USING MIMIC MODELS TO EXAMINE DETERMINANTS OF VAT GAP IN LITHUANIA

: In recent years analysis of economic loss attributed to different aspects of shadow economy has attracted much attention of both academics and policy makers. Recent statistical data shows that new member states have on average a 9 percent higher VAT gap than the older members of the European Union. Knowing that economies of emerging markets rely on the VAT for a substantially higher percentage of their government revenues, it is very important to understand the determinants limiting revenue mobilization in those countries. In Lithuania, the VAT gap increased dramatically after the crisis of 2008 , and now is one of the largest in the EU. However, few studies have empirically tested some hypotheses about the VAT as a revenue-raising instrument in the country. The purpose of this study is to identify the determinants significantly influencing the size of the VAT gap in Lithuania using the MIMIC method for quarterly data of the period 2000-2013. The applied MIMIC model indicated that two factors (General government consumption expenditure and inflation) have a statistically significant impact on the VAT gap in the long-run. The results of the eMIMIC model show that two determinants (inflation and household deposits) have a statistically significant influence on the gap in the short-run. The authors believe that the key findings of the study can be used as one of the supporting tools in adjusting Lithuanian pro-growth tax policy and improving administration of VAT taxes.


Introduction
Value Added Tax (VAT) revenue is one of the most important sources of the state's income. According to the latest annual data on the implementation of the National Budget presented by the Ministry of Finance of the Republic of Lithuania, it amounted to 40.76 percent of the state budget income. Analyses of economic trends in the various phases of the economic cycle highlight the problem of the shadow economy, particularly the VAT compliance gap, which is henceforth simply called the "VAT gap". e most commonly used de nition describes the VAT gap as the "di erence between the theoretical tax liability according to the tax law and the actual revenue collected" (CASE, 2013, p.18). Tax evasion and tax avoidance are widely believed to be important causes of ine ciency in the functioning of the market, limiting the country's capacity to mobilize money and implement their economic and social policies.
VAT gaps have a very wide dispersion range across countries. One of the ndings presented in the report of the "Study to quantify and analyse the VAT gap in the EU-27 Member States" commissioned by the EC is that in 2011 the largest VAT gap as a share of GDP was in Romania, Latvia, Greece and Lithuania (7.9,4.7,4.7,and 4.4 percent,respectively) (CASE, 2013). Naturally, be er understanding of determinants of the VAT gap as a response to economic events or policy decisions in Lithuania is required.
ere is a cause -e ect relationship between the VAT gap and many macroeconomic variables, for example, a shortfall of the National Budget revenue, decline in the GDP, decrease in additional wages and other indicators that re ect negative trends in the economy. Since causes determining tax revenue and the strength of their impact are di erent for each type of the tax, it is not appropriate to assess all the revenues as a single variable. Consequently, in this study we decided to analyse separate economic factors which may have statistically signi cant in uence on the VAT gap. It should be mentioned that there is no single methodology for precise estimating of the VAT gap; its results could not be safely used as a basis for practical application. Having conducted a critical review of the methods in this eld we decided to apply the most appreciated method for our study -Multiple Indicators and Multiple Causes (MIMIC) model, where the VAT gap is treated as a latent variable.
e main purpose of this study is to review the various methods estimating the VAT gap and, using MIMIC models for quarterly 2000-2013 period data, to identify the determinants signi cantly in uencing the VAT gap in Lithuania. e paper is organized as follows: e following part discusses the methods for quantifying the VAT gap and existing estimates. Further, the analysis of the variables in uencing either the VAT gap or VAT performance used in the MIMIC models is reviewed. In the next part of the paper, the construction and analysis of the long run eMIMIC models is presented. e h part analyses the results of the short run eMIMIC models, including comments on the economic interpretation. e sixth section describes some limitations of the study and suggestions for the future research. In conclusions section the results are summarized and discussed.

Review of Literature
VAT non-compliance problems are widely studied in scienti c literature. Historically, M. G. Allingham and A.Sandmo (1972) were among the rst authors who published the paper on tax evasion. e study mainly focused on the individual tax-payers' decision to avoid taxes. Later on, it became more important to concentrate on the VAT gap measurement and identifying factors having in uence on such a gap. Basically, there are two main approaches in the eld to estimate the tax gap: macro (top-down) and micro (bo om -up). Macro methods allow researchers to calculate the VAT gap at the macroeconomic level and are preferred when analysing indirect taxes. Micro methods focus on direct taxes in the sense that they measure missing tax income based on samples of individual tax-payers (Gemmell & Hasseldine, 2012). e macro or top -down method was used to estimate the VAT gap in the "Study to quantify and analyse the VAT gap in the EU -25" over the period from 2000 to 2006 carried out by a London-based economic consultancy company Reckon (2009). Total accrued tax receipts were compared with a theoretical tax liability calculated from general economic data. However, when using this method the structural information about the most fraudulent companies or economic sectors is lost. Additionally, the use of this method in order to calculate the VAT gap involves more disadvantages: rstly, particularity of available data, and, secondly, part of taxable activities, such as construction of own dwelling or exceptions to small business, is outside the National accounts; thirdly, it is di cult to determine whether the National accounts estimates are accurate. e study used the ESA 95 standard, which requires that in uence of the shadow economy should be included in the National accounts data, so the accuracy and the quality of the data depends on how logically and properly calculations of the shadow economy are performed. However, total estimated liabilities of the VAT tax are calculated as a sum of total household consumption, gross xed capital formation, other consumption, which contains government intermediate and nal consumption expenditure, intermediate consumption of other sectors and adjustments that are related to small business exemption, company cars, business environment and changes in worth. It should be noted that top-down estimation method of the compliance gap was also used in the recent CASE (2013) study.
One of the bo om -up (micro method) analyses was performed by the specialists of the Swedish National Tax Agency (2008). An extensive survey, which was intended to help determination of the behaviour of the taxpayers under di erent circumstances, tax rates and so on, was conducted to identify the di erence between the o cial sources of household consumption expenditure and those obtained by the survey results.
Hanousek and Palda (2002) used the bo om -up method to describe evolution of tax evasion over time and to get a detailed view on the structure of it. e major disadvantage of such (micro) methods is that the main source of data is a survey, which is di cult to be controlled. Moreover, the respondents can interpret the same terms di erently or can be simply afraid to tell the truth. On the other hand, if the same parameters are estimated using di erent sources of data, they can produce imprecise and sometimes con icting results. e VAT gap, the calculation of which is based on the above discussed methods, is widely used in the econometric models. However, as it was mentioned earlier, these methods may measure the VAT gap incorrectly. erefore, it was decided to use a di erent model in this study -Multiple Indicators and Multiple Causes (MIMIC) model. e MIMIC model is a special type of the structural equation model that speci es the causal relationships among observable variables and an unobservable variable. e major advantage of the MIMIC model is that the main a ention is paid to the latent or unobserved variable, for example, such a hardly measurable variable as the VAT gap, which we can investigate and evaluate only indirectly, and assess its e ects on directly monitored variables. All the methods described above designed to estimate the size of the VAT gap consider just one indicator that is supposed to include all the e ects of the VAT gap. But it is obvious that it is very di cult to evaluate all these e ects correctly and accurately. By contrast, the MIMIC method is quite di erent from those and is based on the statistical theory of "unobserved variables, which considers multiple causes and multiple indicators of the phenomenon to be measured" (Schneider, 2006, p.48).
e MIMIC model has become very popular to be applied in measuring hidden economy and the tax gap in recent years. It is well appreciated among the scientists. D. Giles and L.Tedds (2002) have used the MIMIC method in order to evaluate underground economy in Canada, A. Bühn and F. Schneider (2008) in France. R. Dell' Anno (2006) applied it in order to nd plausible answers to the following questions: What are the dynamics and size of the Portuguese shadow economy (as percentage of the o cial GDP) in the last thirty years (from 1977 to 2004)? What are the main causes of shadow economy? What kind of economic policies could be e ective in reducing shadow economy? C.-M. Ene and A. Ştefănescu (2011) have also used the MIMIC approach in their work "Size and implication of Underground Economy in Romania -a MIMIC approach". e general structure of the MIMIC model is presented in Figure 1: As we see from Figure 1, formally, the MIMIC model consists of two parts: the structural equation model and the measurement model. e structural equation is speci ed by this equation: Where χ T t = (χ 1t , χ 2t , ..., χ qt ) is a (1 × q) vector of a set of observable time series variables (causes), γ T t = (γ 1t , γ 2t , ..., γ qt ) -(1 × q) vector of coe cients in the structural model, which describes the causal relationship between the latent variable η t and its causes; ς t is the error term, which represents the unexplained component. Symbol T henceforth means that an appropriate vector is transposed.
Latent variable (η) describes the endogenous variables that depend on the measurement errors (the measurement model): where y T t = (y 1t , y 2t , ..., y pt ) is a (1 × p) vector of individual endogenous time series variables (indicators) y jt = (1, ..., p), ε t = (ε 1t , ε 2t , ..., ε pt ) is a (p × 1) vector of disturbances where every ε jt , (j = 1, ... , p) is a white noise term the covariance matrix of which (p × p) is given by Θ ε . λ j (j = 1, ... , p) is a (p × 1) vector of regression coe cients λ. Both structural noise ς, as well as measurement error ε are represented by normal distribution and are linearly independent of each other. In order to create the model, the following assumptions were taken: 1) E(η t ) = E(χ t ) = E(ς t )= E(y t ) = E(ε t ) = 0 -means are equal to 0; 2) E(χ t ς T t ) = E(ς t χ T t ) = 0 -the error terms in the structural model do not correlate with the causes; 3) E(χ t ε T t ) = E(ε t χ T t ) = 0 -the error terms in the measurement model do not correlate with the causes; 4) E(η t ε T t ) = E(ε t η T t ) = 0 -the error terms in the measurement model do not correlate with the latent variable; 5) E(ς t ε T t ) = E(ε t ς T t ) = 0 -the error terms in the structural model do not correlate with the error terms in the measurement model; 6) E(ς 2 t ) = σ 2 -the variance of the error terms in the structural model is a constant.
By using equations (1) and (2) the MIMIC model covariance matrix Σ (3) can be de ned. It reveals the structure between the observable variables and the latent variable: As the latent variable is unobserved, its size is unknown, so the model parameters must be evaluated using the relationships between variance and covariance of the observed variables. e aim of the assessment procedures is to nd values for the parameters γ and λ and also the values of covariance matrix, ψ and (where -is the (q × q) covariance matrix of the causes χ t , ψ -is the variance of ς t and ε -is (p × p) covariance matrix of the white noise term) which are compiled to matrix, which is as close as possible to the covariance matrix of observed variables and indicators, i.e., all χ t and all y t . e following MIMIC model was considered as a long-run MIMIC model in this study. e aim of such a model was to nd the trends and mutual associations between the variables during all the period (from 2000 to 2013). However, it is also very important to examine an instantaneous relationship between variables. erefore, an error correction MIMIC (eMIMIC) model was used, where the long run equilibrium errors together with causal variables were evaluated (Bühn & Schneider, 2008). us, a er adding the long run equilibrium errors (the number of the errors must be equal to the number of indicators) to the long run MIMIC model, the short run eMIMIC model was constructed. e long run equilibrium errors are found by cointegrating the variables. If a stationary linear combination of non-stationary variables exists, the variables are co-integrated (Enders, 1995). While creating the model, due to the fact that only non-stationary variables can be co-integrated, a stationary variable (if it exists) must be used as an exogenous variable.
In summary, analysis of scienti c literature reveals that there are almost no econometric models which would be suitable in the analysis of the VAT gap. Most of them are based on the principle that primarily the theoretical revenue of VAT is calculated and only a er that the econometric models are constructed and, according to the results of the models, appropriate conclusions are drawn. However, such techniques of the VAT gap calculation are not always su cient and do not determine the situation when incorrect and inaccurate conclusions are being made. erefore, the most appropriate method is the MIMIC model, in which the VAT gap is considered to be a latent variable. On the one hand, it is associated with a set of observable variables and, on the other, -with the causal variables, which a ect the VAT gap activity.

Selection of variables used in the MIMIC model
e level of tax evasion, or the VAT gap, depends on a number of di erent factors. ere are numerous studies describing the variables likely to a ect non-compliance. Sometimes the study results may di er meaningfully depending not only on the use of the VAT gap estimation method, but also on the selected indicators of the economic variables. erefore, it is very important to choose variables very precisely in order to get the most accurate results. Based on the analysis of scienti c literature (Allingham & Sandmo, 1972;Christie & Holzner, 2006;Schneider, 2006;Schneider & Bühn, 2007;Nerre, 2008;Bühn & Schneider, 2008;Fathi & Esmaeilian, 2012), the variables believed to determine the VAT gap were selected for empirical work: expenditure, in ation, gross xed capital formation, additional amount of wage and money on deposit; cash equivalents. As stated in the literature (Tedds, 2002), development of the public sector, i.e., increasing government expenditure or economic regulation is o en one of the incentives to take informal or illegal activities. at is why the rst variable which is likely to a ect the VAT gap, General Government consumption expenditure (GGCE), is chosen.
In ation (INFL) is de ned as a sustained increase in the general level of prices of goods and services. Along with the increase in the in ation, consumer purchasing power decreases. Such a situation for both consumers and producers, who want to avoid negative e ects of the in ation, may encourage them to look for the alternatives such as purchasing goods and / or services illegally at a relatively low price. e in ation is calculated according to the EU methodology and using statistical data on consumer price changes in the consumption pa ern of households (the harmonized consumer price index) (Statistics Lithuania, 2014). e subject's decision to carry out the tax obligations is to a great extend determined by the mood of the taxpayers, expectation for the future and the total economic situation in the country. As a result, the selected variable that should in uence the mood of the taxpayers is an additional amount of wages (AAW), which was calculated as a di erence between the average and the minimum wages. is variable indicates how much money above the minimum wage workers receive. e growth of this amount may be associated with the higher quality of life -individuals who receive higher wages can spend more money on consumption or saving, i.e., investments, ceteris paribus. On the other hand, in terms of the employers, decline in the wages can be associated with decision to conceal the income, respectively, to pay the salaries in an "envelope" and thus to evade tax obligations.
Another variable of the model is household deposits (HD). e growth of wages does not necessarily mean that consumption will grow, too. Households decide what to do with their free money: release it for consumption or for saving. If they decide to save (for example, to put money on a deposit), then the country's economy will not grow to the extent that it could at the given period. e last determinant is gross xed capital formation (GFCF), which otherwise is considered as investments and represents physical capital replenishment. It is logical to assume that when the national economy is growing, the business must ensure a su cient supply of goods and services in order to survive and to be competitive in the market.
is increase of supply is inseparable from the greater need of funds for investment. erefore, it is appropriate to analyse whether the investments tend to be nanced from the "saved" money, i.e., concealed income, or whether growing investment leads to higher revenue and reduces the incentives to evade tax obligations. e rst indicator -real GDP per capita (rGDP) -is one of the most important variables in the model. e real GDP (measured at constant prices (the chain-linking method)) rather than the nominal (nGDP) is used in the analysis in order to avoid the in uence of the in ation. e studies suggest that income which is earned in the informal economy increases GDP growth, since some of it is released in the formal economy (Krumplytė, 2010). So, national recession could lead to a tendency of individuals to save money instead of paying VAT. On the other hand, there are more opportunities to circumvent the law, and tax evasion may become easier when the economy grows. In addition, part of the "shadow" money is released o cially, which leads to economic growth. e second indicator is VAT revenue managed by the State Tax Inspectorate (VATR). It is evident that not ful lling tax liabilities on time or not ful lling at all (both intentionally (for example, fraudulently avoiding to pay VAT) and unintentionally (for example, due to a lack of knowledge, taxpayers complete the VAT declaration incorrectly and pay less tax accordingly)), directly a ects the VAT revenue. According to the Republic of Lithuania Law on Tax Administration, there are two institutions that are responsible for the VAT revenue collection: the State Tax Inspectorate and the Customs of the Republic of Lithuania (Chapter IV, Art. 15). However, there are some di erences in the structure and the nature of work between these two institutions. Because of these di erences and in order to make the study more accurate, VAT revenue which is managed by the State Tax Inspectorate was selected for our empirical work. e third indicator is cash and cash equivalents (MONEY) (the money that is in the company's accounts and short -term (up to 3 months), i.e. liquid, investments, which can be quickly converted to cash and the risk of the change value is negligible) (5 BAS of Business accounting standards, 2008). is indicator was selected because money is used not only in formal economy, but also in informal -money is also needed in order to carry out the illegal transactions on which the relevant taxes are not paid. us, the growth of the informal economy should increase the demand for money.
Quaterly data for the period of 2000-2013 were collected from various sources: General Government consumption expenditure, in ation, additional amount of wage, real GDP per capita and cash and cash equivalents were obtained from the O cial Statistics Portal of Statistics Lithuania; money on deposit data was extracted from the "Report on nancial market state and execution of functions" that is prepared by the Central Bank of the Republic of Lithuania; gross xed capital formation was taken from the Eurostat Statistics Database; VAT revenue from the "Data on the Implementation of the National Budget" prepared by the Ministry of Finance of the Republic of Lithuania.
Prior to initiating the econometric model, the data needs to be prepared -seasonally adjusted and made stationary. ese procedures are necessary in order to get the correct results and reasonable conclusions. It should be noted that this model formation is not mentioned in most of the articles, which could mean that not all the results of these models are reliable. In this study, rst of all, part of the variables, i.e., those which have multiplicative decomposition, were logaritmized (for example, the case of Cobb -Douglas production function). ese include: General Government consumption expenditure, the gross xed capital formation, the additional amount of wages, the households deposits, VAT revenue managed by the STI, real GDP per capita and cash and cash equivalents, i.e. variables, which are calculated as a percentage value of other variables or indicators and cannot gain negative values. e la er condition is relevant due to the fact that this procedure cannot be performed for negative or equal to 0 values. Since quarterly data are used in the model, it is possible that the seasonal component can be statistically signi cant. In order to avoid that in uence which could distort the results, the variables were seasonally adjusted. is procedure was performed using the command "decompose" of the so ware R. Depending on the mathematical expressions of the variables, the suitable method of the seasonal adjustment was selected: multiplicative model for the logaritmized variables (here the seasonal variations are roughly constant through the series) and additive for the other variables (here the seasonal variations are changing proportionally to the level of the series).
en, to overcome the problem of spurious regressions, all the variables were transformed into stationary ones. It is o en omi ed or not emphasized that this step is performed in the econometric models. In order to nd the order of integration, several unit root tests: Augmented Dickey -Fuller (ADF), Elliot Rothenberg Stock (ERS), Phillips -Perron (P -P), Kwiatkowski, Phillips, Schmidt & Shin (KPSS) and Zivot -Andrews (Z -A) were run. All of these tests were performed at a 95 percent con dence level, i.e., at a 5 percent probability of error.  Notes: * e number in parenthesis shows the order in which the process is integrated. For example, we say that the process is integrated of order 1 if it is calculated according to the formula ΔY t = Y t -Y t -1 .

** Number of lags
Source: calculated by the authors with the use of R so ware.
Based on the results of these tests, it can be concluded that the variables are not stationary and it is necessary to di erentiate them, moreover, part of the variables have from one to three periods to be lagged. In addition, Z -A test showed that GFCF has a unit root with a structural break in the intercept which occurred in 2008 Q3. For this reason, GFCF was used as an exogenous variable to nd the number of cointegrating vectors. Z -A test showed that VATR also has a unit root with a structural break at the 18th observation, but including this break in the model is not considered as appropriate for the following reasons: the critical value of this test is -5.34 (1 % level) and it is slightly di erent from the calculated value -5.36, so hypothesis H 0 cannot be rejected. In addition, calculated break point is quite close to the beginning of the observationstherefore, it is probable that the structural break occurred at the beginning of the investigation period, i.e. ,when Lithuania became a member of the European Union.
Prepared-logaritmized and seasonally adjusted data was used to estimate the MIMIC and eMIMIC models with the use of R so ware. e following packages were used to estimate the models: lavaan, urca, vars, semPlot, Hmisc, tseries, lmtest and fArma.

Construction and analysis of the long run MIMIC models
It was estimated that the three variables (AAW, rGDP, GGCE) are stationary with 1 to 3 period lags, so in order to nd the best structure of the MIMIC model, the variables were included both with and without lags. To compare the models the following criteria were used: 1. χ 2 -Chi-square -a compatibility criterion which is used to verify if observed distribution is compatible with the theoretical one (p-value must be more than 0.05); 2. DF -Degrees of eedom -a criterion which is calculated using the following formula: 0.5 × (p + q) × (p + q + 1) -t, where p is a number of indicators, q is a number of causes and t is a number of free parameters; 3. RMSEA -Root mean square error of approximation; if RMSEA is less than 0.05, it means that the model is appropriate. RMSEA values can vary from 0.0 to 1.0; 4. AIC -Akaike information criterion is a criterion used for selecting among nested econometric models. e preferred model is the one with the minimum AIC value. Firstly, the long run MIMIC model with ve causal variables and three indicators was constructed. A er evaluating the statistical signi cance of the causal variables, the least statistically signi cant causal variables were eliminated one by one until all remaining variables were statistically signi cant (estimated values of the information criteria are summarized in Table 2). e statistical signi cance was assessed by using z statistics. Since the critical values of z statistics vary depending on the degrees of freedom, p-value was used: the variable was considered as statistically signi cant when p-value < 0.05. e MIMIC model presented in Figure 2 shows that both statistically signi cant causal variables have positive e ect on the VAT gap: GGCE -0.156 (at signi cance level of 0.043) and INFL -4.713 (at signi cance level of 0.010). It should be noted that because each of these variables was used at a stationary state, interpretation of the calculated estimates would be: 1 percent change in GGCE increases the VAT gap by 0.156 notional units, ceteris paribus; 1 percent change in INFL increases the VAT gap by 4.713 notional units, ceteris paribus. According to the latest data provided by Statistics Lithuania (2014), one of the highest growths of the Government spending in absolute terms was on social protection (from 5.77 billion Litas in 2001 to 13.5 billion Litas in 2012). Although it is only a part of the Government spending, partial observations can be made. Rising expenditure on social protection means that people who are on low income are less interested to work, because the bene t from work is not su cient enough for them to become active labour market participants. Although people have less revenue, there is more free time for other activities. On the other hand, lower expenses do not allow the business to develop. In order to operate in a competitive environment, it has to nd nancial resources by other means. One of the alternatives is a failure to comply with the tax obligations, i.e., instead of paying taxes, including VAT, business may spend the money on the technological capacity building or increasing workers' salaries, etc. e obtained results show that the growth of the VAT gap can be explained by the rising in ation, ceteris paribus. e individuals are very sensitive about the rising price level because it has a direct e ect: purchasing power is declining. When in ation is low, overall price level changes slightly, but prices of particular goods and / or services that are relevant to certain individuals may actually have increased, and it reduces the purchasing power of customers nevertheless. In order to maintain the current level of consumption, individuals are forced to look for additional sources of income -both legal (e.g., looking for a new job) and illegal (e.g., engaging in illegal activity, hiding income and thereby avoiding tax compliance) ways. If individuals do not intend to search for additional sources of income and reduce the consumption of less necessary goods and / or services, the revenue of relevant companies decreases as well. e result is a similar situation as in the case of GGCE increase -rising in ation increases the VAT gap.
According to the results, the remaining variables (HD, AAW and GFCF) were not statistically signi cant. e inclusion of HD in the model was based on the consideration that it would have a positive e ect on the VAT gap, ceteris paribus. However, it was found that this variable was not statistically signi cant and the direction of the impact cannot be de ned. On the other hand, the estimated coe cient of HD was negative in the primary model, so it tentatively suggests that positive growth in the changes of HD (since the variable was integrated of order 2) determines the higher VAT gap. It implies that higher household savings are not conducive to business as demand for goods and services decreases, consequently, the National Budget income is reduced because the tax revenues are not being collected and the VAT gap tends to grow.
Another not statistically signi cant causal variable was AAW. Although increasing additional amount of wages should reduce the VAT gap, the estimate of DU was negative, moreover, this variable was not statistically signi cant. e reason for this result can be the fact that individuals who receive xed salary are able to be er plan their budgets, so the concealment of income and / or wage payment in the "envelopes" in order to evade tax obligations is less likely.
e study results show that the changes of gross xed capital formation do not a ect the VAT gap. One of the reasons can be that the changes of these investments during the analysed period from 2000 to 2013 are not considerable enough to signi cantly a ect the businesses decision whether to carry out the tax obligations or not.
ere were no statistically signi cant indicators in the long run MIMIC models: p-value of both the indicators VATR and MONEY was close to 1. It is evident that the VAT gap should negatively a ect the VAT revenue. However, based on our results, it cannot be stated that the trend is either positive or negative. MONEY was not statistically signi cant in the rst models, still it is considered to be important to the assessment of the VAT gap, because transactions aimed to reduce or avoid the VAT liability are performed in cash. e close evaluation of the models indicates that inclusion of the lagged variables in the model was not expedient because none of them were statistically signi cant. It can be stated that the taxpayer's decisions are determined not by the previous but by the current period information -it is likely that decisions are made impulsively and based on the latest information. A er all, if decisions were made prudently, it would take time to analyse all the available information and nd the most e ective and appropriate solutions.
It should be noted that the MIMIC method has not been modelled yet to analyse the factors of the VAT gap in the case of Lithuania. Some of our results are in line with other researchers' ndings. F. Schneider and A. Bühn in their study "Shadow Economies and Corruption All Over the World: Revised Estimates for 120 Countries" (2007) have analysed the shadow economy and the VAT gap in three groups of countries: developing countries over 1999 to 2006, Eastern European and Central Asian countries over 1999 to 2006 and High income OECD countries over 1995 to 2006. Lithuania belongs to the second group, and as the MIMIC estimation results show, the three most statistically signi cant causal variables in this model were business freedom (t statistics was -7.85), scal freedom (-3.95) and in ation rate (2.88). As we can see from the results, in ation rate has statistically signi cant positive e ect just as it was estimated in our research. However, this comparison should be evaluated carefully rst of all because of the different time periods analysed. F. Schneider and A. Bühn's study covered a period from 1999 to 2006; our research involved a period from 2000 to 2013, so in the rst study inuence of the 2008 crisis was not accounted for. Moreover, other causal variables were di erent in these two models, that is why there is no further reason to compare them.

Construction and analysis of the short run eMIMIC models
In order to derive a short run eMIMIC model it is necessary to include the long run equilibrium errors (the number of which must be equal to that of indicators) in the long run MIMIC model. When designing the eMIMIC model it was discovered that inclusion of all the variables in the model did not yield any statistically reliable data of the existence of 3 cointegrating vectors. erefore, a er exclusion of one of the indicators (rGDP) two co-integrating vectors were found. In order to get reliable, fair and accurate results, rGDP was not included in the estimation of the short run eMIMIC model.
To determine the number of the co-integrating vectors the Johansen procedure was used. e procedure consists of two tests: the Trace test and the Maximum eigenvalues test. During these tests vector autoregression (VAR (p)) model is composed (Lütkepohl & Krätzig, 2004). Optimal number of lags (the errors are uncorrelated at lag 1 (p = 1)) was determined by using the autocorrelation function (ACF). e variable stationarity tests identi ed that there can be structural breaks in two variables: GFCF and VATR (this structural break is likely to be statistically insigni cant), therefore additional Lütkepohl -Saikkonen -Trenkler test was performed in order to test the co-integration rank. is test implies a possibility of the structural breaks when testing for unit root processes. Due to the large number of variables and a relatively short time series it was not possible to calculate the theoretical values of λ trace . Since GFCF is stationary with a structural break, it was decided to take GFCF as an exogenous variable in these tests, i.e., we searched for a stationary combination of non -stationary variables, considering that there is a stationary variable with a structural break. e numbers of characteristic roots that are statistically di erent from unity are conducted by using the following test statistic in the Trace test: n LR(r) = -T * Σ ln(1 -λ i ). (4) where r -is the number of co-integrating vectors, T -the number of usable observations, λ i -the eigenvalues of matrix π. e following sequence of null hypothesis is tested during this procedure: H 0 : r = 0, there are no co-integrating vectors; H 1 : r > 0, there is at least one co-integrating vector. e null hypothesis is rejected when LR(r) > theoretical λ trace . en the following hypothesis is tested: H 0 : r ≤ 1 -there is one or less than one co-integrating vector; H 1 : r > 1 -there is at least one co-integrating vector. e procedure of the rejection of the null hypothesis is similar to the former case. e test is completed when the null hypothesis is not rejected at 5 percent probability of error. e obtained results of the Trace test are presented in Table 3 (the results of the Maximum eigenvalue test were similar, so they were not included in this paper). Table  3 shows that the null hypothesis, which claims that there are 2 or less co-integrating vectors, cannot be rejected at a 5 percent level of signi cance because in this case the theoretical test statistics was lower than the estimated one (51.70 < 53.12). According to the p-value of the model compatibility chi -square (χ 2 ) criteria, the most relevant model is the one which includes all the causal variables; p-value of the last model (which was without GFCF, AAW and GGCE) was over 0.05 as well. It means that empirical distribution of all the models is compatible with the theoretical one. Other criteria used to compare the models were RMSEA and AIC. Results of both the criteria suggested that the most suitable is the last model, where RMSEA p-value and meaning of AIC were respectively 0.210 and 1568.16 (see Table 4). Based on all these results it could be stated that the last model is the best for further analysis. As it can be seen from Figure 3, there were no statistically signi cant causal variables in this evaluated eMIMIC model -p-value for both INFL and HD variables exceeds 0.05. However, in the course of this work, instead of GFCF, another variable -index of economic freedom -was included in the model both with HD and without HD (i.e., with the assumption that consumption is directly a ected by growing AAW); it was calculated that both INFL and HD were statistically signi cant. When the model with three causal variables GGCE, INFL and HD was evaluated, no statistically signi cant variables were identi ed, p-value of the least signi cant variable (GGCE) was not very high -it did not exceed 0.15. It would be inappropriate to say that none of the used causal variables have no statistically signi cant e ect on the VAT gap in the short run, therefore INFL and HD in uence should be evaluated. e estimated coe cient of INFL was the same as in the long run MIMIC model. It means that a positive change of in ation increases the VAT gap, ceteris paribus. It follows that in order to prevent an increase in the VAT gap, a stable price level should be maintained. As it is mentioned in the strategy of the monetary policy of ECB, price stability is de ned as a year-on-year increase in the Harmonised Index of Consumer Prices (HICP) for the euro area of below 2% (ECB, 2015). In order to pursue the stable price level, in ation rate should be maintained below but close to 2 percent over the medium term. e estimated coe cient of another variable -HD was also positive: growing propensity to save, i.e., the allocation of available resources not to consumption but to deposits may be the reason for the growth of the VAT gap in the short run, ceteris paribus. is variable was not statistically signi cant in the long run, which means that business takes into account the changes in the preferences of household savings in the short run, but adapts to them in the long run and copes with these challenges in other ways than avoiding tax obligations.
Similarly to the long run MIMIC model, there were no statistically signi cant lagged variables and indicators in the short run eMIMIC model. ese results may be explained by the fact that the impacts of the causal variables eliminate each other and the amount of the VAT gap remains constant over the long term, regardless of the outside e ects ( the variables which were used in the research), whereas taxpayers systematically a empt to avoid their tax obligations. It was found that the VAT gap does not have statistically signi cant in uence on the indicators of the short run eMIMIC model.

Limitations and suggestions for further research
Some limitations of our study should be also noted. First of all, there are doubts about the clear theoretical de nition of the "VAT gap": this concept can include some other possible elements such as the level of socio -economic development or social welfare etc. Moreover, all the estimates depend on the limited availability of data and the subjective decisions of the authors. Although the inclusion of all the variables in our models was based on the scienti c literature in the eld, due to the fact that not all the data was available during all the investigation period (for example, consumer con dence) or some of the data was not available at all (for example, the weighted average VAT rate), it was not possible to estimate the in uence of some of the meaningful variables on the VAT gap.
In addition to the above considerations, all the results were obtained making certain assumptions, e.g., that the error terms in the measurement model do not correlate with the latent variable. at speci cation of the MIMIC model simpli es description of the functioning of the economic system. Finally, the MIMIC model itself has the limitations as there may be other unidenti ed variables potentially correlated with the VAT gap. e study intended to determine the signi cant factors, therefore the coe cients obtained should be understood as approximations rather than exact gures.
Nevertheless, the limitations mentioned above do not a ect the general appropriateness of the MIMIC method in estimating determinants of the VAT gap.
In the future studies, in order to be er understand the nature and "composition" of the VAT gap, it would be important to deepen the knowledge on a set of other observable macroeconomic factors, such as turnover, labour market activity rate, the weighted average VAT rate, e ciency of the State Tax Inspectorate performance, assurance of measures on executing tax obligations, etc. Moreover, in real life, relationships between economic variables are not exactly linear. erefore further work is required to analyse non-linear relationships between variables both in the MIMIC and eMIMIC models.

Conclusions
e VAT gap in Lithuania being one of the largest in the EU de nitely in icts a signi cant loss on public nance. erefore it is very important to understand what determinants limit the country's capacity to mobilize revenue. e literature review suggests that the MIMIC model is one of the most reliable methods of measuring the VAT gaps.
e results of the estimated long run MIMIC model obtained show that only two out of ve causal variables have a statistically signi cant in uence on the VAT gap: the changes in General Government consumption expenditure and the changes in in ation. e growth of changes of the General Government consumption expenditure determines the growth of the VAT gap, ceteris paribus (1 percent changes in GGCE increases the VAT gap by 0.156 notional units). Since the core part of these expenditures in absolute terms was allocated to social protection, it may be assumed that growing sponsorship to this sector determines the fact that people ge ing low income are less interested to work, because the bene t from work is not su cient enough for them to become active labour market participants. Such people spend less money on consumption, which reduces the opportunity for business development.
e VAT gap growth in the long run can be explained by changes in in ation growth, ceteris paribus (1 percent change in INFL increases the VAT gap by 4.713 notional units); i.e., individuals, in order to maintain at least equal level of consumption, are forced to look for additional sources of income by other means, for example, engaging in illegal activity, hiding income and thereby avoiding tax compliance.
Due to the fact that there were no statistically signi cant indicators in the long run MIMIC model, it can be concluded that the impact of the causal variables eliminates each other, i.e., the amount of the VAT gap is permanent in the long run -regardless of the outside e ects, and the taxpayers systematically a empt to avoid their tax obligations.
e results of the short run MIMIC model obtained show that only two out of ve causal variables have statistically signi cant in uence on the VAT gap: in ation and household deposits. Positive changes of the in ation increase the VAT gap, ceteris paribus. us, in order to maintain at least the same level of the VAT gap, it is important to ensure price stability in the country. It decreases not only the uctuation of consumer purchasing power, but also the VAT gap. e growth of the changes in household deposits (HD) may be the reason why the VAT gap increases in the short run, ceteris paribus. In the long run this causal variable was not statistically signi cant, so it can be concluded that business takes into account the changes in the preferences of household savings in the short run, but adapts to these changes in the long run. e evaluation of both MIMIC and eMIMIC models indicated that there are no statistically signi cant indicators, which means that the VAT avoidance related business decisions cannot be taken spontaneously, i.e., in compliance only with the changes in causal variables used in the model. Decisions to carry out the tax obligations or not may be determined by many microeconomic and macroeconomic factors which were not included in this research or are hard to be measured.
It is important to mention that involvement of the lagged variables in the long run MIMIC model was not expedient, because none of them were statistically signi cant. erefore, it is most probable that both in the long and the short run the taxpayers make decisions based on the latest information, rather than depending on the long run trends.
Finally, we believe that the present study delivers reliable estimates and expands previous research on VAT evasion. e results of the models applied can be used not only as a basis for further discussion in this area, but also as one of the potential supporting tools in adjusting Lithuanian tax policy and VAT administration.