Data

Data are from World Bank

## [1] "NE.GDI.FTOT.ZS" "NE.GDI.FTOT.KD" "SL.TLF.TOTL.IN" "NY.GDP.PCAP.KD"
## [5] "SP.POP.TOTL"

Correlation matrix:

##           lgdp        lC        lL
## lgdp 1.0000000 0.9866900 0.7572515
## lC   0.9866900 1.0000000 0.7513212
## lL   0.7572515 0.7513212 1.0000000

Model 1

Cobb-Doublas production function:

\[ GDP = a C^b L^c\]

## 
## Call:
## lm(formula = lgdp ~ lC + lL, data = f2)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.95769 -0.15345  0.00571  0.20939  1.13132 
## 
## Coefficients:
##             Estimate Std. Error t value             Pr(>|t|)    
## (Intercept)  2.04901    0.33528   6.111         0.0000000112 ***
## lC           0.94815    0.02137  44.361 < 0.0000000000000002 ***
## lL           0.04419    0.02613   1.692               0.0932 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3292 on 127 degrees of freedom
##   (86 obserwacji zostało skasowanych z uwagi na braki w nich zawarte)
## Multiple R-squared:  0.9741, Adjusted R-squared:  0.9737 
## F-statistic:  2392 on 2 and 127 DF,  p-value: < 0.00000000000000022
##  [1] "coefficients"  "residuals"     "effects"       "rank"         
##  [5] "fitted.values" "assign"        "qr"            "df.residual"  
##  [9] "na.action"     "xlevels"       "call"          "terms"        
## [13] "model"

## 
##  studentized Breusch-Pagan test
## 
## data:  m0
## BP = 14.628, df = 2, p-value = 0.0006661
##  lag Autocorrelation D-W Statistic p-value
##    1       0.1265414      1.717711   0.102
##  Alternative hypothesis: rho != 0

##  45 185 
##  29 114
## 
##  Shapiro-Wilk normality test
## 
## data:  m0$residuals
## W = 0.97736, p-value = 0.02842
##       lC       lL 
## 2.296125 2.296125
## Analysis of Variance Table
## 
## Response: lgdp
##            Df Sum Sq Mean Sq   F value               Pr(>F)    
## lC          1 518.19  518.19 4781.1737 < 0.0000000000000002 ***
## lL          1   0.31    0.31    2.8617              0.09316 .  
## Residuals 127  13.76    0.11                                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Panel estimation

## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = lgdp ~ lC + lL, data = f2.p, model = "within")
## 
## Unbalanced Panel: n = 163, T = 1-32, N = 4208
## 
## Residuals:
##      Min.   1st Qu.    Median   3rd Qu.      Max. 
## -0.630734 -0.070458  0.001466  0.066159  0.894414 
## 
## Coefficients:
##     Estimate Std. Error t-value              Pr(>|t|)    
## lC 0.3409135  0.0058837  57.942 < 0.00000000000000022 ***
## lL 0.8294965  0.0155783  53.247 < 0.00000000000000022 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    426.24
## Residual Sum of Squares: 75.005
## R-Squared:      0.82403
## Adj. R-Squared: 0.81689
## F-statistic: 9466.21 on 2 and 4043 DF, p-value: < 0.000000000000000222
## Oneway (individual) effect Random Effect Model 
##    (Swamy-Arora's transformation)
## 
## Call:
## plm(formula = lgdp ~ lC + lL, data = f2, model = "random", index = c("iso3c", 
##     "year"))
## 
## Unbalanced Panel: n = 163, T = 1-32, N = 4208
## 
## Effects:
##                   var std.dev share
## idiosyncratic 0.01855 0.13621 0.192
## individual    0.07787 0.27905 0.808
## theta:
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.5614  0.9097  0.9140  0.9081  0.9140  0.9140 
## 
## Residuals:
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -0.70480 -0.08693  0.00691  0.00223  0.09727  1.03025 
## 
## Coefficients:
##             Estimate Std. Error z-value              Pr(>|z|)    
## (Intercept) 5.543724   0.149031  37.199 < 0.00000000000000022 ***
## lC          0.421680   0.006051  69.688 < 0.00000000000000022 ***
## lL          0.615494   0.012880  47.786 < 0.00000000000000022 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1750.9
## Residual Sum of Squares: 100.66
## R-Squared:      0.94267
## Adj. R-Squared: 0.94265
## Chisq: 20200.7 on 2 DF, p-value: < 0.000000000000000222
## 
##  Hausman Test
## 
## data:  lgdp ~ lC + lL
## chisq = 162.41, df = 2, p-value < 0.00000000000000022
## alternative hypothesis: one model is inconsistent
## Pooling Model
## 
## Call:
## plm(formula = lgdp ~ lC + lL, data = f2.p, model = "pooling")
## 
## Unbalanced Panel: n = 163, T = 1-32, N = 4208
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -2.58990 -0.18054  0.02712  0.19521  2.30904 
## 
## Coefficients:
##              Estimate Std. Error t-value              Pr(>|t|)    
## (Intercept) 2.7442157  0.0629049  43.625 < 0.00000000000000022 ***
## lC          0.8861260  0.0039553 224.034 < 0.00000000000000022 ***
## lL          0.0968770  0.0050570  19.157 < 0.00000000000000022 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    17647
## Residual Sum of Squares: 578.78
## R-Squared:      0.9672
## Adj. R-Squared: 0.96719
## F-statistic: 62001.6 on 2 and 4205 DF, p-value: < 0.000000000000000222
## 
##  F test for individual effects
## 
## data:  lgdp ~ lC + lL
## F = 167.62, df1 = 162, df2 = 4043, p-value < 0.00000000000000022
## alternative hypothesis: significant effects
## 
##  Lagrange Multiplier Test - (Breusch-Pagan)
## 
## data:  lgdp ~ lC + lL
## chisq = 17533, df = 1, p-value < 0.00000000000000022
## alternative hypothesis: significant effects

Results

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