⼀⽂读懂动态⾯板门槛模型及stata操作
Hansen（2000）将“门槛回归”模型的基本形式定义为：
其中，作为解释变量的xi是⼀个m维的列向量。qi被称为“门槛变量”， Hansen（2000）认为门槛变量既可以是解释変量xi中的⼀个回归元，也可以作为⼀个独⽴的门槛变量。
⽽⾯板门槛模型已经⼴泛应⽤到实证研究中，2015年开发出来的xthreg命令可以进⾏hansen所提出的门槛回归模型。Hansen's(1999)模型是静态的另外固定效应回归估计要求协变量是强外⽣变量，估计值是⼀致的。——然⽽，在许多实际应⽤程序中，强外⽣性可能具有限制性。因此,Seo and Shin (2016)将该模型扩展到动态⾯板模型。
假设如下⼀个动态⾯板门槛模型：
xit可能包含滞后因变量，即xit为Y的滞后期，qit是门槛变量。
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语法格式
动态⾯板门槛模型命令为xthenreg，语法格式为：
xthenreg depvar [varlist (q x1 x2 ...)] [if] [in] [, options]
其中depvar是因变量，⽽indepvars是解释变量变量。
使⽤该命令前需要注意：
1. xtset应该在运⾏之前完成。此外，变量必须为事先按(i)⾯板变量和(ii)时间变量排序。（xtset should be done before running this. Moreover variables must be sorted by (i) panel variable and (ii) time variable beforehand.）
2. 需要强平衡的⾯板数据（Strongly balanced panel data is required.）
3.Inputs 应该把 y q x1 x2 …… , 其q为门槛变量， x1 和 x2这些称为解释变量（Inputs should be put as y q x1 x2 …… , where q is the threshold variable and x1 x2 ……are other independent variables.）
4. moremata library is required since this command use mm quantile func-
tion.
5. When there are endogeneous independent variables, endogenous option
should be set. For example, if x1 is exogeneous and x2 is endogeneous,
the input must be y q x1, endo(x2).
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option选项介绍
endogenous(varlist) species endogeneous independent variables. The endogeneous variables must be excluded from
endogenous(varlist) species endogeneous independent variables. The endogeneous variables must be excluded from the list of independent variables before the comma.
inst(varlist) species the list of additional instrumental variables.
staticsets the model static. The default model is dynamic. In contrast
with dynamic model, static model does not automatically include L.y as inde-
pendent variable.
kink sets the model kink.
grid _ num(integer)determines the number of grid points to estimate the thresh-
stata怎么发音
old . The default is 20.
trim _ rate(real)determines the trim rate when constructing a grid for es-
timating r. The default is 0.4.
h_0(real)determines a parameter for Silverman's rule of thumb used to ker-
nel estimation. The default is 1.5.
boost(integer) The number of bootstrapping for linearity test. The default
is 0.
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案例应⽤介绍
我们应⽤我们的⽅法来评估肥胖对⼯⼈⽣产⼒的影响。肥胖是⽤体重指数(BMI)来衡量的，体重(公⽄)除以⾝⾼(⽶)的平⽅。BMI在25到30之间的⼈被认为超重，BMI在30或更⾼的⼈被视为肥胖。
使⽤数据来⾃British Cohort Study，我们研究了BMI与⼯作时间的关系。更多的详细讨论见Kim(2019)。
加载数据后，⾸先需要声明数据是panel。xthenreg的默认模型是⼀个动态模型。因为我们认为是静态的模型，⽽不是动态模型，我们使⽤静态选项。
案例1：:
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usehour, clear xtset ilabel time xthenreg hourbmi hsize, endo(bmi) inst(bweight bmic bmim bmid hsize) kink static
结果为：
In this example, we can obtain the same results by collecting all exogenous variables into one place with exo option as follows.
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xthenreg hour bmi, endo(bmi) exo(hsize) inst(bweight > bmic bmim bmid) kink static
We can also change the set of included and excluded instruments using the inst option. The number of moment conditions varies accordingly.
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xthenreg hour bmi hsize, endo(bmi) inst(bweight bmic bmim bmid) kink static
We can estimate the model with a restriction on the sample.
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xthenreg hour bmi ifregion== 1, endo(bmi) exo(hsize) inst(bweight bmic bmim bmid) kink static
Next we consider discontinuity in BMI eect without imposing a kink in the model.
By taking rst difference, we obtain the following model and estimate it with only static option.
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xthenreg hour bmi, endo(bmi) exo(hsize) inst(bweight bmic bmim bmid) static
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References
[1] Adam, C. S., and Bevan, D. L. (2005). Fiscal decits and growth in developing countries," Journal of Public Economics, 89(4), 571-597.
[2] Giacomini, R., Politis, D. N., & White, H. (2013). A warp-speed method for conducting Monte Carlo experiments involving bootstrap estimators,"Econometric theory, 29(3), 567-589.
[3] Hansen, B. E. (1999). Threshold eects in non-dynamic panels: Estimation,testing, and inference," Journal of econometrics, 93(2), 345-368.
[4] Hidalgo, J., Lee, J., and M.H. Seo (2019). Robust Inference for Threshold Regression Models," Journal of Econometrics, to appear.
[5] Khan, M. S., and Ssnhadji, A. S. (2001). Threshold eects in the relationship between ination and growth," IMF Sta papers, 48(1), 1-21.
[6] Kim, Y-J. (2019). The eect of weight on work hours," working paper.
[7] Seo, M. and Y. Shin (2016). Dynamic panels with threshold eect and endogeneity," Journal of Econometrics, 195: 169-186.
[8] Wang, Q. (2015). Fixed-eect panel threshold model using Stata," The Stata Journal, 15(1), 121-134.
[9] Zhang, Y., Zhou, Q., and Jiang, L. (2017). Panel kink regression with an unknown threshold," Economics Letters, 157, 116-121.
157, 116-121.

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