4. Model Specification

There is an acute need to develop this new discretion model that accounts for granularity: In this study, granularity is postulated to help resolve the discretion puzzle (see Box 2.5 in Sect.​ 2.​4.​2) but the models of many existing studies in the literature only take limited granularity into account (see Sects.​ 1.​1 and 2.​2.​3). The new model—which is empirically-validated in Chap.​ 5—allows the study to test its hypotheses in Chap.​ 6. As Chap.​ 7 shows, this fulfils the research objective of working towards resolving the discretion puzzle.

See Chap.​ 2 (e.g. Agarwal et al. 2009; Barnabas and Mekoth 2010; Bloom et al. 2008; Bowen et al. 2008; Caza 2007, 2011; Chang and Wong 2004; Cheng et al. 2006; Davis et al. 1997b, pp. 27–43; Dicke and Ott 2002, p. 468; Fox and Hamilton 1994, p. 74; Gammelgaard et al. 2010; Groves et al. 1994; He et al. 2009; Khanchel 2009; Xiaoyang Li 2007; Marin and Verdier 2006; Spremann 1987, p. 18; Stano 1976; Vargas Sánchez 2005, p. 19; Venaik 1999; Werner and Tosi 1995; Xu et al. 2005; Zhang 1997).

This is possible due to the representativeness of the sample, as discussed in Sect.​ 5.​5.​4 (Fogiel 2000, pp. 158–160; Garson 2002, pp. 139–196; Gliner and Morgan 2000, p. 148; Wooldridge 2002, pp. 298–299).

In line with the contributions of the theories highlighted in the literature review summary Table 2.​12 in Sect.​ 2.​4, the new discretion model integrates the theoretical context specified by managerial discretion theory (e.g. the potentially multidimensional construct of discretion and the antecedents of discretion) and the theoretical mechanisms specified by principal-agent theory and stewardship theory (e.g. direct and moderating effects). In line with the empirical literature (see Sects.​ 2.​1 and 2.​2), the theories are woven into the new model with more fine-grained granularity than in many previous studies (see references in the introduction to this chapter).

Sect.​ 2.​3.​1 has reviewed many contributions to managerial discretion theory subsequent to Hambrick and Finkelstein’s (1987) seminal work, which are built on in this study’s model (e.g. Abrahamson and Hambrick 1997; Berman et al. 2005; Carpenter and Golden 1997; Caza 2007, 2011; Chen 2006; Crossland 2007; Crossland and Hambrick 2007; Datta et al. 2003; Finkelstein and Boyd 1998; Finkelstein and Hambrick 1990; Finkelstein and Peteraf 2007; Haleblian and Finkelstein 1993; Hambrick and Abrahamson 1995; Hambrick et al. 1993; Hutzschenreuter and Kleindienst 2007; Keegan 2006; Keegan and Kabanoff 2008; Key 2002; Li and Zhao 2004; Magnan and St-Onge 1997; Quigley and Hambrick 2009; Rajagopalan and Finkelstein 1992; Thomas and Peyrefitte 1996; Zhang and Li 2008b; Zhang et al. 2006a, b).

As described in Sect.​ 2.​3.​1, population ecology regards organisations as entities within populations and in the process of evolution, those organisations with favourable organisational competences—such as routines of large organisations (e.g. Baum 1996; Singh and Lumsden 1990) and the reputation and reproducibility of more mature organisations (e.g. Freeman et al. 1983; Hannan and Freeman 1984; Stinchcombe 1965)—successfully adjust to environmental structural changes (e.g. innovations) and thereby survive.

As explained in Sect.​ 2.​3.​1, strategic choice theory assumes that there is a group of influential decision-makers (i.e. the ‘dominant coalition’) who actively make strategic choices (i.e. ‘Managerial Action’ in Fig. 4.2) that determine organisational outcomes (Datta et al. 2003, p. 102; Pegels et al. 2000, p. 911). These decision-makers engage in an evaluation of the current situation, which is influenced by e.g. environmental conditions, rewards expected by resource providers, and the prior ideology of the decision-makers (Child 1972, p. 18), i.e. environmental, organisational, and managerial influences.

See Sect.​ 2.​1.​2 (e.g. Barnabas and Mekoth 2010; Bloom et al. 2008; Caza 2007, 2011; Chang and Wong 2003; Cheng et al. 2006; Dicke and Ott 2002, p. 468; Fox and Hamilton 1994, p. 74; Gammelgaard et al. 2010; He et al. 2009; Marin and Verdier 2006; Spremann 1987, p. 18; Vargas Sánchez 2005, p. 19; Xu et al. 2005).

For example, a given manager might use additional discretion for making capital investments in a way that improves performance but use additional discretion for hiring workers in a way that reduces performance.

For instance, a construct such as firm size would act as an antecedent if managers in larger firms tended to systematically possess different degrees of discretion than did managers in smaller firms.

As noted in Sect.​ 2.​3.​1.​2, managerial antecedents include ‘Managerial Activities’ (Finkelstein and Peteraf 2007, pp. 237–243) in addition to ‘Managerial Characteristics’ (Hambrick and Finkelstein 1987, pp. 378–389), which, due to their theoretical origins in principal-agent theory, are discussed in Sect. 4.1.2 below.

In addition to potentially impacting on performance, it has been empirically demonstrated that discretion may significantly affect managerial power (Carpenter and Golden 1997), managerial compensation (Finkelstein and Boyd 1998; Magnan and St-Onge 1997; Rajagopalan and Finkelstein 1992; Werner and Tosi 1995; Wright and Kroll 2002; Zhang and Xie 2008), workers’ incentives (Groves et al. 1994), a successor chief executive officer’s age (Wang 2009), top management team tenure, trust (Perrone et al. 2003), strategic attention (Abrahamson and Hambrick 1997), environmental commitment (Aragon-Correa et al. 2004), pricing (Cameron 2000), organisational knowledge creation (Oh 2002), and research and development (Zhang et al. 2006a, b).

The letters a, c, d, and m in parentheses on the arrows in Fig. 4.3 correspond to the algebraic notation used in Sect. 4.3 for specifying the empirical discretion model. These types of structural relationships are derived from the methodological literature (e.g. Aiken and West 1991; Arnold 1982; Baron and Kenny 1986; Carte and Russell 2003; Chin et al. 1996, 2003; Cohen 1978; Cronbach 1987; Eggert et al. 2005; Finney et al. 1984; Henseler and Fassott 2010; Homburg and Giering 2001; Iacobucci and Duhachek 2003; Irwin and McClelland 2001; Jaccard and Turrisi 2003; Kenny and Judd 1984; Rigdon et al. 1998; Shrout and Bolger 2002; Simon 1954; Venkatraman 1989).

As explained in Sect.​ 2.​3.​1.​1, the influences on strategic choice (\( M \)) are investigated further in upper-echelon theory, which focuses on the ‘Managerial’ contingencies in Fig. 4.3 by contending that the cognitive bases and values (i.e. knowledge, ordering, and preferences) of top managers strongly influence their processing of complex information from environmental and organisational stimuli and thus their strategic choices (Aragon-Correa et al. 2004; Galavan 2005; Galavan et al. 2009; Hambrick et al. 1993; Hambrick and Mason 1984; Hutzschenreuter and Kleindienst 2007; Manner 2010; Pegels et al. 2000). It is argued that these cognitive bases and values can be measured by observable managerial background characteristics (e.g. age, education, and socioeconomic roots), and it has been confirmed that such demographics are empirically related to strategic choices and performance (see Carpenter et al. 2004; Hambrick 2007).

For example, if larger firms granted more capital investment discretion, and additional capital investment discretion improved performance, then the mediating effect of firm size via capital investment discretion on performance could help explain the performance differences by firm size. While this mediating effect is included in Fig. 4.3 to offer a complete theoretical discretion model that can be harnessed in future research (see Chap.​ 7), mediating effects are not investigated in order to fulfil the present study’s research objective.

See Sect.​ 2.​3.​2 on principal-agent theory (e.g. Agrawal and Knoeber 1996; Baysinger and Butler 1985; Berger et al. 1997; Brush et al. 2000; Chang and Wong 2003; Childs and Mauer 2008; Denis et al. 1997; Eisenhardt 1989; Fama 1980; Fama and Jensen 1983a, b; He et al. 2009; Jensen 1986; Jensen and Meckling 1976; Jensen and Murphy 1990; Jensen and Ruback 1983; Laffont and Martimort 2002; Lang et al. 1995; Levinthal 1988; Ongore 2011; Shleifer and Vishny 1997; Spremann 1987; Thépot 2007; Thomsen and Pedersen 2000; Walters 1995; Wang et al. 2008; Weidenbaum and Jensen 1993; Werner and Tosi 1995, p. 1673; Xu et al. 2005; Zou 1989) and Sect.​ 2.​3.​3 on stewardship theory (e.g. Albanese et al. 1997; Arthurs and Busenitz 2003; Corbetta and Salvato 2004; Davis et al. 1997a, b; Dicke and Ott 2002; Donaldson 1990; Donaldson and Davis 1989, 1991, 1993, 1994; Eddleston and Kellermanns 2007; Fox and Hamilton 1994; Lane et al. 1999; Liu and Cai 2004; Miller and Le Breton-Miller 2006; Mills and Keast 2009; Muth and Donaldson 1998; Salvato 2002; Tian and Lau 2001; Tosi et al. 2003; Van Slyke 2007; Vargas Sánchez 2001, 2004, 2005; Zahra 2003).

This general theoretical discretion model is tailored to the present study’s research objective in Sect. 4.1.3.

As explained in Sect.​ 2.​1.​1, managerial discretion theory defines discretion as the extent to which a manager has multiple courses of action across various domains of his/her work that he/she is aware of and that are acceptable to the parties that possess power to constrain the manager (Abrahamson and Hambrick 1997, p. 513; Carpenter and Golden 1997, p. 187; Caza 2007, p. 27; Chang and Wong 2003, p. 2; Crossland 2007, p. 1; Crossland and Hambrick 2007, p. 767; Finkelstein and Boyd 1998, p. 179; Finkelstein and Hambrick 1990, p. 484; Hambrick and Abrahamson 1995, p. 1427; Hambrick and Finkelstein 1987, pp. 371–378; Rajagopalan and Finkelstein 1992, p. 32).

As described in Sect.​ 2.​4.​4, managerial discretion theory, principal-agent theory, and stewardship theory have all focused on top management as the unit of analysis but also apply to middle management, as analysed in this study (see Caza 2007, pp. 7–8; Davis et al. 1997b, p. 25; Jensen and Meckling 1976, p. 309).

As explained in Sect.​ 2.​3.​3.​2, stewardship theory tends not to address the antecedents of discretion, neither explicitly nor implicitly. What stewardship theorists term ‘antecedents’ (e.g. Davis et al. 1997b, pp. 27–43) was explained to relate to moderating effects and is thus modelled as moderating effects in Fig. 4.4.

As discussed in Sect.​ 2.​3.​2.​2, multiple courses of action count towards a manager’s (agent’s) discretion only if they ‘lie within the zone of acceptance of powerful parties’ (principal; Hambrick and Finkelstein 1987, p. 378). Principal-agent theory’s assumption of asymmetric information (i.e. the inability of the principal to fully monitor the agent’s actions; see assumption 2 in Sect.​ 2.​3.​2.​1; e.g. Eisenhardt 1989, p. 59; Jensen and Murphy 1990, p. 226; Khanchel 2009, p. 97; Levinthal 1988, p. 153; Spremann 1987, p. 3; Van Slyke 2007, p. 162; Werner and Tosi 1995, p. 1673) widens the zone of acceptance of the principal, since to the extent that the principal cannot monitor the agent’s activities and thus hold him/her accountable, the principal is bound to accept the agent’s actions (e.g. Spremann 1987, p. 10). The more difficult it is for the principal to monitor the agent’s activities, the more latitude (i.e. discretion) the agent has in choosing additional courses of action, even if they are against the principal’s best interests. Hence, the asymmetry of information (i.e. the inability of the principal to fully monitor the agent’s actions) gives the agent additional managerial discretion.

As explained in Sect.​ 2.​3.​2, it is possible to assume that the principal is less performance-maximising than the agent, in which case managerial discretion may positively affect performance (Chang and Wong 2003, pp. 1–7). However, this assumption is rarely made in principal-agent theory (Thomsen and Pedersen 2000, p. 690). The literature on principal-agent theory therefore generally contends that managerial discretion has a negative direct effect on performance (e.g. Caza 2007, p. 10; Caza 2011; Chang and Wong 2003, p. 7; Davis et al. 1997b, p. 38; Hutzschenreuter and Kleindienst 2007, p. 4; Jensen and Murphy 1990; Zhao et al. 2010).

As explained in Box 2.3 in Sect.​ 2.​3.​3.​2, stewardship theory’s assumptions create two theoretical mechanisms that contribute to the positive predicted direct effect of discretion on performance (\( d>0 \)). First, additional discretion allows stewards to shift organisational outcomes closer to their preferred outcomes, which are assumed to be equally or more performance-maximising than those preferred by the principal (see assumption 4). Second, higher discretion strengthens the steward’s motivation to improve performance (see assumption 1).

As Sect.​ 2.​4.​3 shows, these divergent predictions of principal-agent theory and stewardship theory motivate the present study to test Hypothesis 4 in an effort to work towards resolving the discretion puzzle. To this end, the moderating effects discussed below likewise motivate Hypothesis 2 and Hypothesis 3 (see Sect.​ 2.​4.​2).

As depicted in Fig. 4.3 in Sect. 4.1.1, environmental, organisational, and managerial contingencies (i.e. ‘Influences on Strategic Choice’ \( M \)) may influence the way that managers make their strategic choices (e.g. Child 1972, 1997, 2002; Child et al. 2003; Elbanna and Child 2007; Hitt and Tyler 1991; Hrebiniak and Joyce 1985; Judge and Zeithaml 1992; Marlin et al. 1994; Miles and Snow 1978; Stienstra et al. 2004), and these influences (\( M \)) can have a ‘Moderating Effect (m)’ on the impact of discretion (\( D \)) on performance (\( P \)).

As to assumption 1, agents in principal-agent theory are assumed to maximise their self-serving utility functions interests (e.g. Albanese et al. 1997, p. 609; Chang and Wong 2003, p. 25; Davis et al. 1997b, pp. 20–22; Dicke and Ott 2002, p. 464; Eisenhardt 1989, pp. 58–59; Jensen and Meckling 1976; Jensen and Murphy 1990, pp. 225–226; Levinthal 1988, p. 153; Spremann 1987, p. 3; Thomsen and Pedersen 2000, p. 690; Van Slyke 2007, p. 162; Werner and Tosi 1995, p. 1673), whereas stewards in stewardship theory are assumed to maximise their pro-organisational utility functions (e.g. Davis et al. 1997b, pp. 24–26; Dicke and Ott 2002, p. 464; Eddleston and Kellermanns 2007, p. 549; Khanchel 2009, pp. 98–99; Mills and Keast 2009, p. 13; Muth and Donaldson 1998, pp. 5–6; Vargas Sánchez 2005, p. 19). As to assumption 4, principal-agent theory mostly assumes that the principal’s interests are more aligned with maximising performance than those of the agent (e.g. Chang and Wong 2003; Eisenhardt 1989; Jensen 1986; Jensen and Meckling 1976; Jensen and Murphy 1990; Shleifer and Vishny 1997; Spremann 1987; Thomsen and Pedersen 2000), whereas stewardship theory assumes that the steward’s interests are at least as performance-maximising as the principal’s interests (e.g. Albanese et al. 1997, p. 609; Davis et al. 1997b, pp. 24–25; Dicke and Ott 2002, p. 464; Donaldson 1990, p. 377; Donaldson and Davis 1994, p. 159; Khanchel 2009, p. 98; Liu and Cai 2004, pp. 3–4; Tosi et al. 2003, p. 2054; Van Slyke 2007, p. 164; Vargas Sánchez 2005, pp. 17–18).

As these influences (moderators) shift the manager’s natural predisposition to performance maximisation towards those of an agent (i.e. assumption 1: self-serving utility maximisation and assumption 4: less performance-maximising interests than the principal), the impact of discretion on performance becomes more negative. By contrast, as these moderators shift towards stewardship (i.e. assumption 1: pro-organisational utility maximisation and assumption 4: interests equal to or more performance-maximising than those of the principal), the impact of discretion on performance becomes more positive (see Sects.​ 2.​3.​2.​2 and 2.​3.​3.​2).

A control-oriented management philosophy entails a risk orientation of control mechanisms rather than trust, a short-term time frame rather than a long-term time frame, and cost control rather than performance enhancement objectives (Davis et al. 1997b, pp. 32–37; Van Slyke 2007, p. 164).

As to assumption 2, principal-agent theory and stewardship theory assume that the principal cannot fully monitor the manager’s actions due to post-contractual asymmetric information (see Sects.​ 2.​3.​2 and 2.​3.​3; e.g. Davis et al. 1997b, pp. 23–24; Eisenhardt 1989, p. 59; Fox and Hamilton 1994, p. 78; Jensen and Murphy 1990, p. 226; Khanchel 2009, p. 97; Levinthal 1988, p. 153; Spremann 1987, p. 3; Van Slyke 2007, p. 162; Werner and Tosi 1995, p. 1673).

In addition to the nature of managerial activities and monitoring control mechanisms having a ‘Moderating Effect (m)’ in Fig. 4.4 in that they can influence how a given level of discretion is utilised so as to increase or decrease performance, it was discussed above that these variables can have a respectively positive and negative ‘Direct Effect (a)’ on the manager’s level of discretion as antecedents (see Table 2.​9 in Sect.​ 2.​3.​2.​2).

This dampening effect of stricter monitoring control mechanisms on the positive impact of discretion on performance under stewardship theory can be traced back to the two theoretical mechanisms derived in Box 2.3 in Sect.​ 2.​3.​3.​2. First, monitoring control mechanisms can constrain the steward to act more in line with the principal’s best interests, which might be less performance-maximising than those of the steward—leading to lower performance improvement from discretion. Second, monitoring control mechanisms might reduce the steward’s motivation and thus the positive effect of granting discretion to improve performance (e.g. Aghion and Tirole 1997; Argyris 1964; Burkart et al. 1997, pp. 693–694; Corbetta and Salvato 2004; Davis et al. 1997b, pp. 21–25; Dicke and Ott 2002, p. 468; Donaldson and Davis 1991, p. 51, Donaldson and Davis 1993, pp. 215–216; Eddleston and Kellermanns 2007, p. 548; Frey 1993; Khanchel 2009, p. 98; Xiaoyang Li 2007; Liu and Cai 2004, pp. 3–4; Tosi et al. 2003, p. 2054; Van Slyke 2007, pp. 162–165; Vargas Sánchez 2004, p. 3, 2005, p. 18; Xu et al. 2005).

As to assumption 3, principal-agent theory and stewardship theory assume that the manager’s managerial action is rational in terms of tending to produce the outcomes that the agent intends (see Sects.​ 2.​3.​2 and 2.​3.​3; e.g. Albanese et al. 1997, p. 610; Davis et al. 1997b, pp. 20–22; Werner and Tosi 1995, p. 1673).

This three-way interaction is visualised by the arrows in Fig. 4.4 and is explained in detail in Box 2.2 in Sect.​ 2.​3.​3.​2, which shows, among other things, that it is consistent with seemingly opposing views in the literature (e.g. Caza 2007, p. 13; Chang and Wong 2003, p. 24; Cheng et al. 2006, pp. 341–342; Hayek 1945, pp. 524–526; Xiaoyang Li 2007).

It should be noted that scholars have empirically tested a number of the moderators embedded in Fig. 4.4 and at times have found significant evidence as noted in Chap.​ 2, but have generally only tested a subset of moderators and rarely considered their potential three-way interaction (see Sects.​ 2.​3.​2.​2 and 2.​3.​3.​2; e.g. Caza 2007, 2011; Cheng et al. 2006; Mills and Keast 2009; Van Slyke 2007; Vargas Sánchez 2001, 2004; Wang et al. 2008; Zhang and Li 2008b). This motivates the present study to build on these relevant moderators and combine them in the general theoretical discretion model that recognises their interactions.

The way that such potential three-way interactions are treated in the present study is to combine the multi-group comparison approach for testing moderating effects (e.g. Arnold 1982; Henseler and Fassott 2010, pp. 719–721; Rigdon et al. 1998, p. 1; Venkatraman 1989, p. 426) with the product term approach for testing moderating effects (e.g. Carte and Russell 2003, pp. 480–495; Chin et al. 2003, pp. 196–200; Irwin and McClelland 2001, p. 105), as described for the empirical discretion model in Sect. 4.3. In simple terms, the model allows firm size (one moderator) to differently influence how a manager uses discretion according to whether the firm type (another moderator) is a Chinese firm or a multinational.

Likewise, when the ‘Moderating Effect (g)’ specifies the manager to choose agency behaviour (\( d<0 \)) rather than stewardship behaviour (\( d>0 \)), then strengthening the manager’s ability, knowledge and information or freeing him/her from monitoring control mechanisms (\( M \)) might aggravate discretion’s negative performance impact (which is the opposite of when the manager chooses stewardship behaviour).

In addition to working towards tailoring the model to the present study and translating it into the empirical discretion model, the parsimonious representation in Fig. 4.6 highlights the flexibility to enrich the theories embedded into the model by testing whether a variable of one theory has an effect postulated in another theory (while also allowing to model only those variables and effects that are specified in the original theories). The present study, for instance, tests whether firm size (i.e. an antecedent from managerial discretion theory with ‘Direct Effect (a)’ and an environmental circumstance from population ecology with ‘Control Effect (c)’) also has a ‘Moderating Effect (m)’ as variables in strategic choice theory, principal-agent theory, and stewardship theory.

Section 2.​3.​1 has also discussed environmental antecedents not related to ‘Industry’, such as national-level or macro-environmental factors (e.g. Bloom et al. 2008; Crossland 2007; Crossland and Hambrick 2007).

For instance, performance may be higher in higher-technology industries than in lower-technology industries (see Sect.​ 5.​3.​3; e.g. Albors et al. 2008; Ang 2008; Bound et al. 1984; Griliches and Mairesse 1990; Hausman et al. 1984; Sarkar et al. 2006).

There is literature in support of both positive effects of firm size on discretion (e.g. Caza 2007, p. 19; Galbraith 1967; Reid 1968; Williamson 1963, p. 1032) and negative effects of firm size on discretion (e.g. Aldrich 1979; Baum 1996; Finkelstein and Hambrick 1990, p. 493; Hambrick and Finkelstein 1987, pp. 379–384; Mintzberg 1978; Tushman and Romanelli 1985; Zohar and Luria 2005).

Economies of scale (Caza 2007, p. 12), the liability of smallness (Singh and Lumsden 1990), and inherent predictability and processes favoured by natural selection (Baum 1996) all support a positive ‘Control Effect (c)’ of firm size on performance. Empirical evidence has confirmed such a positive relation between size and performance in some cases, even in the context of middle management discretion (e.g. Caza 2007, pp. 19–23).

In contrast to organisational variables such as firm size, which can affect performance directly via e.g. natural selection in population ecology (i.e. ‘Control Effect (c)’), the managerial variables in Fig. 4.6 take effect on performance only via managerial action and thus via discretion (i.e. the latitude of managerial action): When a manager has zero discretion and therefore has no multiple courses of action to choose from, there will be no performance effect from strengthening his/her ability, knowledge, and information if discretion remains zero. If strengthening his/her ability, knowledge, and information increases managerial discretion by allowing him/ her to perceive multiple courses of action (i.e. ‘Direct Effect (a)’), then there may be an effect on performance, but only via the chosen managerial action (i.e. ‘Direct Effect (d)’), which leads to the ‘Mediating Effect (d ⋅ a)’.

As the utility function \( U\left( {L,\cdot } \right) \) is not further specified, it can accommodate both self-serving utility functions assumed in principal-agent theory and pro-organisational utility functions assumed in stewardship theory (Sects.​ 2.​3.​2 and 2.​3.​3; e.g. Albanese et al. 1997, p. 609; Chang and Wong 2003, p. 25; Davis et al. 1997b, pp. 20–22; Dicke and Ott 2002, p. 464; Eddleston and Kellermanns 2007, p. 549; Eisenhardt 1989, pp. 58–59; Jensen and Meckling 1976; Jensen and Murphy 1990, pp. 225–226; Khanchel 2009, pp. 98–99; Levinthal 1988, p. 153; Mills and Keast 2009, p. 13; Muth and Donaldson 1998, pp. 5–6; Spremann 1987, p. 3; Thomsen and Pedersen 2000, p. 690; Van Slyke 2007, p. 162; Werner and Tosi 1995, p. 1673).

While denoted by scalars for the sake of simplicity, managerial action (\( L \)) and managerial discretion (\( D \)) may be viewed as multidimensional vectors with dimensions related to the domains of the manager’s work in which managerial discretion (\( D \)) is granted and managerial action (\( L \)) can thus take place (see Sect. 4.3).

The present study treats such potential three-way interactions by combining the multi-group comparison approach for testing moderating effects (e.g. Arnold 1982; Henseler and Fassott 2010, pp. 719–721; Rigdon et al. 1998, p. 1; Venkatraman 1989, p. 426) with the product term approach for testing moderating effects (e.g. Carte and Russell 2003, pp. 480–495; Chin et al. 2003, pp. 196–200; Irwin and McClelland 2001, p. 105).

Chapter 3 explains that the present study chooses this unit of analysis due to both the particular need to clarify the performance impact of discretion at the middle management level in China (see Caza 2007, p. 1; Yougen Li and Zhao 2003, p. 6; Zhang and Li 2008a, pp. 37–38) and the applicability of the theories in the new theoretical discretion model to middle management (see Caza 2007, pp. 7–8; Davis et al. 1997b, p. 25; Jensen and Meckling 1976, p. 309).

For example, some plant managers may have been granted the discretion to hire full-time permanent shop floor workers without involving top management, whereas others may be required to seek prior authorisation from top management at corporate headquarters in China before taking managerial action to hire workers. Section 2.​1.​1 has thus defined managerial discretion as the extent to which the plant manager has multiple choices across such domains as making capital investments, hiring workers, introducing new products, and sales & marketing activities that he/she is aware of and that are acceptable to corporate headquarters in China. Section 4.2.2 demonstrates that the present study’s selection of the four domains of managerial discretion (\( D \)) that are displayed in Fig. 4.7 is consistent with the domains chosen by various scholars in recent research.

Similarly, with different types of firms attracting different people, the ‘Psychological Characteristics’ and ‘Expectations’ in Fig. 4.6 that stewardship theorists have argued influence how managers use discretion might differ between Chinese firms and multinationals, as could ‘Compensation Control Mechanisms’ from principal-agent theory (see Box 2.6 in Sect.​ 2.​4.​2).

For example, Caza (2007, pp. 12–20) argues that a larger firm with multiple units (here plants) that are similar to that led by the (plant) manager under consideration provide the principal with more informational bench-marks to assess the (plant) manager’s performance and thus potentially constrain his/her misconduct.

Section 4.3 takes the third and final step towards developing the new discretion model by specifying the structural model for each relationship. This completes the translation into the empirical discretion model.

Figure 4.12 in Sect. 4.3.1 adds the arrows omitted in Fig. 4.8. The labelling of the leftmost shapes has been simplified and the constructs have been given the algebraic symbols used in Sect. 4.3 (\( P \) for Performance, \( D{}_1 \) to \( D{}_4 \) for the dimensions of Discretion, and \( A{}_1 \) to \( A{}_2 \) for the Antecedents of discretion). As explained in Box 4.1 in Sect. 4.1.2, Antecedents have been regrouped to include influences on managers, antecedents, and environmental circumstances with no loss of generality. ‘Firm Type’ has no measurement model and no algebraic symbol, as it is modelled by the multi-group comparison approach (see Sect. 4.3; e.g. Arnold 1982; Henseler and Fassott 2010, pp. 719–721; Rigdon et al. 1998, p. 1; Venkatraman 1989, p. 426) and thereby denotes whether a given plant manager’s firm is a domestic Chinese firm or a foreign multinational.

The measure for middle management performance is based on a practice evaluation tool developed and employed by McKinsey & Company, a leading global management consulting firm. The tool has been tested and published in Bloom and Van Reenen (2007) for middle management performance in France, Germany, the United Kingdom, and the United States of America. Examining 18 relevant aspects of management, specially-trained interviewers assess the extent to which the managers’ practices reflect best practices as defined on a scoring grid. The indicators are combined into a measure for middle management performance.

For instance, Caza (2007) measures the performance of research and development units as a latent variable with four non-financial reflective indicators, namely an evaluator’s rating of the R&D unit’s innovation, quality, success in reaching R&D goals, and contributions to the science field.

The selection of these management practices can also be justified on practical grounds (see Sect.​ 5.​3.​1).

The purified six-indicator performance measure is shown to exhibit even higher levels of construct validity (i.e. lower measurement error) in the context of the present study and greater parsimony, while retaining sufficient breadth of content so as to capture the domain of the theoretical construct of middle management performance (e.g. Coltman et al. 2008; Diamantopoulos and Siguaw 2006, p. 271; Rossiter 2002).

Summated scales calculate single scores from multiple indicators before they enter the empirical model, such as unweighted averages. They tend to conceal measurement error by aggregating indicators outside of the model’s theoretical context (Chin et al. 2003, p. 194). In this sense, summated scales are inferior to measurement models in structural equation models that allow latent variables to be endogenously determined from multiple indicators within the model’s theoretical context (Chin et al. 2003, p. 197; Herrmann et al. 2006).

Coltman et al.’s (2008) criteria include three theoretical criteria (i.e. the nature of the construct, the direction of causality, and the characteristics of the indicators) and three empirical criteria (i.e. the indicator intercorrelation, the indicator relationships with construct antecedents and consequences, and the measurement error and collinearity). For instance, applying their criterion of indicator intercorrelation, the high value of Cronbach’s alpha (see Sect.​ 5.​2.​3) suggests that the indicators have similar underlying true scores and supports a reflective measurement model.

Seminal work has postulated and empirically confirmed that it is the discretion a manager perceives rather than some objective degree of discretion that matters for predicting managerial behaviour (see Sect.​ 2.​1.​1; e.g. Carpenter and Golden 1997, p. 202; Caza 2007, 2011; Galavan 2005; Galavan et al. 2009; Glaister et al. 2003; Hambrick and Finkelstein 1987, p. 373; Key 2002; Walters 1995; Zhao et al. 2010).

While the exact choice of areas of the manager’s work differs in the literature, some domains of managerial action tend to be measured more frequently than others. E.g. Cheng et al. (2006) combine data from surveys of different years and retain only those indicators that were assessed in every year. This results in eight areas of the manager’s work, which Table 4.3 classifies according to the taxonomy used for performance-relevant firm resources in Barney’s (1991, p. 101) resource-based view of the firm. Similar indicators have also been put forward in other recent studies (see references in Table 4.3). When benchmarking the areas of work selected for the present study against those from the literature in Table 4.3, it becomes apparent that the chosen indicators represent the content domain of the theoretical construct of discretion. Specifically, the indicators related to physical and human capital resources are very similar, and the discrepancies in the indicators related to organisational capital resources appear justifiable: Strategic decisions such as mergers appear less relevant in this study (which examines middle management) than in many extant studies (that analyse top management), and new product introduction discretion and sales & marketing discretion have appeared in various existing studies (e.g. Cheng et al. 2006; Glaister et al. 2003; Marin and Verdier 2006).

The z-transformations ensure comparability between the indicators and are recommended for the computation of moderating effects in the context of the present study, as discussed in Sect. 4.3 (Aiken and West 1991, pp. 35–129; Finney et al. 1984; Henseler and Fassott 2010, pp. 727–729).

As discussed in Sect.​ 2.​1.​2, principal-agent theory, stewardship theory, and many empirical studies tend to treat discretion as unidimensional, whereas managerial discretion theory hints that discretion might be multidimensional (e.g. Barnabas and Mekoth 2010; Bloom et al. 2008; Carpenter and Golden 1997, p. 195; Caza 2007, pp. 26–82, Caza 2011; Chang and Wong 2003; Huiyuan Chen 2006; Cheng et al. 2006; Dicke and Ott 2002, p. 468; Finkelstein and Peteraf 2007, p. 245; Fox and Hamilton 1994, p. 74; Gammelgaard et al. 2010; Groves et al. 1994, p. 190; Hambrick and Abrahamson 1995, p. 1439; Hambrick and Finkelstein 1987, pp. 371–402; Hambrick et al. 1993, p. 409; He et al. 2009; March and Simon 1958; Marin and Verdier 2006; Perrone et al. 2003, pp. 422–423; Spremann 1987, p. 18; Vargas Sánchez 2005, p. 19; Xu et al. 2005).

As estimates of industry technology intensity based on empirical data from mainland China are not available, the OECD’s international estimates are used as proxies on the grounds of their broad coverage of 18 countries. Using official correspondence tables, the present study translates the Standard Industrial Classification (SIC) codes recorded for each of the 467 firms in the study’s database from the ORIANA dataset (see Sect.​ 5.​5) into the International Standard Industrial Classification (ISIC) codes used by the OECD. In this way, the OECD’s data on R&D intensities at the industry branch level is linked to the 467 firms in this study’s sample.

Indirect R&D intensity is calculated on the basis of the OECD input–output matrices (Loschky 2008, p. 3).

Indirect R&D intensity ranges from 0.50 % in ‘Chemicals excluding pharmaceuticals’ to 1.85 % in ‘Medical, precision and optical instruments’ (Loschky 2008, p. 7). Normalising direct and indirect R&D intensities to z-scores makes their scales comparable in terms of the relative degree of industry technology intensity.

In particular, as the conceptual domain of the two indicators differs in that direct R&D intensity relates to the production of technology and indirect R&D intensity relates to the use of technology (Hatzichronoglou 1997, p. 5), the indicators are not interchangeable and cannot be dropped individually without altering the meaning of the construct. Consequently, a formative measurement model would be more appropriate than a reflective one. The view that direct and indirect R&D intensity are formative indicators, i.e. separate causes of industry technology intensity, is also substantiated by the fact that the pairwise correlation coefficient between the indicators is as low as 0.53 in the present study’s sample of all 467 firms. This demonstrates that industry branches which devote a large proportion of their turnover to R&D (i.e. direct R&D intensity) do not necessarily make use of the most advanced capital goods (i.e. equipment) and intermediate inputs.

Across all firms in the study’s representative sample, the average plant employs approximately 800 employees (see Sect.​ 3.​1), which is more than the average plant across firms with only one plant (approximately 650 employees; see above). The total number of employees in mainland China in the sample has an approximate arithmetic mean of 1,100 and a geometric mean of 800 for Chinese firms, and an approximate arithmetic mean of 1,400 and a geometric mean of 1,000 for multinationals (see Sect.​ 7.​5.​2).

The control effect of firm size on performance indeed turns out to be statistically more significant when firm size is measured with rather than without diminishing returns to the number of employees.

This is possible due to the representativeness of the sample (see Sect.​ 5.​5.​4; Fogiel 2000, pp. 158–160; Garson 2002, pp. 139–196; Gliner and Morgan 2000, p. 148; Wooldridge 2002, pp. 298–299).

The reader can find a more complete description of the modelling methodology in Sect.​ 5.​1.​1, which demonstrates that PLS is the most appropriate modelling methodology for the present study.

In PLS, the measurement model consists of equations that compute values for the constructs themselves (i.e. scores for the constructs/latent variables) based on the variables that can be measured directly (i.e. the indicators/manifest variables). The structural model contains a set of regression-like equations to represent the causal relationships between the constructs, such as between discretion and performance (see Sect. 4.3.1).

The reasoning in Sect.​ 5.​1.​1 follows the literature on factors determining the suitability of the two alternative types of structural equation models in order to achieve statistical conclusion validity (e.g. Bliemel et al. 2005, p. 11; Chin and Newsted 1999, pp. 314, 337; Falk and Miller 1992, p. 5; Fassott 2005, p. 26).

Chin and Newsted (1999, p. 315) view the estimation of the means and location parameters as a third stage.

As described in Box 5.6 in Sect.​ 5.​3, reflective measurement models posit that the latent variable (e.g. performance) is an underlying factor that causes the variation in the reflective indicators (i.e. the performance indicators). Formative measurement models reverse causality, defining the latent variable (e.g. discretion) as a weighted average of its formative indicators. While in the reflective case the algorithm chooses loadings to minimise errors in the structural and measurement models, in the formative case weights are computed to minimise errors in the structural model irrespective of the explained variance in the measurement model.

When estimating a given instrument variable, it is assumed that the values of the neighbouring latent variables (both antecedents and consequences) are known—which is why the method is called partial least squares. Weighting schemes include (a) Wold’s centroid scheme, which uses the signs of the correlation coefficients, (b) Lohmöller’s factorial scheme, which uses the correlation coefficients themselves, and (c) the structural or path weighting scheme, which uses the regression coefficient for antecedents and correlation coefficients for weighting consequences. As the factorial scheme considers both the direction and strength of the correlations to neighbouring latent variables, the algorithm chooses latent variables emphasising high correlations with a few variables (squared deviations are minimised), whereas the centroid scheme emphasises correlations with many neighbouring variables (absolute deviations are minimised). Esposito Vinzi et al. (2010, p. 53) recommend the path weighting scheme, while acknowledging that the centroid scheme adapts well when the indicators in a block correlate strongly, and that the factorial scheme is often better suited when these correlations are weaker. As explained in Sect.​ 5.​4.​3, the present study chooses the path weighting scheme and finds that its results are robust to alternative weighting schemes.

Starting from the manager’s utility maximisation problem, Box 4.1 has derived these three equations as a synthesis of managerial discretion theory, principal-agent theory, and stewardship theory in line with the study’s new general theoretical discretion model (see Figs. 4.4 and 4.6 in Sect. 4.1.2). Equation (4.12) models discretion (\( D \)) as a function of antecedents/influences on managers (\( A \)), i.e. \( D=a\cdot A+{\varepsilon_D} \). Equation (4.13) models performance (\( P \)) as a function of discretion (\( D \)) and antecedents/influences on managers (\( A \)), i.e. \( P=d\cdot D+c\cdot A+m\cdot \left( {D\cdot A} \right)+{\varepsilon_P} \). Finally, Equation (4.14) models the ‘Moderating Effect (g)’ when \( A=0 \), i.e. \( {{\left. g \right|}_{A=0 }}=\left. {{{{\partial P}} \left/ {{\partial D}} \right.}} \right|{}_{A=0}^{II }-\left. {{{{\partial P}} \left/ {{\partial D}} \right.}} \right|{}_{A=0}^I=\left( {{d^{II }}-{d^I}} \right)+\left( {{m^{II }}\cdot {A^{II }}-{m^I}\cdot {A^I}} \right)={d^{II }}-{d^I} \).

As the notation used for scalars, vectors, and matrices varies in the literature (e.g. Gentle 2007, pp. 479–491; Harville 2008, pp. 1–10; Knapp 2007, pp. xxi–xxiv), the present study chooses among the available notation in a way to distinguish scalars, vectors, and matrices unequivocally while maintaining the distinction between lower-case letters for parameters (i.e. effects) and upper-case letters for variables (i.e. constructs). Hereby, letters in italics represent scalars (e.g. \( P \)), letters in normal face represent vectors (e.g. \( \mathrm{ D} \)), and letters in bold face represent matrices (e.g. \( \mathbf{a} \)). The transposition of a vector or matrix is denoted by a prime (e.g. \( \mathbf{m}^{\prime} \)).

The final arrow in Fig. 4.7, i.e. ‘Mediating Effect (d ⋅ a)’, is modelled implicitly by Equations (4.15) and (4.16), and can be calculated based on the individual parameters contained in the vector \( \mathrm{ d} \) and the matrix \( \mathbf{a} \). The disturbance or error terms can be viewed as additional adjustment terms to make the left-hand sides of the equations equal to the right-hand sides (Gentle 2007, p. 490). With the PLS algorithm (see Box 4.3 in Sect. 4.3), the expected value of the error terms is zero (Betzin and Henseler 2005, p. 53). In particular, \( {\varepsilon_P} \) is the error term when modelling performance (\( P \)) as a function of the dimensions of discretion (\( \mathrm{ D} \)) and antecedents (\( \mathrm{ A} \)), as specified in Equation (4.16). Likewise, \( {\upvarepsilon_{\mathrm{ D}}} \) is the column vector of the error terms \( {\varepsilon_{{{D_1}}}} \), \( {\varepsilon_{{{D_2}}}} \), \( {\varepsilon_{{{D_3}}}} \), and \( {\varepsilon_{{{D_4}}}} \), which are the respective error terms for the four dimensions of discretion \( {D_1} \), \( {D_2} \), \( {D_3} \), and \( {D_4} \)

As explained in Sects.​ 7.​5, 7.​5.​2, and 7.​6, this study recognises the limitations implied by modelling linear rather than non-linear effects. In particular, the linear effects model tendencies that quantify whether discretion tends to improve, not alter or reduce performance over specific domains of discretion rather than quantify which degrees of discretion maximise performance. Within the sample’s domains of discretion, extending discretion is thus modelled as having the same impact on performance regardless of its level.

In order to prevent the product term from including any direct effects of \( \mathrm{ D} \) and \( \mathrm{ A} \), all the components of the product term, i.e. \( \mathrm{ D} \) and \( \mathrm{ A} \), must be included in the structural model in direct form (Carte and Russell 2003, pp. 480–495; Cohen 1978; Cronbach 1987; Henseler and Fassott 2010, pp. 718–719; Irwin and McClelland 2001, p. 105). This requirement is met by including the direct effects \( \mathrm{ d}\cdot \mathrm{ D} \) and the control effects \( \mathrm{ c}\cdot \mathrm{ A} \) in Equation (4.16).

For the ‘average’ firm, i.e. when all variables are at their average levels, the mediating effect of a given antecedent (e.g. \( {A_2} \)) via discretion (e.g. \( {D_1} \)) on performance (\( P \)) is equal to the product of the direct effect of the antecedent on discretion (\( {a_{1,2 }} \)) and the direct effect of discretion on performance (\( {d_1} \))—i.e. here \( {d_1}\cdot {a_{1,2 }} \). Furthermore, modelling control effects (\( \mathrm{ c} \)) of the independent variables (\( \mathrm{ A} \)) on the dependent variable (\( P \)) allows the model to determine whether any particular mediation is partial or complete in nature. While the analysis of mediating effects lies outside the scope of the research objective, Equation (6.1) in Sect.​ 6.​1 empirically establishes a partial mediating effect of firm size via capital investment discretion on performance.

It should be noted that Equation (4.17) fundamentally differs from Equations (4.15) and (4.16) in that there are only parameters and no dependent or independent variables (there are thus no error terms). Hence, instead of entering into the partial least squares algorithm (see Sect. 4.3) as a specified structural equation, Equation (4.17) is evaluated based on the algorithm’s output, simply as the difference between parameters estimates.

It should be noted that the structural model in Equations (4.15)–(4.17) is a completely general specification of the theoretical discretion model in the sense that it can contain any number of antecedents and dimensions of discretion, not only the two antecedents (\( {A_1} \), \( {A_2} \)) and four types of discretion (\( {D_1} \), \( {D_2} \), \( {D_3} \), \( {D_4} \)) specified in this study. It is not until the second step that the structural model is specified with respect to these constructs.

E.g. Equation (4.19) states that the level of capital investment discretion granted to a plant manager (\( {D_1} \)) depends on industry technology intensity (\( {A_1} \)) as well as firm size (\( {A_2} \)). As all constructs are normalised to means of zero and variances of unity (see Sect. 4.2), the structural path coefficient \( {a_{1,1 }} \) in Equation (4.19) measures the direct effect of \( {A_1} \) on \( {D_1} \) in terms of the number of standard deviations by which capital investment discretion is predicted to adjust when industry technology intensity is increased by one standard deviation. Analogous interpretations can be made for each antecedent and dimension of discretion. The subscripts specify which parameters belong to which constructs (e.g. \( {a_{1,2 }} \) belongs to \( {D_1} \) and \( {A_2} \), whereas \( {a_{2,1 }} \) belongs to \( {D_2} \) and \( {A_1} \)). Being specified at the level of the measured constructs, Equations (4.19)–(4.22) fully define the empirical discretion model’s structural model for the impact of the antecedents on discretion.

The matrix \( \mathbf{m}^{\prime} \), which is the matrix of the moderating effects \( \mathbf{m} \) transposed to a two-by-four matrix, is multiplied with the column vector \( \mathrm{ D} \), which can be treated as a four-by-one matrix. The resulting two-by-one matrix is transposed to a one-by-two matrix and multiplied by the column vector \( \mathrm{ A} \), which can be treated as a two-by-one matrix. The resulting one-by-one matrix can be treated as a scalar (e.g. Gentle 2007, p. 7).

As above, the subscripts on the structural path coefficients denote the constructs to which the parameters pertain. For instance, the structural path coefficient \( {d_4} \) measures the direct effect of sales & marketing discretion (\( {D_4} \)) on performance (\( P \)), and \( {c_2} \) measures the control effect of firm size (\( {A_2} \)) on performance. The parameter \( {m_{4,2 }} \) measures the moderating effect of firm size (\( {A_2} \)) on the impact of sales & marketing discretion (\( {D_4} \)) on performance (\( P \)). This can easily be seen by rearranging Equation (4.23) to \( P=\ldots +{d_4}{D_4}+ \) \( \ldots +{m_{4,2 }}\cdot \left( {{D_4}\cdot {A_2}} \right)+\ldots =\ldots +\left( {{d_4}+{m_{4,2 }}\cdot {A_2}} \right){D_4}+\ldots \). The impact of \( {D_4} \) on \( P \) for every increase in \( {D_4} \) by one standard deviation is given by \( \left( {{d_4}+{m_{4,2 }}\cdot {A_2}} \right) \), i.e. is moderated by \( {A_2} \) (firm size) with the parameter \( {m_{4,2 }} \).

The raw data on the indicators of capital investment discretion (\( {D_1} \)) and firm size (\( {A_2} \)) are measured in monetary amounts and in numbers of employees, respectively, i.e. their variances are initially interpretable. Yet after the logarithmic transformations described in Sect. 4.2, their variances become non-interpretable.

The first stage of the two-stage approach estimates the latent variable scores of all constructs in the model without the interaction terms. The second stage takes these latent variable scores as the single indicators of the constructs and adds the interaction terms as the product of the interacting variables’ latent variable scores. In this way, the constructs are not re-estimated in the presence of the product term, which ensures that the interaction term represents the exact interaction of the interacting variables.

For example, the scalar \( {g_2} \) measures the difference in the direct effect of hiring discretion on performance (\( {d_2} \)) that prevails in Chinese firms (\( d_2^{Chinese } \)) versus multinationals (\( d_2^{Multi. } \)). This represents the moderating effect of firm type on the direct effect of hiring discretion (\( {D_2} \)) on performance (\( P \)).

In the way explained in Sect. 4.2 for Fig. 4.8, the labelling in Fig. 4.12 (i.e. empirical discretion model) has been simplified compared to the labelling in Fig. 4.7 (i.e. theoretical discretion model) in Sect. 4.1.3.

Comparative statics (or comparative-static analyses) compare the different values in a dependent variable (e.g. performance) that result from changes in an independent variable (e.g. discretion) or a parameter while holding all other variables and parameters constant (e.g. Dowling 2000, p. 284; Hirschey 2009, p. 99). In line with the literature (e.g. Dowling 2000, pp. 284–291), these comparative statics are derived from the system of multiple structural equations in Box 4.6 (i.e. the structural model) as partial derivatives. This makes it possible to investigate the impact of any given dimension of discretion on performance while holding all other dimensions of discretion and antecedents constant (i.e. ceteris paribus).

Firm size (\( {A_2} \)) measures by how many standard deviations a firm exceeds (geometric) average size in terms of its number of employees in mainland China (see Box 7.4 in Sect.​ 7.​5.​2 for a conversion formula). In the study’s representative sample of 467 firms, the average-sized Chinese firm (defined by \( A_2^{Chinese }=0 \)) has approximately 800 employees in mainland China and the average-sized multinational (defined by \( A_2^{Multi. }=0 \)) has approximately 1,000 employees in mainland China. As \( {A_2} \) logarithmically transforms the number of employees (see Sect. 4.2.4), these average numbers of employees are geometric means. The arithmetic means are higher: approximately 1,100 employees for Chinese firms and 1,400 employees for multinationals, because before the logarithmic transformation the firm size distribution exhibits stronger positive skewness. Given that all latent variables (including all antecedents) are normalised to means of zero and variances of unity in SmartPLS (Ringle et al. 2005), antecedents are equal to zero when they reach their average levels. Moreover, this normalisation of all constructs standardises the model’s parameters (i.e. structural path coefficients). They thus reveal the relative impact of the predictors, i.e. the number of standard deviations by which a dependent variable is predicted to change when an independent variable is increased by one standard deviation (Aiken and West 1991, pp. 35–129; Finney et al. 1984; Henseler and Fassott 2010, pp. 727–729).

If variables are centred to means of zero, then when the moderator variable reaches its mean value (i.e. zero), the total impact of the independent on the dependent variable measures the direct effect of the independent on the dependent variable (Aiken and West 1991, p. 37; Finney et al. 1984; Henseler and Fassott 2010, p. 728).

Differentiating Equation (4.40) (i.e. the total impact of new product introduction discretion on performance) with respect to firm size (A ₂) yields the parameter of the moderating effect (m _3,2). It thus measures by how much discretion’s performance impact changes when firm size is adjusted upwards by one standard deviation.

Figure 4.12 visualises the ‘Direct Effect (a)’ of firm size on the level of discretion (e.g. Caza 2007, pp. 30–56; Hambrick and Finkelstein 1987, pp. 378–389; Walters 1995; Zhang et al. 2006a) and the ‘Control Effect (c)’ of firm size on the level of performance (e.g. Baum 1996; Berman et al. 2005, p. B5; Chang and Wong 2003, p. 21; Datta et al. 2003, p. 101; Gammelgaard et al. 2010, p. 9; Haleblian and Finkelstein 1993, p. 853; Khanchel 2009, p. 100; Misangyi 2002, p. 62; Singh and Lumsden 1990; Xu et al. 2005, p. 9; see Sect. 4.1.2).

As explained in Sect. 4.1.2, three-way interaction stems from synthesising the moderating effects derived from principal-agent theory and stewardship theory in Chap.​ 2 into the present study’s new discretion model.

Whereas testing Hypothesis 2 for the average-sized firm (A ₂ = 0) in Sect.​ 6.​2.​2 can focus on testing whether or not g ₃ in Equation (4.43) is zero, generalising Hypothesis 2 to the non-average-sized firm (A ₂ ≠ 0) in Sect.​ 6.​2.​3 requires this study to further investigate whether or not (m _3,2 ^Chinese  − m _3,2 ^Multi.) in Equation (4.44) is zero.

The ‘Mediating Effect (d ⋅ a)’ is thus the product of the ‘Direct Effect (a)’ of firm size on discretion and in turn the ‘Direct Effect (d)’ of discretion on performance, as visualised in the new discretion model (see Fig. 4.12).

These mediating effects are tested in Sect.​ 6.​1 by following the recommendations in the literature, e.g. Chin et al. (2003, pp. 195–211), Cohen (1988, pp. 410–413), Eggert et al. (2005, pp. 105–106), Götz and Liehr-Gobbers (2004, pp. 730–731), Herrmann et al. (2006, pp. 57–61), Iacobucci and Duhachek (2003), Krafft et al. (2005, pp. 83–85), Shrout and Bolger (2002, pp. 430–432), Sobel (1982), and Venkatraman (1989, pp. 429–430).

This is possible due to the representativeness of the sample (see Sect.​ 5.​5.​4; Fogiel 2000, pp. 158–160; Garson 2002, pp. 139–196; Gliner and Morgan 2000, p. 148; Wooldridge 2002, pp. 298–299).

This section builds on the foundations of hypothesis testing in the literature of statistics and econometrics (e.g. Fogiel 2000, pp. 158–190; Greene 2003, pp. 892–896; Gujarati 2004, pp. 119–139; Hayashi 2000, pp. 33–45; Salvatore and Reagle 2002, pp. 87–95; Spanos 1986, pp. 213–311; Wooldridge 2002, pp. 116–154).

The predictor specification states that the conditional expectations of the dependent variables in measurement models (i.e. their systematic parts) are linear functions of their independent variables: \( \mathrm{ E}({x_{ij }}|{\xi_i})={\lambda_{0j }}+{\lambda_{ij }}{\xi_i} \) for reflective and \( \mathrm{ E}({\xi_i}|{x_{ij }})=\sum {{\omega_{ij }}{x_{ij }}} \) for formative measurement models. Error terms thus have zero means and are uncorrelated with the variables on their block (Esposito Vinzi et al. 2010, pp. 50–51).

The following discussion on bootstrapping is based on the discussion of bootstrapping in the literature (e.g. Chin 1998, pp. 318–320; Efron and Gong 1983, pp. 40–46; Efron and Tibshirani 1993, pp. 145–147; Esposito Vinzi et al. 2010, pp. 59–60; Krafft et al. 2005, p. 83; Tenenhaus et al. 2005, p. 176; Thas 2010, pp. 335–337).

The superscript ^Chinese is omitted on the parameters in this example in order to stress that the two-tailed t-test with bootstrapping equally applies to Chinese firms (d ₁ ^Chinese ) and multinationals (d ₁ ^Multi.).

For the sake of simplicity, the two alternative hypotheses in Sect.​ 6.​2.​4 for Hypothesis 4 (i.e. H ₄ ¹:d ₁ < 0 and H ₄ ²:d ₁ > 0 for capital investment discretion’s direct effect d ₁) are combined herein into H ₄ ^1′:d ₁ ≠ 0.

For these two-tailed tests, the p-values estimate the probability that, given that the null hypothesis is true (i.e. the population parameter is zero), a sample drawn from the population will contain a sample parameter value that is at least as far from zero (i.e. from the null hypothesis value of the parameter) as the estimated sample parameter value. The p-value is also known as the exact or observed level of significance, since it is the lowest level of significance at which the null hypothesis can be rejected. It therefore also measures the probability of committing a Type I error, which is the probability of rejecting H ₀ when H ₀ is true. In line with the recommendations in the literature (e.g. Gujarati 2004, pp. 136–138), this study mostly reports the p-values for the hypothesis tests rather than comparing whether the t-statistics exceed a critical value from a predetermined level of significance, such as 1 % or 5 %, in order to report the exact level of statistical significance. The p-values are calculated for the estimated t-statistic from bootstrapping using a Student’s t-distribution with two tails and degrees of freedom depending on the number of bootstrap pseudo samples.

While the p-values reported in the present study correspond to two-tailed tests (e.g. H ₄ ⁰:d ₁ = 0 versus H ₄ ^1′:d ₁ ≠ 0), due to the symmetry of the t-distribution the reader can compute the p-values on one-tailed tests (e.g. H ₄ ⁰:d ₁ = 0 versus H ₄ ¹:d ₁ < 0 only) as half of the p-values reported here for the two-tailed tests.

The product term approach for testing moderating effects (see Sect. 4.3.1; e.g. Carte and Russell 2003, pp. 480–495; Chin et al. 2003, pp. 196–200; Irwin and McClelland 2001, p. 105), which is used for the metric antecedent of firm size (A ₂) in this study, can in principle also be applied to dichotomous categorical variables, such as firm type, by using a dummy moderator (Henseler and Fassott 2010, p. 721; Qureshi and Compeau 2009, p. 199). Nevertheless, as explained in Sect. 4.3.1, the multi-group comparison approach is chosen instead due to its suitability for three-way interactions (Henseler and Fassott 2010, p. 722).