Effects of Measurement Error on the Output Gap in Japan

Potential output is the largest amount of products that can be produced by fully utilizing available labor and capital stock; the output gap is defined as the discrepancy between actual and potential output. If data on production factors contain measurement errors, total factor productivity (TFP) cannot be estimated accurately from the Solow residual(i.e., the portion of output that is not attributable to labor and capital inputs). This may give rise to distortions in the estimation of potential output and the output gap. The primary purpose of this paper is to discuss theoretically how measurement errors and quality changes in production factors affect estimates of potential output and the output gap. The main results are (1) that effects of quality changes in production factors can be left in the Solow residual for correct estimation of potential output and the output gap, but (2) that measurement errors in utilization of capital stock and labor should be removed. Estimation of Japan's output gap, in particular, may be distorted by the absence of data on capacity utilization in non-manufacturing sectors. To resolve this problem, we consider two definitions of output gap and compare their performance. The first definition (the conventional output gap) assumes capacity utilization to be 100 percent in non-manufacturing sectors. Then we fit a certain trend to the Solow residual and define the trend as TFP and the regression residual as the measurement error of capacity utilization in non-manufacturing sectors. The second definition (the new output gap) uses data on electricity consumption to directly estimate capacity utilization in non-manufacturing sectors. In this case, we can take the Solow residual to be TFP. Next, we compare the performance of the two definitions of output gap in terms of their consistency with the reference dates of business cycle and with various DIs in Short-Term Economic Survey of Enterprises in Japan published by the Bank of Japan, including the business conditions DI. We show that the new output gap is superior to the conventional output gap. Furthermore, when the new output gap is used in a Phillips curve, estimates of parameters are more stable than when we use the conventional output gap. These results suggest that the new output gap is a suitable measure of slackness in the Japanese economy.