通货膨胀与劳动力变动率的关系：USA的协整检验
Inflation as a function of labor force change rate: cointegration test for the USA
摘要：
发达经济体的通货膨胀率与劳动力变动率之间存在线性滞后关系，p（t）= A1 dLF（t-t1）/LF（t-t1）+A2。对于美国，A1=4.0，A2=-0.03075，t1=2年。它提供了一个RMS预测误差（RMFSE）为0.8%，在1965年至2002年期间的两年期（最好的其他通货膨胀预测模型）。对这种关系进行了协整检验。这两个变量是根据一个单位根的存在下，在一系列和它的第一个差异的情况下，整合的顺序。两种方法的协整检验：恩格尔-格兰杰一个基于单位根检验的残差，包括各种规格测试和Johansen协整秩检验的VAR表示的基础上。这两种方法都证明了变量之间存在协整关系，并且在以往的研究中揭示的长期均衡关系成立。通过格兰杰因果检验，证明了劳动力变动是一个弱外生变量，是考虑时间提前和存在协整关系的自然结果。VAR和VECM表示不提供RMSFE的任何显著改进。该方程有许多应用：从纯粹的理论-宏观经济和人口变量之间的稳健基本关系，到实际的-两年期内准确的样本外通胀预测和基于劳动力预测的长期预测。这种关系的预测能力与劳动力估计的不确定性成反比。因此，未来的通货膨胀研究计划应该从显著提高劳动力估计的准确性开始。
英文摘要：
A linear and lagged relationship between inflation and labor force change rate, p(t)= A1dLF(t-t1)/LF(t-t1)+A2 was found for developed economies. For the USA, A1=4.0, A2=-0.03075, and t1=2 years. It provides a RMS forecasting error (RMFSE) of 0.8% at a two-year horizon for the period between 1965 and 2002 (the best among other inflation forecasting models). This relationship is tested for cointegration. Both variables are integrated of order one according to the presence of a unit root in the series and its absence in their first differences. Two methods of cointegration testing are applied: the Engle-Granger one based on the unit root test of the residuals including a variety of specification tests and the Johansen cointegration rank test based on the VAR representation. Both approaches demonstrate that the variables are cointegrated and the long-run equilibrium relation revealed in previous study holds. According to the Granger causality test, the labor force change is proved to be a weakly exogenous variable - a natural result considering the time lead and the existence of a cointegrating relation. VAR and VECM representations do not provide any significant improvement in RMSFE. There are numerous applications of the equation: from purely theoretical - a robust fundamental relation between macroeconomic and population variables, to a practical one - an accurate out-of-sample inflation forecasting at a two-year horizon and a long-term prediction based on labor force projections. The predictive power of the relationship is inversely proportional to the uncertainty of labor force estimates. Therefore, future inflation research programs should start from a significant improvement in the accuracy of labor force estimations.
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