Flattening the organization: the effect of organizational reporting structure on budgeting effectiveness

Abstract

This study investigates whether increasing a superior’s span of control improves the effectiveness of the budgeting process. We characterize the superior’s utility function as consisting of utilities for norm enforcement and wealth, leading the superior to reject profitable projects believed to contain excessive slack. We develop theory to predict that superiors become more willing to reject projects as their span of control increases. Further, subordinates anticipate superiors’ behavior and reduce slack as span of control increases. Experimental results are consistent with these predictions. As span of control increases, superiors show a greater willingness to reject projects that they believe contain excessive slack, and subordinates submit budgets with less slack. The net result is that superiors earn more profit per subordinate under an expanded span of control. Our study suggests that increasing span of control can improve the effectiveness of the budgeting process, an important component of most firms’ control environments.

Appendices

Appendix

In this appendix, we describe a specific utility function to illustrate the intuition behind our hypotheses. Our setting is a modification of the capital budgeting setting used in a number of recent experimental studies (for example, Evans et al. 2001; Rankin et al. 2003; Hannan et al. 2006). Project completion requires the subordinate’s presence and funding provided by the superior. The cost of the project is uniformly distributed as c∈[c _min , c _max ], and revenue, R, is equal to c _max . The expected total surplus from the project is given by R − E(c). Note, however, that for all realizations of c ∈[c _min , c _max ], the actual surplus, R − c, is greater than or equal to zero, and so the superior should prefer funding the project to rejecting it. Revenue and the probability distribution over costs are common knowledge; however, only the subordinate ever knows the actual cost. Because of the subordinate’s private information, the superior uses participatory budgeting to elicit a cost report from the subordinate.

We assume that the superior has an acceptable level of slack, S, which is determined by a social norm. Our laboratory study does not provide the level of interaction required for the formation and calibration of a unique social norm. For this reason, we expect our participants to apply whatever social norms they bring into the laboratory, most likely those of fairness and honesty. For example, the norm of pure honesty (no slack) would mean that S = 0, whereas the norm of fairness would mean that S equals a fair proportion of the estimated surplus (for example, a 50–50 split). The specific social norm is likely to differ across individuals and organizations, but the implication for the span of control is the same regardless of the specific social norm that determines S in any given case. We further assume that the superior compares S with his or her estimate of slack in the subordinate’s budget, $c_{i}^{report} - E^{j} (c_{i} |c_{i}^{report} )$, where $c_{i}^{report}$ is subordinate i’s budget report and $E^{j} (c_{i} |c_{i}^{report} )$ is superior j’s subjective assessment of the expected cost of the project, conditional on subordinate i’s report. We use a subjective assessment because there is evidence of considerable heterogeneity in the processes individuals use in updating probabilities (Zizzo et al. 2000; Charness and Levin 2005). The result of this comparison, denoted $p_{i}^{j}$, is superior j’s estimate of the degree to which the level of slack in subordinate i’s report violates a social norm, and we assume that $p_{i}^{j}$ is increasing in $c_{i}^{report}$.

We characterize the utility function of each superior, j, as:

$$ u^{j} = u^{j} (y,p_{i}^{j} , \ldots ,p_{i}^{j} ) $$

where y denotes the superior’s pecuniary payoff, and $p_{i}^{j}$ is the superior’s estimate of the degree to which the level of slack in subordinate i’s budget violates a social norm. Alternatively, $p_{i}^{j}$ can be interpreted as the degree of certainty with which the principal perceives that a social norm has been violated. This estimate affects the superior’s tradeoff between accepting the project and receiving utility through wealth or rejecting the project and receiving utility through enforcing a social norm. Utility is increasing in y at a decreasing rate. Also, utility from enforcing a social norm is increasing in $p_{i}^{j}$. In other words, the greater the estimated social norm violation, the more utility the superior receives from rejecting the project and thereby punishing the subordinate for incorporating excess slack in the budget.²⁹

This formulation of the superior’s utility function implies that the span of control affects the superior’s project acceptance decisions. We illustrate this point with a simple example, using the actual parameters from the experiment. This example is illustrated in Exhibit 1. For simplicity (and consistent with strong evidence that individuals deviate significantly from perfect Bayesian updating [Zizzo et al. 2000; Charness and Levin 2005]), we replace $E^{j} (c_{i} |c_{i}^{report} )$ with E(c) and $p_{i}^{j}$ with p _i . That is, for the numerical example we make the simplifying assumption that E(c) is pre-determined based on the ex ante probability distribution of costs. Consider a situation with a superior and two subordinates with c uniformly distributed between 1 and 30 for each subordinate. Revenue (R) is known to equal 30, and the expected cost E(c) = 15.5, hence the expected surplus = 14.5 for each subordinate’s project. Each subordinate’s project cost is independently determined, and each subordinate submits a cost report to the superior. As described previously, S is the superior’s acceptable level of slack and p _i , the superior’s estimate of the degree to which the level of slack in the subordinate’s budget violates a social norm.

Consider the following characterization of the superior’s utility function.

$$ u = a\left[\sum\limits_{i = 1}^{2} {d_{i} } (y_{i} )\right]^{.5} + b\sum\limits_{i = 1}^{2} {\left[(1 - d_{i} )p_{i} \right]} $$

where

$$ d_{i} = \left\{ \begin{array}{ll} 1 & {\text{if}}\;{\text{the}}\;{\text{superior}}\;{\text{accepts}}\;{\text{subordinate}}\;i\hbox{'} {\text{s}}\;{\text{project}} \\ 0 & {\text{if}}\;{\text{the}}\;{\text{superior}}\;{\text{rejects}}\;{\text{subordinate}}\;i\hbox{'} {\text{s}}\;{\text{project}} \\ \end{array} \right. $$

$$ y_{i} = R - c_{i}^{report} $$

$$ p_{i} = \left\{ {\begin{array}{ll} {[c_{i}^{report} - E(c)] - S} & \quad{{\rm if}\,[c_{i}^{report} - E(c)] > S} \\ 0 &\quad {{\rm if}\,[c_{i}^{report} - E(c)] \le S\,({\rm no social norm violation})} \\ \end{array} } \right. $$

Two aspects of this utility function are important to note. First, the decision related to each individual subordinate’s project affects only one component of the utility function. If the subordinate’s project is accepted, the wealth component, y, is increased, and the social norm component, p _i, is not changed. The reverse is true for project rejections. Second, the form of the function differs across the wealth and social norm components. For the wealth component, we use the square root function to reflect the decreasing marginal utility for wealth. We sum the surplus earned from each subordinate’s project before taking the square root to reflect the fungibility of wealth, resulting in a function that is not additively separable by subordinate. For the social norm component, we use a simple linear function, which satisfies the requirement of additive separability by subordinate.³⁰

The relative importance a superior places on the wealth and social norm-related components of utility are represented by a and b, respectively. Principal-agent analyses typically assume a = 1 and b = 0, that is, only utility for wealth matters. In that case, the issue of trading off the utility for wealth and the utility for enforcing a social norm is irrelevant. Therefore, all projects are accepted, and the number of subordinates reporting to the superior does not matter.

When b > 0, the superior receives utility from preventing subordinates from incorporating excessive slack in their budgets. Let a = b = 1, so that the superior places equal weight on the wealth and social norm-related components of utility. Assume that the superior uses a fairness social norm, whereby fairness is defined as an equal split of the expected surplus. In that case, S = [R − E(c)]/2 = [30 − 15.5]/2 = 7.25. Consider the case when subordinates one and two submit cost reports of 22 and 24, respectively. Facing either subordinate one or subordinate two, the superior would choose to accept the project because for each individual subordinate, the utility for wealth is greater than the utility for enforcing a social norm (u = 2.83 vs. u = 0.00 for subordinate one and u = 2.45 vs. u = 1.25 for subordinate two). However, if the superior faces both subordinates, the superior receives greater utility from accepting subordinate one’s project only (u = 4.08) than from accepting both subordinates’ projects (u = 3.74). Therefore, the superior would accept the project with the lower cost report and reject the project with the higher cost report.³¹

1.1 Additional analysis: superior’s utility function

To provide further insights into the processes responsible for our behavioral observations, we provide descriptive data from Experiment 1 to evaluate the reasonableness of our characterization of the superior’s utility function. Specifically, we compare actual decisions with three benchmarks: random, pure wealth maximization, and the predicted decision using our characterization of the superior’s utility function. We use the parameters from the example described above (that is, a = b = 1, S = 7.25, exponent on wealth = 0.5, exponent on social norm = 1) to compute the latter benchmark. Of course, these parameters are individually specific, and so our predictions are noisy to the extent that actual parameters differ from our example parameters. Nonetheless, these data provide a useful benchmark for evaluating our characterization of the superior’s utility function. We use only periods 1 through 4 to make these comparisons, because these are the periods in which superiors made individual accept/reject decisions for each project. However, the results are inferentially identical if we include all periods.

In the low span condition, the superior makes one binary decision (accept or reject). If we were to repeatedly generate a random model and compare that with the superior’s decision, it would converge to 50% accuracy. The random benchmark therefore provides 50% accuracy in predicting decisions in the low span condition. A model assuming wealth maximization (that is, a = 1 and b = 0) predicts that all projects will be accepted. In Periods 1 through 4, 70.8% of projects were accepted. Therefore, the wealth maximization benchmark improves on the random benchmark, increasing accuracy from 50 to 70.8%. Our model predicts that projects will be accepted as long as the utility of wealth from accepting the project exceeds the utility of norm enforcement from rejecting it. Given our assumed parameters, our model predicts that all cost reports ≥25 would be rejected and that all others would be accepted. This model accurately predicts the decisions of our low span superiors 77.1% of the time, improving accuracy slightly over the wealth maximization benchmark. Whereas this degree of accuracy provides a reasonable level of assurance for our model, the high accuracy rates of the other two benchmarks do not allow much room for improvement.

The richer decision context in the high span condition allows for a more rigorous comparison across benchmarks. In this richer context, our model provides substantial predictive improvement compared with the other two benchmarks. In the high span condition, the superior makes a binary decision for three projects, and therefore, a random benchmark provides 12.5% (0.5 × 0.5 × 0.5) accuracy in predicting all three of the superior’s accept/reject decisions. A pure wealth maximization model predicts that all three projects are accepted 100% of the time. All three projects were accepted in only 20.3% of the observations,³² therefore the wealth maximization benchmark modestly improves accuracy over the random benchmark. In contrast, our model improves accuracy substantially. We calculated the predicted decision given our assumed parameters as well as the three cost reports actually submitted each period and found that our model predicts the actual pattern of project accept/reject decisions with 82.8% accuracy. Thus, our evaluation provides substantial support for our characterization of the superior’s utility function.

Although our goal is not to develop an exhaustive representation of the superior’s utility function, we investigate whether two additional factors may be descriptive of our results. First, the superior may experience disutility from treating subordinates inequitably, which suggests adding a third component to the superior’s utility function. This would lead to consistent acceptance and rejection decisions in the high span condition for subordinates who submitted similar cost reports. However, whether this would lead to more acceptances or more rejections in the high span compared to low span condition depends on the relative weight the superior places on the utilities for wealth, norm enforcement, and inequity. Given that 24% of the time, the spread between the acceptance and rejection decision is one dollar, we conclude that any disutility the superiors experience for treating the subordinates inequitably is not a major factor in our setting. Second, the superior may mentally represent the setting as a tournament, thereby maximizing utility subject to a constraint on the number of projects accepted. This would lead superiors in our high span condition to be consistent across periods in the number of projects selected. Given that none of the superiors chose the same acceptance rate across the first four periods (when decisions were made on a project-by-project basis rather than with a pre-specified cutoff) and fewer than half chose the same rate in more than two of these periods, it is unlikely that they mentally represented their decision as a tournament.³³ Thus it does not appear warranted to include either factor in our model.

Exhibit 1: Comparing utility from wealth to utility from norm enforcement

This illustration assumes the utility function presented in the Appendix:

$$ u = a\left[\sum\limits_{i = 1}^{2} {d_{i} } (y_{i} )\right]^{.5} + b\sum\limits_{i = 1}^{2} {\left[(1 - d_{i} )p_{i} \right]} $$

where

$$ d_{i} = \left\{ \begin{array} {ll} 1 & {\text{if}}\;{\text{the}}\;{\text{superior}}\;{\text{accepts}}\;{\text{subordinate}}\;i\hbox{'} {\text{s}}\;{\text{project}} \\ 0 & {\text{if}}\;{\text{the}}\;{\text{superior}}\;{\text{rejects}}\;{\text{subordinate}}\;i\hbox{'} {\text{s}}\;{\text{project}} \\ \end{array} \right. $$

$$ y_{i} = R - c_{i}^{report} $$

$$ p_{i} = \left\{ {\begin{array}{ll} {[c_{i}^{report} - E(c)] - S} & {{\rm if}\,[c_{i}^{report} - E(c)] \geq S} \\ 0 & {{\rm if}\,c_{i}^{report} - E(c)] \le S\,({\rm no social norm violation})} \\ \end{array} } \right. $$

This illustration assumes that the superior applies a social norm of equity. Recall that revenue (R) is known to equal 30, and the expected cost [E(c)] = 15.5, hence the expected surplus = 14.5 for each subordinate’s project. (As discussed in the Appendix, we make the simplifying assumption that E(c) is pre-determined based on the ex ante probability distribution of costs). Equity implies that this surplus will be divided equally by the superior and the subordinate. Therefore, a norm of equity implies that the accepted level of slack (S) = 7.25. On an expectation basis, a cost report above 22.75 (15.5 + 7.25) is perceived as a violation of the social norm.

Panel A: One project with a reported cost of 22

A cost report of 22 does not violate a social norm of fairness, and so no utility is gained from norm enforcement. However, accepting the project leads to wealth of 30 − 22 = 8. Utility from wealth = 8^.5 ≈ 2.83;³⁴ utility from norm enforcement = 0. The project will be accepted.

Panel B: One project with a reported cost of 24

A cost report of 24 violates a social norm of fairness, and so the superior gains utility from norm enforcement if the project is rejected. However, accepting the project leads to wealth of 30 − 24 = 6. Utility from wealth = 6^.5 ≈ 2.45; utility from norm enforcement = 24 − 22.75 = 1.25. The project will be accepted.

Panel C: Two projects with reported costs of 22 and 24

If two cost reports are received, one for 22 and one for 24, the superior will implicitly order the projects by attractiveness. The cost report of 22 is most attractive, and this project will be accepted, yielding utility from wealth of 8^.5 ≈ 2.83, as described in Panel A. The cost report of 24 will then be evaluated. The incremental utility from wealth (assuming the project is accepted) of 14^.5–8^.5 ≈ 0.91 is lower than the utility from norm enforcement (24 − 22.75 = 1.25). Therefore, this project will be rejected.