model using the set of 4 indica-

tors seems highly accurate for the time period considered. The following table displays the predic-

tions of the model (forecast_revenue) versus the real revenue collected (RPPT _SLD) until May

2019 for the Comunidad de Madrid region using predictions of the partial indicators.





31

Figure 19

RECURSIVE ONE STEP AHEAD FORECAST FOR THE RPTT AND SLD TAX REVENUES AND 95% CONFIDENCE

LIMITS. TIME SPAM: APRIL 2015,MAY 2019





32

5. CONCLUSION

As mentioned in the introduction, the final aim of this paper is to propose a methodology that

successfully combines indicators approaching activity in the real estate sector to generate a fore-

casting model for RPTT and SLD tax revenue .The model has proved to approximate the actual

and future revenue collection in each AC applying the actual tax rates to a forecasted tax base.

This tax base is the result of an ARX model using as regressors some of the indicators of the real

estate market.

Two alternative models have being considered for estimating the tax base for each AC with differ-

ent time intervals (annual and monthly models). In order to perform forecast evaluation and to

assess the performance of the proposed time series model compared to the existing normative

model we illustrate the following results during the time span 2009-2016:

Figure 20

EVOLUTION OF THE INDEX CORRESPONDING TO THE TAX REVENUES RELATED TO RPTT AND SLD

ACCORDING TO NORMATIVE COLLECTION COMPARED WITH THE REAL ACTUAL COLLECTION

The model of prediction of the normative collection currently used for the calculation of the fi-

nancing system of the Spanish AC is based on estimating the growth of the RPTT and SLD tax

revenues based on the sum of the final tax revenues for the PIT, VAT and special manufacturing

taxes received in each AC in the year (x) with respect to those received related to the same con-

cepts in 2009, in homogeneous terms and without regulatory capacity.

This model presents important distortions in the annual comparison, where sometimes the real

values collected are 2.5 times greater than the normative ones and, therefore, those taken into

account in the financing model, remaining, on the contrary, reduced in occasions to little more

than half. But the fact that is more dangerous is that this distortion is also observed when calcu-

lating the average of a sufficient period of years (for example taking into consideration the time

span 2009-2016) when the differences between predictions from the current model and the val-

ues of real collection differ in a range of more than 100 points .





33

The danger lies in the fact that those Spanish AC that are expected to collect RPTT and SLD tax

revenues above the real value will have their funding diminished, although this circumnavigation

occurs in only two cases and with differences of a maximum of 20%.

But the opposite case is also dangerous from the National Treasury point of view, since it means

that the collection capacity of the RPTT and SLD has been underestimated by adding unnecessary

system resources for other concepts.

The problem is even greater in terms of equity since the existence of a medium-term average

range of 100 points means that some ACs have an improvement in funding compared to others

that double the collection of tax considered.

The following table shows the evolution of the index corresponding to the tax revenues related to

RPTT and SLD tax collection according to the time series model compared with the real revenue

collection.

Figure 21

EVOLUTION OF THE INDEX CORRESPONDING TO THE TAX REVENUES RELATED TO RPTT AND SLD

COLLECTION ACCORDING TO TIME SERIES MODEL COMPARED WITH THE REAL ACTUAL COLLECTION

As shown in Figure 21 according on the time series model, the annual distortions are much

smaller as there is a variation of more than 27% and less 21%. Considering the eight years period

from 2009 to 2016 the fluctuations range in the average is even smaller, barely reaching 10 per-

centage points, 10 times lower than with the current prediction model.

The conclusion is that with the proposed model of time series a more tight allocation of resources

to the ACs could be made, respecting the principle of sufficiency in the financing and, at the same

time, greatly improve the same model in terms of equity.





34

References

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común: un análisis crítico y datos homogéneos para 2009 y 2010”, mimeo, Instituto de Análisis

Económico (CSIC). (http://ideas.repec.org/p/aub/autbar/917.12.html)

DE LA FUENTE, A. (2014): “La evolución de la financiación de las comunidades autónomas de régimen

común, 2002-2012”, FEDEA Estudios sobre la Economía Española, nº. 2014-07, Madrid.

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Sankhyā: The Indian Journal of Statistics, Series A, 329-358.





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ANNEX 1

RESULTS OBTAINED BY THE ANNUAL FORECASTING MODELS FOR THE RPTT AND SLD TAX

REVENUE BY AUTONOMOUS COMMUNITIES

Andalucia:





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Aragón:





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Principado de Asturias:





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Illes Balears:





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Canarias:





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Cantabria:





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Castilla-La Mancha





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Castilla y León:





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Cataluña:





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Extremadura:





45

Galicia:





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C. de Madrid:





47

Región de Murcia:





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La Rioja:





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C. Valenciana:





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ANNEX 2

ANNUAL MODEL'S EQUATIONS BY AUTONOMOUS COMMUNITY

Equations for ARX model:

In all equations the variable ls2008 stands for the level shift and is the error term.

Andalucia:

Aragón:

Principado de Asturias:

Illes Balears:

Canarias:

Cantabria:

Castilla la Mancha:

Castilla y León:

Cataluña:

Extremadura:





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Galicia:

C. de Madrid:

Región de Murcia:

La Rioja:

C. Valenciana:

PAPELES DE TRABAJO · 2020. 1. 7. · Papeles de Trabajo del Instituto de Estudios Fiscales 9/2019...

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