Table 2

Estimation of firm efficiency, using a panel stochastic Frontier model

Family firmsNon-family firms
ParameterEstimatet-statisticp-valueEstimatet-statisticp-value
lnBE0.8378*116.700.0000.7755*178.090.000
DEBT0.4054*7.920.0000.6041*16.520.000
CAPEX0.0390*3.920.000−0.0032*−2.170.030
RND−0.0021−1.670.0950.0088*4.870.000
XRD_D0.1286*4.690.0000.1282*5.860.000
ADV−0.8359*−2.210.0270.47171.880.060
XAD_D0.0774*3.640.000−0.0183−1.170.241
PPEN−0.8644*−12.650.000−0.8940*−18.680.000
EBITDAAT3.2439*37.350.0001.9655*42.800.000
CONST8.1060*134.460.0009.0098*220.030.000
Coefficients on standard deviation σu
IVOL42.233012.030.00034.020920.450.000
CONST−2.4380−5.480.000−0.4362−0.700.485
No. obs 8,812  18,319 
Wald 203.26  638.80 
p-value 0.000  0.000 

Note(s): The table presents estimation results from a panel data stochastic frontier analysis of corporate efficiency. The estimated frontier is of the form lnmei,t = β0 + nβnXn,i,t + θi + vi,t − ηi − ui,t, where lnme is the log of market value of shareholder equity, and θi, vi, ηi and ui are error terms representing firm effects, estimation error, persistent inefficiency, and transitory inefficiency, respectively. Similar to Kumbhakar et al. (2014), θi, vi, ηi and ui have distributions that are normal, normal, half-normal, and truncated-normal. Following Kumbhakar et al. (2014) we let β = [β0, β1, …, βi, …βn], and then express the frontier model as lnmei=α0+f(Xi;βi)+αi+εi,t, where α0=α0E(ηi)E(ui,t); αi = θi − ηi + E(ηi); and ɛi,t = vi,t − ui,t + E(ui,t). Then the model is estimated in three stages. In the first step, a standard fixed effects model is used to estimate βˆ and a residual εˆ. In the second step, εˆ is used to estimate time-varying inefficiency ui,t from the relation ɛi,t = vi,t − ui,t + E(ui,t). Third, similar to Step 2, we estimate persistent inefficiency ηi from the relation αi = θi − ηi + E(θi). The explanatory variables in X comprise the following quantities. LNBE denotes the log of book value of shareholder's equity. DEBT denotes the ratio of long-term debt to total assets. CAPEX denotes the ratio of capital expenditures to total sales. RND denotes expenses on research and development, divided by total sales. ADV denotes expenses on advertising, divided by total sales. XRD_D and XAD_D represent dummy variables for missing observations on RND and ADV, respectively. PPEN denotes the ratio of property, plant and equipment to total assets. EBITDAAT denotes EBITDA divided by total assets. ivol denotes idiosyncratic volatility as assessed by the Fama-French three-factor model, evaluated using daily returns over the previous fiscal year. We include dummies for the 48 Fama-French industry classifications. The distribution of the one-sided error term ui is assumed to be truncated normal, similar to Reifschneider and Stevenson (1991) and Kumbhakar et al. (2014). The distribution's standard deviation σu is allowed to vary depending on idiosyncratic volatility, as in Habib and Ljungqvist (2005). The standard deviation is modeled as σu,i,t = γ0 + γ1ivoli,t−1, where ivol denotes the idiosyncratic volatility of firm returns computed over the fiscal year. σv and σu denote the standard deviation of the symmetric and one-sided error terms in equation (3), respectively. Wald denotes the Chi-square test statistic for joint significance of the model. Our sample comprises nonfinancial, nonutility firms in the Compustat database. An asterisk ∗ denotes parameters significant at the 0.05 level. The sample period comprises fiscal years 1992–2018

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