AI 中文总结
本文提出一种带自适应加权组惩罚的面板数据拐点估计方法，可恢复拐点数量与位置，通过蒙特卡洛模拟验证其有限样本性质，并将其应用于宏观金融中债务与增长的关系研究。
AI 中文摘要
许多经济和金融关系可能是逐渐变化而非突变的。我们研究一类面板数据模型，其中系数向量在日历时间上连续且分段线性，存在有限个未知的拐点日期，系数斜率在这些日期处发生变化。我们提出一种惩罚最小二乘估计量，对系数路径的二阶差分应用自适应加权组惩罚，并建立渐近理论证明，该估计量以趋近于1的概率同时恢复拐点的数量和位置。据我们所知，这是首个在固定效应下估计时变系数路径中未知数量共同拐点日期的面板框架。我们证明端点斜率以常规的三次区间长度速率收敛，内部斜率则以由自身及相邻区间长度决定的速率收敛。我们还开发了逐系数扩展方法，允许个体回归元在不同日期出现拐点。蒙特卡洛模拟证据支持该方法具有良好的有限样本性质，我们通过宏观金融中的一个应用实例说明该方法，具体是债务与增长之间的关系。
英文摘要
Many economic and financial relationships may change gradually rather than abruptly. We study panel data models in which the coefficient vector is continuous and piecewise linear in calendar time, with a finite number of unknown kink dates at which its slope changes. We propose a penalised least squares estimator that applies adaptive weighted group penalties to the second differences of the coefficient path, and develop asymptotic theory showing that it recovers both the number and the locations of the kinks with probability approaching one. To our knowledge, this is the first panel framework to estimate an unknown number of common kink dates in a time-varying coefficient path under fixed effects. We establish that endpoint slopes converge at the usual cubic regime-length rate and interior slopes at rates determined by their own and adjacent regime lengths. We also develop a coefficient-by-coefficient extension allowing individual regressors to kink at different dates. Monte Carlo evidence supports the good finite sample properties, and we illustrate the method through an application in macro-finance, specifically the relationship between debt and growth.
