Shadow Economy in Portugal: computation by different approaches

Shadow Economy in Portugal: computation by different approaches by Sónia Cristina Leite Sousa Master in Economy and Business Administration Advisers: Óscar Afonso and Paulo Vasconcelos Porto, September of 2014 i Biographical note Sónia Cristina Leite Sousa, was born on September 27, 1988, in Oporto. She began her studies in the academic year 2007/2008 at the School of Economics and Management, University of Porto, having completed the first degree in Management in 2011. On the same year, she joined the Economics and Business Administration Master’s degree in the same institution. Chose to join this project given the multidisciplinary nature of the course which enabled her to get a solid background knowledge in management. Allowed her also to obtain the necessary skills to face the many challenges of the labour market. Started working in management areas since September 2011, giving at the same time, mathematics and economics explanations classes. ii Acknowledgments I would like to express my gratitude to the Professors Óscar Afonso and Paulo Vasconcelos, for the valuable help and guidance I received throughout the preparation of this study. I also thank all my teachers by broadening my horizons of knowledge. I could not forget to express my gratitude to my family, specially my parents, Carlos and Cristina, thank you for having me brought to the world. To Frederico Oliveira, I appreciate the patience and support you have always given me, especially in difficult times which allowed me to proceed with this project. To my friend Daniela Silva, thank you for all the help and good advice that motivated me to move on. To my colleague Manuel Nogueira, a special thanks for the collaboration and all aid that you have given. Moreover, I want to mention all friends and colleagues who directly or indirectly contributed to make this study a reality. iii Abstract In a period of financial and economic turmoil, it is of paramount interesting to quantify the Shadow Economy (SE). It is a phenomenon present in all countries, regardless of their level of development. In Portugal, the latest data reveals that its share reached 25.40% of the observed GDP in 2011 (Afonso and Gonçalves, 2012). For the determination of SE the author used the Electricity Consumption Method (ECM) and the Structural Model of Multiple Indicators and Multiple Causes, the MIMIC model, which is an econometric analysis, firstly proposed by Jöreskog, and Goldberg (1975). Several other methods can alternatively be used. The purpose of this dissertation is to analyse different approaches and to comprehend the evolution of the Shadow Economy in Portugal until 2011, through the perspective of several authors. Furthermore, it is also intended to estimate its Portuguese value in 2012 and 2013, through the use of ECM and the MIMIC model. The electricity consumption is regarded as the single best physical indicator of overall (both official and unofficial) economic activity moving in sync with GDP. MIMIC model is based on structural modelling using the Shadow Economy as a latent variable considering several causes and indicators of the SE. According to the results, the relative size of the SE in Portugal has increased over the last decades (1970-2013). According to the ECM, it increased from 9.31% of GDP in 1970 to 19.23% of GDP in 2013, while the MIMIC approach shows increase of the shadow economy from 8.18% of GDP in 1970 to 25.62% of GDP in 2013. In the final phase is developed a new method to estimate the size of SE based on the combination of the two previous methods. Keywords: Shadow Economy, GDP, Methods to Estimate the Shadow Economy, ECM, MIMIC Model, Portugal iv Resumo Num período de turbulência financeira e económica é deveras interessante quantificar a Economia Não Registada (ENR). Esta é um fenómeno presente em todos os países, independentemente do seu nível de desenvolvimento. Em Portugal, os últimos dados revelam que o seu peso atingiu 25.40% do PIB observado em 2011 (Afonso e Gonçalves, 2012). Para a determinação deste indicador, a autora utilizou o Método do Consumo de Electricidade (MCE) e o Modelo Estrutural de Múltiplos Indicadores e as Causas Múltiplas, o modelo MIMIC, que consiste numa análise econométrica, em primeiro lugar proposto por Jöreskog e Goldberg (1975). Vários outros métodos podem ainda ser usados. O objetivo desta dissertação é analisar as diferentes abordagens e compreender a evolução da ENR em Portugal até 2011, através da perspectiva de vários autores. Além disso, também tem como objetivo estimar o seu valor para Portugal em 2012 e 2013, através do MCE e do modelo MIMIC. O consumo de energia elétrica é considerado o melhor indicador físico da totalidade da atividade económica (tanto oficial e não oficial) que se movimenta em sincronia com o PIB. O modelo MIMIC é baseado em modelos estruturais que usa a ENR como uma variável latente, considerando várias causas e indicadores da ENR. De acordo com os resultados apresentados neste trabalho, o tamanho relativo da ENR em Portugal tem aumentado ao longo das últimas décadas (1970-2013). De acordo com o MCE, passou de 9.31% do PIB em 1970 para 19.23% do PIB em 2013, enquanto que a abordagem MIMIC mostra aumento da Economia Não Registada de 8.18 % do PIB em 1970 para 25.62 % do PIB em 2013. Na fase final é desenvolvido um novo método de estimativa para o tamanho da ENR com base na combinação dos dois métodos anteriores. Palavras Chave: Economia Não Registada, PIB, Métodos para Estimar a Economia Não Registada, MCE, Modelo MIMIC, Portugal v Contents 1. Introduction ............................................................................................................... 1 2. Shadow Economy: definition, causes and consequences .......................................... 3 2.1. Definition of Shadow Economy ......................................................................... 3 2.2. Causes of Shadow Economy .............................................................................. 6 2.3. Consequences of Shadow Economy ................................................................ 11 2.4. The Shadow Economy in Portugal ................................................................... 13 3. Methods to Estimate the Size of the Shadow Economy .......................................... 16 3.1. Direct Approaches: the Survey and Tax Auditing Method .............................. 16 3.2. Indirect Approaches ......................................................................................... 18 3.2.1. The Discrepancy between National Expenditure and Income Statistics .. 18 3.2.2. The Discrepancy between the Official and Actual Labour Force............. 18 3.3. The Models Approach ...................................................................................... 19 3.3.1. The Transactions Approach ...................................................................... 19 3.3.2. The Currency Demand Approach ............................................................. 20 3.3.3. The Physical Input (Electricity Consumption) Method ............................ 21 3.3.4. The MIMIC Model ................................................................................... 24 4. Estimation of the size of Shadow Economy in Portugal ......................................... 27 4.1. Computation of the Shadow Economy by Physical Input Method .................. 27 4.2. Computation of the Shadow Economy by MIMIC Model............................... 30 4.3. The Shadow Economy as an average between ECM and MIMIC Model ....... 40 5. Conclusions ............................................................................................................. 43 References ....................................................................................................................... 45 Appendix A: MIMIC model data, stationary and co-integration data ............................ 50 Appendix B: Estimations for the 2013 value .................................................................. 52 Appendix C: ECM, MIMIC and other authors data ....................................................... 53 vi List of Figures Figure 1. Definition of “Shadow Economy”, “Black Economy” and “Black Activities” 4 Figure 2. Main Causes of the Increase of the Shadow Economy ..................................... 8 Figure 3. Size and development of tax evasion (in % of GDP) in Portugal and in 38 OECD countries average accounting for indirect taxation and self-employment as driving forces .................................................................................................................... 9 Figure 4. Average relative impact (in %) of the Shadow Economy determinant’s in Portugal and the average of 38 OECD countries (1999-2010) ....................................... 12 Figure 5. The Shadow Economy in GDP (%) in Portugal 1970-2011 ........................... 13 Figure 6. The Shadow Economy according to the different authors (1989/90 – 2009/10) ........................................................................................................................................ 14 Figure 7. Size of the Shadow Economy of Portugal and 27 EU - Countries average over 2003–2013 (in % of GDP) .............................................................................................. 14 Figure 8. Quantification methods of the Shadow Economy ........................................... 16 Figure 9. General Structure of a MIMIC Model ............................................................. 26 Figure 10. Evolution of Electricity Consumption and of GDP in Portugal from 1970 to 2012 ................................................................................................................................ 27 Figure 11. Size of SE in Portugal (% of GDP) by Electricity Consumption Method .... 28 Figure 12. SE annual growth by ECM vs GDP annual growth, 1970 to 2013 ............... 29 Figure 13. MIMIC Model 6-1-3 ..................................................................................... 32 Figure 14. MIMIC Models 6-1-3, 5-1-3b, 5-1-3c ........................................................... 36 Figure 15. Size of SE in Portugal (% of GDP) by MIMIC Model ................................. 37 Figure 16. SE annual growth by MIMIC model vs GDP annual growth, 1970 to 2013 40 Figure 17. Size of SE in Portugal (in % of GDP) by MIMIC and ECM model ............. 41 Figure 18. Size of SE in Portugal (in % of GDP) by several authors ............................. 42 Figure B.1. Social Security Revenue - Estimation for the 2013 value ........................... 52 Figure B.2. Social Security Expenditure - Estimation for the 2013 value ...................... 52 vii List of Tables Table 1. Taxonomy of types of underground economic activities ................................... 5 Table 2. Portugal’s Corruption Perceptions Index from 1995 to 2013 ........................... 10 Table 3. Size of SE in Portugal (% of GDP) by Electricity Consumption Method ........ 29 Table 4. MIMIC models estimated ................................................................................. 34 Table 5. Size of SE in Portugal (% of GDP) by MIMIC Model ..................................... 36 Table 6. Size of SE (in % of GDP) - Average between ECM and MIMIC Model ........ 41 Table A.1. Data used in the MIMIC Model estimation for the SE, 1970-2013 ............. 50 Table A.2. Stationary analysis ........................................................................................ 51 Table A.3. Co-integration analysis ................................................................................. 51 Table C.1. Size of SE (% of GDP) of Portuguese Economy, 1970-2013 ....................... 53 Table C.2. Size of SE (% of GDP) in Portugal between 1970-2013 – Several authors . 54 1 1. Introduction The growth of the underground, informal, illegal economy or any other name that will be used is a global phenomenon. Recent studies indicate that the size of this part of the economy, that does not pay tax or is not measured, regulated or even not operate within the law, is higher than many economists thought and presents a high growth. The shadow economy did not attract the attention of economists until the sixties when it became the subject of study. In 1972, from a study of the International Labour Organization (ILO), the subject gains prominence and its study momentum. In fact, Dixon (1999) states that the shadow economy drew little attention until recently. This attitude changed after the first estimates of SE. They showed just how large it might be. From there, the population in general and the government have become concerned with the phenomenon due mainly to its effect on tax evasion. The shadow economy reduces the credibility of official statistics, makes it difficult to choose public policies and produces unequal competition with companies of the official sector. Nowadays, the Shadow Economy evaluation is still quite controversial as there are disagreements about the definition of the concept of shadow economic activities and about their estimation procedures. Several meaningful outcomes have already been written by Schneider and Enste (2000), and Feld and Schneider (2010), yet a widely definition has not been adopted. The theoretical studies have advanced several reasons why pointing people to operate in the shadow economy. The most often mentioned factors are the high taxes, high labour costs and the strong regulation of economy. Empirical studies, in turn, face a big problem that resides in fact of trying to measure something that is not observable (by its nature), which in itself is an arduous task. The present study attempts to arrange the development of literature, including its theoretical and empirical aspects of their disputes, with a view to developing a index to measure the evolution of the shadow economy in Portugal. This present dissertation is organized as follows: chapter 2 defines the concept of SE and explores its main causes and consequences in the official economy. Chapter 3 8 (citizens’ attitudes toward the state), which describes the readiness of individuals (at least partly) to leave their official occupations and enter the SE, tends to increase the size of the SE. In the market labour, the unemployment rate and the self-employment are also considered causes of the SE. In literature is assumed that an unemployed individual has more incentives to work in SE activities, however this assumption depends on the educational and cultural aspects. There are people who prefer working in the official economy because of the social benefits and labour protections, to increase their income, they can also add to their official activity a shadow activity. At the same time, increased activities in the informal sector may be expected to be reflected in shorter working hours in the official economy. Concerning self-employment, it is well known that selfemployers understate their incomes to authorities (Dell’Anno, 2007). So, it is expected that an increase in this variable will positively influence the size of SE. Figure 2. Main Causes of the Increase of the Shadow Economy The size of tax evasion (Figure 3) has decreased from 1999 to 2001 and from 2004 to 2009. After 2001, this indicator increased until 2003, a possible explanation for such development maybe the 9/11 and all negative consequences derivate from it. In 2010 it is also notice an increase, possibly due to the economic and financial world crises that 9 broke down in 2008. It is notorious that Portugal and the 38 OECD countries average have a similar trend, although Portugal displays a differential, about +1%, which is a remarkable difference. Figure 3. Size and development of tax evasion (in % of GDP) in Portugal and in 38 OECD countries average accounting for indirect taxation and self-employment as driving forces Source: Schneider and Buehn (2012) Another worrying cause is bribery. Corruption is a symptom of over-regulation, as well as Shadow Economy. Governments must have economic freedom in all conceivable areas, so that bribery and SE can diminish through time. Economic freedom with a strong rule of law will foster a culture of investment, job creation and institutional respect (Eiras, 2003). There is a negative relationship between economic freedom and Shadow Economy, that is, as economic freedom is reduced the Shadow Economy assumes a greater share of the GDP. In repressed countries in their economic freedom the Shadow Economy weighs 40.25% in the GDP, while in countries with high economic freedom the weight drops to 16.37% (Barbosa et al., 2013). 2 2,5 3 3,5 4 4,5 5 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Portugal Average 10 Table 2. Portugal’s Corruption Perceptions Index from 1995 to 2013 Year Index Rank Total Countries Rank/Total Countries 1995 5,56 22 41 54% 1996 6,53 22 54 41% 1997 6,97 19 52 37% 1998 6,5 22 85 26% 1999 6,7 21 99 21% 2000 6,4 23 90 26% 2001 6,3 25 91 27% 2002 6,3 25 102 25% 2003 6,6 25 133 19% 2004 6,3 27 146 18% 2005 6,5 26 159 16% 2006 6,6 26 163 16% 2007 6,5 28 180 16% 2008 6,1 32 180 18% 2009 5,8 35 180 19% 2010 6 32 178 18% 2011 6,1 32 183 17% 2012 6,3 33 176 19% 2013 6,2 33 177 19% Source: Transparency International The Corruption level within a country is another factor that increases SE activities.The Corruption Perceptions Index 1 (Table 2) shows that corruption has been decreasing in Portugal between edge years. In 2013, Portugal belongs to the 19% cleanest countries of the sample, however it is important to notice that the worst years were in 1995 with 5.56 and in 2009 with 5.8. There is no consensual and unique study perspective of the impact of these factors in the development of Shadow Economy. These causes, either major or minor, change for different countries. Nevertheless, as small or insignificant a cause can be, its influence in the evolution of Shadow Economy should be taken into account by researchers to avoid mistakes. Only through meticulous study is possible to aid politicians in the fight for decreasing the size of Shadow Economy. 1 The Corruption Perceptions Index ranks countries and territories based on how corrupt their public sector is perceived to be. A country or territory’s score indicates the perceived level of public sector corruption on a scale of 0 - 10, where 0 means that a country is perceived as highly corrupt and 10 means it is perceived as very clean. A country's rank indicates its position relative to the other countries and territories included in the index. 11 2.3. Consequences of Shadow Economy The development of SE has different outcomes in the official economy. Inequality and unfairness of the economic system is one of them, as there are individuals who seek the same products cheaper in the SE by not paying taxes. One hypothesis for the negative correlation between the formal and informal sector may be due to an increase in the SE that leads to a reduction in tax revenue and, therefore, a smaller quantity and quality of public goods and services made available to society. Thus, it could occur a reduction of economic growth, under the premise of a tax burden higher than the optimum, and a weak compliance with state institutions (Loayza, 1996). This proposition becomes true, to the extent that a public infrastructure is a key to economic growth. Another form submitted for negative explanation of this correlation is through a model, prepared by Asea (1996), which is based on the fact that the production technology depends of public services funded by taxes. Adding to the fact that the SE does not pay taxes, but fines and fees, which, in most cases, are not used to finance public services required to impulse economic growth. If a SE is growing faster than the official and the resources are moving up to informality, as a result of a likely high taxation, increase regulation or another previously pointed cause, it is clear that official statistics of economic growth will be undervaluing the real growth of the entire economy. Therefore, it can be deduced that a fast growth of SE contributes to a decrease in observed economic growth (Feige, 1979). The observed economic growth may be being taken into account by the governments when they set their economic policies and it also could be observed in official unemployment statistics, presenting in this case a likely overestimation regarding the real situation (Gutmann, 1979). Another negative consequence of SE is disincentive for foreign investment. Since foreign investments are usually more regulated, their produced goods can potentially be uncompetitive in comparison with the domestic competitors who are functioning in the SE. 12 Nevertheless, according to Asea (1996), the SE may lead to more competitiveness, greater efficiency and can limit governmental activities through an environment of urban demand and small scale production, adding dynamism and entrepreneurship to the economy. The SE can, therefore, contribute to the creation of markets, increase financial resources, printing a positive correlation between economic growth and informality. Through some studies, Schneider and Enste (2000) present that around 66% of income generated by the SE, is immediately spent in the official sector, with positive effects on economic growth and revenues with indirect taxes, for instance VAT (value added tax). A study by Schneider and Buehn (2012) revealed the impact of SE in different areas, from 1999 to 2010, in which the size of SE in Portugal was 22.7% of GDP, and the average of 38 OECD countries was 20.3% of GDP. The results are shown in the figure below. Figure 4. Average relative impact (in %) of the Shadow Economy determinant’s in Portugal and the average of 38 OECD countries (1999-2010) Source: Schneider and Buehn (2012) Figure 4 reveals that the main impact of SE in Portugal is in self-employment and indirect taxes, with approximately 30% each. This is also true for the average of 38 OECD countries, but with more featured for the indirect taxes. The third is 0 5 10 15 20 25 30 35 Personal income tax Indirect taxes Tax morale Unemployment Selfemployment GDP growth Business freedom Average Portugal 13 0% 5% 10% 15% 20% 25% 30% unemployment, whether for Portugal and for the average of 38 OECD countries, followed by tax morale in Portugal’s case and personal income tax for the average of 38 OECD countries. The main difference between the two cases is self-employment, where Portugal has more or less 10% than the average of the 38 OECD countries. The opposite occurs for personal income tax, where the last has about 5% more than Portugal. 2.4. The Shadow Economy in Portugal In recent years there have been appearing some studies about the Shadow Economy in Portugal, namely of the recent studies by Barbosa et al. (2013), Schneider (2010, 2013), and Afonso and Gonçalves (2010, 2012). Figure 5. The Shadow Economy in GDP (%) in Portugal 1970-2011 Source: Afonso and Gonçalves (2012) Based on the continuous study developed by Afonso and Gonçalves in 2010, updated in 2011 and 2012, “A Economia Registada em Portugal”, the author prepared Figure 5, according to the data displayed by the source. The model used was the MIMIC 6-1-3 (six causes, one latent variable and three indicators). As it is shown, the percentage of the Shadow Economy in Portugal is increasing from 9.4% in 1970 to 24.8% in 2010. In three decades, according with this estimation, the size has grown about 264%. 14 From the results shown in Figure 6 it is possible to see a guide line between all perspectives. Every author used the MIMIC Model for the estimation of the size and development of Shadow Economy. The majority of the approaches illustrate that after 2007/08 the size of the Shadow Economy has increased. Figure 6. The Shadow Economy according to the different authors (1989/90 – 2009/10) Source: Barbosa et al. (2013) Figure 7. Size of the Shadow Economy of Portugal and 27 EU - Countries average over 2003–2013 (in % of GDP) Source: Schneider (2013c) 17,0% 18,0% 19,0% 20,0% 21,0% 22,0% 23,0% 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Portugal 27 EU-Countries / Average (unweighted) 15 Figure 7 was prepared by the author, according to the information in “Size and Development of the Shadow Economies of Portugal and 35 other OECD Countries from 2003 to 2013: Some New Facts” by Schneider (2013). Through it is possible to comprehend, that from 2003 to 2013, these 27 highly developed countries show a further decline of the shadow economies. The main reason for this development is the recovery of the official economy in most countries (Schneider, 2013). In that decade, in Portugal’s case, the deceleration is also noticed. It is important to emphasise the growth of the Shadow Economy due to the world economic crisis, between 2008 and 2009, both in Portugal and the 27 EU - Countries Average. 16 3. Methods to Estimate the Size of the Shadow Economy As mentioned in the previous chapter, estimating the size of a Shadow Economy is a tough and demanding task. Three different types of methods (Figure 8) are most regularly implemented: the direct, the indirect and the model approach (Schneider, 2005). Figure 8. Quantification methods of the Shadow Economy 3.1. Direct Approaches: the Survey and Tax Auditing Method Direct methods, as the name suggests, attempt to measure Shadow Economy directly, among economic agents who carry it out. Survey methods consists on making inquiries of voluntary response, usually along the households, including questions about participation in Shadow Economy activities or on income earned in activities of this nature. Sample surveys designed to estimate the shadow economy are widely used in a number of countries. This approach has the advantage of allowing to obtain detailed information about the structure of the Shadow DIRECT •SURVEY •TAX AUDITING INDIRECT •DISCREPANCY BETWEEN NATIONAL EXPENDITURE AND INCOME STATISTICS •DISCREPANCY BETWEEN THE OFFICIAL AND ACTUAL LABOUR FORCE MODEL •TRANSACTIONS •CURRENCY DEMAND •PHYSICAL INPUT •MIMIC 17 Economy, but the results are very sensitive to the way the questionnaire is formulated (Schneider, 2005). Moreover, it has the disadvantages of any inquiry procedure: the credibility of the results depends greatly on the respondent’s willingness to cooperate, on the ability to inquiry a representative sample and on the achievement of true answers to the questions. Audit methods use personal tax returns for income groups and audits them to identify those who are misreporting or hiding their actual income. The model considers cases in which individuals choose the fraction of income they report to the IRS, while facing stochastic probabilities of being audited. If individuals are caught evading taxes this year the IRS examines their tax returns for the previous year as well. In this simple, specification of the model, unreported income is either discovered by an IRS audit in the year that follows the tax filing, or is discovered when the taxpayer is audited and caught evading the following year, or else is never discovered (Engel and Hines, 1999). The fiscal auditing programs can find discrepancies between income declared for tax purposes and that measured by selective checks. This kind of software is created to estimate the amount of undeclared taxable income, in that perspective, they may also be used to calculate the Shadow Economy. For Schneider (2005) this approach shows many difficulties. First of all, using tax compliance information is equivalent to using a (possibly biased) sample of the population. The selection of tax payers for tax audit is not usually random but based on properties of submitted (tax) returns that indicate a certain likelihood of (tax) fraud. Consequently, such a sample is not a random one of the whole population, and estimates of the shadow based upon a biased sample may not be accurate. Secondly, estimates based on tax audits reflect only that portion of shadow economy income that the authorities succeed in discovering, and this is likely to be only a fraction of hidden income. This method drastically understates the underground economy as it only measures tax evasion and does not include production of illegal goods and services. 24 3.3.4. The MIMIC Model The previous methods are designed to calculate the size and development of the SE. However, they consider just one indicator (Schneider, 2005). It is notorious that SE effects show up simultaneously in the production, labour, and monetary markets. An even more important critique is that the causes that determine the size of the SE are taken into account only in some of the monetary approach studies that usually consider one cause, the burden of taxation. The Structural Model of Multiple Indicators and Multiple Causes, MIMIC model, due originally to Frey and Pommerehne (1984), is a special case of the models of structural equations (SEM – Structural Equation Models), which explicitly considers multiple causes leading to the existence and growth of the Shadow Economy, as well as the multiple effects over time. It has the particularity that the latent variables are formative and reflective items at the same time. The MIMIC Model treats the Shadow Economy as a latent variable and estimates parameters that relate the latent variable to the causes and indicators respectively, as illustrated in Figure 9. Applying this model to Shadow Economy measurement has become increasingly popular in recent years with applications across many developed and developing countries (e.g., Loayza, 1996; Bajada and Schneider, 2005; Schneider, 2007). However, as Breusch (2005) indicates, the estimated parameters in such model can only recognise the relative size of the Shadow Economy in each year. For Schneider (2013), the MIMIC estimation procedure can be described in three steps. 1. Modelling the Shadow Economy as an unobservable (latent) variable; 2. Description of the relationships between the latent variable and its causes in a structural model; 3. The link between the latent variable and its indicators is represented in the measurement model. The structural equation model, according to Buehn and Schneider (2008), is given by: ηt = γ′xt + ςt (3.6) 25 Where  ηt represents the latent variable, the value of SE in year t;  γ′ = (γ1, γ2,...,γq) a (1 × q) vector of coefficients in the structural model describing the “causal” relationships between the SE and its causes;  x′t = (x1t, x2t,…,xqt) is a (1 × q) vector of time series variables as indicated by the subscript t. Each time series xit, i = 1,…,q is a potential cause of the latent variable ηt;  ςt represents the unexplained component; The MIMIC model assumes that the variables are measured as deviations from their means and that the error term does not correlate to the causes, i.e. E (ηt) = E (xt) = E (ςt) = 0 and E (xt ς′t) = E (ςt x′t) = 0. The variance of ςt is abbreviated by ψ and Φ is the (q × q) covariance matrix of the causes xt. The measurement model represents the link between the latent variable and its indicators, i.e. the latent unobservable variable is expressed in terms of observable variables. It is specified by: yt = ληt + εt , (3.7) Where  y′t = (y1t, y2t,…,ypt) is a (1 × p) vector of individual time series variables yjt j = 1,…,p;  εt = (ε1t, ε 2t,…, ε pt) is a (1 × p) vector of disturbances where every εjt , j = 1,…,p is a white noise error term. Their (p × p) covariance matrix is given by Θε.  The single λj, j = 1,…,p in the (1 × p) vector of regression coefficients λ, represents the magnitude of the expected change of the respective indicator for a unit change in the latent variable. 26 Figure 9. General Structure of a MIMIC Model Source: Buehn and Schneider (2008) Like the MIMIC model’s causes, the indicators are directly measurable and expressed as deviations from their means, that is, E(yt) = E(εt) = 0. Moreover, it is assumed that the error terms in the measurement model do not correlate either to the causes xt or to the latent variable ηt, hence, E (xt ε′t) = E (εt x′t) = 0 and E (ηt ε′t) = E (εt η′t) = 0. A final assumption is that the εt does not correlate to ςt, i.e. E (ε t ς′t) = E (ςt ε′t) = 0. Figure 9 displays the common structure of the MIMIC model. 27 4. Estimation of the size of Shadow Economy in Portugal As seen in the previous sections, there are several researchers that calculate the size and growth of SE. In this chapter the author estimates the size of SE according to the Physical Input Method for the period of 1970 to 2012 and the MIMIC Model between 1970 and 2013. Then a combination of the achieved results will be presented as the compute of SE for that period of time. 4.1. Computation of the Shadow Economy by Physical Input Method In this section the Kaufmann and Kaliberda electricity consumption method will be applied to estimate the size of SE in Portugal. The following stages are involved in estimating the SE for Portugal through this approach. First, it is needed to gather data for the electricity consumption and GDP at constant prices growth rates. The electricity consumption data was obtained from World Bank for the period of 1970 to 1993 and from Pordata between 1994 and 2012. And the growth rate of GDP at constant prices (base year 2006) was acquired through Pordata for the period of 1970 and 2012. From Figure 10 it is possible to see that the two variables present a similar behaviour between 1970 and 2012. Figure 10. Evolution of Electricity Consumption and of GDP in Portugal from 1970 to 2012 Source: World Bank and Pordata -6 -4 -2 0 2 4 6 8 10 12 Growth Rate of Electricity Consumption Growth rate of GDP at constant prices (base year 2006) 28 y = 0,0002x3- 0,0175x2+ 0,6408x + 7,876 R² = 0,976 5 7 9 11 13 15 17 19 21 23 25 According to Kaufmann and Kaliberda (1996), the output elasticity of electricity consumption is taken as one. After having the growth rates, an initial value of the SE is needed to derive the estimated results for the period of 1970 and 2012. For this purpose, it was assumed the size of SE in 1970, which was, according to Afonso and Gonçalves (2012), 9.31% of the GDP. The formula used to compute the size of SE by this approach is (3.3), which is exhibited in the previous chapter. Figure 11 presents the outputs of the SE in Portugal for the period between the years 1970 and 2012. Even though the relative size of the SE within the GDP is strongly dependent on the SE base year and can be misleading, it is nuclear to mention that the dynamic trend of SE in GDP is not affected, regardless the initial base value. Figure 11. Size of SE in Portugal (% of GDP) by Electricity Consumption Method Source: Own calculations The output indicates that the SE general trend as a percentage of the GDP between 1970 and 2012 in Portugal is increasing, from 9.31% to 20.95%, respectively. The value size of SE in year 2013 was estimated through the equation shown in figure above, the outcome was 19.23% of GDP (consult annual results in Table C.2 Appendix C). 29 Table 3. Size of SE in Portugal (% of GDP) by Electricity Consumption Method Years 1970- 73 1974- 77 1978- 81 1982- 85 1986- 89 1990- 93 1994- 97 1998- 01 2002- 05 2006- 09 2010- 13 ECM 9.23 11.24 13.01 14.61 15.64 15.90 16.35 17.50 19.68 20.89 20.70 Source: Own calculations In Table 3 are shown the average results for the size of SE. Starting from 1970 until 1989 the SE is increasing quickly, by one to two percent per year, it starts with 9.23% in 1970-1973 and finishes with 15.64% in 1986-1989. Between 1990 and 2009 it also rises but not so fast. The 2010-2013 SE estimation is an exception, it decreases to 20.70%. During the years 1973-1977, the annual growth rate of the Electricity Consumption is much greater than the annual growth rate of the GDP for the same period. The annual difference is between four to nine percent, that why the SE is fast growing. According to the Kaufmann/Kaliberda method, this leads to the conclusion that the total economic activity (including the industry and the households) are using more electricity to produce goods and services that are not captured by the recorded official GDP. From Figure 12 it is possible to realize that in 1970-2013, SE and GDP growth rates display symmetric behaviour, with the exception of the years 2010 and 2011, where the trend is the same. This means that when the official economy grew, the SE decreased. Figure 12. SE annual growth by ECM vs GDP annual growth, 1970 to 2013 Source: Own calculations and Pordata -10,00 -5,00 0,00 5,00 10,00 15,00 SE GDP 30 It is important to mention some problems with this approach. Not all shadow activities require a lot of electricity power, which allows measurement of only a part the SE. Overtime there is technical progress and the consumption of electricity, per unit product, is reduced. Finally, the electricity consumption is different across sectors, the tertiary sector does not employ as much electricity as the secondary. 4.2. Computation of the Shadow Economy by MIMIC Model In this section, the MIMIC Model is used to estimate the size of Shadow Economy between 1970 and 2013. The causes and indicators of SE used in this work are based on the associated literature (Schneider and Enste, 2000; Dell’Anno, 2008; Enste, 2010) and the available data for Portugal. Are cited as potential causes:  the weight of direct taxes and social security contributions 2 in the Gross Domestic Product (GDP), DTSSC;  the weight of indirect taxes in GDP, IT;  the weight of subsidies and social transfers 3 in GDP, SUBSSC;  the weight of real government consumption in GDP, GE - variable used as a proxy for the burden of regulation;  the percentage of self-employment, SEMP;  the unemployment rate, UR. The relationship between these variables and the SE is supposed to be given by the following structural formula: ηt= β1DTSSCt+β2ITt+β3SUBSSCt+β4GEt+β5SEMPt+β6URt+ςt (4.1) It is expected that a variation in size of SE is given by the following: 2 The value for this variable in 2013 was estimated, see Figure B.1. in Appendix B. 3 The value for this variable in 2013 was estimated, see Figure B.2. in Appendix B. 31  the amount of currency in circulation outside the banking system (per capita), CURR;  the percentage of participation in the workforce, LFPR;  real GDP per capita, GDP - this latter variable is used as the scale variable, the value of the associated coefficient is fixed to +1 or -1 to establish the relative magnitude of other indicators. Considering Schneider (2005), the scale coefficient is set to be as +1 and, in line with Dell’Anno et al. (2007), the sign of the coefficient is adjusted (if necessary) according to the methodology reductio ad absurdum. The measurement equations are used: CURRt = λ1ηt+ ε1 (4.2) LFPRt = λ2ηt+ ε2 (4.3) GDPt = +1.ηt+ ε3 (4.4) The data sources and the concrete specification of the variables are displayed in Table A.1 of Appendix. The MIMIC model base used was a 6-1-3 model (six causes, a latent variable and three indicators), shown in Figure 13, which has been progressively modified by omitting some of its non-statistically significant variables, in order to try to optimize the model. As Duncan (1975, pp.149) mentions: “The meaning of the latent variable depends completely on how correctly, precisely and comprehensively the causal and indicator variables correspond to the intended semantic content of the latent variable.” Following the theoretical considerations in chapter 2, eight hypotheses were developed below (all ceteris paribus), which will be empirically tested by using the MIMIC model: 1. An increase in direct and social security contributions increases SE. 2. An increase in indirect taxation increases the SE. 3. An increase in government expenditure rises the SE. 4. An increase in subsidies and social security contributions, leads to a decrease in SE. 32 5. The higher self-employment, the more people work in SE activities. 6. The higher unemployment, the more people work in SE activities. However, the theory suggests that the coefficient of unemployment can have a positive or negative sign. The development of the SE can occur alongside the development of the formal economy, or it can occur in moments of crisis in the formal economy. 7. An increase in monetary transactions, implies a rise in shadow economy activities. 8. The lower labour force participation rate, the more people work in SE activities. However, the expected coefficient sign of this variable is ambiguous, since there is no consensus in the literature on the effects of SE in LFPR. Figure 13. MIMIC Model 6-1-3 The statistical processing of data begins with the preparation of two tests for nonstationary of all variables in the model. It was used the econometric software Gretl, version 1.9.90, which was released in May 2014. 33 The first test performed was the Augmented Dickey-Fuller (ADF) test. The second test made was the Kwiatkowski Phillips-Schmidt-Shin (KPSS) test. The results are shown in Table A.2 in Appendix A, therefore it may be concluded that a large number of variables are I (1), since the ADF test does not reject the null hypothesis of the series not be stationary and KPSS test did not reject the alternative hypothesis of the series not to be stationary. The KPSS test appeared to decrease the uncertainty that often the ADF and Phillips-Peron (PP) tests evidenced. According to Kwiatkowski-Phillips-Schmidt- Shin, this test complements the analysis of traditional unit root tests (ADF and PP). Then the Engle-Granger two-step Approach (1987) was prepared, to verify if all cause variables are co-integrated with each of the indicator variables. The results obtained from the estimations are shown in Table A.3 in Appendix A. The residuals of the cointegration relationship of each regression are analysed using the ADF test. If the causes are co-integrated with the indicators, then it is expected the rejection of the null hypothesis of a unit root in the regression residuals of each equation, using the ADF test. Table A.3 in Appendix A shows that, to the usual significance levels, the null hypothesis in all residuals can be rejected, which means the causes are co-integrated with each indicator. According to Dell’ Anno et al. (2007), the detection of multivariate normality is vital to preserve the statistical properties of estimators. The “chi-square” test is used to evaluate if the models fit with the dataset. If the variables are not (multivariate) normally distributed, the maximum likelihood estimators may produce biased standard errors and an ill-behaved “chi-square” test of the overall model fit. The tests made displayed that the variables do not reject the null hypothesis of following a normal distribution. The cause and indicator variables will be used without any differentiation treatment to estimate the long-term equilibrium of MIMIC model translated in equations (4.1; 4.2; 4.3; 4.4), Breusch (2005). The estimated coefficients for maximum likelihood method are shown in Table 3. The cause variables are all expressed in percentage, which allows the direct comparison of their coefficients in order to evaluate the importance of these variables in the formation of SE. 40 -15 -10 -5 0 5 10 15 20 SE GDP nowadays. From that point on, Portugal has never been able to fully recover and in addition a political crisis was installed. In 2011 it was necessary to make a request for financial assistance, and so in 2013 the SE achieved its highest value 25.62% of GDP. Figure 16. SE annual growth by MIMIC model vs GDP annual growth, 1970 to 2013 Source: Own calculations and Pordata The MIMIC model has also some drawbacks. It is calculated based on an existing estimation of SE for a base year, which is one of the problematic aspects of the latent variable method. Giles and Tedds (2002) claim that there is no guarantee that the model can reflect the exact share of the shadow economy, since the causes and indicators may reflect other economic phenomena; the flexibility offered by the MIMIC model does not prevent the use of variables difficult to measure, which may contain errors. 4.3. The Shadow Economy as an average between ECM and MIMIC Model In this section, a comparison between the two used methods is made. Figure 17 shows the output of the two approaches. It is possible to see that until 1988, the ECM model presented higher values for the size of SE, after that year the MIMIC model displayed bigger estimations. In 1987 the size of SE in percentage of official GDP by ECM model was 15.30% and 14.24% by MIMIC model, in 1988 it was 15.54% and 16.33%, 41 respectively. Both approaches show a positive growth for the under taken period (1970- 2013). Figure 17. Size of SE in Portugal (in % of GDP) by MIMIC and ECM model Source: Own calculations In Table 6 are shown the average estimated results for the size of SE in each four years, from 1970 to 2013, through the average of ECM and MIMIC model outcomes (the annual estimations are presented in table C.2 in Appendix C). Table 6. Size of SE in Portugal (in % of GDP) - Average between ECM and MIMIC Model Years 1970- 73 1974- 77 1978- 81 1982- 85 1986- 89 1990- 93 1994- 97 1998- 01 2002- 05 2006- 09 2010- 13 MIMIC 8.79 10.91 9.72 12.18 15.21 18.56 19.09 21.01 22.16 23.06 23.60 ECM 9.23 11.24 13.01 14.61 15.64 15.90 16.35 17.50 19.68 20.89 20.70 Average 9.01 11.08 11.37 13.39 15.42 17.23 17.72 19.25 20.92 21.97 22.15 Source: Own calculations 0 5 10 15 20 25 30 MIMIC Model ECM Model 42 In that period of time, the SE in percentage of GDP has always increased, starting in the period 1970 to 1973 with 9.01% and ending in 2010 to 2013 with 22.15%. For that period of time, the average annual growth rate of SE in GDP is 2.26%. Hence, Portugal displays for the MIMIC model, ECM and their average, a positive growth trend for the period under study. Figure 18. Size of SE in Portugal (in % of GDP) by several authors Source: Own calculations, Schneider (2005, 2013a), Afonso e Gonçalves (2009, 2012) As Figure 18 presents, SE in Portugal displays a growing tendency, which is in accordance to the estimated outcomes of Afonso and Gonçalves (2009, 2012), and with Schneider up to 2003, afterwards Schneider’s results are decreasing until 2013 (for further enlightening see table C.2 in Appendix C). 0,00 5,00 10,00 15,00 20,00 25,00 30,00 Average (ECM + MIMIC) Schneider Afonso and Gonçalves 43 5. Conclusions This dissertation provides a detailed description about a phenomenon called Shadow Economy and an attempt to estimate its size in Portugal over the period 1970 up to 2013. The SE definition, the estimation procedures and the acceptance of its effects on the official economy are not consistent, although there are several studies on the matter. For measuring the size of SE were developed several models. Among the most commonly used are the physical input approach, with relevancy for the electricity consumption method (ECM) and MIMIC models. These two were the approaches chosen for the computation of the size of SE. Through the Kaufmann - Kaliberda model the author achieved the following results: the size of SE evolved from 9.31% of GDP in 1970 to 19.23% of GDP in 2013. The SE presented a positive growth tendency and its annual growth rate a symmetric behaviour while comparing to the annual growth rate of GDP. Through the MIMIC model the author attained the following estimations: the size of SE evolved from 8.18% of GDP in 1970 to 25.62% of GDP in 2013. The SE also showed a positive growth trend. The main causes that contribute the most for the formation and growth of SE are the direct taxes and social security contributions and the indirect taxes, according to the MIMIC model. Therefore, the weight of SE in the official GDP can be reduced if a reduction in the tax burden occurs. The unemployment rate is another cause that plays an important role in explaining the SE in Portugal. The coefficient sign associated with this variable is mainly negative, which indicates that the unemployed individuals prefer having a job in the official economy instead of shadow economy. It is important to mention that the values obtained for SE should be seen as approximations, due to the constraints imposed by the available data and the used models. Therefore, the author combined two methods to estimate the evolution of SE in the period between 1970 and 2013 in Portugal, using the ECM and MIMIC model, since there is no optimum model to compute the size of SE. 44 By combining the two used methods, its average revealed that the size of SE evolved from 8.75% of GDP in 1970 to 22.43% of GDP in 2013. For the period 1970-2013, it was estimated that the average annual growth rate of SE is 2.26% and for the GDP is on average 2.76%. 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