Configuring a profile-deviation-analysis to statistical test complementarity effects from balanced management control systems in a configurational fit approach

Abstract

This paper develops novel test formulas able to test performance effects from balancing control forms in management control systems using the notion of complementarity. Extant research has underlined the importance of researching and understanding complementarity effects stemming from multiple control forms—i.e., management control systems. In configurations of management controls, a number of control forms work interdependently. In some cases, these interdependencies produce complementarity effects, which previous literature has not captured in full, as synergy effects from interdependencies in configurations are often treated implicitly or tested too reductionistic. Previously used statistical test techniques and formulas have not been fully developed to test performance effects using a configurational fit approach that accounts for complementarity effects from balancing multiple control forms and roles of management accountants (finance functions). In configurations of management control systems, control forms and/or roles of management accountants can be balanced to fit local optima for each control form, and simultaneously fitting the distance, i.e. balance, to other control forms/roles, in which the latter can produce complementarity effects. This balance type of complementarity is a subset of the broader notion of complementarity. To move research forward, new formulas are developed that is suited to testing complementarity effects from balancing management control forms. In this way, the black box of how configurations of control forms produce performance is being opened, yet not completely, to better examine how they collectively produce performance. The developed test formulas are illustrated using survey-data on whether multiple roles of management accountants can affect performance in a complementing manner given the strategy of the company they serve.

Appendices

Appendix A: A calculation example

This appendix will show a simple calculation example of the basic formula presented in the paper. The example is based on the same numbers as in Fig. 1, but with an extra CV.

The formula is: Y_{(Performance)} = β₀ + β₁(|X − x| + |Y − y| + |Z − z|) + β₂(|A − a| + |B − b| + |C − c|).

Let us assume the ideal configuration as having the values:

$$ \begin{array}{*{20}c} {{\text{X}} = 4} & {{\text{Y}} = 2} & {{\text{Z}} = 3} \\ \end{array} $$

And the values for one specific organization (that does not constitute part of the ideal configuration) are:

$$ \begin{array}{*{20}c} {{\text{x}} = 4} & {{\text{y}} = 2} & {{\text{z}} = 3} \\ \end{array} $$

Then

$$ \begin{aligned} {\text{Y}}_{{ ( {\text{Performance)}}}} &=\upbeta_{0} +\upbeta_{1} \left( {\left| {4 - 5} \right| + \left| {2 - 1} \right| + \left| {3 - 3} \right|} \right) +\upbeta_{2} \left( {\left| {(4 - 2) - (5 - 1)} \right|} \right) \\ & \quad + \left| {\left( {(4 - 3) - (5 - 3) + \left| {(2 - 3) - (1 - 3)} \right|} \right)} \right|\\ &\downarrow \\&{\text{Y}}_{{ ( {\text{Performance)}}}} =\upbeta_{0} +\upbeta_{1} \left( {1 + 1 + 0} \right) +\upbeta_{2} \left( {2 + 1 + 1} \right) \\&\downarrow\\& {\text{Y}}_{{ ( {\text{Performance)}}}} =\upbeta_{0} +\upbeta_{1} (2) +\upbeta_{2} (4) \end{aligned} $$

This is calculated for all cases outside the ideal configurations. This will change the values of the small capital letters, x,y,z. It should be noted that there are often multiple ideal configurations. The beta values will also be negative; otherwise, it is difficult to interpret.

Calculation examples of the possible extensions/alterations of the basic formula are not presented in this appendix.

Appendix B

Questionnaire item on strategy

Strategy
Please indicate the description of firms below that fit the most to your firm
Prospector	These businesses are frequently the first-to-market with new product or service concepts
	They do not hesitate to enter new market segments where there appears to be an opportunity
	These businesses concentrate on offering products that push performance boundaries
	Their proposition is an offer of the most innovative product, whether based on dramatic performance improvement or cost reduction
Analyzer	These businesses are seldom ‘first-in’ with new products or services or to enter emerging market segments
	However, by carefully monitoring competitors’ actions and customers’ responses to them
	They can be ‘early-followers’ with a better targeting strategy, increased customer benefits, or lower total costs
Defender	These businesses attempt to maintain a relatively stable domain by aggressively protecting their product–market position
	They rarely are at the forefront of product or service development; instead they focus on producing goods or services as efficiently as possible
	These businesses generally focus on increasing share in existing markets by providing products at the best prices
Reactor	These businesses do not appear to have a consistent product–market orientation
	They primarily act to respond to competitive or other market pressures in the short term

Questionnaire items on three roles of finance functions (management accountants)

Role	Variable	Question
		Please indicate the frequency of which the finance function perform the following activities
Adhocracy	X	Develops and evaluates investment opportunities for the business (for example involvement in new markets, or investment in new production facilities)
Compete	Y	Advices other functions (departments) with respect to reaching financial and non-financial goals
Control	Z	Variance analysis of cost and revenue incurred in other functions (departments)
		1: never, 2: very rarely, 3: rarely, 4: occasionally, 5: frequently, 6: very frequently, 7: always

Appendix C

Documentation of all formulas to prepare data analysis from excel before testing. Showing the first 13 cases (answers/companies). Ideal profile values (used in Column F, G, H) are calculated before using the average of 10% best performers for each of the four strategy groups. Notice the head-line counts as the first row

A	B	C	D	E	F	G	H	I	J	K	L	M
email (hidden)	Comp. No	x	y	z	X_ideal	Y_ideal	Z_ideal	X_minus_x_absolute_city_block	Y_minus_y_absolute_city_block	Z_minus_z_absolute_city_block	α_TOTAL_diff_city_block	a_x_minus_y
	1	4.0	3.0	3.0	Part of ideal profile							1.00
	2	1.0	2.0	5.0	Part of ideal profile							− 1.00
	3	1.0	3.0	4.0	Part of ideal profile							− 2.00
	4	4.0	3.0	4.0	2.0	2.7	4.0	2.00	0.33	0.00	2.33	1.00
	5	4.0	5.0	6.0	2.0	2.7	4.0	2.00	2.33	2.00	6.33	− 1.00
	6	2.0	4.0	7.0	2.0	2.7	4.0	0.00	1.33	3.00	4.33	− 2.00
	7	3.0	6.0	6.0	2.0	2.7	4.0	1.00	3.33	2.00	6.33	− 3.00
	8	4.0	6.0	7.0	2.0	2.7	4.0	2.00	3.33	3.00	8.33	− 2.00
	9	2.0	4.0	5.0	2.0	2.7	4.0	0.00	1.33	1.00	2.33	− 2.00
	10	7.0	5.0	7.0	2.0	2.7	4.0	5.00	2.33	3.00	10.33	2.00
	11	6.0	7.0	7.0	2.0	2.7	4.0	4.00	4.33	3.00	11.33	− 1.00
	12	5.0	4.0	3.0	2.0	2.7	4.0	3.00	1.33	1.00	5.33	1.00

A	B	N	O	P	Q	R	S	T	U	V	W	X	Y
email (hidden)	Comp. No	b_y_minus_z	c_x_minus_z	A_ideal	B_ideal	C_ideal	A_minus_a_absolute	B_minus_b_absolute	C_minus_c_absolute	δ_TOTAL_difF_A_B_C	interaction_α_δ_1	interaction_δ_2	interactions_in_α_3
	1	0.00	1.00
	2	− 3.00	− 4.00
	3	− 1.00	− 3.00
	4	− 1.00	0.00	− 0.67	− 1.33	− 2.00	1.67	0.33	2.00	4.00	9.33	4.56	0.67
	5	− 1.00	− 2.00	− 0.67	− 1.33	− 2.00	0.33	0.33	0.00	0.67	4.22	0.11	13.33
	6	− 3.00	− 5.00	− 0.67	− 1.33	− 2.00	1.33	1.67	3.00	6.00	26.00	11.22	4.00
	7	0.00	− 3.00	− 0.67	− 1.33	− 2.00	2.33	1.33	1.00	4.67	29.55	6.78	12.00
	8	− 1.00	− 3.00	− 0.67	− 1.33	− 2.00	1.33	0.33	1.00	2.67	22.22	2.11	22.67
	9	− 1.00	− 3.00	− 0.67	− 1.33	− 2.00	1.33	0.33	1.00	2.67	6.22	2.11	1.33
	10	− 2.00	0.00	− 0.67	− 1.33	− 2.00	2.67	0.67	2.00	5.33	55.12	8.45	33.66
	11	0.00	− 1.00	− 0.67	− 1.33	− 2.00	0.33	1.33	1.00	2.67	30.21	2.11	42.33
	12	1.00	2.00	− 0.67	− 1.33	− 2.00	1.67	2.33	4.00	8.00	42.66	19.89	8.33

Appendix D: Alternative approaches to calculate complementarity from a balance approach

In this appendix, three possible extensions/alterations to the main formula (found in Sect. 3.2.1) are presented. First, a possible third section (β₃) is added to the formula below. It is the interaction between α and δ, both of which are explained in the previous section. This interaction term represents a complementarity effect resulting from having CVs closer to the ideal state and having the ideal balance between these CVs. Thus, the return from being close to the ideal state will increase if the balance between the same CVs is close to the ideal balance. In this respect, an incomplete implementation of management control forms twarts performance more than if only the effects from α or δ are significantly present. It is expected that all beta values including the interaction term are negative. Adding this interaction term is inspired by Cao et al. (2009) and by Bedford et al. (2018). Cao et al. (2009) also operationalize an interaction term for the balance between exploration and exploitation strategies’ effect on performance. Yet, they do not operate with nonsymmetrical ideal states.

$$ {\text{Y}}_{{ ( {\text{Performance)}}}} =\upbeta_{0} +\upbeta_{1}\upalpha +\upbeta_{2}\updelta +\upbeta_{3}\upalpha \updelta +\upvarepsilon $$

(1)

A second possible complementarity extension to the basic formula presented in the previous section could be interaction effects between the distances used to calculate δ. This represents the complementarity effect on performance by having reduced the imbalance between CVs simultaneously. Hence, it is the joint product effect of having CVs closer to the right balance between sets of CVs.³⁰ It can be understood as complementarity effects between relations of CVs, which is not just complementarity between CVs, but also between relations.³¹ If all three betas are significantly negative, the performance effect stems from CVs (1) being closer to the ideal state, (2) being more balanced as in the ideal state, and (3) having their joint effect more in balance.

$$ {\text{Y}}_{{ ( {\text{Performance)}}}} =\upbeta_{0} +\upbeta_{1}\upalpha +\upbeta_{2}\updelta +\upbeta_{3} \left( {\left| {{\text{A}} - {\text{a}}} \right| \cdot \left| {{\text{B}} - {\text{b}}\left| { + } \right|{\text{A}} - {\text{a}}} \right| \cdot \left| {{\text{C}} - {\text{c}}\left| + \right|{\text{B}} - {\text{b}}} \right| \cdot |{\text{C}} - {\text{c}}|} \right) +\upvarepsilon $$

(2)

A third possible complementarity extension or alteration of the basic formula is to add a section containing the interactions between the distances to ideal states of the CVs. This will be the interaction of the distances contained in α. Hence, the performance effect from one CV getting closer to the ideal state depends on the level of the distance that the other CVs have to the ideal state.

This is closer to the conventional complementarity test with an interaction term³² representing the joint product of CVs with complementarity effects when the distance to the ideal state is minimized for multiple CVs. This is especially the case if β₂ is insignificant. Therefore, if only β₁ and the interaction term are significant, and thus β₂ is not, it would still be an interesting finding of complementarities, as it represents a conventional complementarity effect without any distinct respect to the balance between control forms. Yet, the ideal state of CVs may still be nonsymmetrical. Thus, maximizing is not always better. When β₂ is insignificant, or absent from the formula, this represents a complementarity notion that could be described as “doing a thing closer to the ideal level increases the returns of doing other things closer to their ideal level.”

If all three betas are significantly negative, the performance effect stems from CVs being closer to the ideal state, balancing them more as in the ideal state, and the joint effect of them being closer to the ideal state.

$$ {\text{Y}}_{{ ( {\text{Performance)}}}} =\upbeta_{0} +\upbeta_{1}\upalpha +\upbeta_{2}\updelta +\upbeta_{3} \left( {\left| {{\text{X}} - {\text{x}}} \right| \cdot \left| {{\text{Y}} - {\text{y}}\left| { + } \right|{\text{X}} - {\text{x}}} \right| \cdot \left| {{\text{Z}} - {\text{z}}\left| + \right|{\text{X}} - {\text{x}}} \right| \cdot |{\text{Z}} - {\text{z}}|} \right) +\upvarepsilon $$

(3)

In sum, both the base formula and the three possible alterations/extensions all comply with the definition of complementarities provided by Brynolfsson and Milgrom (2013). The formulas just show different ways of how the complementarity effect arises from configurations. Thus, they are different ways to operationalize their notion of complementarity. This should help to open the black box, yet not completely, of how relations between multiple control forms produce complementarity effects in configurations of control forms.