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What happens if a taxpayer does not spontaneously pay the additional tax amount he is charged? Well, after a while, coercive collection procedures will be deployed by the tax authorities. However, as we have seen above, these procedures are highly ineffective, as they only collect about the 5% of the overall credits claimed against the audited taxpayers.

Indeed, data shows that coercive procedures take place in almost 40% of cases, although its distribution is not uniform: they are more frequent if the tax bill is high, as reported in Table 1.2 (again, tax claim values are in thousands of euros).

Table 1.2. Number of coercive procedures per tax claim interval

Tax claim	Coercive procedures	Total
	No	Yes
[0 - 1]	578	158	736
[1 - 2]	476	155	631
[2 - 5]	1,268	477	1,745
[5 - 10]	1,072	572	1,644
[10 - 20]	745	603	1,348
[20 - 50]	511	653	1,164
[50 - 100]	159	274	433
[100+]	90	237	327
Total	4,899	3,129	8,028

Table 1.2 is actually a double frequency table, which can be used to investigate the existing relationship between the two categorical variables, Coercive procedures and Tax claim (they both take on values that are labels). Recall that given characters X and Y, X is independent from Y if for all Y values, the relative distribution of X does not change. Therefore, a quick glance at Table 1.2 shows that Coercive procedures depend on the values taken by Tax claim.

In a more formal way, following the Openstax (2013) notation, we could also perform a test of independence for these variables, by using the well-known test statistic for a test of independence:

where O is the observed value, E is the expected value, calculated as (row total)(column total) over total number surveyed.

Given the values in Table 1.2, the test would let us reject the hypothesis of the two variables being independent at a 1% level of significance: therefore, from the data, there is sufficient evidence to conclude that Coercive procedures are dependent on the Tax claim level.

It is easy to calculate, from Table 1.2, for each tax claim interval, the total coercive procedures rate, the tax notices rate and the coercive procedures within that tax claim interval rate (all of these ratios are depicted in Figure 1.4).

A close look at Figure 1.4 shows that until the tax claim is “low” (less than € 10,000; please note that the intervals are in thousands of euros), the blue line, i.e. the percentage of tax notices, is above the purple one, i.e. the percentage of coercive procedures, while for higher values of tax claim, the blue line is under the purple one. This is quite strong evidence that coercive procedures are not independent from tax claim.

As a result, the red line shows that the higher the tax claim, the higher the percentage of procedures within the tax claim range itself, up to over 70% in the last and, apparently, most desirable range.

Therefore, with just one model in place, whose task is to recognize interesting taxpayers, the tax authorities would risk facing many cases of coercive procedures. Thus their ability to ensure tax collection may be seriously jeopardized.

We therefore need to find a way to discover, among the most interesting taxpayers, the most solvent ones, the most willing to pay.

Figure 1.4. Coercive procedures and tax claim. For a color version of this figure, see www.iste.co.uk/dimotikalis/analysis2.zip

We can start by observing that a taxpayer with no properties will probably not be willing to pay his dues. Therefore, a second model only focusing on a few features indicating whether the taxpayer owned some kind of assets or not is built, in order to predict if a tax notice will end in an enforced recovery proceeding or not.

Once both models are available, the taxpayer selection process is held in such a way that undertakings will only be audited if judged worthy by both models.