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In this study, we developed multivariate model for the study of the impact of treasury single account (TSA) on the performance of banks in Nigeria. From the study, we discovered that there was no significant difference between the period before and after the introduction of the TSA policy on the performance of banks in Nigeria. In Diamond Bank Nigeria Plc, we observed that there were negative relationships between liquidity ratio and capital adequacy with correlation coefficient of -0.093; liquidity ratio and credit to customers with correlation coefficient of -0.312; capital adequacy and credit to customers with correlation coefficient of -0.176. On the other hand, from the analysis on first bank, we observed that there were both positive and fairly strong relationships between the liquidity ratio and capital adequacy with correlation coefficient of 0.626; negative relationship between liquidity ratio and credit to customers with correlation coefficient of -0.880 and finally, negative relationship between capital adequacy and credit to customers with correlation coefficient of -0.165.

Treasury single account is a banking arrangement put in place to control multiple accounts created by ministries, departments and agencies, (MDAs). The primary objective of a TSA is to ensure effective aggregate control over government cash balances. The consolidation of cash resources through a TSA arrangement facilitates government cash management by minimizing borrowing costs. In the absence of a TSA, idle balances are maintained in several bank accounts. Until the introduction of TSA in Nigeria, MDAs which generate revenue, have the multiplicity of accounts in commercial banks, use part of the revenue generated to fund their operations and then remit the surplus to the federation account. As a result, agencies pay into government account what they deem fit. The result of this situation includes leakages of funds, embezzlement of public funds, and inability of a government to know the exact amount in its account [

There were speculations that the introduction of TSA will badly affect the operations of commercial banks in Nigeria. For TSA to work effectively there must be daily clearing of and consolidation of cash balances into the central account. TSA can cover all funds earmarked and budgetary accounts or even funds held in trust by government. All Ministries, Departments and Agencies are expected to remit their revenue collections to this account through the individual commercial banks who act as collection agents. But all monies collected by these banks will have to be remitted to the Consolidated Revenue Accounts with the CBN at the end of each banking day. Remita is the Central payment platform supporting the payments of Federal Government and MDAs under the TSA, as it is widely accepted and connected online to all the DMBs and sizeable number of Micro Finance Banks (MFBs) and Primary Mortgage Institutions (PMIs). TSA allows complete and timely information on government cash resources; improves appropriation control; improves operational control during budget execution; enables efficient cash management; reduces bank fees and transaction costs; facilitates efficient payment mechanisms; improves bank reconciliation and quality of fiscal data; lowers liquidity reserve needs. The custody of the TSA in Nigeria is with the central bank. However, the balances in commercial banks should be cleared every day and all government cash balances should be consolidated in one central account of the treasury at the central bank [

TSA issue did not start with president Buhari administration in Nigeria. Actually, the former President Goodluck Jonathan initiated the policy but could not implement it before he left office on 29 May 2015 [

Treasury single account is a pool in which all government revenue is collected and controlled by the Central Bank of Nigeria, with the view to boost the economy and reduce corruption [

Treasury Single Account was introduced in Nigeria as a result of numerous corrupt practices that exist in the Country’s public accounting system, lack of transparency and accountability [

[

Multivariate data are data collected on several dimensions or characteristics of the same individual or item or experimental trial. To test for difference between mean vectors of two populations, Hotelling’s T^{2} statistic and F statistic were used [

We shall develop multivariate analysis model for the research since we are considering many dependent variables from each bank at the same time and their effects compared simultaneously, multivariate analysis provide the best model for such a problem. Multivariate statistics has the ability to use the few data from 2015 to 2017 from the banks when the TSA was introduced in combination with the large data from the banks on the same subject when TSA was not introduced. We shall determine the Hotelling’s T^{2} statistic; Mahalanobi’s D^{2} statistic and F distribution for the problem. We shall also determine the multivariate distribution for the data and test the hypothesis that there was no significant difference on these parameters before and after the introduction of TSA against the alternative hypothesis which state the contrary. The test statistics are stated as follows:

T 2 = n 1 n 2 n 1 + n 2 D 2 (1)

where T^{2} is as explained above; n_{1} is the sample data from the respective banks before the introduction of TSA in Nigeria; n_{2} is the sample data from the respective banks after the introduction of TSA in Nigeria and D^{2} is the Mahalanobi’s D^{2} statistic.

D 2 = ( X ¯ 1 − X ¯ 2 ) T S − 1 ( X ¯ 1 − X ¯ 2 ) (2)

where ( X ¯ 1 − X ¯ 2 ) T is the difference in the sample mean vector of the first and the second sample data; the superscript T denote the transpose of T; and S − 1 denote the inverse of dispersion matrix or the inverse of the variance covariance matrix.

F c a l = ( n 1 + n 2 − p − 1 ) p ( n 1 + n 2 − 2 ) ⋅ T 2 (3)

where F_{cal} denote the value of F distribution statistic calculated; p denote the parameters being estimated and other notations retain their usual meanings as defined earlier.

F t a b = F ( α ) ; p , ( n 1 + n 2 − p − 1 ) (4)

where F_{tab} denote F tabulated, this is the value of F as it is stated in the standard F tables and (α) denote the level of significance under which we make our inference about the impact of TSA on banks’ performance in Nigeria.

We shall determine the covariance and the correlation on the performance of banks in Nigeria before and after the introduction of TSA in Nigeria.

In trying to achieve the above, we shall state some hypothesis that should be tested as follows:

1) Ho: X ¯ 1 = X ¯ 2 vs H_{1}: X ¯ 1 ≠ X ¯ 2

Ho: denote the null hypothesis which says that there is no significant difference between the performance of banks in Nigeria before and after the introduction of TSA. Vs stand for versus; and H_{1}: stand for the alternative hypothesis which says that there is significant difference between the performance of banks in Nigeria before and after the introduction of TSA. Hypothesis is an assumption to be tested; it could be true or false. If it is true, we accept the null hypothesis and reject the alternative but if it is the contrary, we accept otherwise. We stated the hypothesis because there is a need for us to test whether there is a significant difference in the performance of banks before and after the introduction of TSA in Nigeria using the three indicators we referred to as parameters in this study or not. Null hypothesis (Ho) supports the assumption that there was no significant difference in the performance of banks before and after the introduction of TSA in Nigeria, while the alternative hypothesis (H_{1}) states the contrary.

2) We shall state the decision rule as follows:

Accept Ho: if F_{cal} < F_{tab} and reject if otherwise. F_{cal} denotes the value of F distribution calculated while F_{tab} denotes the tabulated value of F-distribution as it is stated in any standard F statistical tables. The two values are used to make inference about the stated hypothesis.

We shall make conclusion as follows:

Since F_{cal} > F_{tab} (F_{cal} < F_{tab}), we reject Ho (accept Ho) and conclude that there is significant (no significant) difference between the performance of banks in Nigeria before and after the introduction of TSA.

Where X_{1} = Liquidity Ratio; X_{2} = Capital Adequacy Ratio; X_{3} = Credit.

Diamond Bank Nigeria Plc | |||
---|---|---|---|

Year | L.R. (%) | C.A.R. (%) | Credit (M) |

2008 | 111.11 | 109.27 | 41.8 |

2009 | 122.02 | 82.25 | 92.2 |

2010 | 132.68 | 110.41 | 76 |

2011 | 114.15 | 175.35 | 61.9 |

2012 | 124.79 | 141 | 78.1 |

2013 | 110.16 | 149.21 | 77.1 |

2014 | 111.09 | 151.69 | 96.5 |

2015 | 119.2 | 178.91 | 111.8 |

2016 | 97.33 | 124.45 | 162.4 |

2017 | 115.84 | 135.84 | 88.7 |

Source: Diamond Bank Nigeria Plc.

First Bank Nigeria Limited | |||
---|---|---|---|

Year | L.R. (%) | C.A.R. (%) | Credit (M) |

2007 | 108.831 | 30.7 | 222.2 |

2008 | 137.63 | 69.7 | 476.4 |

2009 | 118.64 | 47.19 | 752.2 |

2010 | 121.03 | 31.8 | 1151.2 |

2011 | 114.67 | 26.74 | 1366.8 |

2012 | 110.46 | 22.45 | 1645.5 |

2013 | 107.44 | 18.68 | 1841.4 |

2014 | 109.6 | 20.05 | 2036.9 |

2015 | 110.69 | 28.49 | 1594.8 |

2016 | 110.83 | 25.26 | 1897.2 |

2017 | 114.98 | 27.9 | 1298.5 |

Source: First Bank Nigeria Limited.

X ¯ D , o = [ 118.00 131.31 74.81 ] ; X ¯ D , n = [ 110.79 146.40 120.97 ]

where D = Diamond Bank Nigeria Plc; o = Financial Operation before TSA (old); n = Financial Operation after TSA (new) and B = First Bank Nigeria Limited.

X ¯ D , o − X ¯ D , n = [ 7.21 − 15.09 − 46.16 ]

The dispersion matrix is stated as follows

( n i − 1 ) S i 2 = [ ∑ x 1 2 − n x ¯ 1 2 ∑ x 1 x 2 − n x ¯ 1 x ¯ 2 ∑ x 1 x 3 − n x ¯ 1 x ¯ 3 ∑ x 1 x 2 − n x ¯ 1 x ¯ 2 ∑ x 2 2 − n x ¯ 2 2 ∑ x 2 x 3 − n x ¯ 2 x ¯ 3 ∑ x 1 x 3 − n x ¯ 1 x ¯ 3 ∑ x 2 x 3 − n x ¯ 2 x ¯ 3 ∑ x 3 2 − n x ¯ 3 2 ]

where n_{1} and n_{2} respectively stand for the first and second samples respectively.

( n 1 − 1 ) S 1 2 = [ 449.28 − 735.92 210.77 − 735.92 6101.25 − 212.57 210.77 − 212.57 2036.21 ]

( n 2 − 1 ) S 2 2 = [ 277.40 515.53 − 798.84 515.53 1650.22 − 868.20 − 798.84 − 868.20 2839.47 ]

( n 1 + n 2 − 2 ) S = [ 726.68 − 220.39 − 588.07 − 220.39 7751.47 − 1080.77 − 588.07 − 1080.77 4875.68 ]

The pooled dispersion matrix is

S = [ 90.84 − 27.55 − 73.51 − 27.55 968.93 − 135.10 − 73.51 − 135.10 609.46 ]

And the correlation coefficients between the parameters of interest are

FUTO Micro-Finance Bank | |||
---|---|---|---|

Year | L.R. (%) X_{1} | C.A.R. (%) X_{2} | Credit (M) X_{3} |

2008 | 111.11 | 109.27 | 41.8 |

2009 | 122.02 | 82.25 | 92.2 |

2010 | 132.68 | 110.41 | 76 |

2011 | 114.15 | 175.35 | 61.9 |

2012 | 124.79 | 141 | 78.1 |

2013 | 110.16 | 149.21 | 77.1 |

2014 | 111.09 | 151.69 | 96.5 |

Diamond Bank Nigeria Plc | |||
---|---|---|---|

Year | L.R. (%) X_{1} | C.A.R. (%) X_{2} | Credit (M) X_{3} |

2015 | 119.2 | 178.91 | 111.8 |

2016 | 97.33 | 124.45 | 162.4 |

2017 | 115.84 | 135.84 | 88.7 |

ρ 1.2 = − 27.55 90.84 × 968.93 = − 0.093

ρ 1.3 = − 73.51 90.84 × 609.46 = − 0.312

ρ 2.3 = − 135.10 968.93 × 609.46 = − 0.176

S − 1 = [ 0.0125 0.0006 0.0016 0.0006 0.0011 0.0003 0.0016 0.0003 0.0019 ]

T 2 = n 1 n 2 n 1 + n 2 ( x ¯ ( 1 ) − x ¯ ( 2 ) ) 1 S − 1 ( x ¯ ( 1 ) − x ¯ (2) )

T 2 = 7 × 3 7 + 3 ( 4.1821 ) = 8.7824

F c a l = n 1 + n 2 − p − 1 p ( n 1 + n 2 − 2 ) ⋅ T 2

F c a l = 10 − 3 − 1 3 ( 10 − 2 ) × 8.7824 = 2.1956

F t a b = F 3 , 6 ( 0.05 ) = 4.76

1) Hypothesis

Ho : X ¯ D , o = X ¯ D , n vs X ¯ D , o ≠ X ¯ D , n

Since F_{cal} < F_{tab}, we accept Ho: and reject H_{1}: and conclude that there is no significant difference between the two means (the period before the introduction of TSA and the period after the introduction of TSA) on Liquidity Ration (L.R.), Capital Adequacy Ratio (C.A.R.) and Credit to customers in the Diamond Bank Nigeria Plc (

Also

X ¯ B , o = [ 116.04 39.66 1186.58 ] ; X ¯ B , n = [ 112.17 27.22 1596.83 ]

X ¯ B , o − X ¯ B , n = [ 3.87 12.44 − 410.25 ]

First Bank Nigeria Limited | |||
---|---|---|---|

Year | L.R. (%) X_{1} | C.A.R. (%) X_{2} | Credit (M) X_{3} |

2007 | 108.831 | 30.7 | 222.2 |

2008 | 137.63 | 69.7 | 476.4 |

2009 | 118.64 | 47.19 | 752.2 |

2010 | 121.03 | 31.8 | 1151.2 |

2011 | 114.67 | 26.74 | 1366.8 |

2012 | 110.46 | 22.45 | 1645.5 |

2013 | 107.44 | 18.68 | 1841.4 |

2014 | 109.6 | 20.05 | 2036.9 |

First Bank Nigeria Limited | |||
---|---|---|---|

Year | L.R. (%) X_{1} | C.A.R. (%) X_{2} | Credit (M) X_{3} |

2015 | 110.69 | 28.49 | 1594.8 |

2016 | 110.83 | 25.26 | 1897.2 |

2017 | 114.98 | 27.9 | 1298.5 |

( n 1 − 1 ) S 1 2 = [ 693.58 1246.66 − 23629.10 1246.66 5644.37 104.73 − 23629.10 104.73 3019.84 ]

( n 2 − 1 ) S 2 2 = [ 9.64 1.26 − 1252.65 1.26 5.37 − 809.86 − 1252.65 − 809.86 179.26 ]

( n 1 + n 2 − 2 ) S = [ 703.22 1247.92 − 24881.75 1247.92 5649.74 − 705.13 − 24881.75 − 705.13 3199.10 ]

S = [ 78.14 138.66 2764.64 138.66 627.75 − 78.35 2764.64 − 78.35 355.46 ]

ρ 1.2 = 138.66 78.14 × 627.75 = 0.626

ρ 1.3 = − 2764.64 78.14 × 355.46 = − 0.880

ρ 2.3 = − 78 627.75 × 355.46 = − 0.165

S − 1 = [ 0.0000 0.0000 − 0.0004 0.0000 0.00016 0.0001 0.0004 0.00001 0.0000 ]

T 2 = n 1 n 2 n 1 + n 2 ( x ¯ ( 1 ) − x ¯ ( 2 ) ) 1 S − 1 ( x ¯ ( 1 ) − x ¯ (2) )

T 2 = 8 × 3 8 + 3 ( 0.4727 ) = 1.0313

F c a l = n 1 + n 2 − p − 1 p ( n 1 + n 2 − 2 ) ⋅ T 2

F c a l = 11 − 3 − 1 3 ( 11 − 2 ) × 1.0313 = 0.2674

F t a b = F 3 , 7 ( 0.05 ) = 4.35

2) Hypothesis

Ho : X ¯ u , o = X ¯ u , n vs X ¯ u , o ≠ X ¯ u , n

Since F_{cal} < F_{tab}, we accept Ho: and reject H_{1}: and conclude that there is no significant difference between the two means (the period before the introduction of TSA and the period after the introduction of TSA) on Liquidity Ration (L.R.), Capital Adequacy Ratio (C.A.R.) and Credit to customers of First Bank Nigeria Ltd.

The multivariate normal distribution for this problem is given bellow as;

f ( x ) = ( 2 π ) p / 2 | S | − 1 / 2 exp { − 1 / 2 ( X ¯ 1 − X ¯ 2 ) T S − 1 ( X ¯ 1 − X ¯ 2 ) } ; − ∞ < x < ∞

where p = 3; | S | is the determinant of the respective pooled dispersion matrices from the respective banks; X ¯ 1 = ( X ¯ D , o ; X ¯ B , o ) and X ¯ 2 = ( X ¯ D , n ; X ¯ B , n ) and other symbols in the distribution retains their usual meaning as explained earlier. Hence, our model is a trivariate normal distribution.

In the analysis carrying out Diamond Bank Nigeria Plc and First Bank Nigeria Limited on the impact of TSA on the Banks’ liquidity ration, capital adequacy and credit (availability) to customers, it was discovered that there were no significant differences between the period before and after the introduction of the TSA policy. In both cases, we accept the null hypothesis (Ho). These showed that there were no significant differences in liquidity ration; capital adequacy; and credit to the customers between the two periods on banks’ performance.

Contrary to the speculations that TSA will affect banks’ liquidity, capital adequacy and credit to customers, it was observed that the reverse was the case. Though TSA removes excess money banks collect from the floating government money which may affect other aspect of the banks’ operation, there was no indication from our research that the introduction of TSA affects liquidity ratio, capital adequacy and credit. Irrespective of the perceived difficulties created by the introduction of TSA to banks in Nigeria, banks still put up their houses together and maintain a balance in these three parameters.

Finally, from the analysis on Diamond Bank Nigeria Plc, we observed that there were negative relationship between liquidity ratio and capital adequacy with correlation coefficient −0.093, liquidity ratio and credit to customers with correlation coefficient −0.312 and between capital adequacy and credit to customers with correlation coefficient of −0.176. On the other hand, from the analysis on first bank, we observed that there were both positive and strong relationships between the liquidity ratio and capital adequacy with correlation coefficient of 0.626; there was negative relationship between liquidity ratio and credit to customers with correlation coefficient of −0.880 and negative relationship between capital adequacy and credit to customers with correlation coefficient of −0.165. The results from both banks were consistent. Finally, we established the distribution of the developed multivariate model for the problem under study.

Ogbonna, C.J. and Amuji, H.O. (2018) Analysis of the Impact of Treasury Single Account on the Performance of Banks in Nigeria. Open Journal of Statistics, 8, 457-467. https://doi.org/10.4236/ojs.2018.83029