《高级宏观学教学》panel threshold modeltheory and application课件.ppt
Panel Threshold Model: Theory and Application,Threshold effectPanel threshold modelComputation methodApplication,Panel Threshold Model: Theory,Threshold effect,门限效应：变量之间的关系取决于门限变量的状态，即当门限变量低于门限值或者高于门限值时，回归方程的系数也不同。以单门限模型为例。,Threshold effect门限效应：变量之间的关系取决,Threshold effect,门限效应由于其直观的含义，门限模型在金融市场和宏观经济政策研究中得到广泛应用。金融约束对企业投资的影响。是否负债率较高、较低的企业其金融约束对投资的影响存在明显差异。一体化程度对经济增长的影响。是否收入越低的国家其经济一体化对经济增长的影响越大。央行利率政策对通货膨胀的响应。是否低、高通货膨胀的国家其央行对通胀率的响应存在明显差异。,Threshold effect门限效应由于其直观的含义，门,Threshold effect,对于门限值的检验：beta1=beta2。但是，在备择假设下多了一个未知参数gamma（称作冗余参数，nuisance parameter)。这种情况下传统的检验统计量不再有效。这种情况下的模型也一直没有得到很好的应用，直至Andrews（1983）等给出统计量的分布。注：如果gamma为已知常数，则模型的估计与检验（Chow)与传统方法相同。,Threshold effect对于门限值的检验：beta1,Threshold effect,Threshold effect,Threshold effect,案例:. sysuse lifeexp. scatter lexp gnppc,Threshold effect案例:,Threshold effect,时间序列门限自回归模型TAR、Self-Exciting TAR等。,Threshold effect时间序列门限自回归模型TAR,Panel Threshold ModelSpecification,单门限模型：,Panel Threshold ModelSpecif,Panel Threshold ModelEstimate beta given gamma,Panel Threshold ModelEstima,Panel Threshold ModelEstimate gamma,Panel Threshold ModelEstima,Panel Threshold ModelEstimate gamma,设门限序列Gamma共S个数值,Panel Threshold ModelEstima,Panel Threshold ModelEstimate gamma,Part 1: Compute Threshold series:Quan=mm_quantile(Thr, 1, (Trim1-Trim)Trunc=Thr:=Quan1 :& Thr:=Quan2Sethr=select(Thr,Trunc)Sethr=uniqrows(Sethr) /* ascending distinct value */,Panel Threshold ModelEstima,Panel Threshold ModelEstimate gamma,Part 2: Estimate single thresholdfor (i=1;i=rows(Sethr);i+) Thtemp=Sethridumreg(N,T,THR,Thtemp,y,IX,RX,RSS=., uf=., fe)SeRSSi=RSS minindex(SeRSS,1,loc=.,w=.)Thfinal=Sethrloc1,1RSSfinal=SeRSSloc1,1,cdumreg(N,T,THR,Thfinal,y,IX,RX,RSS=., uf=., fe,Sigsq=.)LR=(SeRSS:-RSS)/Sigsq,Panel Threshold ModelEstima,Panel Threshold ModelEstimate gamma,Panel Threshold ModelEstima,Panel Threshold ModelTest Threshold Effect,Note: 第3步中，F统计量与没有关系，因此DGP中的可以任意设定。,Panel Threshold ModelTest T,Panel Threshold ModelTest Threshold Effect,设自举次数为Iters。,Panel Threshold ModelTest T,Panel Threshold ModelTest Threshold Effect,Part 3: Test threshold effect* Regress linear model, extact residual u(residual).* Regress single-threshold model, extract yhat,F.for (i=1;iF)/rows(Fstat)Fcrit=mm_quantile(Fstat, 1, (0.900.950.99),Panel Threshold ModelTest T,Panel Threshold ModelTest Threshold Effect,Bootstrap number = 100- | RSS Sig2 Fstat Prob Crit_10 Crit_5 Crit_1-+- Threshold_0 | 464.9505 3.3692 . . . . . Threshold_1 | 382.9400 2.7353 29.9824 0.0000 9.3880 10.1582 12.6432 Threshold_2 | 373.2608 2.6661 3.6304 0.9600 15.2674 18.2482 20.7824-,Panel Threshold ModelTest T,Panel Threshold ModelConfidence interval,Panel Threshold ModelConfid,Panel Threshold ModelConfidence interval,Part 4：Confidence interval/* find the location of threshold */for (i=1; i=1; i-) if (LRicrit) breaklow=Thri+1/* Upper: Minimum of ThrThreshold */for (i=loc+1; icrit) breakupp=Thri-1,Panel Threshold ModelConfid,Panel Threshold ModelConfidence interval,Threshold estimation: Alpha = 0.0500- | Threshold Lower Upper-+- Th_1 | 4.4565 4.4135 4.4860-,Panel Threshold ModelConfid,Panel Threshold ModelModel estimation,= Linear regression (fixed effect):Sum of Squared Residual: RSS = 464.9505Standard error of regression: Se = 3.3692R-squared: R2 = 0.4783- | Coef Std t prob-+- drgdp | -0.1100 0.0468 -2.3524 0.0201 dcpi | 0.6049 0.0545 11.0948 0.0000- = Threshold Regression: threshold number= 1.00Sum of Squared Residual: RSS = 382.9400Standard error of regression: Se = 2.8157R-squared: R2 = 0.5703- | Coef Std t prob-+- drgdp_1 | -0.0895 0.0519 -1.7259 0.0866 dcpi_1 | -0.0703 0.1388 -0.5067 0.6132 drgdp_2 | -0.0682 0.0659 -1.0349 0.3026 dcpi_2 | 0.5504 0.0683 8.0532 0.0000-,Panel Threshold ModelModel,Panel Threshold ModelMultiple thresholds,以双门限模型为例，其他模型依此类推。,Panel Threshold ModelMultip,Panel Threshold ModelEstimate thresholds,如果利用普通的格点搜寻，需要迭代计算（NT）2。显然，实践当中这不太可行。根据(Chong, 1994; Bai, 1997; Bai and Perron, 1998)，序贯估计具有一致性。,Panel Threshold ModelEstima,Panel Threshold ModelMultiple thresholds,双门限模型：Step 1: 估计单门限模型 - Th1Step 2: 给定Th1，估计第二个门限值 - Th21，CIStep 3: 给定Th21，重新估计第一个门限值 - Th22，CI三门限模型：Step 1: 估计双门限模型 - Th21，Th22Step 2: 给定Th21、Th22，估计第三个门限值 - Th31, CIStep 3: 给定Th31、Th22，重新估计第二个门限值 - Th32,CIStep 4: 给定Th31、Th32，重新估计第一个门限值 - Th33,CI,Panel Threshold ModelMultip,Panel Threshold ModelTest double threshold effect,Note:在第3步中，DGP中的为单门限模型的估计量。,Panel Threshold ModelTest d,Panel Threshold ModelConfidence interval,Panel Threshold ModelConfid,Panel Threshold ModelExample,Hansen(1999). cd d:stata10panel. use hansen1999, clear. xtptm i q1-qd1, rx(c1) thrvar(d1) trim(0.01) grid(393) thnum(3) iters(300),Panel Threshold ModelExampl,Panel Threshold ModelExample,Wu and Wang(2008). cd d:stata10panel. use res4, clear. xtptm depr, rx(drgdp dcpi) thrvar(dcpi) thnum(2) trim(0.10) iters(100),Panel Threshold ModelExampl,其他扩展,（1）多门限变量（2）动态面板门限模型,其他扩展（1）多门限变量,谢谢！,高级宏观学教学panel_threshold_model_theory_and_application课件,
