MURDER DATASI

library(wooldridge)
data(murder)
library(rmarkdown)
paged_table(murder)

I. Cinayet mahkumlarının geçmişteki infazları caydırıcı bir etkiye sahipse beta 1’in işareti ne olur? beta 2’nin sahip olması gereken işaret hakkında ne düşünüyorsunuz?

I. Bir eyalette infaz artıyorsa cinayetlerin azalmasını bekleriz bu yüzden beta 1’in işaretinin (-) olmasını bekleriz.

summary(lm(mrdrte ~ exec + unem + d90 + d93 , data = murder))
## 
## Call:
## lm(formula = mrdrte ~ exec + unem + d90 + d93, data = murder)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -9.130 -3.119 -1.211  1.379 67.810 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  -1.8644     3.0695  -0.607  0.54452   
## exec          0.1628     0.1939   0.839  0.40268   
## unem          1.3908     0.4509   3.085  0.00243 **
## d90           2.6753     1.8169   1.472  0.14302   
## d93           1.6073     1.7748   0.906  0.36659   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 8.955 on 148 degrees of freedom
## Multiple R-squared:  0.07609,    Adjusted R-squared:  0.05112 
## F-statistic: 3.047 on 4 and 148 DF,  p-value: 0.01897
  1. Sadece 1990 ve 1993 yıllarını kullanarak soru I’deki eşitliği havuzlanmış SEKK ile tahmin ediniz. Birleşik hatadaki serisel korelasyon problemini göz ardı ediniz.Caydırıcı bir etkiye dair herhangi bir delil buldunuz mu?
library(plm)
murderpd <- pdata.frame(murder, index =c("state", "year"))
summary(murderpd)
##        id         state     year        mrdrte            exec       
##  Min.   : 1   AK     :  3   87:51   Min.   : 0.800   Min.   : 0.000  
##  1st Qu.:13   AL     :  3   90:51   1st Qu.: 3.900   1st Qu.: 0.000  
##  Median :26   AR     :  3   93:51   Median : 6.400   Median : 0.000  
##  Mean   :26   AZ     :  3           Mean   : 8.071   Mean   : 1.229  
##  3rd Qu.:39   CA     :  3           3rd Qu.:10.200   3rd Qu.: 1.000  
##  Max.   :51   CO     :  3           Max.   :78.500   Max.   :34.000  
##               (Other):135                                            
##       unem             d90              d93            cmrdrte       
##  Min.   : 2.200   Min.   :0.0000   Min.   :0.0000   Min.   :-2.6000  
##  1st Qu.: 4.900   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:-0.4000  
##  Median : 5.800   Median :0.0000   Median :0.0000   Median : 0.3000  
##  Mean   : 5.973   Mean   :0.3333   Mean   :0.3333   Mean   : 0.8422  
##  3rd Qu.: 7.000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.: 1.3000  
##  Max.   :12.000   Max.   :1.0000   Max.   :1.0000   Max.   :41.6000  
##                                                     NA's   :51       
##      cexec              cunem             cexec_1            cunem_1       
##  Min.   :-11.0000   Min.   :-5.80000   Min.   :-11.0000   Min.   :-5.8000  
##  1st Qu.:  0.0000   1st Qu.:-1.07500   1st Qu.:  0.0000   1st Qu.:-1.9500  
##  Median :  0.0000   Median : 0.30000   Median :  0.0000   Median :-1.0000  
##  Mean   :  0.1863   Mean   : 0.00588   Mean   : -0.2745   Mean   :-0.8863  
##  3rd Qu.:  0.0000   3rd Qu.: 1.00000   3rd Qu.:  0.0000   3rd Qu.: 0.0000  
##  Max.   : 23.0000   Max.   : 3.60000   Max.   :  5.0000   Max.   : 3.1000  
##  NA's   :51         NA's   :51         NA's   :102        NA's   :102
coklu <- plm(mrdrte ~ exec + unem + d90 + d93 , data = murder, model = "pooling")
## Warning in pdata.frame(data, index): duplicate couples (id-time) in resulting pdata.frame
##  to find out which, use, e.g., table(index(your_pdataframe), useNA = "ifany")
summary(coklu)
## Pooling Model
## 
## Call:
## plm(formula = mrdrte ~ exec + unem + d90 + d93, data = murder, 
##     model = "pooling")
## 
## Unbalanced Panel: n = 51, T = 3-3, N = 153
## 
## Residuals:
##    Min. 1st Qu.  Median 3rd Qu.    Max. 
## -9.1301 -3.1194 -1.2107  1.3794 67.8099 
## 
## Coefficients:
##             Estimate Std. Error t-value Pr(>|t|)   
## (Intercept) -1.86439    3.06952 -0.6074 0.544523   
## exec         0.16275    0.19393  0.8392 0.402685   
## unem         1.39079    0.45087  3.0847 0.002432 **
## d90          2.67533    1.81693  1.4724 0.143024   
## d93          1.60732    1.77477  0.9056 0.366594   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    12845
## Residual Sum of Squares: 11868
## R-Squared:      0.076089
## Adj. R-Squared: 0.051119
## F-statistic: 3.04715 on 4 and 148 DF, p-value: 0.018975

Etkileşim terimlerinin çoğu anlamsız ve caydırıcı bir etki görünmüyor. En büyük katsayı 1990 almıştır, son üç yıldaki toplam infazdan ve yıllık infaz oranından fazladır.

  1. 1990 ve 1993’ü kullanarak eşitliği sabit etkilerle tahmin ediniz. Sadece iki yıla ait verileri kullanmanız nedeniyle ilk farkları kullanabilirsiniz. Şimdi, caydırıcı bir etkiye dair herhangi bir delil var mıdır? Bu delil ne kadar güçlüdür?
library(plm)
murderpd <- pdata.frame(murder, index =c("state", "year"))
summary(murderpd)
##        id         state     year        mrdrte            exec       
##  Min.   : 1   AK     :  3   87:51   Min.   : 0.800   Min.   : 0.000  
##  1st Qu.:13   AL     :  3   90:51   1st Qu.: 3.900   1st Qu.: 0.000  
##  Median :26   AR     :  3   93:51   Median : 6.400   Median : 0.000  
##  Mean   :26   AZ     :  3           Mean   : 8.071   Mean   : 1.229  
##  3rd Qu.:39   CA     :  3           3rd Qu.:10.200   3rd Qu.: 1.000  
##  Max.   :51   CO     :  3           Max.   :78.500   Max.   :34.000  
##               (Other):135                                            
##       unem             d90              d93            cmrdrte       
##  Min.   : 2.200   Min.   :0.0000   Min.   :0.0000   Min.   :-2.6000  
##  1st Qu.: 4.900   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:-0.4000  
##  Median : 5.800   Median :0.0000   Median :0.0000   Median : 0.3000  
##  Mean   : 5.973   Mean   :0.3333   Mean   :0.3333   Mean   : 0.8422  
##  3rd Qu.: 7.000   3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.: 1.3000  
##  Max.   :12.000   Max.   :1.0000   Max.   :1.0000   Max.   :41.6000  
##                                                     NA's   :51       
##      cexec              cunem             cexec_1            cunem_1       
##  Min.   :-11.0000   Min.   :-5.80000   Min.   :-11.0000   Min.   :-5.8000  
##  1st Qu.:  0.0000   1st Qu.:-1.07500   1st Qu.:  0.0000   1st Qu.:-1.9500  
##  Median :  0.0000   Median : 0.30000   Median :  0.0000   Median :-1.0000  
##  Mean   :  0.1863   Mean   : 0.00588   Mean   : -0.2745   Mean   :-0.8863  
##  3rd Qu.:  0.0000   3rd Qu.: 1.00000   3rd Qu.:  0.0000   3rd Qu.: 0.0000  
##  Max.   : 23.0000   Max.   : 3.60000   Max.   :  5.0000   Max.   : 3.1000  
##  NA's   :51         NA's   :51         NA's   :102        NA's   :102
pdim(murderpd)
## Balanced Panel: n = 51, T = 3, N = 153

51 kişiden 3 yıl boyunca toplam 153 tane gözlem toplanmıştır.

withinmodel <- plm(mrdrte ~ exec  + unem + d90 + d93 + factor(year)*exec + year , data = murder, model = "within")
## Warning in pdata.frame(data, index): duplicate couples (id-time) in resulting pdata.frame
##  to find out which, use, e.g., table(index(your_pdataframe), useNA = "ifany")
summary(withinmodel)
## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = mrdrte ~ exec + unem + d90 + d93 + factor(year) * 
##     exec + year, data = murder, model = "within")
## 
## Unbalanced Panel: n = 51, T = 3-3, N = 153
## 
## Residuals:
##       Min.    1st Qu.     Median    3rd Qu.       Max. 
## -26.693360  -0.684805  -0.056137   0.687376  13.402922 
## 
## Coefficients: (3 dropped because of singularities)
##                       Estimate Std. Error t-value Pr(>|t|)  
## exec                -0.1660867  0.2768209 -0.6000  0.54993  
## unem                 0.2282087  0.3034049  0.7522  0.45380  
## d90                  1.5477421  0.7995912  1.9357  0.05585 .
## d93                  1.7016588  0.7430442  2.2901  0.02420 *
## exec:factor(year)90  0.0075527  0.3136208  0.0241  0.98084  
## exec:factor(year)93  0.0266765  0.1896223  0.1407  0.88842  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    1311.5
## Residual Sum of Squares: 1215
## R-Squared:      0.073558
## Adj. R-Squared: -0.46687
## F-statistic: 1.27037 on 6 and 96 DF, p-value: 0.27826

1990 yılı istatiksel olarak anlamsızdır. 1993 yılının 0,01 anlamlı olduğunu görüyoruz.

randommodel <- plm(mrdrte ~ exec  + unem + d90 + d93 + I(cexec^2) + year , data = murderpd, model = "random")
summary(randommodel)
## Oneway (individual) effect Random Effect Model 
##    (Swamy-Arora's transformation)
## 
## Call:
## plm(formula = mrdrte ~ exec + unem + d90 + d93 + I(cexec^2) + 
##     year, data = murderpd, model = "random")
## 
## Balanced Panel: n = 51, T = 2, N = 102
## 
## Effects:
##                    var  std.dev share
## idiosyncratic   0.5854   0.7651 0.005
## individual    106.1862  10.3047 0.995
## theta: 0.9476
## 
## Residuals:
##     Min.  1st Qu.   Median  3rd Qu.     Max. 
## -1.36973 -0.46929 -0.12669  0.32637  3.83832 
## 
## Coefficients: (2 dropped because of singularities)
##               Estimate Std. Error z-value  Pr(>|z|)    
## (Intercept)  8.9214366  1.7891607  4.9864 6.152e-07 ***
## exec         0.0059700  0.1265524  0.0472   0.96237    
## unem        -0.0188165  0.1609622 -0.1169   0.90694    
## d90         -0.3520064  0.2135355 -1.6485   0.09926 .  
## I(cexec^2)  -0.0068039  0.0076242 -0.8924   0.37217    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    64.721
## Residual Sum of Squares: 59.026
## R-Squared:      0.087985
## Adj. R-Squared: 0.050376
## Chisq: 9.35789 on 4 DF, p-value: 0.052751
library(stargazer)
## 
## Please cite as:
##  Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.
##  R package version 5.2.3. https://CRAN.R-project.org/package=stargazer
stargazer(murderpd, withinmodel, randommodel, type = "text", column.labels = c("OLS","RE","FE"))
## 
## ===========================================
## Statistic  N   Mean  St. Dev.  Min    Max  
## -------------------------------------------
## id        153 26.000  14.768    1      51  
## mrdrte    153 8.071   9.193   0.800  78.500
## exec      153 1.229   3.791     0      34  
## unem      153 5.973   1.681   2.200  12.000
## d90       153 0.333   0.473     0      1   
## d93       153 0.333   0.473     0      1   
## cmrdrte   102 0.842   4.290   -2.600 41.600
## cexec     102 0.186   2.951    -11     23  
## cunem     102 0.006   1.658   -5.800 3.600 
## cexec_1   51  -0.275  2.192    -11     5   
## cunem_1   51  -0.886  1.734   -5.800 3.100 
## -------------------------------------------
## 
## ================================================
##                         Dependent variable:     
##                     ----------------------------
##                                mrdrte           
##                             OLS            RE   
##                             (1)           (2)   
## ------------------------------------------------
## exec                      -0.166         0.006  
##                           (0.277)       (0.127) 
##                                                 
## unem                       0.228         -0.019 
##                           (0.303)       (0.161) 
##                                                 
## d90                       1.548*        -0.352* 
##                           (0.800)       (0.214) 
##                                                 
## d93                       1.702**               
##                           (0.743)               
##                                                 
## exec:factor(year)90        0.008                
##                           (0.314)               
##                                                 
## exec:factor(year)93        0.027                
##                           (0.190)               
##                                                 
## I(cexec2)                                -0.007 
##                                         (0.008) 
##                                                 
## Constant                                8.921***
##                                         (1.789) 
##                                                 
## ------------------------------------------------
## Observations                153           102   
## R2                         0.074         0.088  
## Adjusted R2               -0.467         0.050  
## F Statistic         1.270 (df = 6; 96)   9.358* 
## ================================================
## Note:                *p<0.1; **p<0.05; ***p<0.01

AİRFARE DATASI

library(plm)
data("airfare")
library(rmarkdown)
paged_table(airfare)
airfaremodel <- pdata.frame(airfare, index = c("id","year" ) )
summary(airfaremodel)
##    year            id            dist            passen            fare      
##  1997:1149   1      :   4   Min.   :  95.0   Min.   :   2.0   Min.   : 37.0  
##  1998:1149   2      :   4   1st Qu.: 505.0   1st Qu.: 215.0   1st Qu.:123.0  
##  1999:1149   3      :   4   Median : 861.0   Median : 357.0   Median :168.0  
##  2000:1149   4      :   4   Mean   : 989.7   Mean   : 636.8   Mean   :178.8  
##              5      :   4   3rd Qu.:1304.0   3rd Qu.: 717.0   3rd Qu.:225.0  
##              6      :   4   Max.   :2724.0   Max.   :8497.0   Max.   :522.0  
##              (Other):4572                                                    
##     bmktshr           ldist            y98            y99            y00      
##  Min.   :0.1605   Min.   :4.554   Min.   :0.00   Min.   :0.00   Min.   :0.00  
##  1st Qu.:0.4650   1st Qu.:6.225   1st Qu.:0.00   1st Qu.:0.00   1st Qu.:0.00  
##  Median :0.6039   Median :6.758   Median :0.00   Median :0.00   Median :0.00  
##  Mean   :0.6101   Mean   :6.696   Mean   :0.25   Mean   :0.25   Mean   :0.25  
##  3rd Qu.:0.7531   3rd Qu.:7.173   3rd Qu.:0.25   3rd Qu.:0.25   3rd Qu.:0.25  
##  Max.   :1.0000   Max.   :7.910   Max.   :1.00   Max.   :1.00   Max.   :1.00  
##                                                                               
##      lfare          ldistsq          concen          lpassen      
##  Min.   :3.611   Min.   :20.74   Min.   :0.1605   Min.   :0.6931  
##  1st Qu.:4.812   1st Qu.:38.75   1st Qu.:0.4650   1st Qu.:5.3706  
##  Median :5.124   Median :45.67   Median :0.6039   Median :5.8777  
##  Mean   :5.096   Mean   :45.28   Mean   :0.6101   Mean   :6.0170  
##  3rd Qu.:5.416   3rd Qu.:51.45   3rd Qu.:0.7531   3rd Qu.:6.5751  
##  Max.   :6.258   Max.   :62.57   Max.   :1.0000   Max.   :9.0475  
## 
indexdata <- pdata.frame(airfare, index = c("id", "year"))
pdim(indexdata)
## Balanced Panel: n = 1149, T = 4, N = 4596
pvar(indexdata)
## no time variation:       id dist ldist ldistsq 
## no individual variation: year y98 y99 y00
poolmodel <- plm(lpassen ~ fare + dist + passen + bmktshr + I(ldist^2) + year, data = airfaremodel , airfaremodel = "pooling" )
summary(poolmodel)
## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = lpassen ~ fare + dist + passen + bmktshr + I(ldist^2) + 
##     year, data = airfaremodel, airfaremodel = "pooling")
## 
## Balanced Panel: n = 1149, T = 4, N = 4596
## 
## Residuals:
##        Min.     1st Qu.      Median     3rd Qu.        Max. 
## -2.17315683 -0.03750978  0.00081035  0.03994864  1.98735732 
## 
## Coefficients:
##             Estimate  Std. Error  t-value  Pr(>|t|)    
## fare     -4.3260e-03  1.3776e-04 -31.4030 < 2.2e-16 ***
## passen    5.4114e-04  2.2967e-05  23.5623 < 2.2e-16 ***
## bmktshr   1.6054e-01  3.9765e-02   4.0374 5.523e-05 ***
## year1998  1.5337e-02  6.0027e-03   2.5550   0.01066 *  
## year1999  5.0585e-02  6.1888e-03   8.1737 4.160e-16 ***
## year2000  1.0955e-01  6.6880e-03  16.3808 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    128.1
## Residual Sum of Squares: 70.409
## R-Squared:      0.45035
## Adj. R-Squared: 0.26602
## F-statistic: 469.9 on 6 and 3441 DF, p-value: < 2.22e-16
withinmodel <- plm(lpassen ~ fare + dist + passen + bmktshr + I(ldist^2) + year, data = airfaremodel , airfaremodel = "within" )
summary(withinmodel)
## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = lpassen ~ fare + dist + passen + bmktshr + I(ldist^2) + 
##     year, data = airfaremodel, airfaremodel = "within")
## 
## Balanced Panel: n = 1149, T = 4, N = 4596
## 
## Residuals:
##        Min.     1st Qu.      Median     3rd Qu.        Max. 
## -2.17315683 -0.03750978  0.00081035  0.03994864  1.98735732 
## 
## Coefficients:
##             Estimate  Std. Error  t-value  Pr(>|t|)    
## fare     -4.3260e-03  1.3776e-04 -31.4030 < 2.2e-16 ***
## passen    5.4114e-04  2.2967e-05  23.5623 < 2.2e-16 ***
## bmktshr   1.6054e-01  3.9765e-02   4.0374 5.523e-05 ***
## year1998  1.5337e-02  6.0027e-03   2.5550   0.01066 *  
## year1999  5.0585e-02  6.1888e-03   8.1737 4.160e-16 ***
## year2000  1.0955e-01  6.6880e-03  16.3808 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    128.1
## Residual Sum of Squares: 70.409
## R-Squared:      0.45035
## Adj. R-Squared: 0.26602
## F-statistic: 469.9 on 6 and 3441 DF, p-value: < 2.22e-16
randommodel <- plm(lpassen ~ fare + dist + passen + bmktshr + I(ldist^2) + year, data = airfaremodel, airfaremodel = "random" )
summary(randommodel)
## Oneway (individual) effect Within Model
## 
## Call:
## plm(formula = lpassen ~ fare + dist + passen + bmktshr + I(ldist^2) + 
##     year, data = airfaremodel, airfaremodel = "random")
## 
## Balanced Panel: n = 1149, T = 4, N = 4596
## 
## Residuals:
##        Min.     1st Qu.      Median     3rd Qu.        Max. 
## -2.17315683 -0.03750978  0.00081035  0.03994864  1.98735732 
## 
## Coefficients:
##             Estimate  Std. Error  t-value  Pr(>|t|)    
## fare     -4.3260e-03  1.3776e-04 -31.4030 < 2.2e-16 ***
## passen    5.4114e-04  2.2967e-05  23.5623 < 2.2e-16 ***
## bmktshr   1.6054e-01  3.9765e-02   4.0374 5.523e-05 ***
## year1998  1.5337e-02  6.0027e-03   2.5550   0.01066 *  
## year1999  5.0585e-02  6.1888e-03   8.1737 4.160e-16 ***
## year2000  1.0955e-01  6.6880e-03  16.3808 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Total Sum of Squares:    128.1
## Residual Sum of Squares: 70.409
## R-Squared:      0.45035
## Adj. R-Squared: 0.26602
## F-statistic: 469.9 on 6 and 3441 DF, p-value: < 2.22e-16
library(stargazer)
stargazer(poolmodel, withinmodel, randommodel, type = "text", column.labels = c("OLS","RE","FE"))
## 
## ===========================================================
##                                  Dependent variable:       
##                            --------------------------------
##                                        lpassen             
##                               OLS         RE         FE    
##                               (1)        (2)        (3)    
## -----------------------------------------------------------
## fare                       -0.004***  -0.004***  -0.004*** 
##                             (0.0001)   (0.0001)   (0.0001) 
##                                                            
## passen                      0.001***   0.001***   0.001*** 
##                            (0.00002)  (0.00002)  (0.00002) 
##                                                            
## bmktshr                     0.161***   0.161***   0.161*** 
##                             (0.040)    (0.040)    (0.040)  
##                                                            
## year1998                    0.015**    0.015**    0.015**  
##                             (0.006)    (0.006)    (0.006)  
##                                                            
## year1999                    0.051***   0.051***   0.051*** 
##                             (0.006)    (0.006)    (0.006)  
##                                                            
## year2000                    0.110***   0.110***   0.110*** 
##                             (0.007)    (0.007)    (0.007)  
##                                                            
## -----------------------------------------------------------
## Observations                 4,596      4,596      4,596   
## R2                           0.450      0.450      0.450   
## Adjusted R2                  0.266      0.266      0.266   
## F Statistic (df = 6; 3441) 469.900*** 469.900*** 469.900***
## ===========================================================
## Note:                           *p<0.1; **p<0.05; ***p<0.01