# A decision-making model

We have already recalled that politicians^{5} are the only actors who can decide which policy is delegated to a RA, as well as the degree of independence and accountability the agency enjoys. In this section, I develop a formal model of decision-making that mimics the choice regarding the amount of independence an RA receives. The model can include both country-specific and policy-specific factors. It must be pointed out that the choice to establish a RA must not be identified as something distinct from the choice regarding the degree of independence enjoyed by the agency. It is a choice that already includes a decision on a certain level of bureaucratic discretion. Going from regulation through ministerial bureaucracy, for instance, to regulation through a RA can be interpreted as an increase in the degree of independence. Therefore, for the purpose of this chapter, it is not necessary to distinguish the two decisions.^{6}

The basic model takes into account only the decision regarding *political independence* and *political accountability.* Following the definitions given in Section 3, independence and accountability can be seen as two alternative 'factors of production' that politicians decide to 'combine' according to a certain production function.

Let us posit that *I e* R[0; n] and *A e* R[0; n], where *I* is independence and *A* is accountability, and *n e* R]0; +^{7}

This particular form implies that, although the marginal rate of technical substitution is not the same for every combination of the two variables (see Figure 5.1),^{8} accountability cannot be increased without reducing (to a certain extent) independence, and vice versa.

The politicians' 'production function' represents all the combinations of independence and accountability that produce the same regulatory output: *O = f (I*, A), so that it can be written as a Cobb-Douglas utility function:

where *a* and *в* are two values such that *а, в e* R[0; 1] and *a* + *в =* 1. *a* and *в* represent the factors affecting the 'marginal productivity' of *I* and A. If there are *j* factors (denoted as *a)* that make independence beneficial with respect to accountability, and *k* factors (denoted as b) that make accountability beneficial with respect to independence, *a* and *в* can be expressed as follows:

*Figure 5.1* Different combinations of independence and accountability depending on different values of y

For instance, if these factors are *a _{x} =* 0.4,

*a*= 0.5 and Ъ = 0.6,

_{2}In order to simplify the model, and without loss of generality, we can write the production function as:

where *у = ^{a}* and

*у*e ]0; +

Given the 'isocosts' as expressed in Equation 5.1, we can rewrite the production function as:

The combination of independence and accountability that maximizes the regulatory output while minimizing the cost can be derived by calculating the first derivative of this function with respect to *I*, that is:

Thus, for any value of *у*]0; *I* is obtained by the equation above for *I: ^{9}
*

Figure 5.1 illustrates that for high values of *у*, politicians will give the agency considerable independence and will keep it accountable to a very low degree. Conversely, the lower *у* is, the more the agency will be kept accountable - and the more its independence will decrease.

The model can be tested empirically by verifying whether it correctly predicts the degree of independence and accountability accorded to a RA given certain factors that are supposed to make them more or less beneficial for the regulatory output. Using the same notation as in Equations 5.3 and 5.4, we can rewrite Equation 5.8 as:^{10}

So, for instance, with *n =* 1, *a _{1} =* 0.4,

*a*0.5 and

_{2}=*b*0. 6, the values of

_{1}=*I*and

*A*employed will be: