Limit Theory for Locally Flat Functional Coefficient Regression

Functional coefficient (FC) regressions allow for systematic flexibility in the responsiveness of a dependent variable to movements in the regressors, making them attractive in applications where marginal effects may depend on covariates. Such models are commonly estimated by local kernel regression methods. This paper explores situations where responsiveness to covariates is locally flat or fixed. In such cases, the limit theory of FC kernel regression is shown to depend intimately on functional shape in ways that affect rates of convergence, optimal bandwidth selection, estimation, and inference. The paper develops new asymptotics that take account of shape characteristics of the function in the locality of the point of estimation. Both stationary and integrated regressor cases are examined. Locally flat behavior in the coefficient function has, as expected, a major effect on bias and thereby on the trade-off between bias and variance, and on optimal bandwidth choice. In FC cointegrating regression, flat behavior materially changes the limit distribution by introducing the shape characteristics of the function into the limiting distribution through variance as well as centering. Both bias and variance depend on the number of zero derivatives in the coefficient function. In the boundary case where the number of zero derivatives tends to infinity, near parametric rates of convergence apply for both stationary and nonstationary cases. Implications for inference are discussed and simulations characterizing finite sample behavior are reported

Economic Fluctuations in Japan during the Interwar Period -- Re- estimations of the LTES Personal

To date, most research on Interwar Period economic fluctuations in Japan has been based on Estimates of Long-term Economic Statistics of Japan (LTES), edited by Kazushi Ohkawa et al. Regardless, the LTES data are just one set of estimations. They require scrutiny, especially for the measurement of personal consumption, which has a high weight in GNE. This paper re-estimates the LTES personal consumption expenditures by adjusting the estimation methods for certain expense categories and deducting imputations (which may have a large measurement error), and then calculates real GDP (adjusted real GDP) focusing on the market economy. The re-estimation presents no major changes from the LTES in the shape of the economic fluctuations of the 1920s, when the Japanese economy continuously posted gunbalanced growth.h From the Showa Depression forward, however, while the LTES shows continued positive real GDP growth, the re-estimation indicates negative growth in adjusted real GDP in 1931. These findings remain robust after considering the bias from the deflator formula. Given the characteristics of national accounts and the measurement error, these re-estimation results suggest that the severity of the Showa Depression may have been underestimated in the prior research.Japanese Economy, Interwar Period, Showa Depression, Great Depression, Personal Consumption, National Accounts, Deflator, Imputation

Economic Fluctuations in Japan during the Interwar Period: Re- Estimation of the LTES Personal Consumption Expenditures

To date, most research on interwar period economic fluctuations in Japan has been based on Estimates of Long-Term Economic Statistics of Japan since 1868 (LTES), edited by Kazushi Ohkawa et al. Regardless, the LTES data are just one set of estimations. They require scrutiny, especially for the measurement of personal consumption, which has a high weight in the gross national expenditure. This paper re- estimates the LTES personal consumption expenditures by adjusting the estimation methods for certain expense categories and deducting imputations (which may have a large measurement error), and then calculates real GDP (adjusted real GDP) focusing on the market economy. The re-estimation presents no major changes from the LTES in the shape of the economic fluctuations of the 1920s, when the Japanese economy continuously posted gunbalanced growth.h From the Showa Depression forward, however, while the LTES shows continued positive real GDP growth, the re-estimation indicates negative growth in adjusted real GDP in 1931. These findings remain robust after considering the bias from the deflator formula. Given the characteristics of the national accounts and the measurement error, these re-estimation results suggest that the severity of the Showa Depression may have been underestimated in the prior research.Japanese economy; Interwar period; Showa Depression; Great Depression; Personal consumption; National accounts; Deflator; Imputation