Estimation of firm efficiency, using a panel stochastic Frontier model
| Family firms | Non-family firms | |||||
|---|---|---|---|---|---|---|
| Parameter | Estimate | t-statistic | p-value | Estimate | t-statistic | p-value |
| lnBE | 0.8378* | 116.70 | 0.000 | 0.7755* | 178.09 | 0.000 |
| DEBT | 0.4054* | 7.92 | 0.000 | 0.6041* | 16.52 | 0.000 |
| CAPEX | 0.0390* | 3.92 | 0.000 | −0.0032* | −2.17 | 0.030 |
| RND | −0.0021 | −1.67 | 0.095 | 0.0088* | 4.87 | 0.000 |
| XRD_D | 0.1286* | 4.69 | 0.000 | 0.1282* | 5.86 | 0.000 |
| ADV | −0.8359* | −2.21 | 0.027 | 0.4717 | 1.88 | 0.060 |
| XAD_D | 0.0774* | 3.64 | 0.000 | −0.0183 | −1.17 | 0.241 |
| PPEN | −0.8644* | −12.65 | 0.000 | −0.8940* | −18.68 | 0.000 |
| EBITDAAT | 3.2439* | 37.35 | 0.000 | 1.9655* | 42.80 | 0.000 |
| CONST | 8.1060* | 134.46 | 0.000 | 9.0098* | 220.03 | 0.000 |
| Coefficients on standard deviation σu | ||||||
| IVOL | 42.2330 | 12.03 | 0.000 | 34.0209 | 20.45 | 0.000 |
| CONST | −2.4380 | −5.48 | 0.000 | −0.4362 | −0.70 | 0.485 |
| No. obs | 8,812 | 18,319 | ||||
| Wald | 203.26 | 638.80 | ||||
| p-value | 0.000 | 0.000 | ||||
| Family firms | Non-family firms | |||||
|---|---|---|---|---|---|---|
| Parameter | Estimate | Estimate | ||||
| lnBE | 0.8378* | 116.70 | 0.000 | 0.7755* | 178.09 | 0.000 |
| DEBT | 0.4054* | 7.92 | 0.000 | 0.6041* | 16.52 | 0.000 |
| CAPEX | 0.0390* | 3.92 | 0.000 | −0.0032* | −2.17 | 0.030 |
| RND | −0.0021 | −1.67 | 0.095 | 0.0088* | 4.87 | 0.000 |
| XRD_D | 0.1286* | 4.69 | 0.000 | 0.1282* | 5.86 | 0.000 |
| ADV | −0.8359* | −2.21 | 0.027 | 0.4717 | 1.88 | 0.060 |
| XAD_D | 0.0774* | 3.64 | 0.000 | −0.0183 | −1.17 | 0.241 |
| PPEN | −0.8644* | −12.65 | 0.000 | −0.8940* | −18.68 | 0.000 |
| EBITDAAT | 3.2439* | 37.35 | 0.000 | 1.9655* | 42.80 | 0.000 |
| CONST | 8.1060* | 134.46 | 0.000 | 9.0098* | 220.03 | 0.000 |
| IVOL | 42.2330 | 12.03 | 0.000 | 34.0209 | 20.45 | 0.000 |
| CONST | −2.4380 | −5.48 | 0.000 | −0.4362 | −0.70 | 0.485 |
| No. obs | 8,812 | 18,319 | ||||
| 203.26 | 638.80 | |||||
| 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 , where ; 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 and a residual . In the second step, 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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