Indonesia is beset by uneven regional resource endowment and interregional income inequalities. Kataoka (2011) concluded that these are largely determined by the labor productivity differential, using the Duro and Esteban (1998) inequality decomposition approach. We empirically explored the extent to which interprovincial differentials in efficiency explain Indonesia's pre- and post-crisis income inequalities, by employing Cheng and Li's (2006) approach. They proposed the interpretive additive inequality decomposition of Theil's second measure by causal factors and showed that interregional income inequality consists strictly of Theil's second measure of productivity as well as of labor participation rates and their interaction terms. Their method improves Duro and Esteban's (1998) inequality decomposition in which terms can take positive or negative values, although a strict Theil index maintains a non-negative value for its property. Moreover, negative decomposition values are hardly interpretive, contributing to overall inequality. To incorporate efficiency factors, we estimated the production frontier and efficiency score of each observation point, using the data envelopment analysis of Coelli et al. (1998). We adopted the piecewise-linear frontier exhibiting variable returns to scale. Efficiency is gauged by standard Farrell output-oriented measures. Our DEA model employs multiple inputs (capital and labor) and a single output to estimate two provincial output values: those without technical inefficiency, assuming variable returns to scale (denoted as ye) and those without scale inefficiency, assuming constant returns to scale (denoted as ys). Using other variables of labor (denoted as l) and actual output (denoted as ya), labor productivity (denoted as ya/L) can be expressed with three multiplicative components: pure labor productivity (denoted as ye/L), pure technical efficiency (denoted as ya/ys), and scale efficiency (denoted as ys/ye). Applying Cheng and Li's (2006) inequality decomposition, interprovincial productivity differentials show the sum of the corresponding Theil second measure components and their interactions. We used annual observations of 26 contiguous provincial output and input factors from 1993 to 2010, sourced from Kataoka's (2013) dataset. Taking into account of the effects of natural resource endowment on the corresponding provinces' economies, two different output values were employed: aggregate GDP and GDP without the oil and gas sector. We found that the impact of technical inefficiency on interprovincial productivity differentials has a declining trend for the observation periods. Cheng, Y.-S. and S.-K. Li., 2006. 'Income inequality and efficiency: A decomposition approach and applications to China', Economics Letters 91 (1): 8-14. Coelli, Tim, Rao, D.S. Prasada, Battese, George E., 1998. An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Publishers, Boston. Duro, Juan Antonio, Esteban, Joan, 1998. Factor decomposition of cross-country income inequality, 1960-1990. Economics Letters 60: 269-275. Kataoka, M., 2013. Capital stock estimates by province and interprovincial distribution in Indonesia, Asian Economic Journal, 27(4): 411-430.
