On R, I have panel dataset with observations for individual, year and variables y, x and z. I am trying to estimate an IV regression so that:
$$y = \beta x + e$$
$$x = \alpha z + u$$
Is there a way to estimate the IV regression while clustering standard errors by individual?
So far I have used ivreg as follows:
my_iv <- ivreg(y ~ x + as.factor(year) |z + as.factor(year),
data = data)
But can't figure out how to include clustered standard errors. Thanks in advance!
We can use lfe::felm.
The formula is specified as y ~ x1 + x2 | f1 + f2 | (Q|W ~ x3+x4) | clu1 + clu2 , where first term is the model, f are the fixed effects, middle term is the instrument and third term the clusters, where we only have clu1 = id.
ivest <- lfe::felm(y ~ x1 + x2 | id + firm | (Q|W ~ x3 + factor(x4)) | id, data = d)
summary(ivest)
# Call:
# lfe::felm(formula = y ~ x1 + x2 | id + firm | (Q | W ~ x3 + factor(x4)) | id, data = d)
#
# Residuals:
# Min 1Q Median 3Q Max
# -1.9436 -0.5140 0.0078 0.4335 2.0452
#
# Coefficients:
# Estimate Cluster s.e. t value Pr(>|t|)
# x1 1.6392 0.5155 3.180 0.00519 **
# x2 0.5039 0.1547 3.257 0.00438 **
# `Q(fit)` 0.9348 0.5148 1.816 0.08608 .
# `W(fit)` 1.2116 0.1048 11.561 9.18e-10 ***
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#
# Residual standard error: 1.051 on 40 degrees of freedom
# Multiple R-squared(full model): 0.8295 Adjusted R-squared: 0.6846
# Multiple R-squared(proj model): 0.7157 Adjusted R-squared: 0.474
# F-statistic(full model, *iid*):6.157 on 34 and 40 DF, p-value: 6.629e-08
# F-statistic(proj model): 85.66 on 4 and 18 DF, p-value: 1.837e-11
# F-statistic(endog. vars):121.7 on 2 and 18 DF, p-value: 3.488e-11
Data:
d <- structure(list(x1 = c(1.37095844714667, -0.564698171396089, 0.363128411337339,
0.63286260496104, 0.404268323140999, -0.106124516091484, 1.51152199743894,
-0.0946590384130976, 2.01842371387704, -0.062714099052421, 1.30486965422349,
2.28664539270111, -1.38886070111234, -0.278788766817371, -0.133321336393658,
0.635950398070074, -0.284252921416072, -2.65645542090478, -2.44046692857552,
1.32011334573019, -0.306638594078475, -1.78130843398, -0.171917355759621,
1.2146746991726, 1.89519346126497, -0.4304691316062, -0.25726938276893,
-1.76316308519478, 0.460097354831271, -0.639994875960119, 0.455450123241219,
0.704837337228819, 1.03510352196992, -0.608926375407211, 0.50495512329797,
-1.71700867907334, -0.784459008379496, -0.850907594176518, -2.41420764994663,
0.0361226068922556, 0.205998600200254, -0.361057298548666, 0.758163235699517,
-0.726704827076575, -1.36828104441929, 0.432818025888717, -0.811393176186672,
1.44410126172125, -0.431446202613345, 0.655647883402207, 0.321925265203947,
-0.783838940880375, 1.57572751979198, 0.642899305717316, 0.0897606465996057,
0.276550747291463, 0.679288816055271, 0.0898328865790817, -2.99309008315293,
0.284882953530659, -0.367234642740975, 0.185230564865609, 0.581823727365507,
1.39973682729268, -0.727292059474465, 1.30254263204414, 0.335848119752074,
1.03850609869762, 0.920728568290646, 0.720878162866862, -1.04311893856785,
-0.0901863866107067, 0.623518161999544, -0.953523357772344, -0.542828814573857
), x2 = c(0.580996497681682, 0.768178737834591, 0.463767588540167,
-0.885776297409679, -1.09978089864786, 1.51270700980493, 0.257921437532031,
0.0884402291595864, -0.120896537539089, -1.19432889516053, 0.611996898040387,
-0.217139845746521, -0.182756706331922, 0.93334632857116, 0.821773110508249,
1.39211637593427, -0.476173923054674, 0.650348560726305, 1.39111045639,
-1.1107888794479, -0.860792586877842, -1.13173868085377, -1.4592139995024,
0.0799825532411612, 0.65320433964919, 1.20096537559849, 1.04475108716773,
-1.00320864683985, 1.84848190167275, -0.666773408757817, 0.105513812456069,
-0.422255881868856, -0.122350171954971, 0.188193034501498, 0.119160957997006,
-0.0250925508674029, 0.108072727942033, -0.485435235846668, -0.504217130687904,
-1.66109907991481, -0.382333726873818, -0.5126502578778, 2.7018910003448,
-1.36211623118972, 0.137256218558607, -1.49362506731629, -1.4704357414368,
0.124702386197007, -0.996639134884037, -0.0018226143047082, -0.428258881425815,
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0.567620594423535, -0.492877353553475, 6.28840653511241e-05,
1.12288964337997, 1.43985574297619, -1.09711376840582, -0.117319560250177,
1.2014984009197, -0.469729580566301, -0.0524694849389963, -0.0861072982370896,
-0.887679017906432, -0.444684004884738, -0.0294448790882381,
-0.413868849057924, 1.1133860233682, -0.480992841653982, -0.433169032600729,
0.696862576552103, -1.05636841317091), id = structure(c(15L,
1L, 6L, 10L, 8L, 19L, 12L, 5L, 10L, 14L, 2L, 6L, 1L, 13L, 15L,
16L, 10L, 17L, 2L, 9L, 4L, 19L, 14L, 7L, 16L, 5L, 19L, 17L, 8L,
10L, 6L, 9L, 8L, 18L, 8L, 10L, 18L, 4L, 9L, 16L, 11L, 6L, 14L,
8L, 9L, 17L, 7L, 13L, 11L, 18L, 9L, 5L, 2L, 3L, 2L, 13L, 15L,
4L, 6L, 19L, 19L, 10L, 1L, 13L, 1L, 4L, 12L, 6L, 11L, 7L, 11L,
5L, 17L, 7L, 12L), levels = c("1", "2", "3", "4", "5", "6", "7",
"9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19",
"20"), class = "factor"), firm = structure(c(10L, 6L, 2L, 12L,
3L, 1L, 13L, 4L, 11L, 9L, 6L, 10L, 7L, 3L, 12L, 2L, 9L, 12L,
10L, 9L, 3L, 7L, 3L, 6L, 13L, 4L, 10L, 2L, 7L, 1L, 2L, 3L, 1L,
10L, 5L, 13L, 2L, 3L, 3L, 10L, 2L, 10L, 4L, 9L, 10L, 13L, 7L,
1L, 4L, 6L, 3L, 12L, 3L, 6L, 12L, 9L, 10L, 7L, 3L, 9L, 2L, 6L,
9L, 8L, 11L, 6L, 5L, 10L, 1L, 9L, 10L, 1L, 12L, 6L, 1L), levels = c("1",
"2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13"
), class = "factor"), u = c(1.50059880011796, -1.1406741536911,
0.496847374722702, 1.4083694575847, -0.62337037345602, -0.741660664568964,
0.376627729983173, -1.31017535156112, 0.0781199235564999, -0.795416769640129,
1.76649494325627, -0.936421828043658, 0.703918293809932, -0.755838819389157,
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-0.388535656201395, -0.669263871638158, 0.704517511710363, -0.827627694647081,
-3.3493240811071, 0.342540952025075, -1.93109788557074, 0.177752576915369,
1.40188419407316, 0.373066264998072, -0.0486032519865556, 2.46346047322287,
0.567606140037349, 0.968840299750039, 2.65141739994693, -0.0344926185009225,
-0.40962669998027, -0.103651100985079, -0.574649379426294, -0.51335141274752,
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0.959600821189023, 0.507252101121057, -0.374112242378446, 1.42044733361966,
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-0.48968148391622, 1.28769545705832, 0.930501447346418, 0.72614069638199,
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0.589847453563791, 3.27667516342197, -0.358336088116629, 1.93500981542015,
1.2290187506713, 3.88766205090481, -0.853662127286324, -2.97033719755537,
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), class = "data.frame")