Predictive and prescriptive analytics of IMTOs using eNaira tokens to remit money to Nigeria.
Published by Dr. Peter Ojo:
In 2012 (Animation circa 2013), we predicted the incoming revolution of POS services in Nigeria and how ordinary people will interact with their bank accounts. This came to pass more than anticipated. We are going on a limb again that eNaira, in harmony with legacy channels, may galvanize how people exchange value. The catalyst will be interoperability with cross-border infrastructure. The IMTOS will pre-mine eNaira, and their agents, local and international, will find more benefits in the value chain than the traditional system because distributed ledgers present a high level of transparency, interoperability, and, most of all, complement the Inter-Bank Settlement System by reducing network congestion. eNaira is necessary not because it has an obvious advantage over the existing mobile wallet but because the timing allows for experimentation with global CBDC and digital assets.
The extract from the 2018 paper explains the inherent economic incentive for digital agents.
If we consider 100 agents/stores in a U.S. city and 100 customers that live in that city and have access to the agents to send money over the next 31 days. Let us consider four money transfer companies A, B, C, D in each of those stores, i.e., the agent/store can decide to use the system of either of the four remittance providers to send the money for the customer.
Assuming that each of the money transfer company can send money to all the destinations (that the customer needs) and that they all have the same fee ($5). We further assume that money transfer companies completion time for sending customers money varies (D=2 minutes, all others — 15 mins) and the same commission for the selling agent ($2.5), it is obvious that the agents will choose by time (not by commission):
· Simple Probability function:
P(A) = P(B) = P(C) = 0, P(D) =1
If they pick by time, the probability will be inversely proportional to time:
P(A) = P(B) = P(C) = 1/15 / (3/15+1/2) = 2/21= 0.095
Figure 1. Quantity of Tokens Sold
P(D) = 1–3*0.095 = 0.714
This means that the most recommended (and chosen) transfer company will be D, based on the transfer time (in the case where the fees and commissions are equal).
Let us consider another situation when all transfer companies (A, B, C, D) have the same fee ($5), time to process the transfer is different (A=B=C=15 mins, D=2 mins), and the commission for the agent is also different (A=B=C=$1.50, D=$3). The question is — which transfer company will be recommended by an agent and which one will be chosen by the client?
If the clients choose solely by time — the probabilities will be the same as above:
P(A) = P(B) = P(C)= 0.095, P(D)=0.714.
If the clients follow the recommendation by the agent — they will be advised to choose by commission, and since the company D is best ranked within this criterion (fee=$3) — the probabilities will remain the same: P(A) = P(B) = P(C)= 0.095, P(D)=0.714.
As a special case — if company A has a lower fee among {A, B, C} — then the probabilities:
P(B) = P(C) = 0, and P(A) =1- P(D)= 1- 0.714 = 0.286.
If they pick by time, then the probability is inversely proportional to time:
P(A) = P(B) = P(C) = 1.5*1/15 / (3*1.5* 1/15 + 3*1/2) = 1/18=0.055
P(D) = 1–3* 1/18 = 5/6 = 0.833
The problem has several layers and ways of analysis. However, we focus on time to complete a transaction and commission to agents. So the probability of picking the fastest time in Q1 and Q2 is the highest — that is agents and customers want the fastest possible time. In Q3 all commissions to agents are the same so again, time took precedence over other factors, so the agent went for option D. Q4 the agents prefer D much more strongly. Agents and Customers like D more than any other remittance provider, therefore agents are more likely to recommend D. The result merely confirms what we could have guessed, but the statistics quantify the result.
We can conclude that agents will be biased towards remittance organizations that offer this Token method. In fact, if the remittance organization that provides this Token covers comparable more corridors than others, one can argue that agents will find it a worthwhile business economic decision to discontinue the relationship with the other remittance organizations. This makes sense because the value proposition is significantly lower than the remittance organization that offers the Token as a means of sending money. Irrespective, we are confident that the reduction in time needed to service customers will drive up the demand for the product over others. Also, the higher the commission paid to agents or stores per Token, the higher the number of agents/stores that’ll be interested in carrying the Token.
Fig. 1 describes the relationship between Commission (C1…C3) and Quantity of Tokens sold.
Figure 2. Number of Tokens sold as a function of time spent with the sender
We argue that the higher the commission paid to agents/stores, the more Tokens they will sell because there is economic incentive to do so, and propensity towards offering the card compared to the other alternatives.
Figure 2. Numbers of tokens sold as a function of Time spent with senders
The chart on Fig. 2 describes Time (T1… T3) spent servicing customers vs. Quantity of cards sold or remittance volume. We argue that the fewer minutes the agents spend with customers, the higher the number of customers they can service and the larger the volume that will come from the agents. In essence, Time is inversely proportional to the number of cards sold. This is so because agents/store wants to be able to go back to servicing customers that come in to patronize their core business and not remittance service.
Linear Regression Model
We can divide the relationships between the phenomena (variables) into two groups: functional and stochastic. Functional (also called deterministic or exact) connection occurs in the case when — on each value of the independent variable X, corresponds only one value of the dependent variable Y. In the stochastic processes, one value of the independent variable corresponds to a whole set of possible values of the dependent variable. So in the stochastic model — we must involve additional component (aside from X) that will influence Y. Thus — the general form of the stochastic model will be:
Y = b1*X + b0 (1)
where b0 is the stochastic element (e.g., an error).
In our system for money remittance we will evaluate the connection between the number of sales points (Agents) as a predictor variable (X), and total revenue in a period — as variable Y. First, we can define a linear connection between these variables, since the increased number will lead to increase in total revenue. Next step is to draw the scattering diagram — to see if a straight line is a good approximation for the empirical values. If yes, we will accept the linear regression model for prediction.
Sample data for our system are given in Table 1, and the scattered diagram is shown in the Fig. 3. The purpose of the regression analysis is to determine the type of the relationship or the dependence between the observed variables. This will be achieved by an appropriate regression model, which will enable us to describe the connection between phenomena, i.e., to predict the values of the dependent variable Y (revenue) for the selected values of the explanatory variable X (number of sales points).
Figure 3. Scatter plot diagram for the Normalized values of the X (No. of agents), Y (Revenue index)
Table 1
According to the equation (1) — we have assumed linear dependence of the two variables (Y=f(X)), thus we proceed to the next stage — evaluation of the unknown parameters: interception value ß0 and slope coefficient ß1. The goal is — on the basis of the sample, to determine the best possible estimates of b0 and b1 and to define the regression line for the sample:
yi = b0 + b1 xi (2)
where yi denotes the value of Y that is its best adjustment to the sample regression line and is called the adjusted value of Y. The estimates b0 and b1 have the same meaning as for the main variables, except that they are related to the sample. As a rule, the regression line in the real values and the sample — varies, because the estimated values of b0 and b1 differ from the actual values of the parameters ß0 and ß1. The reason is simple: the sample is almost never perfectly representative.
On the Fig. 4 — the normalized plot of the sample data about error calculation for the dependence: Revenue index vs. The number of agents is presented.
Figure 4. Normalized plot for the example data from Table 1
While values βo, β1 on the Fig. 4 diagram are constants (intercept and slope of the line) — the samples — b0, b1 can get any value, thus they can only be estimated, and we will treat them as random variables. Between the points on the scatter diagram — it is possible to draw infinitely many straight lines. All of them would, of course, differ in coefficients b0 and b1. The question is: how to draw the correct line between the empirical points that best represents them? These lines should go as close as possible to all comply and thus — give us optimal estimates of b0 and b1. Thus we should proceed by error estimation with the least square method.
The least squares method is based on minimizing the squares deviations of all empirical points from the regression line. We know that due to the stochastic character of the connection, the empirical points will have minor or more significant deviations from the correct line. The vertical deviation (difference) between the actual value yi and the adjusted value — is called a residual i and it is marked by ei:
Figure 5. Overall Yearly Projection
For the real data about the growing number of Agents (available as Excel addendum to this paper) — the resulting revenue prediction diagram is shown in Fig.5.
Regarding the behavior of the agents — it can be assumed that it is determined solely by the commission/time needed and that time/ commission are independent variables. A conditional statistical analysis of how agents will react when faced with slightly more commission / less time in completing a transaction — is shown by the formulas below.
By: Peter Ojo Adapted from the (2018) white paper: Remmittancetoken
Contact us: operations@virtualterminalnetwork.com
