ECONOMIC FLUCTUATIONS AND THE SHADOW ECONOMY: A GLOBAL STUDY

The recent economic crisis re-emphasizes the importance of the economic fluctuations. This study investigates the role of shadow economy in combination with economic factors on the economic instability for 133 economies between 1991 and 2015. Using the system-GMM estimations, this paper shows that a larger shadow economy increases the fluctuations of GDP growth rate in relation to the size and the volatility of shadow economy. Notably, the shadow economy presents an inverted-U relationship with economic instability and this relationship is strongest for low- and lower-middle income economies. Our results identify two categories of drivers for economic fluctuations: the stabilizing factors (the labor force and the TFP) and the enhancing factors (capital investment, consumption, government spending, trade, and FDI inflows). Interestingly, exports increase economic fluctuations while imports decrease them. Finally, we discuss the differences in the determinants of economic instability across low, middle and high incomes countries. This study documented that shadow economy influences the economic fluctuations — our results actually confirm our hypothesis and the impact of shadow economy on the effectiveness of macroeconomic policies. The contribution of this paper is to show the extent to which the impact can affect the economic activities and how institutions can smooth this effect.


Introduction
What generates economic fluctuations is an important issue in macroeconomics. A huge literature deals with the determinants of economic fluctuations from both demand and supply sides; in the short-and the long-run (Kose andRiezman 2001, Wen 2006). The 2008 global financial crisis reemphasized this issue by generating a lot of debates (Christiano, Motto, and Rostagno 2010). This article contributes to these debates by investigating the role of shadow economy in the economic instability. According to Blackburn, Bose, and Capasso (2012), the shadow economy refers to a pervasive feature of the economies throughout the world, which includes all unregistered economic activities that would contribute to the official output if counted (Schneider and Williams 2013). Medina and Schneider (2018) documented that the average size of shadow economy in 158 countries is 31.9 percent over 1991 to 2015, the largest ones (in 2015) are Zimbabwe and Bolivia with respectively 60.6 percent and 62.3 percent of GDP, while the lowest ones are Austria and Switzerland with 8.9 percent and 7.2 percent, respectively. In this context, a key question is: does shadow economy influence economic fluctuations? If yes, to what extent? Does shadow economy enhance economic fluctuations or does it act as a "buffering activity" stabilizing the economies facing with economic the 133 economies have been divided into 3 categories: 62 low-and lower-middle income economies (LMEs), 31 upper-middle income economies (UMEs), and 40 high-income economies (HIEs) in line with the World Bank classification. Using the system-GMM estimations, this article shows that a larger shadow economy increases the fluctuations of GDP growth rate in relation to the size and the volatility of shadow economy. Interestingly, the shadow economy presents an inverted-U relationship with economic instability and this relationship is strongest for LMEs.
The study is structured as follows: the Sect. 2 reviews the literature; the Sect. 3 presents our methodology and data while our results are discussed in Sect. 4. The final section ends this study with conclusions and recommendations.

Literature Review
Economic fluctuations have always been a key issue in macroeconomics (Gambacorta and Marques-Ibanez 2011). The empirical literature identified several drivers of economic instability from both side: demand shocks (Hall 1986) and supply shocks (Gali 1999) but also shocks from economic integration as trade activities and capital flows (Kose and Riezman 2001), shocks from fiscal policy and monetary policy (Creal and Wu 2017) and shocks from the financial sphere (credit supply or stock prices) (Chauvet andGuo 2003, Christiano, Motto, andRostagno 2010). More recently, Furlanetto, Ravazzolo, and Sarferaz (2014) found that financial shocks are actually the major driver of fluctuations while Gilchrist, Yankov, and Zakrajšek (2009) showed that credit market shocks contributed significantly to the US economic fluctuations for the period of 1990-2008. On another point, Konstantakis, Michaelides, and Tsionas (2016) documented that the ten-year bond yields and the elections can play a pro-cyclical role on the Greek business cycle in the period of 1995-2004. Economic fluctuations are also related to human expectations and how the market perceives the level of uncertainty associated with the economic context under consideration. Using survey data in US, Leduc and Sill (2013) found that changes in expected future economic activity act as an important driver for economic fluctuations. Creal and Wu (2017) documented that uncertainty contributes negatively to economic activity when they investigated the relationship between uncertainty about monetary policy and economic fluctuations. Related to this aspect, Forni, Gambetti, and Sala (2017) explained that the Great Recession were exacerbated by the uncertain context generated by media and news.
A particular way of characterizing the uncertainty of a country is to investigate the importance of its shadow economy. Surprisingly, the influence of shadow economy on economic fluctuations is still relatively under-investigated in the literature despite the existence of some research: Mai & Friedrich, 2016;Medina & Schneider, 2018. Because agents operating in shadow economy do not wish to be identified, the estimation of such economy can be tricky. Schinckus (2009) explained that uncertainty is probably the major driver of all economic activities despite the difficulty to estimate it. Fortunately, recent databases about shadow economy (Medina and Schneider 2018) have been developed offering new opportunities for academic research.
Shadow economy refers to all currently unregistered economic activities which if counted, would contribute to the official output (Schneider and Williams 2013). Mai and Friedrich (2016) specifically defined shadow economy as the legal economic and productive activities that would contribute to national GDP if recorded, but it does not include illegal, criminal activities, do-it-yourself, charitable or household activities. In other words, shadow activities refers to all these legal economic activities actually refer to market-based production of goods and services that are deliberately concealed from public authorities to avoid payment of income, value added, other taxes or costs related to legal labour market policy (social security, minimum wages, maximum working hours, safety standards, etc.) (Schneider and Williams 2013).
Shadow economy can also be related to (i) tax evasion since economic agents are not willing to pay when taxes or social security burdens are high (see Tanzi (1999), Schneider (1994) and (ii) the quality of government in implementing and enforcing their regulations (La Porta et al. 1999). A weak institutional quality (associated with bureaucracy, regulatory discretion, rule of law, corruption, and a weak legal system) usually paved the way to a higher level of shadow activities (Friedman et al. 2000). Several studies examined the effects of shadow economy on other economic aspects. While Dreher, Kotsogiannis, and McCorriston (2009) found that corruption and shadow markets have a substitution effect in 145 countries over the period of 2000-2002Choi and Thum (2005) documented that shadow sectors can be perceived as a complementary element to the official economy. In the light of these findings one can question remains: how does shadow economy influence the economic instability?
There exist few studies detailing the link between these two aspects. (Granda-Carvajal 2010, Shapiro 2015. Broadly speaking, the literature explains that unofficial businesses are mostly small and therefore 1) they cannot benefit from economies of scale; and 2) they have a limited financial access (Ferreira-Tiryaki 2008). As a result, informal businesses are likely more exposed to economic instability, which resulting in the fail and overall higher economic fluctuations.
In this study, we use the few existing studies to investigate further these aspects by adding the economic reasoning eventual influence of the shadow economy on the economic instability. First, a higher shadow economy might reduce the government's capability to implement a fiscal policy, especially a counter-cyclical fiscal policy. In other words, an increase of shadow economy reduces government's revenue implying therefore a negative impact on the ability of government to provide public goods and services. Paradoxically, such situation might lead the government to react by increasing the tax rates (Talvi and Végh 2005). Consequently, shadow economy distorts and weakens government roles in its allocation, redistribution and stabilization function (Κάτσιος 2015).
It is also worth mentioning the possible link between shadow economy and the effectiveness of monetary policy. Both fiscal and monetary policies require a precise estimation of the key macroeconomic indicators related to output and unemployment. In this context, shadow economy and its non-declared activities become an important issue. (Fleming, Roman, and Farrell 2000). For instance, the velocity of currency in the official sector is quite difficult to value but it becomes totally impossible to estimate when the shadow economy activities are important (Schneider 2000) leading to the use of biased estimations in conducting monetary policies. Furthermore, shadow banking (Gennaioli, Shleifer, and Vishny 2013) or informal credit (Barslund and Tarp 2008) have also severely misled decision related to monetary policy. In this challenging context, a higher shadow economy implies a higher economic uncertainty complicating the role of central banks in the implementation of monetary policy (that have often been blamed for the turbulences in recent crisis, (Duncan, 2014; (Creal and Wu 2017). Related to that, economic activities taking place in the shadow economy are not protected by any legal framework but these activities are rather ruled by the informal trust between economic agents who usually focus on a short-term horizon. However, a higher shadow economy generally leads to a lower generalized trust in the overall economy (D'Hernoncourt and Méon 2012).
All these aspects influence the investors mood and it might exacerbate economic fluctuations (Forni, Gambetti, and Sala 2017).
In overall, the shadow economy may induce higher economic fluctuations through the links with the effectiveness of macroeconomic policies and the nature of informal businesses, which are far from economies of scales or optimal mix of labor/capital in production, and moreover face with financial constraints. Restrepo-Echavarria (2014)  However, the link between shadow economy and economic fluctuations must be treated in different ways. We mentioned above the potential influence of shadow economy on economic instability. There are also other reasons why shadow economy may have a positive influence in reducing the economic fluctuations. We detail hereafter the reasons for why we decided to investigate further the relationship between shadow economy and economic fluctuations.
Tax evasion, for instance, can actually bring to economic agents additional unexpected benefits offering therefore an advantage for informal sectors in case of economic fluctuations. Second, the informal businesses are small, which mean they are more flexible in changing their production or business model. Third, the cost and the spread effects to the economy of the fail in small businesses will be much more smaller than the fail of large firms so that the informal businesses under recessions may be fail but their failure would have a weaker marginal impact on the economy.
Overall, shadow economy may act as a buffer or a complement for official economic activities in case of large economic fluctuations with less cost and weaker spread impacts. As a result, there is a surprising claim according to which shadow economy in some circumstances, may be useful for the economy depending on its size and the development of the national economy. This study investigates further this surprising claim.  (Christiano, Motto, and Rostagno 2010, Konstantakis, Michaelides, and Tsionas 2016, Fosu 2001, Sordi and Vercelli 2006, Jallab, Gbakou, and Sandretto 2008. β, &detlta; are the usual coefficients and ε is the classical residual term. Details on these data are presented in the table 1. In first step, the influence of economic drivers on the economic instability is investigated. It is worth mentioning that all the lags for explanatory variables are used to avoid the endogenous problem in our dynamic panel data. Therefore, the trade openness is replaced by the 3-year mean of exports to GDP (Mexport) and imports to GDP (Mimport) to examine the channel of trade shocks to economic fluctuations. Next, the shadow economy (se) under three apsects as the 3-year mean of shadow economy to GDP (Mse), the standard deviation of shadow economy to GDP (Stdse) and the square of 3-year mean of shadow economy to GDP, are incorporated in Eq. 1 to examine the roles of the shadow economy in relation to its size, its volatility, and its non-linear relationship with economic fluctuations. The Eq. 2 hereafter details this estimation, 2

Methodology
The data concerning the shadow economy are coming from Medina and Schneider (2018), all other economic variables are extracted from World Development Indicators (World Bank). The data description, unit root test and correlation matrix are presented in table 2 and 3 hereafter,  Table 3 Correlation matrix The data show that the size of the shadow economy is average ranged from over 6% to nearly 71% of official GDP in 133 economies with the average of 31.472% for the whole period of 1991-2015. These results also indicate that there are huge differences in terms of economic integration among countries. Meanwhile, the Levin-Lin-Chu unit-root test (Levin, Lin, and Chu 2002) shows that all variables are stationary at level, which are suitbale for panel estimations.
The Fig. 2 shows that a higher economic fluctuations tends to apperar in higher income economies with high trade openness, high imports to GDP, high FDI inflows, low level of household consumption, low gross capital formation, low domestic credit level, high government expenditure, and labor forces around 50% and 65% percent of total population. To provide a more detailed analysis, we follow the classification proposed by the World Bank to decompose our sample into 62 low-and lower-middle income economies, 31 upper-middle income economies, and 40 high-income economies basing on their average GDP per capita (for the period 1991-2015). We then ran new estimation for our three sub-samples for robustness purposes.
Econometrically, the estimation of dynamic panel data is faced to the issue of endogeneity (Roodman 2006). Anderson and Hsiao (1982) propose first difference method to deal this issue in panel data by combining first differencing with instrumental variables in estimation. Arellano and Bond (1991) develop the GMM estimator and argues that it is a more efficient estimation. But the method in Arellano-Bond GMM estimator faces to the problem of asymptotically and considerable bias in unbalanced panel data (Roodman 2006). The system GMM estimator is then proposed by Arellano and Bover (1995) and extended by Blundell and Bond (1998) and Blundell and Bond (1998) to reduce the bias associated with the fixed effects in short panels as two-step system GMM (Roodman 2009). In this study, the standard two-step system GMM is applied by using one-year lags of independent variables are instrument variables.

Results And Discussion
As detailed in the previous section, we used here a GMM system for the estimations of our dynamic panel data. Related to this methodology, it is worth mentioning that the AR(2) and Hansen tests were not significant implying that our results are consistent and unbiased. The table 4 hereafter shows the determinants of economic fluctuations for the full sample of 133 economies. The positive significant effect of the lag economic volatility on the current ones implies that the economic fluctuations exhibit an exacerbated effect of volatility on the real GDP growth rate. This might lead to a difficult self-enforcing situation when the economic instability can not be stabilized. A higher volatility in a specific year t may stimulate a higher instability in the following period (t + n) if nothing is done. This observation actually supports the Keynesian perspective according governments should take actions in fighting with economic crisis (Sharma 2004). However, such interventions must be planned and balanced since our empirical evidence suggest that a too high increasing in the government expenditures also increase the economic fluctuations. This empirical result is consistent with public theories stating that a large government size with the over public spending can be a major cause for economic crisis (Feldstein 2009).
The increase in gross capital formation, household consumption, trade openness and FDI inflows also increase the volatility of real GDP growth rates. However, the economies with higher income levels, higher level of labour force and TFP present less volatility in real GDP growth rates. The significant positive impacts of gross capital formation on economic volatility refers to the facts that higher capitalized economies face with higher economic fluctuations (King et al. 1987) where shocks related to the marginal efficiency of new investment are stronger (Justiniano, Primiceri, and Tambalotti 2010).
An increasing in the household final consumption expenditures significantly increases the volatility of real GDP growth rate implying that shocks in private consumption can also contribute to overall economic fluctuations (Hall 1986).
The significant negative effect of labour forces and TFP on economic fluctuations show some interesting relationships. Concretely, these results mean that economies with higher labour forces to total population have a better configuration to temper economic turbulences. Conversely, innovations and technological progress not only boost the economic growth but they also temper instability by reducing the economic fluctuations (Bilbao-Osorio and Rodríguez-Pose 2004). These results provide some significant policy implications that we will detail later in this study.
The significant positive impacts of FDI inflows and trade openness on the volatility of the real GDP growth rates confirm the previous empirical studies on the topic. Specifically, a higher level of FDI inflow increases economic fluctuations (Furceri, Guichard, and Rusticelli 2012). Such observation reemphasizes the concerns about the "bad side" of capital flows on domestic economic activities (Furceri, Guichard, & Rusticelli, 2012). Regarding trade openness, the results indicate that international shocks may affect the domestic economic stability through the export channel which is consistent with previous documents (Schmitt-Grohé 1998). This observation is quite straightforward: higher exports to GDP indicate a higher dependence of domestic producers to international customers and therefore a higher volatility of overall economy. In contrast, a higher ratio of import to GDP decreases the volatility of real GDP growth rate. Our results are presented in the following table. The roles of shadow economy in driving economic fluctuations are investigated through three aspects: its size, its volatility and its non-linear relationships. The significant positive influence of shadow economy's size suggests that an important shadow economics may increase the instability in the official sector. This result is consistent with the idea that shadow activities increase the overall uncertainty by limiting/altering the efficiency of fiscal and monetary policies that governments may implement to fight against economic turbulences.
Notably, the square of shadow economy's size has significant negative effects on the volatility of real GDP growth rate. In other words, it appears that we have an inverted-U relationships between the shadow economy and economic fluctuations. In this context, for countries with a low level of shadow economy, an increasing of these shadow activities increases the economic fluctuations contributing therefore to a high economic instability. In contrast, for countries with a relatively high level of shadow economy, an increase in these activities acts as a complement of the official sectors to help to stabilize the official growth. Such observation suggests that policy makers should implement strategies to keep shadow economy below a level for which the whole economy stability does not become dependent of shadow activities. The significant positive impact of shadow economy's volatility on the volatility of real GDP growth rate indicates that fluctuations in shadow economy can be transmitted to the official sector. Because the shadow economy is mainly composed by unknown variables for policy makers, these results also suggest to keep the shadow economy at a low level to reduce its potential impact on national economy.
After a general analysis of our data, we decomposed all results into three sub-samples referring to low-and lower-middle income, upper-middle income, and high-income economies. The results are presented in table 6, 7, and 8.   These results show that economic fluctuations are actually directly related to countries' productive capabilities. In low-income economies where their productive power is mainly based on labour, an increase of capital accumulation can help to stabilize productions and therefore the economy. First, the shadow economy is found to have a significant positive impact on economic fluctuations.
Notably, shadow economy and economic instability have an inverted-U relationship implying that the former increases the latter in countries in which shadow activities are quite limited while shadow economy acts as a stabilizing factor for countries in which shadow activities are important. In addition, it has been shown that the volatility of shadow economy has increases the fluctuations of official economy. This relationship is stronger for the case of low-and lower-middle income economies.
Second, labour force and TFP are a stabilizing factor, while capital investment, consumption, In terms of policy making, our empirical study shows that the stability of a national (low income) economy can actually be dependent of the shadow economy. Such situation can unfortunately create a growth trap for the poorest countries in which stability would depend on shadow activities that would put the official economy and all government actions in a position in which they cannot act properly to generate an economic growth for the country. In such context, our study suggests to keep shadow economy at a low level to reduce its potential impact on national economy.

Declarations
Availability of data and materials Real GDP growth rate (%), 3-year Standard deviation of real GDP growth rate, and the size of Shadow economy to official GDP (%) Figure 1 Real GDP growth rate (%), 3-year Standard deviation of real GDP growth rate, and the size of Shadow economy to official GDP (%)