This paper is devoted to extending the SSCM of Li et al. (2002) from a
cross-sectional framework to the more popular and important panel data framework, which allows for the presence of time-varying technical efficiency. Under the maintained framework, we develop the likelihood function for the composed errors, which cannot be directly estimated by the maximum likelihood due to the presence of nonparametric and smooth coefficient functions. We instead propose a group of estimation procedures adapting from Robinson (1988) and Fan et al. (1996), who develop valid estimation approaches for a semiparametric model. A local least squares method with a kernel weight function is suggested to estimate the smooth coefficient functions. Monte Carlo simulations are used to confirm that our proposed estimators of interest have the desirable property of consistency.
Due to the fact that the SSCM with error components is a quite flexible specification appropriate for describing a general production and/or cost regression relationship with varying coefficients and panel data are getting more important for applied researchers for the past two decades, our modeling offers an alternative and is perhaps preferable to a parametric model. Using international macroeconomic panel data the SSCM suggests that the marginal effects of labor and capital stock are
significantly affected by human capital nonlinearly. In addition, the slope of the estimated L( )z is increasing after z = 6, while the shape of the estimated K( )z is concave after z = 6. A parametric model fails to provide such information. The empirical study appears to support that the SSCM is preferable to the traditional Cobb-Douglas (translog) function in terms of the goodness of fit and the ability of Log-likelihood 1272.84
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extracting valuable information from the data.
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計畫成果自評
本研究案於計畫申請時，係以三年期計畫為藍本進行規劃，打算用三年時 間，逐步探討平滑係數與分量迴歸縱橫資料模型。唯經過評審後被刪成一年期計 畫，時間縮短的結果，只能完成第一部分，故本結案報告內容僅為以平滑係數縱 橫資料模型為主，探討估計生產效率的方法。
本研究成果，主要將平滑係數迴歸模型從橫斷面擴充至縱橫資料模型，並容 許生產無效率項隨時間變動，更符合實際情況。使用 Monte Carlo 模擬方法，證 明本研究建議的估計步驟，可以得到具備一致性的係數估計式，適合用於實證分 析，提供實證研究者更多的選擇，故應有一定的學術價值。