Appended Note 3-10 Estimation of Total Factor Productivity (Agriculture) by Prefecture

(1) Estimation equation
   With respect to the agricultural industry, it is defined as the equation of the production function (Linear homogenous Cobb=Douglas production function) whose productive factors are the social capital stock in all prefectures i in t years, land and labor as stated below.
   


   Y = output, K = social capital stock, Z = arable land, L = number of core persons engaged in agriculture, , , 1-- represents the value of elasticity (rate of increase in Y when the productive factor increases by 1%) for each production factor. The following equation represents the results that we estimated for the agricultural industry with the fixed effect model of prefectures' panel data (The estimation equation shows that the above equation was transformed into a function per number of core persons engaged in agriculture and that the transformation of logarithm was made for it).
   



(2) Estimation results (Estimation period: 1976-2000)
   


   Total factor productivity was calculated as the residual derived by subtracting the contribution of social capital stock, arable land and core persons engaged in agriculture from the growth of gross agricultural production.
   Affected by weather patterns, agricultural production varies greatly from year-to-year. For this reason, data used was the average of five-year periods: e.g. 1976-1980, 1981-1985, 1986-1990, 1991-1995, 1996-2000. In addition, as agricultural production was significantly affected by a cold summer in 1993, it was removed from the sample.

(3) Relationship between land productivity and rice cultivation ratio
   The relationship between land productivity (early half of 1990s (1990-1995) latter half of 1990s (1996-2000)) and rice cultivation ratio (value of rice output included in the gross value of agricultural output for each prefecture in the latter half of the 1990s (1996-2000)) was estimated.
   



(4) Relationship between total factor productivity and rice cultivation ratio
   The relationship between total factor productivity (early half of 1990s (1991-1995) latter half of 1990s (1996-2000)) and rice cultivation ratio (value of rice output included in the gross value of agricultural output for each prefecture in the latter half of the 1990s (1996-2000)) was estimated.