The Correlation and Linear Regression Analysis between Annual GDP Growth Rate and Money Laundering in Albania during the Period 2007-2011 *

This study is the first attempt to investigate the relationship between the annual GDP growth rate and money laundering in the Republic of Albania during the period 2007-2011. The main result of the study: there is a negative correlation between money laundering process and economic growth rate in Albania during the specified period; there is a negative correlation between money laundering and import, but there is a positive correlation between money laundering and the government expenditure, as well a positive correlation between money laundering and export. More concretely: 1) The coefficient of correlation between cases referred in the prosecutor’s office for money laundering (X) and the annual GDP growth rate (Y) is . The equation of the linear regression is 0.74 r   7.2827 0.0585 y x   9 . 2) The coefficient of correlation between cases reported in the police for money laundering (X) and the annual GDP growth rate (Y) is , while the equation of the linear regression is 0.81 r   7.3223 0.024 y x   7.1411 0.01 . 3) The coefficient of correlation between reported CAA (Cases for Alleged Activity) for money laundering (X) and the annual GDP growth rate (Y) is , while the equation of the linear regression is 0.49 r   07 y x   . 4) The coefficient of correlation between government expenditures and the cases referred in the prosecutor’s office for money laundering is 0.72 r  . 5) The coefficient of correlation between government expenditures and the cases reported in the police for money laundering is . 6) The coefficient of correlation between net export and the cases referred in the prosecutor’s office for money laundering is . 7) The coefficient of correlation between the cases referred in the prosecutor’s office for money laundering and unemployment rate is 0.79  r 0.89 r  0.64 r  . 8) The coefficient of correlation between the cases reported in the police for money laundering and unemployment rate is 0.60 r  . 9) The coefficient of correlation between the cases referred in the prosecutor’s office for money laundering and inflation rate is 0.22 r  . 10) The coefficient of correlation between the cases reported in the police for money laundering and inflation rate is . 11) The coefficient of correlation between the cases referred in the prosecutor’s office for money laundering and the investments in Albania is . 12) The coefficient of correlation between the cases reported in the police for money laundering and inflation rate is . 13) The coefficient of correlation between the cases referred in the prosecutor’s office for money laundering and the foreign direct investments in Albania is 0.13 r 

2) The coefficient of correlation between cases reported in the police for money laundering (X) and the annual GDP growth rate (Y) is , while the equation of the linear regression is 0.81 r   7.3223 0.024 y x   7.1411 0.01 .
3) The coefficient of correlation between reported CAA (Cases for Alleged Activity) for money laundering (X) and the annual GDP growth rate (Y) is , while the equation of the linear regression is 0.49 r   07 y x   .4) The coefficient of correlation between government expenditures and the cases referred in the prosecutor's office for money laundering is 0.72 r  . 5) The coefficient of correlation between government expenditures and the cases reported in the police for money laundering is .6) The coefficient of correlation between net export and the cases referred in the prosecutor's office for money laundering is .7) The coefficient of correlation between the cases referred in the prosecutor's office for money laundering and unemployment rate is 0.79  r 0.89 r  0.64 r  . 8) The coefficient of correlation between the cases reported in the police for money laundering and unemployment rate is 0.60 r  . 9) The coefficient of correlation between the cases referred in the prosecutor's office for money laundering and inflation rate is 0.22 r  . 10) The coefficient of correlation between the cases reported in the police for money laundering and inflation rate is .11) The coefficient of correlation between the cases referred in the prosecutor's office for money laundering and the investments in Albania is . 12) The coefficient of correlation between the cases reported in the police for money laundering and inflation rate is .13) The coefficient of correlation between the cases referred in the prosecutor's office for money laundering and the foreign direct investments in Albania is 0.13 r  0.95 r 6 0.979 r   0.973 r   6  .14) The coefficient of correlation between the cases reported in the police for money laundering and the foreign direct investments in Albania is .0.8941 r 

Introduction
Nowadays one of the major issues in the world is anti-money laundering.According to the IMF (International Monetary Funds), money laundering has become one of the most serious activities faced by the international financial community [1].It became harmful because of its necessary coexistence with crime.The value of global money laundering amounted to 2.5 trillion USD (see [2]).However, in 2011, it is estimated to be over 3.0 trillion USD.But before going further, it is necessary to clarify some of the concepts that will be used in this paper.
Definition 1. Illicit money refers to the money that is originated from illicit activities, especially from the criminal ones [2].Definition 2. Money laundering is the process of obscuring the source, ownership or use of funds, usually cash, that are profits of illicit activity [3].
In other words, money laundering is the process of creating the appearance that large amounts of money obtained from serious crimes, such as drug trafficking, human trafficking, weapons trafficking, corruption, counterfeiting of currency, or terrorist activity, originated from legitimate source (see [1,2]).
Definition 3. Guilty of money laundering is that a person hides or disguises the true origin, the source, movement or alienation of money, for which he (she) has knowledge that directly or indirectly derives from illegal activities, especially criminal (see [2,3]).
Remark.This definition is according to the EU's legislation, as well as UN's legislation.Furthermore, it is also used by the World Bank and Interpol.Definition 4. GDP (Gross Domestic Product) is the market value of all finished goods and services within a country during a given period of time.The GDP is given by the formula: Y = C + I + G + NX, where C denotes private consumption, I denotes gross investments, G denotes government spending and NX denotes Net Exports = Exports − Imports (see [1,4]).
According to some recent estimation, money laundering constitutes about 6% -8% of GDP in USA, 7% -9% of GDP in UK, Germany, France, Italy, etc.However, some scientists claim that the amount of official data is underestimated compared to the reality of money laundering process (see [2,3]).Actually, to fight money laundering in nations like America, where the relationship between the amount of money laundering and the annual GDP growth rate is positive, can be a double-edged sword.This happens because if illicit money is not turned into legal capital, they cannot be used into the economy, but only as a capital for illegal activities.While, in other countries of Europe such as France and Germany, the relationship between money laundering and GDP is negative (see [1,2,5]).Regarding the Republic of Albania there is not, yet, any study which analyses with a mathematical statistic method the relationship between money laundering and the annual GDP growth.Hence, our study is a first oriented toward this topic.

Mathematical Model
The linear regression analysis is used to estimate the impact that the process of money laundering has on the economic growth, in the case of Albania over the period January 2007-December 2011.The random variable X denotes the annual number of cases of money laundering, while the random variable Y denotes the corresponding rate of annual real GDP growth.X represents the explanatory variable (input).Y represents the dependent variable (output).The sources of the data are INSTAT (Albanian Institute of Statistics), Bank of Albania (BoA), see [6][7][8] and General Directory for the Prevention of Money Laundering, Albanian Financial Intelligence Unit, AFIU 2011, see [9].The Table 1 contains the data sets for the random variables X and Y.

Main Results
Coefficient of correlation r = −0.74 Coefficient of determination d = 0.55 Linear regression equation y = 7.2827 -0.0585x In Figure 1 using the linear correlation and regression analysis, as well as the given data set, we obtain the following results: The coefficient of correlation between cases referred in the prosecutor's office for money laundering and the annual GDP growth rate is r = −0.74,which (according to Gelfand's classification) indicates a moderate negative correlation between the two random variables.The coefficient of determination is d = r 2 = 55%, which implies that 55% of the total variation in annual GDP growth rate can be explained by the variation in the number of cases of money laundering, while 45% of the total variation in GDP growth rate must be explained by the impact of other factors.The linear regression equation is y = 7.2827 − 0.0585x, where x denotes the number of cases referred in prosecutor's office for money laundering and y denotes the annual GDP growth rate for Albania during the period of January 2007-December 2011.
Coefficient of correlation r = −0.81Coefficient of determination d = 0.66 Linear regression equation y = 7.3223 − 0.0249x In Figure 2 we have used the correlation analysis to measure the strength of the relationship between the cases referred in police for money laundry and annual GDP     Using the regression and correlation analysis we ha ncluded that there is a relationship ent spending and cases referred prosecu ported in the police for money laundering.
In Figure 5 the coefficient of correlation is correspondingly r = 0.72, which indicate a strong positive correlation between the variables.While, the coefficient of determination is respectively d = r 2 = 52% (or is result is interpreted in this way: 52% (or 62%) of the total government spending can be explain by the cases referred in the prosecutor's office (or the ones reported in the police) for money laundering.But, 48% (or 38%) of the total government spending is explain by other factors.
The equation of the linear regression for the cases referred in the prosecutor`s office is y = 339877 + 499.83x,where x denotes the cases referred in prosecutor's office, and y denotes the government spending in the Republic of Albania during the period of time January 2008-December 2010. In

8491x
Using the linear regression and correlation analysis we have concluded that there is a relationship between export and cases referred in the prosecutor's office and the ones reported in the police for money laundering.
The coefficient of correlation between cases referred in the prosecutor's office and the export is r = 0.17, while between cases reported in the police and export is r = 0.50, which indicates, respectively, a weak and a moderate positive correlation between th   prosecutor's office for money laundering, and y denotes the import in the Republic of Albania during the period of January 2008-December 2011.In Figure 10, the equation of the linear regression for the cases reported in the police for money laundering is y = 3440.8+ 0.9103x, where x indicates the cases reported in the police, and y indicates the import during the period of January 2008-December 2011.
Coefficient of correlation r = 0.89 Coefficient of determination d = 0.79 quation of linear regression Using the regression and cor have concluded that there is a relationship between net export and cases referred in the prosecutor's office and reported in the police for money laundering.
In        Using the regression and correlation analysis we have concluded that there is a relationship between investments and cases referred in the prosecutor's office and reported in the police for money laundering.The coefficient of correlation between the cases reported in the prosecutor's office and investments is r = −0.979,while the relationship between the cases reported in the police and the investments is r = −0.9736,which indicate a strong negative e correlation between the va ables.Let us reconsider the relationship between the annual number of cases referred in prosecutor's office for money laundering (denoted by x) and the rate of annual real GDP growth (denoted by y) during the period 1 January 2007-31 December 2011 in Albania.
Given the data set containing n = 5 observations: here x denotes the cases reported in the police, and y denotes the unemployment in the Republic of Albania d  The simple linear regression equation is here ε denotes the random error term, see Bolton and David (2002).
Assume that the mean w   0 E   and the variance A 95% prediction interval for y when x = x * is given by the formula: see [5].
We obtain the following results:  

Th
efficient of correlation r is difficult to obtain in the small sample case.For large random samples this di lty could be overco sher z -transformation, see [5].

Conclusions
it is po egatively correlated with the number of cases of money la ases above m a negative number.However, further researches may be necessary to draw light on this topic, as we had no access to data regarding the exact amount of money laundering he on s the number of cases rmation at our disthe percentage that illicit money occupies on the annual GDP growth rate over January 2007-December 2011.Actually, in other countries, these data are published and availabl or .T ly information available to us wa of money laundering.With this info posal, it is not possible to clearly state e f ientific studies, for instance, in America, Germany, and other 11 countries that have done similar researches.But, in Albania the amount of money laundering is not of public domain anti-money lau tivities.
Some surprising results of this study are: 1) The positive correlation between government expenditure and the number of cases referred in the prose- 2) The positive co penditure and the number of cases reported in police for money laundering (r = 0.79); 3) The positive correlation between export and the number of cases referred in the prosecutor's office for money laundering (r = 0.17); 4) The positive correlation between export and the number of cases reported in police for money laundering (r = 0.50); 5) The positive correlation between the number of cases referred in the prosecutor's office for money laundering and net export (r = 0.89); 6) The positive correlation between the number of cases reported in police for money laundering and net export (r = 0.68); 7) The positive correlation between the number of cases referred in the prosecutor's office for money laundering and annual unemployment rate (r = 0.64); 8) The positive correlation between the number of cases reported in the police and the annual unemployment rate (r = 0.60); 9) The positive correlation between the number of cases referred in the prosecutor's office for money laundering and the inflation rate (r = 0.22); 10) The positive correlation between the number of cases reported in the police and the inflation rate (r = 0.136); 11) The positive correlation between the number of cases referred in the prosecutor's office for money laundering and the foreign direct investments in Albania (r = 0.95); 12) The positive correlation between the number of cases reported in the police and the foreign direct instments in Albania (r = 0.8941).Actually, it is not possible to give a scientific argument for the for the exact amount of money laundering during the years 2007, 2008, 2009, 2010, and 2011 are not published in the Republic of Albania.

Figure 1 .
Figure 1.Relationship between the cases referred in the prosecutor's office for money laundering and the annual GDP growth rate during 2007-2011.
The pearson's coefficient of correlation is r = −0.81,which (according to Gelfand's classification) indicates a st s the number of cases referred in police fo termination d = 0.24 − 0.0107x n r = −0.49indi two ra orted CAA an rong negative correlation between the two random variables.The coefficient of determination is d = r 2 = 66%.This result can be interpreted in this way: 66% of the total variation in GDP growth rate can be explained by the variation in the number of cases referred in police for money laundering.But, 34% of the total variation in GDP growth rate must be explained by the impact of other factors.The linear regression equation is y = 7.27 − 0.024x, where x denote r money laundry, and y denotes the annual GDP growth rate for Albania during the period January 2007-December 2011.Coefficient of correlation r = −0.49Coefficient of de Linear regression equation y = 7.1411In Figure3the coefficient of correlatio cates a moderate negative correlation between the ndom variables.While, the coefficient of determination d = r 2 = 24%.This means that 24% of the total variation in GDP growth rate is explained by the variation of reported CAA (Cases for Alleged Activity), whereas the other 66% is explained by the other factors.The equation for the linear regression analysis is y = 7.1411 − 0.0107x, where x denotes the rep d y denotes the annual GDP growth rate for Albania

Figure 2 .
Figure 2. Relationship between the cases reported in the police for money laundering and the annual GDP growth rate during 2007-2011.

Figure 3 .
Figure 3. Relationship between reported CAA and the annual GDP growth during 2008-2011.

Figure 4 .
Figure 4. Relation between referred CAA and the annual GDP growth rate during 2008-2011.

Figure 6
the equation of the linear regression for the cases reported in the police is y = 341708 + 216.92x,where x denotes the cases reported in the police, and y e variables.The denotes the government spending in the Republi of Albania during the period of time January 2008-December c 2010.Coefficient of correlation r = 0.17 Coefficient of determination d = 0.03 Equation of linear regression y = 912.45+ 2.9765x Coefficient of correlation r = 0.50 Coefficient of determination d = 0.25 Equation of linear regression y = 720.8+ 2.

Figure 5 .
Figure 5. Relation between government spending and cases referred in prosecutor's office during 2008-2010.

Figure 6 .Fi n pr gure 7 .
Figure 6.Relationship between government spending and cases referred in the police during 2008-2010.

Figure 8 .
Figure 8. Relationship between export and cases reported in the police for money laundering during 2008-2011.

Figure 11 ,
the coefficient of correlation is correspondingly r = 0.89, which indicate a strong and moderate positive correlation between the variables.While, the coefficient of determination is respectively % Equation of linear regression y = −2865.7 + 7.5 66x Coefficient of correlation r = 0.68 oefficient of determination d = 0d = 46%).This result is interpreted in this way: 79% (or 46%) of the total net export can be explained by the cases referred in prosecutor's office (or the ones reported in the police) for money laundering.But, 21% (or 54%) of the total net export is explain by other factors.The equation of the linear regression for the cases referred in the prosecutor's office is y = −2865.7 + 7.5446x, where x denotes the cases referred in prosecutor's office, and y denotes the net export in the Republic of Albania

Figure 9 .
Figure 9. Relationship between import and cases referred in prosecutor's office for money laundering.

Figure 10 .
Figure 10.Relationship between import and cases reported

Figure 11 .
Figure 11.Relationship between net export and cases referred in prosecutor's office for money laundering.

Figure 12 .
Figure 12.Relationship between net export and cases reported in the police for money laundering during 2008-2011.

Figure 13 .
Figure 13.The relationship between the cases referred in the prosecutor's office and the annual inflation rate ba in Alnia.

Figure 14 .
Figure 14.Relation between cases reported in the police for money laundering and the annual inflation rate in Albania.
prosecutor's office, and y denotes the unemployment in the Republic of Albania during the period of time January 2008-December 2011.In Figure16the equation of the linear regression for the cases reported in the police is y = 13.086+ 0.0026x, where x denotes the cases reported in the police, and y denotes the unemployment in the Republic of Albania during the period of time January 2008-December 2011.Coefficient of correlation r = −0.979Coefficient of determination d = 0.9584 ficient of determination d = 0.9479 Equation of linear regression y = 4651.4− 30.281x the cases referred in prosecu Equation of linear regression y = 4909.2− 78.788x Coefficient of correlation r = −0.9736Coef ri While, the coefficient of determination is respectively d = r 2 = 0.9584 or d = 0.9479.In Figure 17 the equation of the linear regression for the cases referred in the prosecutor's office is y = 4909.2− 78.788x,where x denotes tor's office, and y denotes the unemployment in the Republic of Albania during the period of time January 2008-December 2011.

Figure 15 .
Figure 15.Relationship between cases referred in prosecutor's office and the annual unemployment rate in Albania.

Figure 16 .Figure 17 .
Figure 16.Relationship between cases reported in the police and the annual unemployment rate in Albania.

Figure 18 .
Figure 18.Relationship between the cases reported in the police and the investments in Albania.

Figure 20 .
Figure 20.The relationship between cases reported in the police and the foreign direct investments in Albania.

sc.
Nevertheless, in our case, where the correlation between the two variables X and Y is negative, ndering policies discourage criminal accutor's office for money laundering (r = 0.72); rrelation between government exve se surprising results, because officially data e Economics of Crime and Money Laun-Similarly, w thesis testing for the param ear regression equation in all relationships e probability distribution for Pearson co fficu me by using the Fi By analyzing the official data available to us during the period of 2007-2011 for the Republic of Albania, ssible to conclude that the economic growth is n undering, because as we have seen in the c entioned the coefficient of correlation "r" is