高管薪酬影响因素——多层线性模型法外文翻译资料

Determinates of Executive Compensation: A Hierarchical Linear Modeling Approach

Owen P. Hall Jr., Kenneth Ko

HIERARCHICAL LINEAR MODELING

Most classical analytic techniques (e.g., OLS) are based on the assumption of independent observations. This assumption is violated when dealing with nested data structures. Typically, managers drawn from a given firm will be more homogeneous than managers that were sampled from the overall population. Managers from the same firm, on some dimensions, tend to exhibit similar characteristics (e.g., organizational background) which suggest that the observations are not fully independent. Therefore, using ordinary least squares regression in these cases tends to generate standard errors that are too small. This leads to a higher probability of concluding that relationships exist between the predictor variables and target variable compared with the case involving independent observations. Two classic approaches in addressing nested data are disaggregation and aggregation. In the former case (disaggregation) firm performance data (Level 2) is assigned to each manager (Level 1). Unfortunately, this results in violating the independence observations assumption since all mangers would be assigned the firm performance scores. In the latter approach (aggregation) average manager characteristics are assigned to the firm. This assignment results in two potentially serious problems: 1) Upwards of 90 percent of individual variability on the target variable is lost (Bryk, 1992); and 2) The target variable can change significantly from individual achievement to average firm achievement.

Furthermore, both analysis strategies limit the ability to separate out manager and firm effects on the target variable (i.e., total executive compensation). Hierarchical linear modeling (HLM) is a relatively new analytical technique which is designed to address problems involving organizational nesting (Pan, 2008; Lee, 2003; Raudenbush, 2002). Many HLM applications consist of a two-level arrangement such as found in this study. However, three and four level configurations are also possible. At Level 1, the parameters (intercept and slopes) representing the relationship between the Level 1 predictors and target variable are estimated (within). At Level 2, the intercepts and slopes for each Level 1 parameter are specified (between). The Level 2 process is analogous to the cross-level main effects model. To further illustrate this process consider a sales organization consisting of three regions each reporting to the general manager. The primary interest of each regional manager is the sales variance within their region while the focus of the general manager is the sales variance between each region.

The basic two-level hierarchical linear model can be characterized as follows:

Level 1 (examples: managers, students)

Y = B₀ B₁*X₁ B₂*X₂ hellip; B_n*X_n R

Level 2 (examples: firms, schools)

B₀ = G₀₀ G₀₁*W₁ G₀₂*W₂ hellip; G_0m*W_m U₀

B₁ = G₁₀ G₁₁*W₁ G₁₂*W₂ hellip; G_1m*W_m U₁

B_n = G_n0 G_n1*W₁ G_n2*W₂ hellip; G_nm*W_m U_n

where: Y is the target variable of interest, X₁, X₂ hellip; X_n are the individual (level 1) and W₁, W₂hellip; W_m are the firm (level 2) predictor variables. The error terms R, U₀, U₁, hellip; U_n represent the residual variance for each equation while B₀, B₁, B₂, B_n are the Level 1 and G₀₀, G₁₀, G_n0, G_nm are the Level 2 intercepts and slopes, respectively. A solution to the above equations is developed simultaneously by combining the two sets of equations (Level 1 and Level 2) into a single mixed model. HLM offers three distinct advantages over the use of traditional OLS in analyzing nested data structures.

bull; HLM separates out the target variable variance into within and between components. Therefore the error terms are not systematically biased.

bull; HLM maximizes the use of the available information.

bull; HLM permits testing for cross-level effects.

One early HLM application in analyzing pay and performance relationships involved professional sports (Todd, 2005). Sports teams like management teams are hierarchical in nature. The results from this study, which linked salary with player experience and performance, revealed that intercepts and slopes varied considerably between teams. One of the advantages in analyzing sports teams in this regard is the availability of extensive individual performance data (e.g., RBI, ERA). Unfortunately, this is not the case for executive management teams. HLM has also seen application in the study of organizational behavior (Gavin, 2002). This study found that the overall leadership style of the organization (Level 2) can play a significant roll in moderating employee hostility (Level 1).

Table 1. Variable mnemonics and definitions