In Japan, after bursting babble economy since the middle of 1990's, the growth rate has not been increasing obviously, and it is said the productivity keeps declining. This period is sometime called "the lost decade". Recently, a number of researchers and the government try to get an answer what did occur in the period, and find an effective policy for raising industrial productivity and growth rate of GDP. Recently, we can use micro level data, for example, the plants and segments data as well as firms' data. It allows empirical researches to make more precise statistical analysis. In estimation of production function of firms, there are problems of endogeneity and self selection due to firm specific productivity shocks and entry/exit decisions. To the best of our knowledge, empirical works have not paid much attention to the limitations of these problems. Then, methodologically, measurement of productivity is an interesting and challenging problem. There are some methods proposed to handle the problems such as Olley and Pakes (1996) and Levinsohn and Petrin (1999, 2003). Here, endogeneity means input levels may not be independent of the "disturbances". The reason is that it is likely each firm determines the input levels depending on the firm-specific productivity, which is observable only for the firm, not econometricians, and thus the "disturbance" in the estimated equation involves the (unobserved) firm specific productivity shock, which should be highly correlated with the input levels, and other ordinary shocks. In the papers referred above, they consider that the endogeneity occurs only in the capital level, not in the labour input. It is a practical matter if this assumption is adequate or not, but if it is incorrect, we will get inconsistent estimates. In this paper, we have developed two kinds of semiparametric instrumental variable estimators, one extending the Robinson's (1988) semiparametric estimator and the other using series expansion of unknown nonparametric function(s). We suppose both capital and labour inputs are correlated with the productivity. We adopt the lag variables of labour and capital as their instruments instead of investment or intermediate inputs unlike Olley and Pakes or Levinsohn and Petrin. Moreover, our econometric model automatically adapts to the effect of exit decision made by each firm. We apply it to plant/segment level panel data of financial report of Japanese firms listed in Tokyo Stock Exchange market. We found different technology of capital and labour among these industries by our estimator and our estimator works better in the empirical study in terms of sign and magnitude of technological parameters of inputs than Levisohn and Petrin (2003)'s estimator. Moreover, using the estimation results, we decompose the so-called total factor productivity (TFP) or Solow residual into the firm specific productivity and other exogenous shocks based on the assumption that the exogenous shocks are uncorrelated with the inputs. Interestingly, we found that the firm specific productivity has not changed much in these five years. The fluctuation of TFP for each firm comes mostly from that of exogenous shocks, which we may think, the demand shock or other macroeconomic shocks. It is sometimes said that the productivity of Japanese economy has declined since the burst of babble economy, it may not be due to the productivity falls of Japanese firms, but due to a simple macroeconomic demand problem. Since we have investigated only some restricted number of industries, we need to extend it to other industries as well. Also, we can see the productivity changes only 2000 similar to 2005, it is not sufficient to make a strong statement. We will also need to extend it to cover 1980's and 1990's as well using some other dataset.
