高級宏觀學(xué)教學(xué)資料panelthresholdmodel-theoryandapplication

1、Panel Threshold Model: Theory and Application,Threshold effect Panel threshold model Computation method Application,Threshold effect,門限效應(yīng)：變量之間的關(guān)系取決于門限變量的狀態(tài)，即當(dāng)門限變量低于門限值或者高于門限值時(shí)，回歸方程的系數(shù)也不同。以單門限模型為例。,Threshold effect,門限效應(yīng)由于其直觀的含義，門限模型在金融市場和宏觀經(jīng)濟(jì)政策研究中得到廣泛應(yīng)用。 金融約束對企業(yè)投資的影響。是否負(fù)債率較高、較低的企業(yè)其金融約束對投資的影響存在明顯差異。 一

2、體化程度對經(jīng)濟(jì)增長的影響。是否收入越低的國家其經(jīng)濟(jì)一體化對經(jīng)濟(jì)增長的影響越大。 央行利率政策對通貨膨脹的響應(yīng)。是否低、高通貨膨脹的國家其央行對通脹率的響應(yīng)存在明顯差異。,Threshold effect,對于門限值的檢驗(yàn)：beta1=beta2。但是，在備擇假設(shè)下多了一個(gè)未知參數(shù)gamma（稱作冗余參數(shù)，nuisance parameter)。這種情況下傳統(tǒng)的檢驗(yàn)統(tǒng)計(jì)量不再有效。這種情況下的模型也一直沒有得到很好的應(yīng)用，直至Andrews（1983）等給出統(tǒng)計(jì)量的分布。 注：如果gamma為已知常數(shù)，則模型的估計(jì)與檢驗(yàn)（Chow)與傳統(tǒng)方法相同。,Threshold effect,Thresh

3、old effect,案例: . sysuse lifeexp . scatter lexp gnppc,Threshold effect,時(shí)間序列門限自回歸模型TAR、Self-Exciting TAR等。,Panel Threshold ModelSpecification,單門限模型：,Panel Threshold ModelEstimate beta given gamma,Panel Threshold ModelEstimate gamma,Panel Threshold ModelEstimate gamma,設(shè)門限序列Gamma共S個(gè)數(shù)值,Panel Threshold Mo

4、delEstimate gamma,Part 1: Compute Threshold series: Quan=mm_quantile(Thr, 1, (Trim1-Trim) Trunc=Thr:=Quan1 :i=rows(Sethr);i+) Thtemp=Sethri dumreg(N,T,THR,Thtemp,y,IX,RX,RSS=., uf=., fe) SeRSSi=RSS minindex(SeRSS,1,loc=.,w=.) Thfinal=Sethrloc1,1 RSSfinal=SeRSSloc1,1,c dumreg(N,T,THR,Thfinal,y,IX,RX,

5、RSS=., uf=., fe,Sigsq=.) LR=(SeRSS:-RSS)/Sigsq,Panel Threshold ModelEstimate gamma,Panel Threshold ModelTest Threshold Effect,Note: 第3步中，F(xiàn)統(tǒng)計(jì)量與沒有關(guān)系，因此DGP中的可以任意設(shè)定。,Panel Threshold ModelTest Threshold Effect,設(shè)自舉次數(shù)為Iters。,Panel Threshold ModelTest Threshold Effect,Part 3: Test threshold effect * Regress

6、 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 Threshold Effect,Bootstrap number = 100 - | RSS Sig2 Fstat Prob Crit_10 Crit_5 Crit_1 -+- Threshold_0 | 464.9505

7、 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 ModelConfidence interval,Panel Threshold ModelConfidence interval,Part 4：Confidence interval /* find the location of threshold *

8、/ for (i=1; i=1; i-) if (LRicrit) break low=Thri+1 /* Upper: Minimum of ThrThreshold */ for (i=loc+1; icrit) break upp=Thri-1,Panel Threshold ModelConfidence interval,Threshold estimation: Alpha = 0.0500 - | Threshold Lower Upper -+- Th_1 | 4.4565 4.4135 4.4860 -,Panel Threshold ModelModel estimatio

9、n,= Linear regression (fixed effect): Sum of Squared Residual: RSS = 464.9505 Standard error of regression: Se = 3.3692 R-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= 1.00 Sum of Squ

10、ared Residual: RSS = 382.9400 Standard error of regression: Se = 2.8157 R-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 ModelMu

11、ltiple thresholds,以雙門限模型為例，其他模型依此類推。,Panel Threshold ModelEstimate thresholds,如果利用普通的格點(diǎn)搜尋，需要迭代計(jì)算（NT）2。顯然，實(shí)踐當(dāng)中這不太可行。根據(jù)(Chong, 1994; Bai, 1997; Bai and Perron, 1998)，序貫估計(jì)具有一致性。,Panel Threshold ModelMultiple thresholds,雙門限模型： Step 1: 估計(jì)單門限模型 - Th1 Step 2: 給定Th1，估計(jì)第二個(gè)門限值 - Th21，CI Step 3: 給定Th21，重新估計(jì)第一個(gè)

12、門限值 - Th22，CI 三門限模型： Step 1: 估計(jì)雙門限模型 - Th21，Th22 Step 2: 給定Th21、Th22，估計(jì)第三個(gè)門限值 - Th31, CI Step 3: 給定Th31、Th22，重新估計(jì)第二個(gè)門限值 - Th32,CI Step 4: 給定Th31、Th32，重新估計(jì)第一個(gè)門限值 - Th33,CI,Panel Threshold ModelTest double threshold effect,Note:在第3步中，DGP中的為單門限模型的估計(jì)量。,Panel Threshold ModelConfidence interval,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) it