The Estimation of Gross Value Added of Sole Proprietors for 2011 in Hungary

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The Estimation of Gross Value Added of Sole Proprietors for 2011 in Hungary

Ildikó Ritzl-Kazimir chief councillor

Hungarian Central Statistical Office

E-mail: Ildiko.Ritzlne@ksh.hu

The purpose of this paper is to demonstrate the new methodology for estimation of sole proprietors’

gross value added (GVA), introduced into the national accounts in 2011. The initiative for the development of the new methodology was that the outputs of previous methods do not harmonise with the system of supply and use tables. The GVA of sole proprietors is a significant contributor to the GVA of Hungary; it is therefore important to have detailed data on these activities.

The developed estimation method takes into account the GVA based on administrative data, and the non- observed GVA is estimated in accordance with the Eurostat recommendation for the separate categories of the non-observed economy. 31% of sole proprietors’

GVA are calculated from administrative data sources, while 69% comprise the estimated non-observed activity in 2011 according to the developed model.

KEYWORDS: Sole proprietors.

Value added.

Non-observed economy.

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T

he paper describes the new method for calculation of registered sole proprietors’ GVA. The objective of the development was to devise a new method that would provide a more accurate picture about the economic performance of sole proprietors through the extensive use of all available information and databases. Moreover, this calculation method complies with EU requirements.

The new method uses sole proprietor administrative data, and estimates separately the economic performance for certain categories of non-observed economies according to the Eurostat [2005] recommendation.

We used the new methodology, which was introduced in 2011, to calculate the individual economic performances of sole proprietors. The results were cast back to 2003 at the four-digit level of Statistical classification of economic activities in the European Community (NACE) Rev. 2 and at the two-digit level of NACE Rev. 2 for the period 1995–2002. The new methodology was presented at the 2012 UNECE Conference of European Statisticians in the Group of Experts on National Accounts (HCSO [2012]). The paper describes this methodology, and includes the results of estimation for the reference year 2011.

The estimation of the non-observed activity was a huge challenge to development. This paper therefore defines it in the first section and describes the main alter- native ways in which the non-observed economy can be estimated. The next section summarises the main characteristics of data sources for sole proprietors in Hungary.

Finally comes the description of the developed method, which includes the calculation of administrative GVA and the estimation of non-observed GVA by categories in the non-observed economy.

1. The definition and estimation of non-observed economy

The non-observed economy involves a very wide range of activities; making any definition of the non-observed economy a difficult task. In addition, a wide variety of names is applied which are often used as synonyms for non-observed economy, yet generally their meanings do not cover the same category. In this paper those activities belong to the scope of non-observed activities that are considered to be production in a statistical sense i.e. activities that use inputs to produce goods and services under the responsibility and supervision of an institutional unit (Eurostat [1996]).

However, administrative data from tax returns and surveys are not available to esti-

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mate their extent. Non-observed activities can be classified into categories by detect- ing reasons behind the lack of administrative data.

Eurostat has already developed an integrated system of tables to take into account non- observed activities in order to suit the data of non-observed economic performance to the system of national accounts, and to ensure the international comparability of data. Eurostat classifies non-observed activities into seven categories by registration of producer, illegali- ty of activity and availability of data labelled with N1–N7 (Eurostat [2005]).

The non-observed activities of sole proprietors can be classified into three categories – N5, N6, and N7 – of the formerly mentioned groups. The group N5 includes the sole proprietors, who have no administrative data from which the GVA could be calculated.

In practice they do not file tax returns. The group N6 includes registered sole proprietors, they have available appropriate administrative data, but it can be assumed that they conceal a part of their income to avoid paying taxes. This activity falls within the scope of non-observed economy. In case of group N7 there is no regular reporting requirement of which the output and GVA of sole proprietors could be calculated.

Detailed knowledge of non-observed economic performance by category provides an opportunity to explore important correlations and to build analysis options. To create an appropriate estimation method, the characteristics of each category must be taken into account. Further help can be gleaned through the OECD handbook (OECD [2002]) and the already mentioned Eurostat [2005] recommendation, which classify the methodological recommendations according to the categories of the non- observed economy. Table 1 contains recommended options for three categories of sole proprietor-related non-observed economy.

Table 1 Procedures for the estimation of sole-proprietor-related non-observed categories

Recommendation Registered but not surveyed sole proprietors (N5)

Deliberate misreport- age (N6)

Statistical deficiencies in data (N7)

Labour input method x x

Supply-use method x

Quantity price method x

Margin approach x

Fiscal and other audit data x x x

Theoretical vs. actual value added tax (VAT)

x

Special and existing survey x x

Expert judgement x x x

Source: Eurostat [2005] p. 25.

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Among these recommended procedures, the labour input method is of great im- portance. The first step in comparison is the estimation of relative labour demand to the level of GDP through the results of the Labour Cost Survey, which is reported by the various economic organisations. The supply side is shown in the Labour Force Survey, which identifies the characteristics of the households on the labour market.

A comparison of supply and demand is possible, if the labour input is standardized, for example if it is converted to the same work unit, such as a full-time equivalent headcount. Conclusions can be drawn about the run of the non-observed labour demand by comparing the supply and demand sides of the labour market. If the labour supply is greater than the demand in any industry; then it refers to the non-observed production.

In the case of supply-use methods, the disequilibrium due to the non-observed activities on the production side will be detected by the supply and use tables for par- ticular products and activities. On the one hand, crosschecking and reconciliation can improve accuracy, consistency and exhaustiveness of estimation alike; on the other hand, estimates can be extrapolated by the coefficients of benchmark tables in time (OECD [2002] p. 84.).

The use of fiscal and other audit data should also be mentioned among the recommended estimation methods. The application of these data is complicated, because the tax offices select the entities for the audits according to their own algo- rithm. This being the case, the results cannot be considered as random samples, so logistic regression cannot be used for estimation of tax evaders. In addition, the differences between the categories of tax returns and definitions of the European Sys- tem of Accounts (ESA) complicate the situation and inspectors do not necessarily cover up all non-observed activities. Nevertheless, all these difficulties do not ex- clude the application of tax audit samples. For example, in France coefficients of value added and output are estimated by the results of VAT audits (OECD [2002]).

The level of non-observed economy can be extrapolated from other comparisons, as well. For example, so-called theoretical VAT can be calculated from the usual data sources of national accounts, and if it is lower than the tax actually collected by the tax authority, it may refer to non-observed activities. The situation is the same with the comparison of the theoretical income tax from the national accounts and the actual income tax revenue of the tax authority.

Participation in the non-observed economy can also be estimated from certain special surveys. The results of such a survey carried out by the Hungarian Central Statistical Office (KSH [1999]) and dated 1997 were used in the compilation of national accounts. The attitudes of participants in non-observed economy were mapped by a survey on corporate and household samples in the early 2000s, repeated in 2007 (Belyó [2008]). However, conclusions can also be drawn from the comparison of the results of surveys initially organized for other purposes. Recommended surveys in-

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cluded the household expenditure survey, the household time-use survey and the Labour Force Survey.

Finally, if there are no available data sources, the estimation of non-observed economic performance can be based on expert judgement; in such cases this must include proper documentation of the questions being asked and how opinions and points of view form the estimation.

2. Data sources for individual enterprises

Sole proprietors are included in the household sector within the national accounts, because most sole proprietors are unincorporated small businesses whose operation cannot or can barely be distinguished from the household.¹ Sole proprietorship may be established in the simplest form without any required start-up capital in Hungary, while sole proprietors are responsible for their business obligations with their total property.

Problems in the value added calculation of sole proprietors are rooted in the wide variety of tax opportunities and consequently the non-uniform and insufficient administrative data sources. In addition, available data may be biased because of the interest in the non-observed economy.

Most of the applicable data comprise the administrative data from tax returns.

However these data are not equally detailed, because sole proprietors may chose from a variety of tax options, so different data content can be included in the submit- ted tax returns.

In 2011, sole proprietors in Hungary were able to report on their income in the form of personal income tax or simplified entrepreneurial tax. Furthermore, some sole proprietors are subject to VAT, depending on their level of revenue.

The simplified entrepreneurial tax scheme is the simplest, providing the least information containing data sources among tax formats. This tax format could be chosen by sole proprietors in 2011 if their business had been running for at least three years and their annual revenue was less than 25 million HUF. The rate of tax was 30% of revenue and costs were not declared in the tax return. (See Act XLIII of 2002 about the value added tax.)

Sole proprietors who did not operate under the simplified entrepreneurial tax scheme had to provide personal income tax returns. In this case they could also choose between two alternatives.

1 In addition, the household sector includes not only the economic performance of sole proprietors but the production of agricultural goods for private own consumption, tips and gratuities, value added of owner- occupied housing, illegal activities as the retail trade of drugs and the value added of prostitution, as well.

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The simpler option was presumptive taxation, which could be chosen under a specified revenue threshold. In this case sole proprietors did not declare their costs, but merely determined their entrepreneurial income with a cost ratio required by law.

Revenue threshold and cost ratio depended on activity, and the ratio was different for full-time and part-time sole proprietors. (See Act CXVII of 1995 about the personal income tax, 52 §.)

Those sole proprietors who were not entitled to presumptive taxation, or did not wish to utilise this opportunity, declared – fairly simplified and itemized – their costs in their personal income tax return. The difference between revenues and costs equalled the entrepreneurial income, which was the tax basis for entrepreneurial personal income tax.

Enterprises with revenue from sales (of products) exceeding HUF 5 million were subject to payment of VAT. (See Act LXXIV of 1992 about the value added tax, Chapter XIII.) The ratio of VAT depended on the nature of the product. In the examined period there products exempt from VAT and 5%, 18% and 25% VAT rates. VAT taxpayers were obliged to declare their costs itemized in their income tax return.

Table 2 Number of sole proprietors, 2011

Activity

Sole proprietors with tax return

Registered sole proprietors without tax return

Total Itemized cost declaration

Subject to presumptive

taxation

Subject to simplified entrepreneuri-

al tax Subject to

VAT

Not subject to VAT

Agriculture 10 726 1 164 4 010 163 203 16 266 Manufacturing 9 561 2 704 9 786 1 098 2 018 25 167 Construction 12 011 5 753 17 499 4 528 1 842 41 633 Retail trade 24 742 9 050 24 560 1 168 929 60 449 Land transport 7 415 1 782 4 735 5 243 364 19 539 Services (without retail trade

and land transport) 33 276 37 275 145 267 13 154 29 096 258 068 Total 97 731 57 728 205 857 25 354 34 452 421 122

Source: HCSO databases of tax returns and Business Register.

Due to the heterogeneity of the sole proprietors’ tax returns, it is impossible to apply a uniform method for the calculation of GVA, since in this case the methodology should be adapted to the limited data content, which can cause significant information loss. Instead, the available detailed data should be exploited, and conclusions

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must also be drawn for the performance of those sole proprietors who do not declare sufficiently detailed information. Therefore, the developed methodology classifies sole proprietors into groups based on available data sources. This distribution is shown in Table 2.

A further problem is that the non-observed activities are well known and wide- spread among sole proprietors. On the one hand, they can underreport their revenue through sales without invoices; on the other, they can declare higher-than-actual costs. The GVA calculated from tax returns data is therefore lower than the true case.

Costs can be even more easily over declared, because in the case of sole proprietors it is hard to separate the household and the business, the household’s expenditure and the cost of business. Non-regular employment is also a problem that may be associ- ated with the reported revenue of the enterprise and in many cases distorts the cost structure (the wages are included in other expenses).

These phenomena are very difficult for the tax authority to detect, since many vi- olate current legislation, and those, which are not legal, may also be hardly observable. It is for this reason that the National Tax and Customs Administration (NTCA) use estimations to define “real” costs and turnover. And of course, those selling without invoices at a test purchase can expect tax audits. (See NAV [2003].) The use of tax audits data in the developed method is therefore also a suitable way to estimate non-value added in calculating sales without invoices and over-reportage of costs.

3. The model

These requirements have been formulated for the new model:

– Data have to be calculated in an adequate, detailed form (industrial and county breakdown);

– Non-observed performance must be clearly determined from the results;

– Results should fit into the system of supply and use tables;

– Calculations are implemented on an annual basis, and so the estimation method has to be relatively simple and at least partially au- tomatable.

The new estimation procedure is based on individual data, such as the value added, while output and intermediate consumption are shown in full detail for observed and non-observed economy, industrial and regional breakdowns.

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Figure 1. The estimation model

A simplified version of the method is shown in Figure 1. In the first step, the GVA of VAT-subject sole proprietors is calculated. On the one hand this value includes the administrative GVA from income tax returns, and on the other the non- observed value added due to VAT evasion and estimated by the model based on VAT audit data. The model separately estimates the population of VAT evaders, while undeclared VAT is calculated by using linear regression. GVA due to VAT evasion is determined by the average net rate of paid VAT.

The next step is the estimation of GVA for groups N5 and N7, something determined – with the exception of some industries – by the ratio of value added and labour input, as well as by the labour input of each business in group N5 and N7.

3.1. The administrative value added of sole proprietors

GVA is the difference between output and intermediate consumption. The output equals the value of goods produced during the current period excepting those trade activities whose output is the trade margin. The intermediate consumption is the value of goods and services used in production process as inputs (Eurostat [1996]).

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Unfortunately, the categories of tax returns are not equivalent to the former categories of the national accounts. In addition, the data available to estimate the trade margin are unreliable and incomplete. Resultantly, output and intermediate consumption are calculated in a simplistic way at an individual level of data.

Using the formula /1/, output is determined by the turnover, with exception of trade, where the output is estimated by the margin ratios of non-financial corporations:

( )

, if 450 479

_ else

j ij

ij ij

m R j

output a

R

⎧⎪ ≤ ≤

= ⎨⎪⎩ , /1/

where

(

^{output a}^_

)

_ij is the output of the VAT-subject sole proprietor (i), which is calculated from the data given by the tax return. The classification of sole proprietors activity is denoted by the index j that is broken down to the three digit level of NACE Rev. 2. Output equals the turnover of sole proprietors from income tax return (R_ij). In the case of trade (the industries 450–470 by NACE classification) insufficient data are available for the margin of sole proprietors, and so the trade margin (mj) is estimated through the average trade margin of corporations at the three digit level of NACE Rev. 2 which have a turnover of five billion HUF at most, and the trade margin is not greater than 60%.

The calculation of intermediate consumption is shown in the following form:

( )

^{1 –}

(

^_

)

, if 450 479 _

else

ij ij j

ij

GVA output a j

output ic a

c

⎧⎛ ⎛ ⎞ ⎞

⎪⎜ ⎜ ⎟ ⎟ ≤ ≤

⎪⎜ ⎟

=⎨⎝⎪ ⎝ ⎠ ⎠

⎪⎩

, /2/

where

(

^{ic _ a}

)

_ij is the intermediate consumption of sole proprietor i in industry j.

With the exception of trade, this value equals the cost of materials, goods and wrap- pings from the income tax returns of sole proprietors (c_ij). In the case of trade this item also includes the costs of goods sold, so the average ratio of value added and output of corporation (

j

GVA output

⎛ ⎞

⎜ ⎟

⎝ ⎠ ) is taken into account at the three digit level of NACE Rev. 2 instead of the data from income tax returns. These ratios are calculated from the data of corporations which have a turnover of up to five billion HUF and a 60% trade margin. The intermediate consumption is estimated by the output from formula /1/.

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The GVA of a sole proprietor i (

(

^{GVA _ a}

)

_ij) is the difference between output and intermediate consumption:

(

^{GVA _ a}

) (

_ij⁼ ^{output _ a}

) (

_ij⁻ ^{ic _ a}

)

_ij^{. /3/}

This method results in 498.4 billion HUF GVA for 2011. The next figure shows the distribution of GVA among industries.

Figure 2. The share of observed gross value added by industries

16%

15%

12%

20%

25%

Agriculture Industry Construction Retail trade Transportation

Services without transportation and retail trade

Source: Own calculation.

3.2. The non-observed value added due to VAT evasion

The non-observed value added due to VAT evasion is estimated by the results of VAT audits (Giczi–Horváth–Ritzlné Kazimir [2013]).

The final number of cases expands retrospectively in time due to appeals and review procedures, and so sufficient sample size is not available either for reference or for the previous year. The sample size is bigger for earlier periods; however, the older the sample, the greater is the risk that the estimation leads to the wrong conclusions, because it is assumed that the behaviour of taxpayers and economic environ- ment have changed in the meantime. Due to this the population of tax evaders is estimated by the utilization of tax audit results of the four years preceding the reference year i.e. the consolidated database contains the results of tax audits of years 2007 to 2010. The unpaid tax is estimated in terms of the undeclared VAT for the

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year 2008. Table 3 contains the number of tax audits by consolidated database and the undeclared tax for 2008.

Table 3 The results of VAT audits among sole proprietors, 2007–2010

Industry

Consolidated database

Undeclared VAT for 2008 (millions of HUF) Number of audited

entrepreneurs

Number of VAT evaders

Agriculture 1 144 599 336

Manufacturing 673 322 191

Construction 1 135 652 531

Retail trade 1 576 747 380

Land transport 762 372 207

Services (without retail trade and land transport) 2 484 1 153 644

Total 7 774 3 845 2 289

Source: Database of tax audits.

The estimation consists of four steps. First, the population of VAT evaders is estimated by the k-nearest neighbour (kNN) method. In the second step the nonpaid VAT is estimated by linear regression, and then the non-observed value added by the industrial average of VAT ratios. Finally, the non-observed output and intermediate consumption are calculated.

The kNN method is a method independent of distribution and a non-parametric classification. The cases are located in the n-dimension space defined by the independent variables. The basis for classification is the distance between the cases, i.e.

each case belongs to the most common category of the predetermined number of nearest neighbours. In this way estimation accuracy is influenced by the set of explanatory variables, the selection of distance measurement and the determination of the number of neighbours. The program employed – the SPSS – has two built-in metric distances, the Euclidean and the city-block (Manhattan) distance.²

2 The Euclidean distance between i and c cases is shown by the next form in the n-dimension space:

( )

²

1 p

Euklidean ij cj

j

d i,c x – x

=

= ∑ . The form of city block or Manhattan distance measure between i and c is

described by the following form: ( )

1 p

city block ij cj

j

d ₋ i,c x – x

=

=∑ . Both distance measure is sensitive to the selection of unit measure, therefore the program transposes the explanatory variables to the interval (0;1), as well.

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Figure 3. Illustration for the kNN method

The kNN method is illustrated in Figure 3, the case marked with an asterisk being classified by the method. Firstly, the three neighbours are selected for the classification, from which two have white and one has black marking. Based on this, the white category is estimated for the case marked with the asterisk. The situation would have been different had the category been estimated by five neighbours. The estimated category will be the black category, because in this scenario the case marked with asterisk has three black and two white nearest neighbours.

Large sample size is an important prerequisite of the method; and so the estimation is based on the consolidated database of available tax audits instead of annual results tax audits.

Tax evasion and the level of undeclared tax can be modelled by the preferences of entrepreneurs, the probability of audits and the expected degree of punishment according to economic theories. However, this information is not available to the HCSO. This being the case, some explanatory variables were selected directly from the VAT and income tax returns, category-type variables from the Business Register of the HCSO, as well as variables calculated from tax returns. The selected indicators describe the circumstances typical of sole proprietor operation and the size of enterprises, because it was assumed that tax avoidance behaviour can be explained through the evaluation of these indicators. (The internet Annex contains the list of explanatory variables. See http://www.ksh.hu/statszemle)

The estimation is made after testing several models with the potential explanatory variables. The kNN method reclassifies the cases of the sample, and whichever model produces the most accurate classification ratio is selected. That is, the version which is accepted is that in which the most tax evaders are classified into the tax evader category and the greatest proportion of non VAT evaders appear as non VAT evaders. The testing undergoes multiple iterations.

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In the first step, the group of explanatory variables is selected, the distance measurement is Euclidean, and the program automatically selects the number of neighbours. Three options are tested; in the first, the program selects from all available variables, while in the second, the explanatory power of variables is tested with logistic regression and a group of variables is selected. Finally, all available variables are weighted into factors, and these factors are the explanatory variables for the kNN model.

In the second step, any change in the number of neighbours is examined according to the previously selected explanatory variables. The program allows automatic selection, besides which the variables are compared with the results of estimation taking three, five and seven neighbours.

Finally, the accuracy of estimation is examined by the city-block (Manhattan) distance measurement, using both the selected explanatory variables and the number of neighbours. The tax evaders probably represent the extreme values in the sample, which is why the city block distance metric should be used, being sensitive to the outliers.

Out of the models tested and described above, the one selected for the year 2011 was that in which the explanatory variables were selected by the program, the number of neighbours was five, and the metric distance was the city block. The exact classification is included in the next table.

Table 4 The result of estimation for tax evaders

Result

VAT audits

Total Ratio of correct

classification (%) VAT evaders Non VAT evaders

Estimation VAT evaders 2 090 1 696 3 786 54.36 Non VAT evaders 1 755 2 233 3 988 56.83

Total 3 845 3 929 7 774 55.61

The consolidated database contains results from 7 774 audits, and the re- estimation on the sample resulted in a classification of 55.61% accuracy. The classification accuracy for the tax evaders and non tax evaders is similar, meaning that the ratio of estimated tax evaders is correct in the sample.

Tax-evasive behaviour depends on risk-averse behaviour, and changes in level can only be seen between different years. Potential tax evaders on the consolidated database can therefore also be looked upon as tax evaders in the reference year. The

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number of estimated VAT evaders in the industries is included in Table A3 of the Annex.

The next step in calculation is the estimation of VAT evasion level by linear regression. Compared with tax avoidance behaviour, which is considered stable, the level of undeclared tax changes from year to year. The level of tax evasion depends on the regulatory framework and changes in market position by entrepreneurs. This being the case, the estimation is not based on the consolidated database, because it contains data for more years; instead, the tax audit sample of the third year preceding the reference period is used in the calculations. The regression model was therefore set for the tax audit data of year 2008, and the undeclared VAT of year 2011 was calculated using the estimated parameters.

The model was adapted for separate industry groups, the opportunities for sole proprietor tax evasion differ depending on business activity. The various industry groups are determined by cluster analysis, in which the number of tax audits and the share of tax evaders by industry are the basis of classification. The following industry groups have been generated: 1. agriculture and land transportation, 2. retail trade, 3. construction, 4. industry and services (without retail trade and land transportation).

The fourth group is divided into industry and services.

Several models were tested, each differing from each other not only in explanatory variables, but in the dependent variable as well, because the main objective was to find the best-fitting model. It was evident that undeclared tax should be used as the dependent variable (sum of undeclared tax is included in Table 3). Experience has shown that a well-fitting model can be built using the ratio of undeclared tax and an indicator based on the VAT returns as a dependent variable.

In agriculture and land transportation, as in construction, the dependent variable was the undeclared tax. In the case of retail trade, the dependent variable was the ratio of undeclared tax and all purchases from the VAT return. The model providing the best results in industry and services is the one where the undeclared tax is compared to the ratio of all sales and purchases as the dependent variable.

The set of explanatory variables includes indicators computed from the tax returns and dummies created by using the categories of the Business Register. The selected variables describe the size of enterprise, the efficiency of production, the relative market position, and the other operating conditions; these variables are similar to ones used in kNN models. The model is set up to increase the prediction accuracy of estimation and to create the best fitting model; in this way the most possible explanatory variables are used. They are not independent of each other, and so the partial interpretation of the parameters is not possible. Information of regression is shown in Table A1.

The estimation of undeclared VAT is followed by calculation of non-observed value added. It is assumed that sole proprietors distort those items of VAT return for

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which they can minimize payable VAT. However, their intention is to submit a relatively realistic tax return in order to reduce the probability of a tax audit.

The average VAT ratio is calculated by the taxable items of VAT returns for the two-digit level of NACE, so the average VAT ratios equal to difference of VAT on sales and purchases and the difference on the taxable items of sales and purchases by industries. So the non-observed value added is the ratio of estimated undeclared VAT and the average VAT ratio:

(

⁶

)

_ij

j

GVA _ N VAT

= ˆt , /4/

where the non-observed value added due to VAT evasion is shown by

(

^{GVA _ N}⁶

)

_ij for industry j and VAT-subject sole proprietor i. vat_ij refers to the estimated undeclared VAT of the VAT-subject sole proprietor i, and ˆt_j is the average VAT ratio for industry j in two-digit level of NACE.

Figure 4. The share of the estimated undeclared VAT and the non-observed value added due to VAT evasion

13%

11%

13%

23%

8%

32%

15%

12%

22%

7%

32% Agriculture

Industry Construction Retail trade Transportation

Inner circle:

undeclared Outer circle:

gross value added

The final step in calculation is the estimation of non-observed output and intermediate consumption resulting from VAT evasion. The tax audit database does not contain information on which item or items of audited returns have been found to be

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distorted. Generally, the tax can be reduced by a combination of concealing sales and over-reporting costs.

Usually the easiest way to conceal sales is the sales without invoices, which is the easiest in the case of sales to households. Our assumption is that the ratio of non- observed output and GVA is equal to the share of sales to households. This proportion is calculated for industries by the ratio of domestic output (without import) and household consumption. The correction of non-observed output and intermediate consumption due to VAT evasion is calculated by using the following formulas

(

output _ N⁶

)

ij=h GVA _ Nj

(

⁶

)

ij, /5/

(

^{ic _ N}⁶

) (

_ij⁼ ^{output _ N}⁶

) (

_ij⁻ ^{GVA _ N}⁶

)

_ij . /6/

In formula /5/

(

^{output _ N}⁶

)

_ij shows non-observed output due to VAT evasion of sole proprietor i in industry j, where the proportion of household consumption in domestic output by NACE is h_j.

Non-observed intermediate consumption is negative, because the VAT evading sole proprietors can over-report their costs; the formula h_j ≤1 also demonstrates this phenomenon. Non-observed output due to VAT evasion is included in Table A3.

3.3. The value added of non-VAT-subject sole proprietors

Those sole proprietors who are not subject to VAT can be divided into two groups. One group includes those sole proprietors, who have tax returns, but whose data are inadequate, incorrect, incomplete or biased. The economic performance of these sole proprietors is included in the non-observed economic category N7. The other group contains those sole proprietors, who do not submit any tax returns (N5).

The number of enterprises by N5 and N7 groups is included in Table 2.

The sole proprietors are small enterprises that are considered nearly perfectly competitive both in input and output markets. Therefore, it is no exaggeration to assume that their production has a constant return to scale. The estimation is based on this assumption and similar in both enterprise groups.

We suppose that the sole proprietors from groups N5 and N7 generated an expected value added per labour input that is equal – with the exception of some industries – to the average ratio of value added and labour input of VAT-subject sole proprietors. The labour input includes both the employees of enterprises and the sole proprietors. The latter has a value of 1, if the entrepreneur is employed full time, but it is 0.5 in the case

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of part-time activities or those performed during retirement. The sole proprietor is employed full time if she or he works more than 36 hours/week for the enterprise.

The GVA of sole proprietors in groups N5 and N7 is the multiplication of the average expected value added per labour input and the labour input. The income tax returns and the entrepreneurial tax returns include the number of employees. In the case of group N5, however, there is no available information about the number of employees.

It is assumed that these entrepreneurs do not have employees, because a significant proportion of sole proprietors does not have employees (87%). In addition, it is likely that the relatively small businesses tend to ignore their obligation to submit tax returns.

In some industries we can not suppose that the return to scale is constant. One example of such an industry is the Activities auxiliary to financial services and insurance activities (Division 66 in NACE Rev. 2). The problem in this case is the nature of work organisation. The sole proprietors are agents or representatives of financial corporations in this industry, working for commissions on concluded transactions.

The agents are usually organized under a multilevel marketing scheme. In such a scenario, the more successful agents manage and monitor the activity of other agents, and receive a commission partly based on their results. The agents at the different levels are sole proprietors; they are not employees of each other.

Nevertheless, a constant return to scale of current costs can be assumed (entry is free to the market; special knowledge of technology is not needed). This also means that the ratio of GVA and output is constant. Output can be equal to turnover in this case. Therefore, the expected value added per labour input of VAT-subject sole proprietors is corrected by the ratio of turnover per capita of group N7 and VAT-subject sole proprietors. This corrected value added per labour input is the basis of calculation for groups N5 and N7. Table 5 shows the data for calculating the correction factor and the expected value added.

Table 5 Correction in the Activities auxiliary to financial services and insurance activities

Denomination VAT-subject sole

proprietors Group N7

Turnover, million HUF 6 553 31 111

Labour input, per person 1 234 18 513

Ratio of turnover and labour input, million HUF/person 5.31 1.68

Correction factor 0.32

Ratio of value added and labour input, million HUF/person 6.02 1.91

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The other two exceptions are Land transport and transport via pipelines and Other personal service activities. In this case, the estimation cannot be based on constant return to scale due to technological differences. The relative greater enterprises in both industries operate using their own fixed capital (for example they have their own delivery trucks, they have their own hairdressing business, etc.). In contrast, smaller enterprises produce with a fixed capital, which is provided either by the cus- tomer or other enterprises (for example, they drive a corporation’s truck, rent a space in a hairdresser’s, etc.). The larger enterprises have a higher value added per labour input, because the fixed capital has to be returned, as well.

The value added of groups N5 and N7 is estimated by logarithmic regression. The dependent variable is the value added of VAT-subject sole proprietor; that is, the sum of administrative value added and non-observable value added due to VAT evasion. The explanatory variable is the turnover of enterprises. The turnover for group N5 is not available, therefore the estimation is based on the data of the previous period. The data of regression is included in Table A2.

To summarize this method, the value added of groups N5 and N7 is estimated by the following formula:

( )

n

( )

66

5 7 49 96

j ij ij ij

j ij

γ GVA _ L L j

GVA _ N N GVA j ;

GVA _ L L else

⎧ =

=⎪⎪⎨ =

⎪⎪⎩

, /7/

where the

(

^{GVA _ N N}^{5 7}

)

_ij defines the sole proprietors i of group N5 or N7 in industry j. The labour input is L_ij, taking that the enterprise produces full time or part time. The ratio of value added and labour input is shown by

(

^{GVA _ L}

)

_j^.^γ^denotes

the correction factor in Activities auxiliary to financial services and insurance activities. The estimated value added by logarithmic regression is GVAn_ij in the industries of Land transport and transport via pipelines and the Other personal service activities.

Consequently, there are two differences between the calculations of value added in groups N5 and N7. For group N7 the calculation takes into account the number of employees, which is not available for group N5. In this scenario, labour input includes only the entrepreneur. The other difference is that in N5 n

GVAij is estimated by the turnover of the previous period.

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Figure 5. The GVA of non-VAT-subject sole proprietors

4% 6%

12%

6%

1%

71%

5%

6%

16%

9%

3%

61% Agriculture

Industry Construction Retail trade Transportation

Inner circle:

N7 Outer circle:

N5

The last step in this method is the calculation of output and intermediate consumption. These are calculated by the average ratio of value added and output of VAT-subject sole proprietors for industries:

( ) ( )

5 7 _ij ⁱ ^ij 5 7 _ij

i ij

GVA _VAT

output _ N N GVA _ N N

output _VAT

⎛ ⎞

⎜ ⎟

=⎜⎝ ⎟⎠

∑

∑ ^, ^/8/

(

^{ic _ N N}^{5 7}

) (

_ij = output _ N N^{5 7}

) (

_ij− GVA _ N N^{5 7}

)

_ij. /9/

The output of sole proprietors from N5 or N7 is shown by

(

output _ N N^{5 7}

)

_ij, which is the multiplication of estimated GVA and ratio calculated from the value added (

(

^{GVA _VAT}

)

_ij) and the output (

(

^{GVA _VAT}

)

_ij) of VAT subjects by industry. Intermediate consumption (

(

^{ic _ N N}^{5 7}

)

_ij) is the difference between the output and GVA. The outputs of groups N5 and N7 are included in Table A3.

4. Summary

This paper has described an improved method for estimating the GVA of sole proprietors. The new bottom-up method meets the objectives of the development.

The structures of value added and ratio of intermediate consumption and output dif-

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fer significantly from the results of the former method. Our experience has shown that this structure better suits the system of supply and use tables. The method calcu- lates the observed value added from administrative data and estimates the performance of the non-observed economy by category. In addition, the economic performance of sole proprietors can be analysed in a sufficiently detailed breakdown at the level of indicator components, as a result of the individual data provided.

In Hungarian national accounts, the estimation of economic performance on the part of sole proprietors has been calculated since 2011 by using the developed method, and figures are available from the reference year 2006. The time series are cast back to 1995. The tax returns and tax audit data are available annually, so estimates can be performed annually.

Our calculations show that the he GVA of sole proprietors for 2011 was 1630.8 billion HUF. A significant share, 69.2% of GVA, is generated in services, of which 9.7% is produced in retail trade, 7.6% in transportation and 51.9% in other services.

The contribution to the production of GVA is relatively lower in other industries.

Agriculture generates 8.6%, industry 9.6% and construction 12.6% of the sole proprietors’ total GVA.

Although only 23% of sole proprietors are subject to VAT, this group produced 40.5% of sole proprietors’ total GVA in the period discussed. The non-observed value added represents 24.5% of the economic performance of those sole proprietors subject to VAT, and this amount is 9.9% of the sole proprietors’ value added. 50.8%

of the sole proprietors’ value added is generated by the non-VAT-subject sole proprietors from group N5. The share of enterprises without tax returns in GVA is only 8.8%, but their number is also small; the ratio is 8.1%.

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