# #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}\$,

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,

``````temp <- tempfile()
con <- unz(temp, "VV-DATA.DAT")
``````

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
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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