Joint audit, audit market structure, and consumer surplus

Abstract

We use a structural application of the discrete choice model to investigate how the introduction of a joint audit policy would affect audit market structure and consumer surplus. We perform this policy evaluation by identifying demand fundamentals in a joint audit regime and applying them to a single audit regime. We find that a joint audit requirement has the potential to change the audit market structure substantially but that the effects are sensitive to the specific policy design. For example, small audit firms gain market share in a joint audit regime but only if an equal sharing of the workload between the two joint auditors is not required. Our counterfactual analysis reveals that the introduction of a joint audit regime would be associated with a substantial loss of consumer surplus. The loss results from restricting clients from giving all of the audit work to their most preferred audit firm, but it is partly offset by gains in consumer surplus deriving from the opportunity to choose the best combination of auditor pairs.

Appendix

Conditional choice probability

The choice probability $Pr_{(j,k)}^{it}$ of choosing a pair of audit firms is:

$$\begin{array}{@{}rcl@{}} Pr^{it}_{(j,k)}&\,=\,&Pr\left( u^{it}_{(j,k)}\!>\!u^{it}_{(n,m)},\forall n\neq i, m\neq k\right)\\ &\,=\,&Pr\left( \varepsilon^{i}_{jkt}\,-\,\varepsilon^{i}_{nmt}\!>\!V_{int}+V_{imt}+{\Gamma}_{it}(n,m)\right.\\ &&\left.-\left( V_{ikt}+V_{ijt}+{\Gamma}_{it}(j,k)\right),\forall n\neq i, m\neq k\right)\\ &\,=\,&{\int}_{A_{00}}\ldots{\int}_{A_{nm}}\ldots{\int}_{A_{56}}dF(\varepsilon^{i}_{jkt}-\varepsilon^{i}_{00t})\ldots dF\left( \varepsilon^{i}_{jkt}-\varepsilon^{i}_{nmt}\right){\ldots} dF\\&&\times\left( \varepsilon^{i}_{jkt}-\varepsilon^{i}_{56t}\right) \end{array} $$

Set A _nm = V _int + V _imt +Γ _it (n,m) −(V _ikt + V _ijt +Γ _it (j,k)), ∀n≠i,m≠k. Given the type 1 extreme value distribution of $\varepsilon _{lkt}^{i}$ for all l and k, the difference of $\varepsilon _{jkt}^{i}-\varepsilon _{nmt}^{i}$ follows the logistic distribution, which yields to a closed form solution for the above integration as,

$${Pr}^{it}_{(j,k)}\,=\,\frac{\mathit{exp}[V_{ikt}\,+\,V_{ijt}\,+\,{\Gamma}_{it}(j,k)]}{\mathit{exp}[V_{i0t}\,+\,V_{i0t}\,+\,{\Gamma}_{it}(0,0)]\,+\,{\sum}^{6}_{l_{2}=l_{1}+1}{\sum}^{5}_{l_{1}=0} exp[V_{il_{1}t}\,+\,V_{il_{2}t}\,+\,{\Gamma}_{it}(l_{1},l_{2})]} $$

Table 9 Variable definitions