带R的系统GMM：IVs的多部分公式和萨根测试结果的问题

我正在研究一个包含N=30个国家和T=15年的面板数据集。我正在使用

R

和

plm

包进行分析。 基于Blundell Bond（1998年）和Arellao Bover（1995年）的研究，我决定使用系统GMM一步模型，只考虑个体效应。 然而，对于如何使用

pgmm

函数，我有点困惑，它需要一个多部分公式来指定带有IVs和我得到的Sargan-Hansen测试结果的模型。 更清楚地说，这里有一些我尝试过的代码示例、估计结果和

sargan

测试。在我的模型中，我考虑滞后因变量和外生回归。为了避免我的文章太长，我只报告模型代码和主要结果，尽可能整洁：

sy_gmm1 <- pgmm(log(GWPcap) ~ lag(log(GWPcap)) + log(GDPcap)|lag(log(GWPcap),2:15) + log(GDPcap), data = europanel, 
                index = c("country","year"), model = "onestep", effect = "individual", transformation = "ld")
        
sy_gmm2 <- pgmm(log(GWPcap) ~ lag(log(GWPcap)) + log(GDPcap)|lag(log(GWPcap),2:15) | log(GDPcap), data = europanel, 
                index = c("country","year"), model = "onestep", effect = "individual", transformation = "ld")
        
sy_gmm3 <- pgmm(log(GWPcap) ~ lag(log(GWPcap)) + log(GDPcap) | lag(log(GWPcap),2) + log(GDPcap), data = europanel, 
                index = c("country","year"), model = "onestep", effect = "individual", transformation = "ld")
        
sy_gmm4 <- pgmm(log(GWPcap) ~ lag(log(GWPcap)) + log(GDPcap)|lag(log(GWPcap),2) | log(GDPcap), data = europanel, 
                index = c("country","year"), model = "onestep", effect = "individual", transformation = "ld")
        
sy_gmm5 <- pgmm(log(GWPcap) ~ lag(log(GWPcap)) + log(GDPcap) | lag(log(GWPcap),2) + lag(log(GDPcap),1:2), data = europanel, 
                index = c("country","year"), model = "onestep", effect = "individual", transformation = "ld")
        
sy_gmm6 <- pgmm(log(GWPcap) ~ lag(log(GWPcap)) + log(GDPcap)|lag(log(GWPcap),2) | lag(log(GDPcap),1:2), data = europanel, 
                index = c("country","year"), model = "onestep", effect = "individual", transformation = "ld")

# Coefficients and p-values of estimates
  
                   Estimate       p.value Model
lag(log(GWPcap)) 0.90340911  1.525370e-86     1
log(GDPcap)      0.06214275  1.965823e-02     1
lag(log(GWPcap)) 0.97250426  0.000000e+00     2
log(GDPcap)      0.02222075  1.383774e-01     2
lag(log(GWPcap)) 0.81905400  2.615214e-47     3
log(GDPcap)      0.10822697  8.291284e-04     3
lag(log(GWPcap)) 0.82343976  4.873484e-16     4
log(GDPcap)      0.11164469  7.294118e-02     4
lag(log(GWPcap)) 0.84762245  2.754039e-87     5
log(GDPcap)      0.09281759  1.636567e-04     5
lag(log(GWPcap)) 0.86280993 3.843798e-104     6
log(GDPcap)      0.08809634  3.325890e-04     6

# Sargan test
                stat  df   p.value
    sargan1 30.00000 128 1.0000000
    sargan2 30.00000 104 1.0000000
    sargan3 30.00000  50 0.9888352
    sargan4 29.64127  26 0.2827384
    sargan5 30.00000  63 0.9998660
    sargan6 30.00000  28 0.3632178

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sy_gmm1交叉帖子：对不起，这是双重帖子。我意识到也许交叉验证更好，因为这更像是一个统计问题，而不是关于代码的问题。对于代码，我只需要找出如何设置公式。如果有必要，我会删除这里的帖子，只留下简历上的一篇。谢谢