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Validity and Reliability of Empirical Discretion Model

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Managerial Discretion and Performance in China

Part of the book series: Contributions to Management Science ((MANAGEMENT SC.))

Abstract

The present chapter holistically assesses the validity and reliability of the study’s calibrated empirical discretion model by applying a new assessment system, i.e. a cascading hierarchy of five evaluation criteria and numerous assessment tests and thresholds defined on the basis of a broad synthesis of state-of-the-art methodological literature. The new assessment system is harnessed to conduct a comprehensive evaluation, which finds that the empirical discretion model indeed fulfils every assessment test of statistical conclusion validity, reliability, construct validity, internal validity, and external validity, even when faced with particularly conservative thresholds from the literature. Thus, the empirical discretion model is empirically-validated and its results can be used with confidence to test the study's four hypotheses and thereby work towards resolving the discretion puzzle. Moreover, this chapter serves as a tutorial for scholars on applying the new assessment system to assessing their own partial least squares (PLS) models holistically in future research.

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Notes

  1. 1.

    See Sect. 5.1 on statistical conclusion validity (e.g. Albers and Hildebrandt 2006, pp. 2–33; Arteaga et al. 2010, p. 164; Backhaus et al. 2006, p. 97; Barroso et al. 2010, p. 437; Baumgartner and Homburg 1996; Bentler and Chou 1987; Bentler and Weeks 1980; Betzin and Henseler 2005, p. 50; Bliemel et al. 2005, pp. 10–11; Bollen 1989, pp. 1–9; Bollen and Davis 1994; Boßow-Thies and Albers 2010, pp. 595–596; Carte and Russell 2003, pp. 480–495; Chin 1995, pp. 315–319, 1998, pp. 318–320, 2000, pp. 1–2, 2001, 2002, p. 94, 2010, p. 670; Chin and Newsted 1999, pp. 309–314; Chow 1960, pp. 595–604; Cohen 1988, pp. 410–413; Coheris Spad 2007; Cortina et al. 2001, pp. 334–359; Diamantopoulos and Schlegelmilch 2006, p. 217; Diamantopoulos and Siguaw 2006, p. 271; Duarte and Raposo 2010, p. 463; Efron and Gong 1983, pp. 40–46; Efron and Tibshirani 1993, pp. 145–147; Eggert et al. 2005, pp. 102–108; Esposito Vinzi et al. 2010, pp. 48–66; Falk and Miller 1992, p. 5; Fassott 2005, pp. 24–29; Fassott and Eggert 2005, pp. 26–32; Finkelstein and Boyd 1998, p. 186; Fornell 1987; Fornell and Bookstein 1982a, pp. 289–302, 1982b, pp. 440–451; Fornell and Larcker 1981, pp. 45–46; Fu 2006; Gallese and Prugent 2007; Garson 2002, p. 144; Götz and Liehr-Gobbers 2004, pp. 727–731; Henseler and Fassott 2010, p. 721; Herrmann et al. 2006, p. 61; Homburg and Baumgartner 1995b; Homburg and Dobratz 1998, p. 450; Hsieh et al. 2008, p. 108; Irwin and McClelland 2001, p. 105; James et al. 1982, pp. 110–112; Jöreskog 1970, 1981; Jöreskog and Sörbom 1982, 1988; Kaplan 2000, pp. 1–12; Krafft et al. 2005, pp. 73–83; Krzanowski 2003, p. xv; Yuan Li 2005; Lohmöller 1987, 1988, p. 126, 1989; MacCallum and Browne 1993, pp. 533–540; Ping 2005, p. 2; Qureshi and Compeau 2009, p. 199; Ringle 2009; Ringle et al. 2005, 2010, p. 205; Rodgers and Pavlou 2003, p. 25; Sánchez 2009, p. 3; Satorra and Bentler 2001; Schepers et al. 2005, p. 504; Scholderer and Balderjahn 2005, pp. 88–94; Temme and Kreis 2005, p. 195; Temme et al. 2006, pp. 1–2; Tenenhaus et al. 2004, pp. 739–742; Tenenhaus et al. 2005, pp. 173–190; van Oppen et al. 2005, p. 19; Wold 1966, 1973, 1975, p. 351, 1980, pp. 70–71, 1982, 1985, 1989), see Sect. 5.2 on reliability (e.g. Albers 2010, p. 411; Albright and Malloy 2000, p. 349; Babbie 1990, p. 187; Bagozzi 1980; Bagozzi and Yi 1988, p. 82; Beyth-Marom 1982; Blalock 1964; Bloom and Van Reenen 2007, pp. 1365–1366; Bollen and Lennox 1991; Carmines and Zeller 1979, pp. 29–62; 1998, p. 320; Churchill 1987; Coltman et al. 2008; Crocker and Algina 1986; Cronbach 1951, p. 297; Diamantopoulos 1999, pp. 447–453; Diamantopoulos and Siguaw 2006, pp. 270–271; Dillman 1978, p. 56; Esposito Vinzi et al. 2010, pp. 50–51; Fornell and Larcker 1981, p. 45; Garson 2002, p. 199; Gliner and Morgan 2000, pp. 312–316; Groves 1990, pp. 226–233; Herrmann et al. 2006, p. 30; Holbrook et al. 2003, pp. 81–86, 109–110; Krafft 1999, p. 124; Krafft et al. 2005, pp. 73–75; Krafft et al. 2003, p. 102; Lavrakas 2008, p. 250; Lichtenstein and Newman 1967; Manski 2004, p. 10; March and Simon 1958, pp. 140–141; Novick and Lewis 1967, pp. 1–13; Nunnally 1978, p. 245; Ping 2005, p. 2; Rossiter 2002, pp. 307–315; Sánchez 2009, p. 3; Scholderer and Balderjahn 2005, pp. 88–89; Schwester 2007, pp. 270–272; Spearman 1904; Tenenhaus et al. 2005, p. 164; Wallsten et al. 1986; Werts et al. 1974), see Sect. 5.3 on construct validity (e.g. Ahuja and Thatcher 2005, p. 446; Albers 2010, p. 411; Albright and Malloy 2000, p. 349; Arnold 1982; Arteaga et al. 2010, p. 164; Bagozzi and Yi 1988, p. 82; Balderjahn 1986, p. 236; Barroso et al. 2010, p. 437; Baumgartner and Homburg 1996; Bido 2007; Blalock 1964; Bohrnstedt 1970, p. 92; Bollen and Lennox 1991, p. 308; Boßow-Thies and Albers 2010, p. 596; Bromley 2002, p. 35; Campbell and Fiske 1959, p. 81; Carmines and Zeller 1979, p. 53; Carte and Russell 2003, pp. 493–494; Caza 2007, p. 40; Chin 1998, p. 318, 2000, pp. 1–2, 2010, p. 670; Chin et al. 2003, p. 194; Churchill 1979, 1987; Coltman et al. 2008; Cronbach and Meehl 1955; Diamantopoulos 1999, pp. 447–453; Diamantopoulos and Siguaw 2006, p. 271; Diamantopoulos and Winklhofer 2001, p. 272; Donsbach and Traugott 2008, p. 364; Duarte and Raposo 2010, p. 463; Eggert and Fassott 2003, pp. 5–9; Esposito Vinzi et al. 2010, pp. 50–51; Esposito Vinzi et al. 2003, p. 5; Fassott and Eggert 2005, p. 32; Fornell and Cha 1994, pp. 71–73; Fornell and Larcker 1981, pp. 45–46; Fornell et al. 1990, p. 1252; Fritz 1995, p. 136; Garson 2002, pp. 195–196; Geisser 1975, pp. 320–328; Gliner and Morgan 2000, pp. 321–322; Götz and Liehr-Gobbers 2004, p. 727; Hahn 2002, p. 104; Helm 2005, pp. 249–252; Henseler and Fassott 2010, pp. 719–721; Herrmann et al. 2006, pp. 24–30; Hinkel 2001, p. 291; Homburg and Baumgartner 1995b, p. 1093; Homburg and Dobratz 1998, p. 450; Homburg and Giering 1996, p. 12; Hsieh et al. 2008, p. 109; Hu and Olshfski 2007, p. 207; Hulland 1999, pp. 198–199; Jarvis et al. 2003, p. 202; Jöreskog and Wold 1982, p. 270; Keil et al. 2000, pp. 312–315; Krafft 1999, p. 124; Krafft et al. 2005, pp. 73–75; Krafft et al. 2003, p. 102; Lohmöller 1989, p. 36; Mosier 1947; Nunnally 1978, p. 111; Ping 2005, p. 1; Qureshi and Compeau 2009, pp. 197–199; Reinartz et al. 2004, p. 298; Rigdon et al. 1998, p. 1; Ringle et al. 2005; Rodgers and Pavlou 2003, p. 25; Rossiter 2002, p. 315; Ruiz et al. 2010, pp. 546–548; Sambamurthy and Chin 1994, pp. 231–232; Sánchez 2009, p. 3; Schepers et al. 2005, p. 504; Seltin and Keeves 1994, p. 4356; Stone 1974; Tenenhaus et al. 2005, pp. 163–174; van Oppen et al. 2005, p. 19; Venkatesh and Morris 2000, p. 126; Venkatraman 1989, p. 426; Wold 1982, p. 10; Zhu et al. 2006, pp. 529–530), see Sect. 5.4 on internal validity (e.g. Abraham et al. 2007, pp. 10–21; Albors et al. 2008; Ang and Straub 1998, p. 544; Ang 2008; Arafat et al. 1999, p. 90; Arnold 1982; Bachman and Schutt 2010, p. 170; Backhaus et al. 2006; Baum 1996; Bloom and Van Reenen 2007, pp. 1375–1381; Bound et al. 1984; Campbell and Fiske 1959, p. 81; Caza 2007, p. 46; Corcoran 2001, p. 154; Davis 1985, pp. 63–64; Diamantopoulos and Siguaw 2006, p. 270; Diamantopoulos and Winklhofer 2001, p. 272; Dibbern and Chin 2005, p. 144; Donsbach and Traugott 2008, p. 364; Eckey et al. 2004, p. 92; Efron and Gong 1983, pp. 37–38; Esposito Vinzi et al. 2010, p. 56; Evans 1987, p. 659; Finkelstein and Boyd 1998, p. 187; Finkelstein and Hambrick 1990, p. 500; Fornell and Bookstein 1982a; Fornell and Cha 1994, pp. 71–73; Galavan, 2005, p. 174; Geisser 1975, pp. 320–328; Götz and Liehr-Gobbers 2004, pp. 727–731; Granger 1969; Grant and Rice 2007, p. 367; Greene 2003, pp. 57–58; Griliches and Mairesse 1990; Gujarati 2004, pp. 342–363; Hair et al. 1998, p. 208; Hannan and Freeman 1977; Hanssens et al. 2003, p. 298; Hatzichronoglou 1997, pp. 12–13; Hausman et al. 1984; Hellevik 1988, p. 38; Helm 2005, pp. 248–249; Henseler and Fassott 2010, pp. 719–721; Herrmann et al. 2006, pp. 55–61; Hu and Olshfski 2007, p. 207; Jaccard and Turrisi 2003, pp. 1–2; Jackman 1975, p. 182; Keuzenkamp 2000, p. 261; Kleinbaum et al. 1998, p. 214; Krafft et al. 2005, pp. 72–80; Kutner et al. 2004; Loschky 2008, pp. 3–7; Motulsky 2003, p. 106; OECD 2005, pp. 167–172; Oliinik 2008, p. 19; Onkelinx and Sleuwaegen 2010; Poncet et al. 2008, pp. 10–12; Rigdon et al. 1998, p. 1; Ringle et al. 2005; Rosenbaum 1989, p. 341; Sánchez 2008, p. 5; Sarkar et al. 2006; Shaughnessy et al. 2005, p. 367; Simon 1954, pp. 471–478; Singh and Lumsden 1990; Stone 1974; Taube, 2005, pp. 4–13; Taube and Ögütçü 2002, pp. 18–23; Temme et al. 2006, p. 18; Tenenhaus et al. 2005, pp. 174–177; Venkatraman 1989, p. 426; Wagner 2002, pp. 287–292; Wald et al. 1988, p. 72; Wooldridge 2002, p. 95), and see Sect. 5.5 on external validity (e.g. Abraham et al. 2007; Bureau van Dijk 2005, p. 2, 2006/2007, p. 2; Fogiel 2000, pp. 158–160; Garson 2002, pp. 139–196; Gliner and Morgan 2000, p. 148; Groves 1990, p. 233; Groves et al. 2009, pp. 54–56; Groves and Lyberg 2001, p. 195; Guojia tongji ju [National Bureau of Statistics] 2003, 2007, 14–1, 14–2, 14–18; McCarty 2003, p. 397; ISIC Rev.3.1; National Bureau of Statistics 2002; Northrop and Arsenault 2007, pp. 235–236; Oliinik 2008; Poncet et al. 2008, p. 8; Ringle et al. 2005; Schofield 2006, pp. 28–29; Schwester 2007, pp. 272–273; Stuart 1984; Temme et al. 2006, pp. 7–8; The American Association for Public Opinion Research 2008, pp. 34–35; United Nations 2007, p. 63; Whyte 2000, p. 62; Wooldridge 2002, pp. 298–299).

  2. 2.

    Note that Campbell (1957) developed the concepts of validity without reference to Cronbach’s (1982) utos system, which was published some 25 years later. Nevertheless, the letters for units, treatments, observations and settings (utos) are used in this section so as to place Campbell’s definitions into a consistent framework.

  3. 3.

    Interestingly, what Campbell defines as external validity (generalising to UTOS) is labelled internal validity by Cronbach (1982). Cronbach (1982) has his own concept of external validity, which concerns whether the study’s findings generalise further to *UTOS, i.e. ‘to domains that have attributes different from those that were sampled’ (Albright and Malloy 2000, p. 344). Cronbach (1982, p. 137) views Campbell’s internal validity as trivial, arguing that because all four elements (utos) simultaneously influence the results of a study, the statements about the causal effect of t alone can only make specific ‘past-tense’ statements about what happened in a particular study context, if generalisation to other contexts is not secured by the study design.

  4. 4.

    Structural equation models (SEM; e.g. Bollen 1989, pp. 1–9; Kaplan 2000, pp. 1–12) are models of complex causal relationships between two or more constructs that cannot be measured directly. These SEM can be estimated using either variance-based (i.e. PLS) or covariance-based methodologies (see below).

  5. 5.

    Putting aside the disadvantage that single-item regression assumes error-free measurement, dealing with multiple indicators in multiple regressions still conceals some measurement error by aggregating indicators outside of the theoretical context (Lohmöller 1989; Wold 1982, 1985, 1989). If instead all indicators are entered into the regression model as separate independent variables, multicollinearity problems may arise. By contrast, building on the idea that ‘one model’s collinearity is another model’s reliability’ (Diamantopoulos and Siguaw 2006, p. 271), for reflective indicators PLS even transforms the threat of multicollinearity into a strength—by measuring constructs as latent variables with higher reliability.

  6. 6.

    In different study contexts, multiple regressions may be preferred to structural equation models, e.g. if there are no relations between constructs, all indicators are formative, exhibit multicollinearity and are thus combined to summated scales (Albers and Hildebrandt 2006, pp. 2–33).

  7. 7.

    Covariance-based SEM (e.g. LISREL) was substantially developed by Jöreskog and Sörbom (e.g. Jöreskog 1970, 1981; Jöreskog and Sörbom 1982, 1988) as well as Bentler (e.g. Bentler and Chou 1987; Bentler and Weeks 1980), whereas variance-based SEM (i.e. partial least squares) was developed as an alternative to covariance-based SEM by Wold (1966, 1973, 1975, 1982) and later by Lohmöller (1987, 1989).

  8. 8.

    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).

  9. 9.

    Scholderer and Balderjahn (2005, p. 94) explain that the restrictive distributional assumptions of the maximum likelihood estimators in covariance-based models can be somewhat relaxed by either estimating using ‘Weighted Least Squares’ (WLS, which however requires very large samples) or still using maximum likelihood estimation for the parameters but correcting the resulting statistics and standard errors with respect to skewness and excess (cf. Satorra and Bentler 2001).

  10. 10.

    The greatest number of predictors in any single regression equation of the empirical discretion model is the number of structural paths going into the performance construct (\( P \)), namely 10 (i.e. four direct effects, two control effects, and four moderating effects; see Equation (4.35) in Box 4.6 in Sect. 4.3.1). Consequently, the required sample size of ten times the largest number of predictors in the empirical discretion model is 100.

  11. 11.

    While the empirical discretion model separates middle management discretion into four single-indicator constructs (see Sect. 4.2.2), one may hypothetically take an alternative model specification as an example for explaining the potential ambiguity in parameter signs: If all four discretion indicators were combined to a single latent variable of ‘overall discretion’ as formative indicators, then ambiguous parameter signs could result. Suppose the indicator \( {x_{21 }} \) (capital investment discretion) had a positive effect on the latent variable \( {\xi_2} \) (overall discretion) whereas the other indicators had negative effects. If then \( {\xi_2} \) had a positive effect on the latent variable \( {\xi_3} \) (performance), then the coefficients between \( {x_{21 }} \) and \( {\xi_2} \) as well as \( {\xi_2} \) and \( {\xi_3} \) could be estimated as both being either positive or negative. In either case, \( {x_{21 }} \) (capital investment discretion) would have a positive effect on \( {\xi_3} \) (performance) and all other indicators a negative effect on performance, given that the product of the two signs would stay positive in both cases. The latent variable score of \( {\xi_2} \) in the former case (‘overall discretion’) would then simply be the negative of the latter case (‘lack of overall discretion’). (Neither of the constructs would, however, be valid, as discretion, i.e. latitude of action, cannot meaningfully be increasing in certain types of discretion and decreasing in other types of discretion.)

  12. 12.

    In the context of the present study, the benefits of the extra features for specifying moderating effects in SmartPLS outweigh the absence of the extra features of some of the other software packages. For example, although SmartPLS is the only software reviewed that does not include a jackknifing resampling procedure (i.e. only blindfolding and bootstrapping; Temme et al. 2006, pp. 8–10), this is not important given that bootstrapping is generally preferred to jackknifing due to a relatively lower standard error (Efron and Gong 1983, pp. 40–46; Efron and Tibshirani 1993, pp. 145–147; Krafft et al. 2005, p. 83; Temme et al. 2006, p. 11). Among the remaining software packages, SPAD-PLS offers the most extra features. While some of these have been demonstrated to be of limited use (Temme et al. 2006, p. 18), the treatment of missing data is most flexible in SPAD-PLS, which offers more advanced imputation methods, such as NIPALS and an EM algorithm (Temme et al. 2006, pp. 9–10). On the contrary, VisualPLS appears to be no better at dealing with missing data than SmartPLS, given that this recently developed software incorrectly transfers missing data codes to LVPLS and hence can lead to erroneous results (Temme et al. 2006, p. 17). In any case, as missing data is not a major issue in the present study (see Sect. 5.5), the use of these extra features is limited here. Finally, SmartPLS provides a finite mixture partial least squares (FIMIX-PLS) routine for detecting unobserved heterogeneity, which yet again is not required for the present study’s research objective.

  13. 13.

    Taking the number of search results when specifying a respective software’s name in the popular online search engine Google as a proxy for the popularity of the software solution, it is found that both PLS-Graph and SmartPLS are by far more prevalent (each with 30,000–35,000 hits) than either VisualPLS (approximately 5,000 hits) or SPAD-PLS (approximately 500 hits; Google, 2009).

  14. 14.

    Additional fit coefficients are assessed in other sections of this chapter, e.g. Dillon-Goldstein’s rho, Cronbach’s alpha, average variance extracted, Stone-Geisser’s \( {Q^2} \), and variance inflation factors.

  15. 15.

    Even higher thresholds, such as the aforementioned \( {R^2}\geq 0.4 \), clearly do not apply to the present study’s research objective, because as described by Homburg and Baumgartner (1995a, p. 172) such thresholds are reserved for studies that aim to explain the dependent latent variable (here performance\( P \)) to the greatest extent possible. By contrast, for studies that investigate the relationships between latent variables—such as the present study, which investigates the impact of middle management discretion on performance—they contend that any value of \( {R^2} \) would be acceptable (i.e. \( {R^2}\geq 0 \)). Hence, given the study’s research objective, the high threshold of \( {R^2}\geq 0.26 \) is stricter than that implied by Homburg and Baumgartner (1995a, p. 172).

  16. 16.

    This reasoning is related to the Chow (1960, pp. 595–604) test, which Henseler and Fassott (2010, pp. 730–732) have suggested as a tenable approximation for multi-group comparisons in PLS models. The Chow test is a parametric test for the null hypothesis that all the parameters in a regression equation are equal between two datasets, which here corresponds to testing at once for the equality of all the structural path coefficients in \(\begin{array}{lll} P=\left( {{d_1}{D_1}+{d_2}{D_2}+{d_3}{D_3}+{d_4}{D_4}} \right)+\left( {{c_1}{A_1}+{c_2}{A_2}} \right)+{\varepsilon_P} \hfill \cr + {m_{1,2 }}\cdot \left( {{D_1}\cdot {A_2}} \right)+{m_{2,2 }}\cdot \left( {{D_2}\cdot {A_2}} \right)+{m_{3,2 }}\cdot \left( {{D_3}\cdot {A_2}} \right)+{m_{4,2 }}\cdot \left( {{D_4}\cdot {A_2}} \right) \end{array} \) (Equation (4.35) in Box 4.6 in Sect. 4.3.1) between Chinese firms and multinationals. The Chow test statistic evaluates the additional explanatory power (i.e. the reduction in the sum of squared residuals) from splitting the model into the two groups rather than pooling them. The additional explanatory power from splitting the empirical discretion model into the two groups of firm types rather than ‘All Firms’ is indicated by the higher values of \( {R^2} \) when splitting the model (see Table 5.4). Details on the moderating effect of firm type are discussed in Sect. 6.2 (Hypothesis 2). As it is of interest to test whether the individual direct effects of discretion (i.e. \( {d_1} \), \( {d_2} \), \( {d_3} \), \( {d_4} \)) differ by firm type rather than the overall model, the dominant parametric test for multi-group comparisons in PLS, namely the pooled t-test proposed by Chin (2000, pp. 1–2), is chosen over the Chow test and other tests (see Sect. 4.3.3).

  17. 17.

    Even when a measurement procedure produces identical measurements every time it is applied to a given phenomenon (i.e. complete reliability, zero random measurement error), these identical measurements may consistently diverge from the true value by a systematic measurement error or bias (i.e. no construct validity).

  18. 18.

    For simplicity, this exposition assumes that there is no systematic measurement error or bias in the error (\( e \)). In particular, a set of assumptions that are sufficient for the full exposition of reliability in this Box are: zero expected error score, zero correlation between the error score and the true score on a given measurement, zero correlation between the error score on a given measurement and the true score on a second measurement, and zero correlation between errors on different measurements (Carmines and Zeller 1979, p. 30).

  19. 19.

    Alternative lower bounds to reliability have been discussed in the literature. For example, theta is a measure of reliability based on principal components analysis and omega is a similar measure based on common factor analysis (Carmines and Zeller 1979, pp. 60–62). As indicators do not have to represent parallel measurements since they can be weighted in an empirical model, these reliability measures weight non-parallel indicators and thereby provide lower bounds to reliability that are closer to the true value of the reliability than alpha. For example, theta is the alpha coefficient for which the indicators have been weighted according to their correlations with the other indicators so as to maximise the value of alpha (V. L. Greene and Carmines 1979). Nevertheless, scholars tend to use Cronbach’s alpha instead of the more accurate lower bounds of theta/omega.

  20. 20.

    Moreover, according to Esposito Vinzi et al. (2010, p. 50) and Tenenhaus et al. (2005, p. 164) a block of a measurement model is considered homogenous and unidimensional if Cronbach’s alpha and Dillon-Goldstein’s rho exceed 0.7.

  21. 21.

    For example, instead of asking the plant manager ‘How much hiring discretion do you have?’, which would give away that discretion was being evaluated, the interviewer would ask ‘To hire a full-time permanent shopfloor worker, what agreement would your plant need from corporate headquarters?’ The interviewer would then allocate the verbal answer to a category on the standardised scoring grid—for instance, awarding the score ‘3’ for an answer such as ‘Requires sign-off from CHQ [corporate headquarters] based on the business case. Typically agreed (i.e. about 80 or 90 % of the time).’ See Sect. 4.2 on the measurement model.

  22. 22.

    For example, due to the ‘double-blind’ nature of the interviews, an interviewer does not know a given plant manager’s performance and the plant manager does not know that his/her performance is being evaluated. Then, instead of asking ‘How strong is your performance in operations management?’ the interviewer poses open questions, such as ‘Can you describe the production process for me?’ or ‘How do you manage inventory levels?’ Depending on the plant manager’s answers to these questions, the specially-trained interviewer then assigns a score for a given management practice according to the exact verbal descriptions in the scoring grid. For example, the top score of 5 is awarded for the first indicator of operations management performance if the following verbal description in the scoring grid is met: ‘All major aspects of modern manufacturing have been introduced (Just-in-time, autonomation, flexible manpower, support systems, attitudes and behaviour) in a formal way.’ By contrast, the lowest score of 1 would be awarded for: ‘Other than JIT [just-in-time] delivery from suppliers few modern manufacturing techniques have been introduced, (or have been introduced in an ad-hoc manner).’ In this way, the interviewers assess the extent to which the managers’ practices along 18 relevant aspects of management reflect best practices as defined on a five-point scoring grid. Similarly, when assessing discretion, there is a defined scoring grid (see Fig. 4.10 in Sect. 4.2.2) and open questions with follow-up crosschecks are posed. For instance, if a plant manager replies that the largest capital investment that the plant can make without prior authorisation from corporate headquarters is zero, then the interviewer would follow up and probe by asking ‘what about buying a new computer—would that be possible?’

  23. 23.

    It shall be noted that the assessment of reliability between indicators applies only to constructs with multiple reflective indicators and not to constructs with multiple formative indicators. In formative measurement models, the indicators represent separate causes of the construct rather than separate measurements of the same true score as in reflective measurement models. Formative indicators therefore do not conform to the classical test theory and reliability estimates discussed above, which expect measurements to covary as they are expected to reflect the same true score (Albers 2010, p. 411; Blalock 1964; Bollen and Lennox 1991; Chin 1998, p. 306; Coltman et al. 2008; Diamantopoulos 1999, pp. 447–453; Diamantopoulos and Siguaw 2006, pp. 270–271; Esposito Vinzi et al. 2010, p. 51; Götz and Liehr-Gobbers 2004, p. 728; Herrmann et al. 2006, p. 30; Krafft 1999, p. 124; Krafft et al. 2005, p. 76; Krafft et al. 2003, p. 102; Rossiter 2002, pp. 307–315; Sánchez 2009, p. 3).

  24. 24.

    The PLS algorithm’s (see Sect. 4.3) loadings computed for the indicators of performance in the empirical discretion model (as used in Dillon-Goldstein’s rho) generally differ from equal loadings (as implicit in Cronbach’s alpha). The loadings here produce visibly higher reliability than equal loadings, since the PLS algorithm weights reflective indicators to maximise the product of the explained variance in the measurement model and the absolute or squared (depending on the weighting scheme) values of the correlations between latent variables in the structural model. The resulting loadings are presented in Table 5.7 in Sect. 5.3.1.

  25. 25.

    Moreover, Sect. 5.2.1 has explained why reliability and construct validity are likely to prevail in the present study on qualitative grounds, given that the study’s measurement procedure uses a standardised scoring system for 467 ‘double-blind’ interviews with plant managers of approximately 45 min each by specially-trained native Chinese graduate students from top business schools, which yields case-study detail for 467 firms.

  26. 26.

    Zero expected error score, zero correlation between the error score and the true score on a given measurement, zero correlation between the error score on a given measurement and the true score on a second measurement, and zero correlation between errors on different measurements (Carmines and Zeller 1979, p. 30).

  27. 27.

    The methods for assessing construct validity synthesised below include both Campbell’s view of convergent and discriminant validity on the one hand and Cronbach’s view of nomological validity on the other hand as well as content validity. As Albright and Malloy (2000, p. 337) explain, ‘Donald Campbell and Lee Cronbach had a long history of mutual respect for and fundamental disagreement with each other’s ideas about experimental validity.’

  28. 28.

    As explained in Sect. 4.3, for reflective constructs the PLS algorithm’s loadings result from maximising the product of the explained variance in the measurement model and the absolute or squared (depending on the weighting scheme) values of the correlations between latent variables in the structural model. By contrast, for formative constructs, the PLS algorithm’s weights result from maximising the absolute or squared values of the correlations between latent variables in the structural model—irrespective of the explained variance in the measurement model, given that formative indicators need not covary. For both types of measurement models, the estimation of loadings/weights takes into account the structural model, which specifies the relationships between the constructs of interest within the study’s theoretical context.

  29. 29.

    As discussed in Sect. 5.2, classical test theory (Carmines and Zeller 1979, pp. 29–36; Scholderer and Balderjahn 2005, pp. 88–89; Spearman 1904) contends that an observed score (\( X \)), such as a reflective indicator, is the sum of the underlying true score that it aims to measure (\( T \)) and measurement error (\( e \)).

  30. 30.

    High loadings of reflective indicators (\( {\lambda_{ij }} \)) are the basis for obtaining high reliability between indicators (see Dillon-Goldstein’s rho in Equation (5.3) in Sect. 5.2) as well as high convergent validity and discriminant validity (see Fornell and Larcker’s (1981, pp. 45–46) average variance extracted in Equations (5.5) and (5.6) below).

  31. 31.

    Scholars have deemed different criteria for reflective indicators as desirable, e.g. \( {\lambda_{ij }}>0.7 \), where construct i explains over 50 % of indicator j’s variation (\( \lambda_{ij}^2 \)), lower thresholds such as \( {\lambda_{ij }}>0.6 \), or simply positive loadings that are statistically significant (e.g. Bagozzi and Yi 1988, p. 82; Balderjahn 1986, p. 236; Carmines and Zeller 1979, p. 27; Eggert and Fassott 2003, p. 5; Herrmann et al. 2006, pp. 24–30). It has been argued that reflective indicators with \( {\lambda_{ij }}<0.4 \) should generally be excluded from the model (Götz and Liehr-Gobbers 2004, p. 727; Hulland 1999, pp. 198–199; Krafft et al. 2005, pp. 73–75).

  32. 32.

    While the conceptual domain of a formative construct thus depends on which indicators are included, it is not necessary to conduct a census of all formative indicators, provided that the selected formative indicators conceptually represent the theoretical domain of interest (Coltman et al. 2008; Rossiter 2002).

  33. 33.

    While mathematically the weights of formative indicators can be either positively or negatively signed, one needs to compare whether the signs are coherent and consistent with the conceptual definition of the theoretical construct (e.g. Fornell et al. 1990, p. 1252; Helm 2005, pp. 249–251). This becomes relevant in Sect. 6.2.1 in terms of supporting the multidimensionality of middle management discretion.

  34. 34.

    On the one hand, certain authors have argued that formative indicators with low, insignificant weights (e.g. below 0.1) should be eliminated on the grounds of model parsimony and statistical fit (e.g. Baumgartner and Homburg 1996; Chin 1998; Jöreskog and Wold 1982, p. 270; Seltin and Keeves 1994, p. 4356). On the other hand, scholars have criticised such elimination as inappropriate if the model is meant to test hypotheses rather than maximise statistical fit (e.g. Hinkel 2001, p. 291; Rossiter 2002, p. 315). In order to balance empirical and theoretical considerations, it has been suggested to exclude low-weight formative indicators only if justifiable on theoretical grounds, even if they do not significantly explain the construct’s variation in the particular sample (Diamantopoulos and Winklhofer 2001, pp. 272–273; Fornell et al. 1990, p. 1252; Helm 2005, pp. 251–252; Helm et al. 2010, p. 523; Krafft et al. 2005, p. 78).

  35. 35.

    This test for discriminant validity is presented for all constructs in the empirical discretion model. Yet it should be noted that for middle management performance (\( P \)) in Sect. 5.3.1, where there are multiple reflective indicators, the Fornell-Larcker criterion (Fornell and Larcker 1981, pp. 45–46) is considered a more suitable test for discriminant validity, as it explicitly accounts for measurement error (Ping 2005, p. 1).

  36. 36.

    For example, in the present study the impact of managerial discretion on performance is viewed as positive in 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) and mostly negative in 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).

  37. 37.

    Middle management performance is measured by a single latent variable with six reflective indicators, where each indicator is a z-score of the extent to which the practices of the plant manager reflect best practices in the fields of operations management, talent management, and target management (see Sect. 4.2.1).

  38. 38.

    In terms of the three classes of performance-relevant firm resources defined by Barney (1991, p. 101), operations management refers to the management of physical capital resources (Williamson 1975), talent management to the management of human capital resources (Becker 1964), and target management to the management of organisational capital resources (Tomer 1987). Target management blends the work of physical and human capital resources and aligns their efforts towards the organisation’s objectives.

  39. 39.

    Based on the literature in Box 5.6 above, the following method for purifying the scale of performance (\( P \)) was applied: The empirical discretion model was initially calibrated with all 18 reflective indicators of performance. Those reflective indicators with unequivocally low loadings (\( {\lambda_{ij }}<0.4 \)) were then excluded, whereas those with unequivocally high loadings (\( {\lambda_{ij }}>0.7 \)) were retained (Carmines and Zeller 1979, p. 27; Eggert and Fassott 2003, p. 5; Götz and Liehr-Gobbers 2004, p. 727; Hulland 1999, pp. 198–199; Krafft et al. 2005, pp. 73–75). A simulation was run for including versus excluding the remaining indicators (i.e. those with \( 0.4\leq {\lambda_{ij }}\leq 0.7 \)). It was necessary to recalibrate the empirical discretion model for the different permutations of indicators because excluding individual indicators can alter the estimates of the performance construct and thereby the loadings of all indicators, given that standardised loadings represent correlations between the indicators and their construct (Esposito Vinzi et al. 2010, pp. 49–50; Lohmöller 1989, p. 36). Throughout the simulations, the results of the structural model (e.g. the direct effects of discretion on performance) remained fully robust, which demonstrates that the particular choice of performance indicators does not affect the conclusions of the present study. Therefore, the final choice of six performance indicators was made so as to optimise the measurement model’s construct validity. In particular, the six indicators selected satisfy all criteria for construct validity, i.e. content validity (e.g. high and significant loadings while retaining sufficient breadth of content), convergent validity (e.g. \( AV{E_i}>0.5 \)), discriminant validity (e.g. \( AV{E_i}>\max \rho_{ib}^2 \)), and nomological validity (see below). In the context of the present study, using the more parsimonious six indicators of performance therefore results in even higher construct validity (i.e. lower error) than when using Bloom and Van Reenen’s (2007) 18 indicators of performance.

  40. 40.

    As explained in Sect. 5.1.2, the similarity of the values for communality (\( Com \)) between Chinese firms and multinationals reflects the invariance of the measurement model for performance across the groups of firms (i.e. the stability of the performance loadings). The same holds true for the average variance extracted (\( AVE \)). Values for both \( Com \) and \( AVE \) are presented in Table 5.8.

  41. 41.

    This equality stems from the fact that standardised loadings represent correlations between each indicator and the corresponding construct (Chin 2010, p. 670; Esposito Vinzi et al. 2010, pp. 50–57; Ringle 2009).

  42. 42.

    As explained in Box 5.7, the present study correctly applies the special settings that are required for the blindfolding algorithm in the PLS software package SmartPLS for properly computing the Stone-Geisser test (Ringle 2009; Ringle et al. 2005; see Box 5.2 in Sect. 5.1.1).

  43. 43.

    The correlations between the performance construct and all the other constructs in the empirical discretion model (\( \rho_{ib } \)) can be inferred from the leftmost columns containing values in Tables 5.18, 5.19, and 5.20 in Sect. 5.4.2.

  44. 44.

    These correlations between the performance construct and the other constructs in the empirical discretion model are the same ones as those used for evaluating the Fornell-Larcker criterion above (i.e. \( r=\rho_{ib } \)). These correlations can be inferred from the leftmost columns containing values in Tables 5.18, 5.19, and 5.20 in Sect. 5.4.2. The second test condition, \( \max |r|<0.7 \), may therefore be rewritten as \( \max {r^2}=\max \rho_{ib}^2<{0.7^2}=0.49 \). It follows that for performance, where \( AV{E_i}>0.50 \), the second test condition (\( 0.49>\max \rho_{ib}^2 \)) is stricter than the first test condition (\( AV{E_i}>\max \rho_{ib}^2 \)). Ping (2005, p. 1) considers the first test condition (Fornell-Larcker criterion) a more suitable test for discriminant validity, because it explicitly accounts for measurement error.

  45. 45.

    High reliability between interviewers (lower bound for reliability exceeds conservative threshold: \( \rho =0.734>0.7 \)) and between indicators (Dillon-Goldstein’s rho is \( \rho =0.86>0.7 \) in Chinese firms, and \( \rho =0.87>0.7 \) in multinationals and all firms; Cronbach’s alpha is \( \alpha =0.80>0.7 \) in Chinese firms, \( \alpha =0.83>0.7 \) in multinationals, and \( \alpha =0.81>0.7 \) in all firms) have been established for performance.

  46. 46.

    For single-indicator constructs (such as hiring discretion), the distinction between reflective and formative measurement models becomes obsolete, since in either case the construct’s latent variable score is simply equal to the (normalised) single indicator (cf. Henseler and Fassott 2010, pp. 723–733).

  47. 47.

    The discussion of the purification of scales in Box 5.6 in the opening of Sect. 5.3 applies only to constructs with multiple indicators (i.e. only to middle management performance \( P \) in the empirical discretion model).

  48. 48.

    With reference to the five steps for establishing content validity outlined in the opening of Sect. 5.3, the listed tests correspond to step 3 (Quantitative assessment of indicators’ loadings/weights and potential purification) and step 5 (Assessment of measurement equivalence.). Given that no indicators of discretion are excluded, step 4 (Qualitative assessment of final indicators) does not apply, as it is identical to step 1. Hence, for the single-indicator constructs of middle management discretion (\( {D_1} \), \( {D_2} \), \( {D_3} \), \( {D_4} \)), industry technology intensity (\( {A_1} \)), and firm size (\( {A_2} \)), the assessment of content validity consists of only step 1 (Qualitative assessment of initial indicators) and in case of middle management discretion step 2 (Quantitative assessment of indicators’ dimensionality). The dimensionality of discretion is treated separately in Sect. 6.2.1.

  49. 49.

    These correlations are taken from the latent variable score correlation matrices in Tables 5.18, 5.19, and 5.20 in Sect. 5.4.2. However, they partly differ from those in the column labelled ‘Maximum | r |’ in Tables 5.18, 5.19, and 5.20, as they are the largest correlations between all—rather than only between independent—latent variable scores.

  50. 50.

    The test for nomological validity that examines the relationship between the firm size construct (\( {A_2} \)) and each discretion construct (\( {D_1} \), \( {D_2} \), \( {D_3} \), \( {D_4} \)) is presented in Sect. 5.3.2 on discretion as well as in Sect. 5.3.4 on firm size, because it simultaneously assesses the validity of both constructs (Carmines and Zeller 1979, p. 25).

  51. 51.

    These correlations are taken from the latent variable score correlation matrices in Tables 5.18, 5.19, and 5.20 in Sect. 5.4.2.

  52. 52.

    Population ecology (see Sect. 2.3.1.1) has emphasised that environmental structural changes, such as innovations in an ‘Industry’, affect performance (\( P \)) via the ‘Control Effect (c)’ (e.g. Aldrich 1979; Baum 1996; Baum and Amburgey 2002; Carroll 1988; Freeman et al. 1983; Hannan and Freeman 1977, 1984; Singh and Lumsden 1990; Tushman and Romanelli 1985; Zohar and Luria 2005). In line with this idea, many empirical studies have included ‘Industry’ variables as control variables with a ‘Control Effect (c)’ (e.g. Chang and Wong 2003, p. 21; Cheng et al. 2006, p. 355; Datta et al. 2003, p. 101; Gammelgaard et al. 2010, p. 9; Khanchel 2009, p. 100; Werner and Tosi 1995, p. 1678).

  53. 53.

    These correlations are taken from the latent variable score correlation matrices in Tables 5.18, 5.19, and 5.20 in Sect. 5.4.2. However, they partly differ from those in the column labelled ‘Maximum | r |’ in Tables 5.18, 5.19, and 5.20, as they are the largest correlations between all—rather than only between independent—latent variable scores.

  54. 54.

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

  55. 55.

    The test for nomological validity that examines the relationship between the firm size construct (\( {A_2} \)) and each discretion construct (\( {D_1} \), \( {D_2} \), \( {D_3} \), \( {D_4} \)) is presented in Sect. 5.3.2 on discretion as well as in Sect. 5.3.4 on firm size, because it simultaneously assesses the validity of both constructs (Carmines and Zeller 1979, p. 25).

  56. 56.

    If one can introduce all necessary control variables into the model so as to allow the model to control for all confounding factors, the remaining associations in the model can be viewed as causal rather than spurious (Sánchez 2008, p. 5; Simon 1954, pp. 477–478). However, even then, identifying the direction of causality requires additional assumptions in order to identify the causal ordering of the variables (i.e. to make the equation system identifiable). Part of these assumptions can be the non-correlation of the error terms, but one must also assume that certain variables bear no causal relation (Simon 1954, pp. 471–473). While the latter may be achieved via temporal precedence with time series (Granger 1969), theoretical reasoning is mostly needed in observational cross-sectional studies. This limitation of observational cross-sectional studies that the direction of causality cannot be empirically verified in general (e.g. Caza 2007, p. 46; Finkelstein and Hambrick 1990, p. 500; Wagner 2002, pp. 287–292) is also applicable to the present study and noted as a limitation in Sect. 7.6.

  57. 57.

    Furthermore, Sect. 5.4.3 demonstrates that the empirical discretion model’s structural relationships are robust to the inclusion of further general control variables (e.g. indirect industry technology intensity and the region of the plant manager’s firm) and noise control variables (e.g. weekday and time of the interview).

  58. 58.

    As noted in Chap. 7, the new discretion model that the present study contributes as a general version of the here calibrated empirical discretion model can potentially control for other confounding factors—either by including control variables as antecedents with control effects (i.e. in the vectors \( \mathrm{ A} \) and \( \mathrm{ c} \)) or by including control variables as grouping variables for multi-group comparisons (i.e. as with firm type herein).

  59. 59.

    As described in Sect. 4.3, in addition to the control effects of industry technology intensity and firm size (c 1 and c 2), these antecedents are allowed other effects in the empirical discretion model. For example, the moderating effects of firm size (m 1,2, m 2,2, m 3,2, m 4,2) are empirically analysed in Sect. 6.2.3. (There are also other effects that could be analysed, such as the direct effects of antecedents on discretion or the mediating effects via discretion on performance. Yet these lie outside of the scope of the research objective.)

  60. 60.

    The improved internal validity of the empirical discretion model when including firm type (see above) is also demonstrated by the finding that the estimated control effect of firm size in all firms (c 2 All = 0.17) is higher than that in either Chinese firms (c 2 Chinese = 0.15) or multinationals (c 2 Multi. = 0.15). When firm type is excluded (as in the column ‘All Firms’ in Table 5.17), then the estimated control effect of firm size spuriously includes some of the effect of firm type, as multinationals here tend to be both larger in size and higher in performance.

  61. 61.

    As noted above and in Sect. 7.6, the limitation of observational cross-sectional studies remains that the direction of causality cannot be empirically verified in general and not all control variables can be tested.

  62. 62.

    In studies that unlike the present study include measurement models with multiple formative indicators, multicollinearity can also threaten the accuracy with which the weights on the formative indicators are estimated. Such studies therefore need to additionally assess the degree of multicollinearity on formative indicators (i.e. predictors) on each block of the measurement model (e.g. Diamantopoulos and Winklhofer 2001, p. 272; Helm 2005, pp. 248–249; Krafft et al. 2005, pp. 79–80; Temme et al. 2006, p. 18).

  63. 63.

    For instance, if the pairwise correlation coefficient between the latent variable scores of capital investment discretion (D 1) and firm size (A 2) were e.g. r(D 1, A 2) = 0.8, the empirical discretion model might potentially not clearly distinguish the direct effect of D 1 on performance (d 1) and the control effect of A 2 on performance (c 2). By contrast, a low value of r(D 1, A 2) would make the threat of multicollinearity less likely.

  64. 64.

    These values imply that the relatively largest threat of multicollinearity in the model is that the variance of the moderating effect parameter on (D 3 ⋅ A 2), m 3,2, is inflated by a factor of less than two. (m 3,2 is the moderating effect of firm size, A 2, on the impact of new product introduction discretion, D 3, on performance, P.)

  65. 65.

    While Campbell and Fiske (1959, p. 81) focus on the validity of the measurement model (see Sect. 5.3), their reasoning is here applied to the validity of the structural model, i.e. to the model’s structural relationships.

  66. 66.

    Both direct industry technology intensity (included as A 1 in the final version of the empirical discretion model) and indirect industry technology intensity (excluded in the model’s final version) were measured as single-indicator constructs with the z-score of the percentage of direct and indirect R&D intensity, respectively, based on the measurement approach of the OECD (Hatzichronoglou 1997, pp. 12–13; Loschky 2008, p. 3; OECD 2005, pp. 167–172). As explained in Sect. 4.2.3, the indicators of direct and indirect R&D intensity could not be meaningfully grouped and rather ought to be separated. Direct R&D intensity gauges the extent to which the firms in the industry branch in which the plant manager’s firm principally operates produce high-technology products themselves. Indirect R&D intensity measures the extent to which these firms use high-technology equipment (e.g. machines) and high-technology intermediate inputs (e.g. components) from their suppliers—i.e. the R&D expenditure embodied in capital goods and intermediate inputs from other industry branches (i.e. suppliers) used in the given industry branch as a proportion of output.

  67. 67.

    The chosen number of bootstrap samples varies in the literature, but often lies between 100 and 1,000 samples for PLS models. Empirical evidence finds that estimates tend to be robust to the chosen number of samples (e.g. Efron and Gong 1983, p. 38; Tenenhaus et al. 2005, p. 176), which is also found in this study. For example, Tenenhaus et al. (2005, p. 176) point out that 100 samples is the default in the PLS software package PLS-Graph, but that ‘a higher number (such as 200) may lead to more reasonable standard error estimates.’ They run the bootstrapping algorithm on a model with 100, 200, 300, 500 and 1,000 samples, with the results being very stable throughout. They choose to use the value of 200 samples for further exposition.

  68. 68.

    The Stone-Geisser test of predictive relevance is described in Box 5.7 in Sect. 5.3. As noted in Box 5.7, the present study has applied the correct settings for the blindfolding algorithm in SmartPLS (see Ringle 2009).

  69. 69.

    As noted above and in Sect. 7.6, the limitation of observational cross-sectional studies remains that the direction of causality cannot be empirically verified in general and not all control variables can be tested.

  70. 70.

    As shown in Fig. 3.3 in Sect. 3.2.2, nearly 30,000 firms with 300–2,000 employees are recorded in official government statistics in the manufacturing sector in China. As the sample of the present study applies to manufacturing firms with 150–5,000 employees, the number of comparable firms in the theoretical population is expected to be even larger. Moreover, with generally one or more plant managers per firm, the number of plant managers is expected to be larger yet, and is therefore here expressed as ‘tens of thousands’.

  71. 71.

    As explained in Sect. 1.3, this study uses a database of 467 plant managers in China that was developed by McKinsey & Company, the London School of Economics, and Stanford University (2008). Hence, when the present study started, the sampling process in Fig. 5.3 (from the theoretical population to the interviews completed) had already been finished, as described in e.g. Bloom et al. (2008, 2009a). Building on this work, the novel contribution of the present section is to blend each stage of the sampling process in Fig. 5.3 with the relevant literature in the field so as to qualitatively establish external validity (see Sects. 5.5.1–5.5.3) and then to quantitatively confirm this validity by virtue of new tests of representativeness (see Sect. 5.5.4).

  72. 72.

    Sampling error refers to unaccountable chance differences among sampling units that make inferences based on the sample inaccurate but are reduced by increasing sample size. Biases here refer to anything that prevents the sample from representing the population and is not reduced by increasing sample size.

  73. 73.

    For example, the ‘rule is if the population is under 200, one does a census. Essentially, there is no way to do a probability sample on populations under 200 and have any useful error rate.’ (Northrop and Arsenault 2007, p. 216). Censuses tend to be conducted only when every response is required, such as for certain government statistics—though notably not for large-scale political polls (e.g. Garson 2002, p. 144).

  74. 74.

    This sampling frame of 30,125 units is depicted as the bar labelled ‘Sampling frame’ in Fig. 5.3 above. The discussion of the sampling frame for the database used in the present study (McKinsey & Company—London School of Economics—Stanford University 2008; see Sect. 1.3) in this section incorporates the related discussions in Bloom et al. (2008, 2009a), blending them with the literature so as to assess external validity.

  75. 75.

    For example, Bureau van Dijk claims to be ‘well-known for its range of company information products, and the high quality IPs [information providers] it works with.’ (Bureau van Dijk 2005, p. 2). As to the ORIANA dataset, Bureau van Dijk identifies ‘the best source of information in each country’ (Bureau van Dijk, company website) and uses Huaxia Credit for China (Poncet et al. 2008, p. 8). In order to mitigate any bias in coverage, Bureau van Dijk applies ‘strict inclusion criteria’ (Bureau van Dijk, company website): To be included in the ORIANA dataset, all public and private companies must satisfy at least one of the following conditions: (a) more than 150 employees, (b) more than USD 10 million turnover, or (c) more than USD 20 million total assets (Bureau van Dijk 2006/2007, p. 2).

  76. 76.

    In order to select firms with 150–5,000 employees, the average number of employees over recent years was calculated based on the ORIANA dataset.

  77. 77.

    The reason is that if the members in the sampling frame systematically differ from the theoretical population, then even a random sample that represents the sampling frame will not represent the theoretical population.

  78. 78.

    Specifically, this number refers to recorded firms in the population with more than 300 employees that also have sales above 30 million RMB and total assets above 40 million RMB.

  79. 79.

    Probability sampling and its significance were explained by the Swiss mathematician Jacques Bernoulli (1654–1705), who reasoned that the difference between the characteristics of a randomly chosen sample and the population would be small and could be expressed by a quantifiable error rate.

  80. 80.

    It was deemed sufficient to contact 1,321 firms from the sampling frame of 30,125 firms, since assuming a reasonable response rate, a sufficiently large sample of a few hundred firms could be obtained.

  81. 81.

    Evaluation apprehension is particularly prevalent in telephone interviews, since individuals tend to prefer face-to-face interviews to telephone interviews due to the personal interaction and mail surveys to telephone surveys due to the greater convenience for participants (Groves 1990, p. 233; Schwester 2007, p. 272).

  82. 82.

    This threat can be decomposed into two parts. First, for a given number of contacts, a lower response rate reduces the sample size and thus increases the sampling error in a calculable manner. Second, if non-responders differ from responders, a lower response rate will bias the sample and make it less representative of the population. In this latter case, where non-response does not randomly occur, ‘the researcher does not mathematically know how the sampling errors have changed’ (Northrop and Arsenault 2007, p. 229).

  83. 83.

    It is possible to calculate a third response rate that treats the 690 cases of ‘scheduling/follow-up’ as refusals (overlooking the fact that they include potential completions). This response rate is 38 %, with 505 completions in the numerator and the sum of 505 completions, 690 scheduling/follow-ups, and 126 refusals in the denominator. Yet the present study views this response rate (38 %) as biased downwards, since it treats the 690 scheduling/follow-ups as refusals—in a similar way as the response rate in Equation (5.7) (90 %) is biased upwards, since it treats the 690 scheduling/follow-ups as completions. Consequently, this study calculates the response rate as in Equation (5.8) (80 %), which treats the 690 scheduling/follow-ups as neither refusals nor completions: As these 690 plant managers neither refused nor completed the interviews, they are similar to non-contacted firms (that contain potential completions and refusals) and thus factored out. Nevertheless, even if one chooses to view the response rate as 38 %, this does not threaten external validity, since the empirical tests in Sect. 5.5.4 decisively demonstrate that the sample is indeed representative.

  84. 84.

    Removing these 19 incorrectly included firms further removes the bias that firms with less than 150 employees would have necessarily contracted and firms with more than 5,000 employees would have necessarily expanded in recent years.

  85. 85.

    The deletion of the 19 cases containing missing values corresponds to the case-wise replacement routine in SmartPLS (Ringle et al. 2005). The alternative routine for treating missing values in SmartPLS is mean replacement, which substitutes the mean computed over all available cases for the missing values—but which may create biased parameter estimates (Temme et al. 2006, pp. 7–8). Given the low proportion of cases with missing values in the present study, it is not surprising that the empirical discretion model’s results are robust (as noted in Sect. 5.4.3) to whether case-wise or mean replacement is applied.

  86. 86.

    As described in Sect. 3.2.2, firms must simultaneously satisfy three size thresholds (i.e. number of people employed, sales volume, and total assets) in order to be allocated to any particular size class. For the sample mean below, however, the size thresholds in terms of sales volume and total assets are disregarded.

  87. 87.

    The number of firms and employees of medium-sized enterprises used to estimate firm size here (30,245 and 23,942,700, respectively) are only provided for the sector ‘industry’ (‘gongye’), which includes ‘Mining’ and the ‘Production and Supply of Electricity, Gas and Water’ as well as manufacturing. Nevertheless, the sector ‘industry’ is likely to be a good proxy for manufacturing given that 92 % of enterprises in ‘industry’ are accounted for by manufacturing firms (Guojia tongji ju [National Bureau of Statistics] 2007, 14–1, 14–2).

  88. 88.

    It should be noted that even though the population mean falls into the confidence interval, there are several limitations of this test due to limited data availability on the population. As stated above, this is at best evidence for 78 % of the sample (firms with 300–2,000 employees). Moreover, there may be inaccuracies from (1) omitting sales volume and total assets when matching the firm size definition, (2) comparing to the population in ‘industry’ rather than only manufacturing, and (3) utilising 2006 instead of 2007 data.

  89. 89.

    North China: Beijing, Tianjin, Hebei, Shanxi, Inner Mongolia. Northeast China: Liaoning, Jilin,Heilongjiang. East China: Shanghai, Jiangsu, Zhejiang, Anhui, Fujian, Jiangxi, Shandong. Central South China: Henan, Hubei, Hunan, Guangdong, Guangxi, Hainan. Southwest China: Chongqing, Sichuan, Guizhou, Yunnan, Tibet. Northwest China: Shaanxi, Gansu, Qinghai, Ningxia, Xinjiang.

  90. 90.

    As data on the exact number of units of analysis in the population by region is not available, three size indicators are calculated from official statistics as proxies: employment in the manufacturing sector, investment in fixed assets in the manufacturing sector, and gross regional product in the sector ‘industry’ (‘gongye’). The National Bureau of Statistics defines ‘industry’ as ‘Manufacturing’, ‘Mining’, and ‘Production and Supply of Electricity, Gas and Water’. As 92 % of enterprises in ‘industry’ are accounted for by manufacturing firms (Guojia tongji ju [National Bureau of Statistics] 2007, 14–1, 14–2), the gross regional product in the sector ‘industry’ may be viewed as a proxy for that of the manufacturing sector.

  91. 91.

    The sample’s SIC codes are translated into ISIC Rev.3.1 codes using official correspondence tables. However, certain three-digit SIC codes in the sample do not correspond to a single two-digit ISIC code. For example, the three-digit US SIC code of 225 contains different types of knitted products, which can either fall under a two-digit ISIC code of 17 (textiles) or 18 (apparel). Likewise, the statistics published by the National Bureau of Statistics present data on certain two-digit ISIC codes in a grouped manner only. For instance, ‘Manufacture of Transport Equipment’ contains multiple ISIC codes (i.e. 34 and 35). In such cases, groups containing multiple ISIC codes were formed so as to provide the most granular breakdown by industry branch that allows representing sample and population data in a compatible format. Consequently, based on the NBS statistics and the actual SIC codes recorded in the sample, the following five groupings were necessary: first, 17, 18; second 20, 36; third 23, 24, 25, 37; fourth 28, 29, 30, 31, 32; fifth 34, 35.

  92. 92.

    The confidence intervals give the possible range of population parameters that the sample reflects with 95 % certainty. Hence this constitutes strong evidence of representativeness. For the manufacture of tobacco products (ISIC code 16), the population proportion of 0.3 % is sufficiently close to that of the sample of 0.2 % to presume that it falls into the confidence interval. Yet as there is only one firm in the sample with ISIC code 16, the binomial approximation to the normal distribution that is generally applied for computing confidence intervals on proportions is not valid and yields a 95 % confidence interval for the proportion of −0.2 % to 0.7 %. As the point estimate from the sample is so close to the population parameter, ISIC code 16 is not merged with other categories in order to preserve maximum granularity.

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Wülferth, H. (2013). Validity and Reliability of Empirical Discretion Model. In: Managerial Discretion and Performance in China. Contributions to Management Science. Physica, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35837-1_5

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