BT4

Mức độ đóng góp của mỗi thành viên là như nhau

Biến phụ thuộc: lngdp

logarit của GDP thực tế theo ngang giá sức mua (lngdp), đo lường bằng đô la quốc tế cố định ở mức giá năm 2021

Biến quản trị

Kiểm soát tham nhũng (cc), ổn định chính trị (pv), tiếng nói và trách nhiệm giải trình (va)

Biến kiểm soát

Đầu tư trực tiếp nước ngoài (fdi), tổng vốn hình thành (gcapf), tiêu dùng chính phủ (gcons) và độ mở thương mại (trad). Tất cả đều tính theo tỷ lệ phần trăm GDP.

Biến giả

Biến giả thu nhập (inc): 0 (thu nhập trung bình thấp) và 1 (thu nhập trung bình cao). (Nước có thu nhập trung bình thấp: 52, nước có thu nhập trung bình cao:56)

Biến giả vùng: Sub–Saharan Africa (ssa), the Middle East and North Africa (mena), South Asia (sa), Latin America (la), Central Asia (ca), East Asia and the Pacific (eap)

Tải dữ liệu

library(tidyverse)
── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4     ✔ readr     2.1.5
✔ forcats   1.0.0     ✔ stringr   1.5.1
✔ ggplot2   3.5.1     ✔ tibble    3.2.1
✔ lubridate 1.9.3     ✔ tidyr     1.3.1
✔ purrr     1.0.2     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors
library(plm)

Attaching package: 'plm'
The following objects are masked from 'package:dplyr':

    between, lag, lead
library(readxl)
Data <- read_xlsx("D:\\ngoctran\\Data4.xlsx")
variable.names(Data)
 [1] "country" "times"   "inc"     "eap"     "ca"      "la"      "mena"   
 [8] "ssa"     "sa"      "fdi"     "gcapf"   "gcons"   "trad"    "va"     
[15] "pv"      "cc"      "gdp"    
Pdata = na.omit(Data)
Pdata$lngdp = log(Pdata$gdp)

Mô hình POOLED OLS

Pooled <- lm(lngdp~eap+ca+la+inc+mena+sa+ssa+fdi+gcapf+gcons+trad+va+pv+cc, data = Pdata)
summary(Pooled)

Call:
lm(formula = lngdp ~ eap + ca + la + inc + mena + sa + ssa + 
    fdi + gcapf + gcons + trad + va + pv + cc, data = Pdata)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.66517 -1.53356  0.05611  1.45950  3.07560 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  9.1542725  0.8047924  11.375  < 2e-16 ***
eap          2.6062645  0.6296399   4.139 4.08e-05 ***
ca           2.2488848  0.6080086   3.699 0.000241 ***
la           1.9187730  0.6643806   2.888 0.004043 ** 
inc          0.1271070  0.1514884   0.839 0.401837    
mena         2.5521349  0.6472252   3.943 9.18e-05 ***
sa           1.6675659  0.6948465   2.400 0.016762 *  
ssa          2.7345106  0.6167600   4.434 1.14e-05 ***
fdi         -0.0031869  0.0029401  -1.084 0.278900    
gcapf       -0.0380422  0.0097135  -3.916 0.000102 ***
gcons       -0.0149623  0.0051758  -2.891 0.004009 ** 
trad        -0.0003258  0.0013914  -0.234 0.814971    
va           0.2822850  0.1372994   2.056 0.040300 *  
pv          -0.1389321  0.1471532  -0.944 0.345555    
cc          -0.0376707  0.1420230  -0.265 0.790930    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 1.612 on 503 degrees of freedom
Multiple R-squared:  0.1046,    Adjusted R-squared:  0.07963 
F-statistic: 4.195 on 14 and 503 DF,  p-value: 5.378e-07

Cài đặt dữ liệu bảng

Pdata %>% pdata.frame(index=c("country","times")) %>% head()
             country times inc eap ca la mena ssa sa      fdi     gcapf
Lebanon-2015 Lebanon  2015   0   0  0  0    1   0  0 4.324692 22.222778
Lebanon-2016 Lebanon  2016   0   0  0  0    1   0  0 5.021740 23.142570
Lebanon-2017 Lebanon  2017   0   0  0  0    1   0  0 4.756779 21.787935
Lebanon-2018 Lebanon  2018   0   0  0  0    1   0  0 4.841403 22.487103
Lebanon-2019 Lebanon  2019   0   0  0  0    1   0  0 3.694133 12.322474
Lebanon-2020 Lebanon  2020   0   0  0  0    1   0  0 5.067130  8.098177
                gcons     trad         va        pv         cc      gdp
Lebanon-2015 103.3369 71.83904 -0.4625397 -1.698364 -0.9014205 15152.15
Lebanon-2016 101.1287 67.72362 -0.5196608 -1.615684 -0.9897533 15732.70
Lebanon-2017 102.8136 68.45543 -0.5761188 -1.622227 -1.0276344 16262.90
Lebanon-2018 104.2612 68.25731 -0.5137916 -1.621536 -1.1326983 16381.15
Lebanon-2019 109.2629 62.98092 -0.5157056 -1.672291 -1.1687958 15693.93
Lebanon-2020 109.2865 50.12980 -0.5552116 -1.621135 -1.1794679 12594.62
                lngdp
Lebanon-2015 9.625898
Lebanon-2016 9.663497
Lebanon-2017 9.696642
Lebanon-2018 9.703887
Lebanon-2019 9.661029
Lebanon-2020 9.441025
Pdata %>% pdata.frame(index=c("country","times")) -> Pdata
Pdata |> pdim()
Unbalanced Panel: n = 74, T = 1-8, N = 518

Mô hình FEM

reg <- "lngdp~inc+eap+ca+la+mena+sa+ssa+fdi+gcapf+gcons+trad+va+pv+cc"
FEM1 <- plm(reg, Pdata, effect = "individual", model="within")

FEM2 <- plm(reg, Pdata, effect = "time", model="within")

FEM3 <- plm(reg, Pdata, effect = "twoway", model="within")

Mô hình REM

REM1 <- plm(reg, Pdata, effect = "individual", model="random")
Models <- list("POOLED" = Pooled,"FEMid"=FEM1,"REMid"=REM1,  "FEMt"=FEM2,"FEMtwoway"=FEM3)
               
modelsummary::modelsummary(Models,
                           statistic = c('{statistic} '),
                            stars = c("*"=0.1, "**"=0.05, "***"=0.01))
POOLED FEMid REMid FEMt FEMtwoway
* p < 0.1, ** p < 0.05, *** p < 0.01
(Intercept) 9.154*** 7.837***
11.375 4.548
eap 2.606*** 2.571 2.606***
4.139 1.531 4.111
ca 2.249*** 2.292 2.249***
3.699 1.391 3.673
la 1.919*** 2.337 1.919***
2.888 1.324 2.869
inc 0.127 -0.014 0.127
0.839 -0.036 0.832
mena 2.552*** 2.269 2.551***
3.943 1.317 3.911
sa 1.668** 1.845 1.670**
2.400 0.987 2.387
ssa 2.735*** 2.856* 2.734***
4.434 1.718 4.402
fdi -0.003 0.000 0.000 -0.003 -0.001
-1.084 -0.333 -0.233 -1.090 -0.393
gcapf -0.038*** -0.024*** -0.026*** -0.038*** -0.026***
-3.916 -2.919 -3.234 -3.882 -3.050
gcons -0.015*** -0.002 -0.001 -0.015*** -0.001
-2.891 -0.369 -0.196 -2.851 -0.227
trad 0.000 0.000 -0.001 0.000 0.000
-0.234 0.009 -0.208 -0.228 0.100
va 0.282** -0.783** -0.328 0.281** -0.832**
2.056 -2.201 -1.345 2.028 -2.306
pv -0.139 0.320 0.075 -0.139 0.326
-0.944 1.428 0.405 -0.934 1.444
cc -0.038 1.052*** 0.463** -0.036 1.087***
-0.265 3.185 2.035 -0.254 3.262
Num.Obs. 518 518 518 518 518
R2 0.105 0.046 0.191 0.105 0.049
R2 Adj. 0.080 -0.129 0.169 0.067 -0.144
AIC 1981.3 1077.3 1166.4 1979.1 1074.3
BIC 2049.3 1111.3 1234.4 2042.9 1108.3
Log.Lik. -974.641
F 4.195
RMSE 1.59 0.67 0.72 1.59 0.67

Các kiểm định

Đa cộng tuyến

Sử dụng mô hình POOLED OLS chỉ với các biến định lượng

Pooled1 <- lm(lngdp~fdi+gcapf+gcons+trad+va+pv+cc, data = Pdata)
car::vif(Pooled1)
     fdi    gcapf    gcons     trad       va       pv       cc 
1.007318 1.201217 1.532778 1.397588 2.408183 3.082034 3.093205 

Không có hiện tượng đa cộng tuyến

Kiểm định có ảnh hưởng cá nhân, thời gian

Pooled <- plm(reg,Pdata, model="pooling" )
plmtest(Pooled)

    Lagrange Multiplier Test - (Honda)

data:  reg
normal = 32.92, p-value < 2.2e-16
alternative hypothesis: significant effects
plmtest(Pooled, effect = "individual")

    Lagrange Multiplier Test - (Honda)

data:  reg
normal = 32.92, p-value < 2.2e-16
alternative hypothesis: significant effects
plmtest(Pooled, effect = "time")

    Lagrange Multiplier Test - time effects (Honda)

data:  reg
normal = -1.9806, p-value = 0.9762
alternative hypothesis: significant effects
plmtest(Pooled, effect = "twoway")

    Lagrange Multiplier Test - two-ways effects (Honda)

data:  reg
normal = 21.878, p-value < 2.2e-16
alternative hypothesis: significant effects
pwtest(Pooled,effect ="individual")

    Wooldridge's test for unobserved individual effects

data:  formula
z = 5.8152, p-value = 6.055e-09
alternative hypothesis: unobserved effect
pwtest(Pooled,effect ="time")

    Wooldridge's test for unobserved time effects

data:  formula
z = -2.8259, p-value = 0.004715
alternative hypothesis: unobserved effect
pwtest(Pooled,effect = c("individual", "time"))

    Wooldridge's test for unobserved individual effects

data:  formula
z = 5.8152, p-value = 6.055e-09
alternative hypothesis: unobserved effect

=> Có đặc trưng riêng, nên mô hình Pooled OLS không phù hợp

Kiểm định FEM & REM

phtest(FEM1, REM1)

    Hausman Test

data:  reg
chisq = 12.278, df = 7, p-value = 0.09178
alternative hypothesis: one model is inconsistent

Mô hình REM tốt hơn

Kiểm định tương quan chuỗi

library(lmtest)
Loading required package: zoo

Attaching package: 'zoo'
The following objects are masked from 'package:base':

    as.Date, as.Date.numeric
bgtest(REM1)

    Breusch-Godfrey test for serial correlation of order up to 1

data:  REM1
LM test = 405.6, df = 1, p-value < 2.2e-16

Có hiện tượng tự tương quan bậc 1

Kiểm định phương sai sai số thay đổi

lmtest::bptest(REM1)

    studentized Breusch-Pagan test

data:  REM1
BP = 79.831, df = 14, p-value = 3.041e-11

Có hiện tượng phương sai sai số thay đổi

Kiểm định phụ thuộc chéo

pcdtest(REM1)
Warning in pcdres(tres = tres, n = n, w = w, form = paste(deparse(x$formula)),
: Some pairs of individuals (23 percent) do not have any or just one time
period in common and have been omitted from calculation

    Pesaran CD test for cross-sectional dependence in panels

data:  lngdp ~ inc + eap + ca + la + mena + sa + ssa + fdi + gcapf +     gcons + trad + va + pv + cc
z = 1.6704, p-value = 0.09485
alternative hypothesis: cross-sectional dependence

Không có hiện tượng phụ thuộc chéo

Hiệu chỉnh sai số

model <- REM1
coeftest(model)

t test of coefficients:

               Estimate  Std. Error t value  Pr(>|t|)    
(Intercept)  7.83651627  1.72320805  4.5476 6.806e-06 ***
inc         -0.01388216  0.38847955 -0.0357  0.971508    
eap          2.57088316  1.67881857  1.5314  0.126308    
ca           2.29168251  1.64732820  1.3912  0.164795    
la           2.33667302  1.76468133  1.3241  0.186060    
mena         2.26920439  1.72362967  1.3165  0.188597    
sa           1.84502971  1.86936287  0.9870  0.324125    
ssa          2.85630925  1.66217935  1.7184  0.086337 .  
fdi         -0.00032245  0.00138603 -0.2326  0.816132    
gcapf       -0.02576579  0.00796826 -3.2336  0.001303 ** 
gcons       -0.00108993  0.00556092 -0.1960  0.844690    
trad        -0.00051695  0.00248731 -0.2078  0.835441    
va          -0.32764960  0.24361599 -1.3449  0.179250    
pv           0.07506964  0.18548640  0.4047  0.685857    
cc           0.46290871  0.22746282  2.0351  0.042365 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coeftest(model, vcovHC)

t test of coefficients:

               Estimate  Std. Error t value  Pr(>|t|)    
(Intercept)  7.83651627  0.84820310  9.2390 < 2.2e-16 ***
inc         -0.01388216  0.36902406 -0.0376 0.9700067    
eap          2.57088316  0.67332122  3.8182 0.0001512 ***
ca           2.29168251  0.49658731  4.6149 4.999e-06 ***
la           2.33667302  0.86746033  2.6937 0.0073025 ** 
mena         2.26920439  0.80211124  2.8290 0.0048553 ** 
sa           1.84502971  0.71310957  2.5873 0.0099525 ** 
ssa          2.85630925  0.67152043  4.2535 2.510e-05 ***
fdi         -0.00032245  0.00049807 -0.6474 0.5176638    
gcapf       -0.02576579  0.00856046 -3.0099 0.0027449 ** 
gcons       -0.00108993  0.00737889 -0.1477 0.8826309    
trad        -0.00051695  0.00319401 -0.1619 0.8714880    
va          -0.32764960  0.36833219 -0.8895 0.3741332    
pv           0.07506964  0.25624603  0.2930 0.7696741    
cc           0.46290871  0.30926002  1.4968 0.1350655    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coeftest(model, vcovHC(model, method = "arellano"))

t test of coefficients:

               Estimate  Std. Error t value  Pr(>|t|)    
(Intercept)  7.83651627  0.84820310  9.2390 < 2.2e-16 ***
inc         -0.01388216  0.36902406 -0.0376 0.9700067    
eap          2.57088316  0.67332122  3.8182 0.0001512 ***
ca           2.29168251  0.49658731  4.6149 4.999e-06 ***
la           2.33667302  0.86746033  2.6937 0.0073025 ** 
mena         2.26920439  0.80211124  2.8290 0.0048553 ** 
sa           1.84502971  0.71310957  2.5873 0.0099525 ** 
ssa          2.85630925  0.67152043  4.2535 2.510e-05 ***
fdi         -0.00032245  0.00049807 -0.6474 0.5176638    
gcapf       -0.02576579  0.00856046 -3.0099 0.0027449 ** 
gcons       -0.00108993  0.00737889 -0.1477 0.8826309    
trad        -0.00051695  0.00319401 -0.1619 0.8714880    
va          -0.32764960  0.36833219 -0.8895 0.3741332    
pv           0.07506964  0.25624603  0.2930 0.7696741    
cc           0.46290871  0.30926002  1.4968 0.1350655    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
coeftest(model, vcovHC(model, type = "HC3"))

t test of coefficients:

               Estimate  Std. Error t value  Pr(>|t|)    
(Intercept)  7.83651627  0.88259658  8.8789 < 2.2e-16 ***
inc         -0.01388216  0.37863041 -0.0367 0.9707674    
eap          2.57088316  0.69926140  3.6766 0.0002618 ***
ca           2.29168251  0.51034732  4.4904 8.823e-06 ***
la           2.33667302  0.89131000  2.6216 0.0090164 ** 
mena         2.26920439  0.83035609  2.7328 0.0065007 ** 
sa           1.84502971  0.74542648  2.4751 0.0136471 *  
ssa          2.85630925  0.69187126  4.1284 4.276e-05 ***
fdi         -0.00032245  0.00071074 -0.4537 0.6502496    
gcapf       -0.02576579  0.00884453 -2.9132 0.0037367 ** 
gcons       -0.00108993  0.00773869 -0.1408 0.8880511    
trad        -0.00051695  0.00345590 -0.1496 0.8811512    
va          -0.32764960  0.38016665 -0.8619 0.3891764    
pv           0.07506964  0.26734783  0.2808 0.7789839    
cc           0.46290871  0.31795820  1.4559 0.1460499    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
t(sapply(c("HC0", "HC1", "HC2", "HC3", "HC4"), function(x) sqrt(diag(vcovHC(model, type = x)))))
    (Intercept)       inc       eap        ca        la      mena        sa
HC0   0.8482031 0.3690241 0.6733212 0.4965873 0.8674603 0.8021112 0.7131096
HC1   0.8607574 0.3744860 0.6832870 0.5039373 0.8802996 0.8139833 0.7236643
HC2   0.8651041 0.3736672 0.6854567 0.5033171 0.8791234 0.8154441 0.7289740
HC3   0.8825966 0.3786304 0.6992614 0.5103473 0.8913100 0.8303561 0.7454265
HC4   0.8806248 0.3774082 0.7116813 0.5075662 0.8835089 0.8396838 0.7435418
          ssa          fdi       gcapf       gcons        trad        va
HC0 0.6715204 0.0004980699 0.008560464 0.007378886 0.003194007 0.3683322
HC1 0.6814596 0.0005054419 0.008687167 0.007488101 0.003241282 0.3737839
HC2 0.6814363 0.0004985957 0.008700271 0.007555284 0.003302414 0.3741682
HC3 0.6918713 0.0007107408 0.008844533 0.007738694 0.003455897 0.3801666
HC4 0.6897694 0.0026530311 0.008813748 0.007776725 0.004000661 0.3770491
           pv        cc
HC0 0.2562460 0.3092600
HC1 0.2600387 0.3138374
HC2 0.2616973 0.3135328
HC3 0.2673478 0.3179582
HC4 0.2664834 0.3155518

Mô hình với các biến tương tác

rem_int <- plm(lngdp~inc+eap+ca+la+mena+sa+ssa+fdi+gcapf+gcons+trad+va+pv+cc+inc:cc+inc:pv+inc:va, data = Pdata,  model = "random")
summary(rem_int)
Oneway (individual) effect Random Effect Model 
   (Swamy-Arora's transformation)

Call:
plm(formula = lngdp ~ inc + eap + ca + la + mena + sa + ssa + 
    fdi + gcapf + gcons + trad + va + pv + cc + inc:cc + inc:pv + 
    inc:va, data = Pdata, model = "random")

Unbalanced Panel: n = 74, T = 1-8, N = 518

Effects:
                 var std.dev share
idiosyncratic 0.5369  0.7327 0.177
individual    2.4893  1.5777 0.823
theta:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.5788  0.8380  0.8380  0.8303  0.8380  0.8380 

Residuals:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-3.3392 -0.3872  0.0402 -0.0085  0.3890  2.7188 

Coefficients:
               Estimate  Std. Error z-value  Pr(>|z|)    
(Intercept)  7.83190410  1.75757420  4.4561 8.347e-06 ***
inc         -0.03483221  0.39558614 -0.0881  0.929835    
eap          2.63591827  1.71892348  1.5335  0.125160    
ca           2.35647844  1.68794686  1.3961  0.162696    
la           2.49319017  1.79514968  1.3888  0.164879    
mena         2.29199115  1.75657412  1.3048  0.191958    
sa           1.99972365  1.90836581  1.0479  0.294697    
ssa          2.96240333  1.70241724  1.7401  0.081839 .  
fdi         -0.00042376  0.00138671 -0.3056  0.759919    
gcapf       -0.02535518  0.00798152 -3.1767  0.001489 ** 
gcons       -0.00190859  0.00560647 -0.3404  0.733536    
trad        -0.00029424  0.00251061 -0.1172  0.906704    
va          -0.65982120  0.34863491 -1.8926  0.058413 .  
pv           0.24384560  0.26008305  0.9376  0.348466    
cc           0.60527157  0.33395253  1.8124  0.069917 .  
inc:cc      -0.25987848  0.45061732 -0.5767  0.564131    
inc:pv      -0.32062515  0.36627634 -0.8754  0.381376    
inc:va       0.59464162  0.46393942  1.2817  0.199940    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Total Sum of Squares:    331.22
Residual Sum of Squares: 268.85
R-Squared:      0.19152
Adj. R-Squared: 0.16403
Chisq: 21.4189 on 17 DF, p-value: 0.20811
rem_region_int1 <- plm(lngdp ~ inc + eap + ca + la + mena + sa + ssa + fdi + gcapf + gcons + trad + va + pv + cc +
                      eap:va + eap:pv + eap:cc +
                      ca:va + ca:pv + ca:cc +
                      ssa:va + ssa:pv + ssa:cc +
                      la:va + la:pv + la:cc,
                      data = Pdata, 
                      model = "random")
rem_region_int2 <- plm(lngdp ~ inc + eap + ca + la + mena + sa + ssa +  fdi + gcapf + gcons + trad + va + pv + cc +
                      mena:va + mena:pv + mena:cc,
                      data = Pdata, 
                      model = "random")
summary(rem_region_int1)
Oneway (individual) effect Random Effect Model 
   (Swamy-Arora's transformation)

Call:
plm(formula = lngdp ~ inc + eap + ca + la + mena + sa + ssa + 
    fdi + gcapf + gcons + trad + va + pv + cc + eap:va + eap:pv + 
    eap:cc + ca:va + ca:pv + ca:cc + ssa:va + ssa:pv + ssa:cc + 
    la:va + la:pv + la:cc, data = Pdata, model = "random")

Unbalanced Panel: n = 74, T = 1-8, N = 518

Effects:
                 var std.dev share
idiosyncratic 0.5104  0.7144 0.163
individual    2.6268  1.6207 0.837
theta:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.5967  0.8460  0.8460  0.8386  0.8460  0.8460 

Residuals:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-3.3773 -0.3612  0.0654 -0.0077  0.3309  2.4452 

Coefficients:
               Estimate  Std. Error z-value  Pr(>|z|)    
(Intercept)  9.23873816  1.93862994  4.7656 1.883e-06 ***
inc          0.03224824  0.41586398  0.0775  0.938190    
eap          1.88592993  1.94647161  0.9689  0.332597    
ca           0.79641868  1.88149254  0.4233  0.672083    
la           1.66299219  2.02623241  0.8207  0.411799    
mena         0.59083231  2.04398527  0.2891  0.772536    
sa           0.62059584  2.16743164  0.2863  0.774627    
ssa          1.58101520  1.87932020  0.8413  0.400197    
fdi         -0.00033893  0.00136809 -0.2477  0.804334    
gcapf       -0.02602981  0.00806295 -3.2283  0.001245 ** 
gcons       -0.00346187  0.00568831 -0.6086  0.542794    
trad        -0.00042297  0.00272782 -0.1551  0.876775    
va          -1.22286507  0.55697058 -2.1956  0.028123 *  
pv           0.66121966  0.36369577  1.8181  0.069055 .  
cc           0.03546819  0.55619748  0.0638  0.949154    
eap:va       0.72703548  0.84608572  0.8593  0.390179    
eap:pv      -0.63032021  0.61299407 -1.0283  0.303825    
eap:cc      -0.77472501  0.75793697 -1.0221  0.306710    
ca:va        0.60365124  0.77987371  0.7740  0.438909    
ca:pv       -0.95443317  0.52482780 -1.8186  0.068978 .  
ca:cc        1.56156081  0.72208619  2.1626  0.030574 *  
ssa:va       1.31279002  0.73237036  1.7925  0.073049 .  
ssa:pv      -0.61316142  0.51910337 -1.1812  0.237526    
ssa:cc      -0.00051870  0.73037085 -0.0007  0.999433    
la:va       -0.84805399  1.15949839 -0.7314  0.464537    
la:pv       -0.22747020  0.83782705 -0.2715  0.786006    
la:cc        1.06708475  1.06907165  0.9981  0.318211    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Total Sum of Squares:    323.92
Residual Sum of Squares: 253.47
R-Squared:      0.21951
Adj. R-Squared: 0.17818
Chisq: 45.7998 on 26 DF, p-value: 0.0096031
summary(rem_region_int2)
Oneway (individual) effect Random Effect Model 
   (Swamy-Arora's transformation)

Call:
plm(formula = lngdp ~ inc + eap + ca + la + mena + sa + ssa + 
    fdi + gcapf + gcons + trad + va + pv + cc + mena:va + mena:pv + 
    mena:cc, data = Pdata, model = "random")

Unbalanced Panel: n = 74, T = 1-8, N = 518

Effects:
                 var std.dev share
idiosyncratic 0.5395  0.7345 0.181
individual    2.4472  1.5643 0.819
theta:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.5750  0.8362  0.8362  0.8284  0.8362  0.8362 

Residuals:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-3.3409 -0.3873  0.0642 -0.0079  0.3720  2.6904 

Coefficients:
               Estimate  Std. Error z-value  Pr(>|z|)    
(Intercept)  7.8097e+00  1.7389e+00  4.4912 7.083e-06 ***
inc         -2.7800e-02  3.9443e-01 -0.0705   0.94381    
eap          2.5212e+00  1.6966e+00  1.4861   0.13726    
ca           2.2456e+00  1.6630e+00  1.3504   0.17689    
la           2.3024e+00  1.7844e+00  1.2903   0.19694    
mena         1.8316e+00  1.7969e+00  1.0193   0.30806    
sa           1.8766e+00  1.8869e+00  0.9946   0.31995    
ssa          2.8793e+00  1.6785e+00  1.7154   0.08627 .  
fdi         -2.8027e-04  1.3892e-03 -0.2017   0.84011    
gcapf       -2.6002e-02  8.0397e-03 -3.2342   0.00122 ** 
gcons       -1.0805e-03  5.6122e-03 -0.1925   0.84733    
trad        -3.4269e-05  2.5663e-03 -0.0134   0.98935    
va          -2.3930e-01  2.7755e-01 -0.8622   0.38859    
pv           8.6431e-02  2.0378e-01  0.4241   0.67147    
cc           4.1715e-01  2.5254e-01  1.6518   0.09857 .  
mena:va     -5.9334e-01  6.4449e-01 -0.9206   0.35724    
mena:pv     -1.3760e-01  5.4725e-01 -0.2514   0.80148    
mena:cc      1.2175e-01  6.7866e-01  0.1794   0.85763    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Total Sum of Squares:    332.83
Residual Sum of Squares: 270.05
R-Squared:      0.19142
Adj. R-Squared: 0.16393
Chisq: 20.448 on 17 DF, p-value: 0.25196