#StackBounty: #estimation #endogeneity Vella and Verbeek's (1998) endogeneity correction terms

Bounty: 50

I’m trying to reproduce Vella and Verbeek’s (1998) analysis and I am struggling to understand how I define their endogeneity correction terms, i.e. $C_i$ and $C_{it}$,
Vella and Verbeek's endogeneity correction terms

I’ve manged to compute two of their models, model 1 and model [3] in Table III (Vella and Verbeek 1998, p. 171), see my working example below, but I cannot figure out how to compute model [5] that include the endogeneity correction terms.

I am sharing what I got in the hope someone can help me move forward,

Loading data,

temp <- tempfile()
download.file("http://qed.econ.queensu.ca/jae/1998-v13.2/vella-verbeek/vv-data.zip", temp)
con <- unz(temp, "VV-DATA.DAT")
VVdata <- read.table(con)
unlink(temp)

Labeling variables,

names(VVdata) <- c('NR', 'YEAR', 'AG', 'BLACK', 'BUS', 'CON', 'ENT', 'EXPER', 'FIN', 'HISP',
                   'HLTH', 'HOURS', 'MAN', 'MAR', 'MIN', 'NC', 'NE', 'OCC1', 'OCC2', 
                   'OCC3', 'OCC4', 'OCC5', 'OCC6', 'OCC7', 'OCC8', 'OCC9', 'PER', 'PRO', 
                   'PUB', 'RUR', 'S', 'SCHOOL', 'TRA', 'TRAD', 'UNION', 'WAGE')

Install packages and lod plm

# install.packages(c("wooldridge", "plm", "stargazer"), dependencies = TRUE)
require(plm)

model [1] and [3]

Pooled.ols.III.1  <- plm(WAGE ~ UNION + SCHOOL + EXPER + I(EXPER ^2 ) + HISP + BLACK + RUR + MAR + HLTH + factor(YEAR) + S + NE + NC + AG + MIN + CON + MAN + TRA + TRAD + FIN + BUS + PER + ENT + PRO, data = VVdata, index=c("NR","YEAR") , model="pooling")
# summary(Pooled.ols.III.1)
Pooled.ols.III.3 <- plm(WAGE ~ UNION + SCHOOL + EXPER + I(EXPER ^2 ) + HISP + BLACK + RUR + MAR + HLTH + factor(YEAR) +  S + NE + NC + AG + MIN + CON + MAN + TRA + TRAD + FIN + BUS + PER + ENT + PRO, data = VVdata, index=c("NR","YEAR") , model="within")

Display using stargazer

stargazer::stargazer(Pooled.ols.III.1, Pooled.ols.III.3, type="text", column.labels=c("III, [1]", "III, [3]"), dep.var.labels = c("log(wage)"), align = TRUE, digits = 3, keep=c("Constant", "UNI", "SCH", "EXP", "I(EXPER2)","HIS","BLAC", "RUR", "MAR", "HLT"))
================================================================
                             Dependent variable:                
             ---------------------------------------------------
                                  log(wage)                     
                     III, [1]                  III, [3]         
                        (1)                       (2)           
----------------------------------------------------------------
UNION                0.148***                  0.077***         
                      (0.017)                   (0.019)         

SCHOOL               0.084***                                   
                      (0.005)                                   

EXPER                0.059***                  0.128***         
                      (0.013)                   (0.010)         

I(EXPER2)            -0.002**                  -0.005***        
                      (0.001)                   (0.001)         

HISP                 -0.059***                                  
                      (0.022)                                   

BLACK                -0.150***                                  
                      (0.023)                                   

RUR                  -0.129***                  0.050*          
                      (0.019)                   (0.029)         

MAR                  0.110***                   0.041**         
                      (0.015)                   (0.018)         

HLTH                  -0.055                    -0.016          
                      (0.054)                   (0.047)         

Constant             0.320***                                   
                      (0.088)                                   

----------------------------------------------------------------
Observations           4,360                     4,360          
R2                     0.265                     0.192          
Adjusted R2            0.260                     0.071          
F Statistic  52.149*** (df = 30; 4329) 34.705*** (df = 26; 3789)
================================================================
Note:                                *p<0.1; **p<0.05; ***p<0.01

Vella, F. and Verbeek, M. (1998). `Whose Wages Do Unions Raise? A Dynamic
Model of Unionism and Wage Rate Determination for Young Men’, Journal of
Applied Econometrics, 13(2), pp. 163-183.

Vella, F. and Verbeek, M. (1999). `Two-step Estimation of Panel Data Models
with Censored Endogenous Variables and Selection Bias’, Journal of Econometrics,
90, pp. 239-263.


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