Problem with instrumental variables regression in XTIVREG2 due to multicollinearity of year dummies

[Valentina Ciriotto]

Dear Stata-list:

I am having difficulties with the command xtivreg2. When I run my regression, the system drops some of my year dummies. I tried to use fe or fd, but the problem is the same. I am using Stata18, and xtivreg210. My panel has n=95 and T=41. xtivreg seems to work, but I would like to use xtivreg2 for the tests. My variables are all continuous, except for year dummies.

This is my code:

xtset Province year
xi:xtivreg2 FLPR (nursery_rate = ln_GDPCCONSTR) Sep NF log_GDP2005pc i.year, fe cluster (Province)

That is the output:

. xi:xtivreg2 FLPR (nursery_rate = ln_GDPCCONSTR) Sep NF log_GDP2005pc i.year, fe cluster (Province)
i.year _Iyear_1951-1991 (naturally coded; _Iyear_1951 omitted)
Warning - collinearities detected
Vars dropped: _Iyear_1973 _Iyear_1978 _Iyear_1991

FIXED EFFECTS ESTIMATION
------------------------
Number of groups = 95 Obs per group: min = 2
avg = 36.5
max = 38
Warning - collinearities detected
Vars dropped: _Iyear_1973 _Iyear_1978 _Iyear_1991

IV (2SLS) estimation
--------------------

Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on Province

Number of clusters (Province) = 95 Number of obs = 3468
F( 41, 94) = 108.98
Prob > F = 0.0000
Total (centered) SS = 10848829.29 Centered R2 = 0.7025
Total (uncentered) SS = 10848829.29 Uncentered R2 = 0.7025
Residual SS = 3227943.215 Root MSE = 30.94

-------------------------------------------------------------------------------
| Robust
FLPR | Coefficient std. err. z P>|z| [95% conf. interval]
--------------+----------------------------------------------------------------
nursery_rate | -.1857237 .5531766 -0.34 0.737 -1.26993 .8984824
Sep | 17.05098 8.422264 2.02 0.043 .5436437 33.55831
NF | -95.04478 25.2899 -3.76 0.000 -144.6121 -45.47748
log_GDP2005pc | 15.13143 54.05821 0.28 0.780 -90.82071 121.0836
_Iyear_1952 | 140.8487 109.4066 1.29 0.198 -73.58436 355.2818
_Iyear_1953 | 131.6268 108.0823 1.22 0.223 -80.21061 343.4642
_Iyear_1954 | 124.9839 104.921 1.19 0.234 -80.65749 330.6252
_Iyear_1955 | 116.8989 101.7531 1.15 0.251 -82.53357 316.3314
_Iyear_1956 | 109.1868 98.55322 1.11 0.268 -83.97396 302.3476
_Iyear_1957 | 102.5229 95.29937 1.08 0.282 -84.26048 289.3062
_Iyear_1958 | 97.71242 91.15555 1.07 0.284 -80.94918 276.374
_Iyear_1959 | 92.68667 87.82716 1.06 0.291 -79.4514 264.8247
_Iyear_1960 | 86.81232 83.67987 1.04 0.300 -77.19722 250.8219
_Iyear_1961 | 82.79502 79.84329 1.04 0.300 -73.69495 239.285
_Iyear_1962 | 79.90715 76.48192 1.04 0.296 -69.99466 229.809
_Iyear_1963 | 65.43609 72.36494 0.90 0.366 -76.39659 207.2688
_Iyear_1964 | 56.00226 66.99057 0.84 0.403 -75.29684 187.3014
_Iyear_1965 | 48.82917 64.06039 0.76 0.446 -76.72689 174.3852
_Iyear_1966 | 38.88355 60.11467 0.65 0.518 -78.93905 156.7061
_Iyear_1967 | 39.32863 55.66573 0.71 0.480 -69.77419 148.4315
_Iyear_1968 | 41.03149 50.95197 0.81 0.421 -58.83254 140.8955
_Iyear_1969 | 40.78152 47.59848 0.86 0.392 -52.50979 134.0728
_Iyear_1970 | 41.43966 43.69138 0.95 0.343 -44.19387 127.0732
_Iyear_1971 | 37.92353 41.151 0.92 0.357 -42.73094 118.578
_Iyear_1972 | 21.44963 39.54252 0.54 0.588 -56.05228 98.95154
_Iyear_1973 | 0 (omitted)
_Iyear_1974 | 22.96776 33.10759 0.69 0.488 -41.92192 87.85744
_Iyear_1975 | 17.71347 30.03025 0.59 0.555 -41.14473 76.57168
_Iyear_1976 | 17.0237 30.56721 0.56 0.578 -42.88694 76.93433
_Iyear_1977 | 39.02033 27.36672 1.43 0.154 -14.61745 92.65812
_Iyear_1978 | 0 (omitted)
_Iyear_1979 | 31.85343 20.16057 1.58 0.114 -7.660561 71.36743
_Iyear_1980 | 30.30293 21.50671 1.41 0.159 -11.84943 72.4553
_Iyear_1981 | 22.02899 16.7729 1.31 0.189 -10.8453 54.90327
_Iyear_1982 | 17.82387 15.4912 1.15 0.250 -12.53832 48.18606
_Iyear_1983 | 14.97719 15.1556 0.99 0.323 -14.72723 44.68162
_Iyear_1984 | 15.5283 15.2084 1.02 0.307 -14.27961 45.33621
_Iyear_1985 | 12.82768 14.1356 0.91 0.364 -14.87759 40.53296
_Iyear_1986 | 12.2171 12.25306 1.00 0.319 -11.79846 36.23266
_Iyear_1987 | 9.856019 11.68595 0.84 0.399 -13.04803 32.76006
_Iyear_1988 | 8.15025 9.981069 0.82 0.414 -11.41229 27.71279
_Iyear_1989 | .2217523 8.197875 0.03 0.978 -15.84579 16.28929
_Iyear_1990 | 1.12541 4.973674 0.23 0.821 -8.622812 10.87363
_Iyear_1991 | 0 (omitted)
-------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 5.346
Chi-sq(1) P-val = 0.0208
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 109.174
(Kleibergen-Paap rk Wald F statistic): 6.253
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Hansen J statistic (overidentification test of all instruments): 0.000
(equation exactly identified)
------------------------------------------------------------------------------
Instrumented: nursery_rate
Included instruments: Sep NF log_GDP2005pc _Iyear_1952 _Iyear_1953 _Iyear_1954
_Iyear_1955 _Iyear_1956 _Iyear_1957 _Iyear_1958
_Iyear_1959 _Iyear_1960 _Iyear_1961 _Iyear_1962
_Iyear_1963 _Iyear_1964 _Iyear_1965 _Iyear_1966
_Iyear_1967 _Iyear_1968 _Iyear_1969 _Iyear_1970
_Iyear_1971 _Iyear_1972 _Iyear_1974 _Iyear_1975
_Iyear_1976 _Iyear_1977 _Iyear_1979 _Iyear_1980
_Iyear_1981 _Iyear_1982 _Iyear_1983 _Iyear_1984
_Iyear_1985 _Iyear_1986 _Iyear_1987 _Iyear_1988
_Iyear_1989 _Iyear_1990
Excluded instruments: ln_GDPCCONSTR
Dropped collinear: _Iyear_1973 _Iyear_1978 _Iyear_1991
------------------------------------------------------------------------------

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