Nothing
Different Variance-Covariance Estimators
In capybara: Fast and Memory Efficient Fitting of Linear Models with High-Dimensional Fixed Effects
knitr::opts_chunk$set(
collapse = TRUE,
comment = "#>"
)
library(capybara)
A very quick verification of Ross (2004) is to obtain the coefficients for the OLS model from table 1:
felm(ltrade ~ bothin + onein + gsp + ldist + lrgdp + lrgdppc + regional +
custrict + comlang + border + landl + island + lareap + comcol +
curcol + colony + comctry | year, data = ross2004)
Formula: ltrade ~ bothin + onein + gsp + ldist + lrgdp + lrgdppc + regional +
custrict + comlang + border + landl + island + lareap + comcol +
curcol + colony + comctry | year
Estimates:
| | Estimate | Std. Error | z value | Pr(>|z|) |
|----------|----------|------------|-----------|-----------|
| bothin | -0.0423 | 0.0159 | -2.6540 | 0.0080 ** |
| onein | -0.0583 | 0.0154 | -3.7722 | 0.0002 ** |
| gsp | 0.8585 | 0.0111 | 77.0829 | 0.0000 ** |
| ldist | -1.1190 | 0.0061 | -183.0863 | 0.0000 ** |
| lrgdp | 0.9159 | 0.0026 | 355.9087 | 0.0000 ** |
| lrgdppc | 0.3214 | 0.0039 | 83.2804 | 0.0000 ** |
| regional | 1.1988 | 0.0360 | 33.2956 | 0.0000 ** |
| custrict | 1.1181 | 0.0374 | 29.8774 | 0.0000 ** |
| comlang | 0.3125 | 0.0110 | 28.3085 | 0.0000 ** |
| border | 0.5257 | 0.0266 | 19.7328 | 0.0000 ** |
| landl | -0.2706 | 0.0093 | -29.0310 | 0.0000 ** |
| island | 0.0419 | 0.0095 | 4.4335 | 0.0000 ** |
| lareap | -0.0967 | 0.0020 | -47.5692 | 0.0000 ** |
| comcol | 0.5846 | 0.0162 | 36.1094 | 0.0000 ** |
| curcol | 1.0751 | 0.1067 | 10.0763 | 0.0000 ** |
| colony | 1.1638 | 0.0312 | 37.3391 | 0.0000 ** |
| comctry | -0.0163 | 0.2623 | -0.0622 | 0.9504 |
Significance codes: ** p < 0.01; * p < 0.05; + p < 0.10
R-squared : 0.648
Adj. R-squared: 0.6479
Fixed effects:
year: 52
Number of observations: Full 234597; Missing 0; Perfect classification 0
This does not involve many fixed effects. However, capybara will be particularly useful to
obtain different standard errors for the same functional form, which is the main focus of
table 4B in Cameron & Miller (2014).
Table 4B shows the following clustering methods that we can replicate with the third part of the
model formula (e.g. y ~ x1 + x2 + ... | fe1 + fe2 | cl1 + cl2) and using the vcov argument
to select how the clustering variables are used:
| vcov value | Description |
|:-----------------|:-----------------------------------------------|
| "iid" | Default OLS (i.i.d. errors) |
| "hetero" | Heteroskedastic-robust (HC0) |
| "cluster" | One-way cluster sandwich |
| "m-estimator" | One-way M-estimator sandwich |
| "dyadic" | Dyadic-robust (Cameron & Miller, 2014) |
Capybara provides an update() method to easily modify the formula for each model, as we need
to change the clustering variables for each model, which avoids error-prone copy-pasting of the full
formula every time.
IID (no cluster part in formula)
fml <- ltrade ~ bothin + onein + gsp + ldist + lrgdp + lrgdppc + regional +
custrict + comlang + border + landl + island + lareap + comcol +
curcol + colony + comctry | year
fit_iid <- felm(
fml,
data = ross2004, vcov = "iid"
)
Heteroskedastic-robust (HC0)
fit_hetero <- felm(
fml,
data = ross2004, vcov = "hetero"
)
One-way: cluster on country-pair (g,h)
Note that multi-part formulas (e.g., y ~ x | fe | cl) are handled by the Formula package. Therefore,
updating those needs an explicit Formula::as.Formula() call if the formula type was not specified initially.
fml2 <- update(Formula::as.Formula(fml), . ~ . | . | pair)
fit_pairs <- felm(
fml2,
data = ross2004, vcov = "cluster"
)
One-way: cluster on country 1 (g)
fit_ctry1 <- felm(
update(fml2, . ~ . | . | ctry1),
data = ross2004, vcov = "cluster"
)
One-way: cluster on country 2 (h)
fit_ctry2 <- felm(
update(fml2, . ~ . | . | ctry2),
data = ross2004, vcov = "cluster"
)
Two-way: cluster on (g) and (h) simultaneously
fit_2way <- felm(
update(fml2, . ~ . | . | ctry1 + ctry2),
data = ross2004, vcov = "cluster"
)
Dyadic-robust: Cameron-Miller (2014) sandwich with cross-dyad correlations
fit_dyadic <- felm(
update(fml2, . ~ . | . | ctry1 + ctry2),
data = ross2004, vcov = "dyadic"
)
With the above models, we can replicate Table 4B from Cameron & Miller (2014) using
summary_table(), another convenience function in capybara to display multiple models side-by-side.
This completely avoids calling summary() on each model and then conducting post-processing to
extract the relevant information for the table.
summary_table(
fit_iid, fit_hetero, fit_pairs, fit_ctry1, fit_ctry2, fit_2way, fit_dyadic,
model_names = c("IID", "Hetero", "Pairs", "Country 1", "Country 2", "2-Way", "Dyadic")
)
| Variable | IID | Hetero | Pairs | Country 1 | Country 2 | 2-Way | Dyadic |
|------------------|--------------------|--------------------------|--------------------|--------------------|--------------------|--------------------|--------------------|
| bothin | -0.042** | -0.042* | -0.042 | -0.042 | -0.042 | -0.042 | -0.042 |
| | (0.016) | (0.018) | (0.053) | (0.122) | (0.107) | (0.122) | (0.186) |
| onein | -0.058** | -0.058** | -0.058 | -0.058 | -0.058 | -0.058 | -0.058 |
| | (0.015) | (0.018) | (0.049) | (0.095) | (0.071) | (0.095) | (0.126) |
| gsp | 0.859** | 0.859** | 0.859** | 0.859** | 0.859** | 0.859** | 0.859** |
| | (0.011) | (0.009) | (0.032) | (0.098) | (0.074) | (0.098) | (0.131) |
| ldist | -1.119** | -1.119** | -1.119** | -1.119** | -1.119** | -1.119** | -1.119** |
| | (0.006) | (0.006) | (0.022) | (0.051) | (0.050) | (0.051) | (0.078) |
| lrgdp | 0.916** | 0.916** | 0.916** | 0.916** | 0.916** | 0.916** | 0.916** |
| | (0.003) | (0.003) | (0.010) | (0.024) | (0.028) | (0.024) | (0.043) |
| lrgdppc | 0.321** | 0.321** | 0.321** | 0.321** | 0.321** | 0.321** | 0.321** |
| | (0.004) | (0.004) | (0.014) | (0.033) | (0.038) | (0.033) | (0.052) |
| regional | 1.199** | 1.199** | 1.199** | 1.199** | 1.199** | 1.199** | 1.199** |
| | (0.036) | (0.029) | (0.106) | (0.222) | (0.185) | (0.222) | (0.333) |
| custrict | 1.118** | 1.118** | 1.118** | 1.118** | 1.118** | 1.118** | 1.118** |
| | (0.037) | (0.035) | (0.122) | (0.165) | (0.176) | (0.165) | (0.235) |
| comlang | 0.313** | 0.313** | 0.313** | 0.313** | 0.313** | 0.313** | 0.313** |
| | (0.011) | (0.011) | (0.040) | (0.081) | (0.065) | (0.081) | (0.111) |
| border | 0.526** | 0.526** | 0.526** | 0.526** | 0.526** | 0.526** | 0.526* |
| | (0.027) | (0.026) | (0.111) | (0.148) | (0.150) | (0.148) | (0.207) |
| landl | -0.271** | -0.271** | -0.271** | -0.271** | -0.271** | -0.271** | -0.271* |
| | (0.009) | (0.010) | (0.031) | (0.069) | (0.079) | (0.069) | (0.110) |
| island | 0.042** | 0.042** | 0.042 | 0.042 | 0.042 | 0.042 | 0.042 |
| | (0.009) | (0.009) | (0.036) | (0.105) | (0.083) | (0.105) | (0.154) |
| lareap | -0.097** | -0.097** | -0.097** | -0.097** | -0.097** | -0.097** | -0.097* |
| | (0.002) | (0.002) | (0.008) | (0.025) | (0.025) | (0.025) | (0.043) |
| comcol | 0.585** | 0.585** | 0.585** | 0.585** | 0.585** | 0.585** | 0.585** |
| | (0.016) | (0.019) | (0.067) | (0.126) | (0.108) | (0.126) | (0.178) |
| curcol | 1.075** | 1.075** | 1.075** | 1.075* | 1.075** | 1.075* | 1.075* |
| | (0.107) | (0.070) | (0.235) | (0.462) | (0.256) | (0.462) | (0.480) |
| colony | 1.164** | 1.164** | 1.164** | 1.164** | 1.164** | 1.164** | 1.164** |
| | (0.031) | (0.023) | (0.117) | (0.193) | (0.115) | (0.193) | (0.209) |
| comctry | -0.016 | -0.016 | -0.016 | -0.016 | -0.016 | -0.016 | -0.016 |
| | (0.262) | (0.205) | (1.081) | (0.884) | (1.077) | (0.884) | (0.859) |
| | | | | | | | |
| Fixed effects | | | | | | | |
| year | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
| | | | | | | | |
| N | 234,597 | 234,597 | 234,597 | 234,597 | 234,597 | 234,597 | 234,597 |
| R-squared | 0.648 | 0.648 | 0.648 | 0.648 | 0.648 | 0.648 | 0.648 |
| SE type | IID | Heteroskedastic-robust | Cluster-robust | Cluster-robust | Cluster-robust | Cluster-robust | Dyadic-robust |
Standard errors in parenthesis
Significance levels: ** p < 0.01; * p < 0.05; + p < 0.10
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capybara documentation built on June 29, 2026, 5:07 p.m.
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knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )
library(capybara)
A very quick verification of Ross (2004) is to obtain the coefficients for the OLS model from table 1:
felm(ltrade ~ bothin + onein + gsp + ldist + lrgdp + lrgdppc + regional + custrict + comlang + border + landl + island + lareap + comcol + curcol + colony + comctry | year, data = ross2004)
Formula: ltrade ~ bothin + onein + gsp + ldist + lrgdp + lrgdppc + regional + custrict + comlang + border + landl + island + lareap + comcol + curcol + colony + comctry | year Estimates: | | Estimate | Std. Error | z value | Pr(>|z|) | |----------|----------|------------|-----------|-----------| | bothin | -0.0423 | 0.0159 | -2.6540 | 0.0080 ** | | onein | -0.0583 | 0.0154 | -3.7722 | 0.0002 ** | | gsp | 0.8585 | 0.0111 | 77.0829 | 0.0000 ** | | ldist | -1.1190 | 0.0061 | -183.0863 | 0.0000 ** | | lrgdp | 0.9159 | 0.0026 | 355.9087 | 0.0000 ** | | lrgdppc | 0.3214 | 0.0039 | 83.2804 | 0.0000 ** | | regional | 1.1988 | 0.0360 | 33.2956 | 0.0000 ** | | custrict | 1.1181 | 0.0374 | 29.8774 | 0.0000 ** | | comlang | 0.3125 | 0.0110 | 28.3085 | 0.0000 ** | | border | 0.5257 | 0.0266 | 19.7328 | 0.0000 ** | | landl | -0.2706 | 0.0093 | -29.0310 | 0.0000 ** | | island | 0.0419 | 0.0095 | 4.4335 | 0.0000 ** | | lareap | -0.0967 | 0.0020 | -47.5692 | 0.0000 ** | | comcol | 0.5846 | 0.0162 | 36.1094 | 0.0000 ** | | curcol | 1.0751 | 0.1067 | 10.0763 | 0.0000 ** | | colony | 1.1638 | 0.0312 | 37.3391 | 0.0000 ** | | comctry | -0.0163 | 0.2623 | -0.0622 | 0.9504 | Significance codes: ** p < 0.01; * p < 0.05; + p < 0.10 R-squared : 0.648 Adj. R-squared: 0.6479 Fixed effects: year: 52 Number of observations: Full 234597; Missing 0; Perfect classification 0
This does not involve many fixed effects. However, capybara will be particularly useful to obtain different standard errors for the same functional form, which is the main focus of table 4B in Cameron & Miller (2014).
Table 4B shows the following clustering methods that we can replicate with the third part of the
model formula (e.g. y ~ x1 + x2 + ... | fe1 + fe2 | cl1 + cl2) and using the vcov argument
to select how the clustering variables are used:
| vcov value | Description |
|:-----------------|:-----------------------------------------------|
| "iid" | Default OLS (i.i.d. errors) |
| "hetero" | Heteroskedastic-robust (HC0) |
| "cluster" | One-way cluster sandwich |
| "m-estimator" | One-way M-estimator sandwich |
| "dyadic" | Dyadic-robust (Cameron & Miller, 2014) |
Capybara provides an update() method to easily modify the formula for each model, as we need
to change the clustering variables for each model, which avoids error-prone copy-pasting of the full
formula every time.
IID (no cluster part in formula)
fml <- ltrade ~ bothin + onein + gsp + ldist + lrgdp + lrgdppc + regional + custrict + comlang + border + landl + island + lareap + comcol + curcol + colony + comctry | year fit_iid <- felm( fml, data = ross2004, vcov = "iid" )
Heteroskedastic-robust (HC0)
fit_hetero <- felm( fml, data = ross2004, vcov = "hetero" )
One-way: cluster on country-pair (g,h)
Note that multi-part formulas (e.g., y ~ x | fe | cl) are handled by the Formula package. Therefore,
updating those needs an explicit Formula::as.Formula() call if the formula type was not specified initially.
fml2 <- update(Formula::as.Formula(fml), . ~ . | . | pair) fit_pairs <- felm( fml2, data = ross2004, vcov = "cluster" )
One-way: cluster on country 1 (g)
fit_ctry1 <- felm( update(fml2, . ~ . | . | ctry1), data = ross2004, vcov = "cluster" )
One-way: cluster on country 2 (h)
fit_ctry2 <- felm( update(fml2, . ~ . | . | ctry2), data = ross2004, vcov = "cluster" )
Two-way: cluster on (g) and (h) simultaneously
fit_2way <- felm( update(fml2, . ~ . | . | ctry1 + ctry2), data = ross2004, vcov = "cluster" )
Dyadic-robust: Cameron-Miller (2014) sandwich with cross-dyad correlations
fit_dyadic <- felm( update(fml2, . ~ . | . | ctry1 + ctry2), data = ross2004, vcov = "dyadic" )
With the above models, we can replicate Table 4B from Cameron & Miller (2014) using
summary_table(), another convenience function in capybara to display multiple models side-by-side.
This completely avoids calling summary() on each model and then conducting post-processing to
extract the relevant information for the table.
summary_table( fit_iid, fit_hetero, fit_pairs, fit_ctry1, fit_ctry2, fit_2way, fit_dyadic, model_names = c("IID", "Hetero", "Pairs", "Country 1", "Country 2", "2-Way", "Dyadic") )
| Variable | IID | Hetero | Pairs | Country 1 | Country 2 | 2-Way | Dyadic | |------------------|--------------------|--------------------------|--------------------|--------------------|--------------------|--------------------|--------------------| | bothin | -0.042** | -0.042* | -0.042 | -0.042 | -0.042 | -0.042 | -0.042 | | | (0.016) | (0.018) | (0.053) | (0.122) | (0.107) | (0.122) | (0.186) | | onein | -0.058** | -0.058** | -0.058 | -0.058 | -0.058 | -0.058 | -0.058 | | | (0.015) | (0.018) | (0.049) | (0.095) | (0.071) | (0.095) | (0.126) | | gsp | 0.859** | 0.859** | 0.859** | 0.859** | 0.859** | 0.859** | 0.859** | | | (0.011) | (0.009) | (0.032) | (0.098) | (0.074) | (0.098) | (0.131) | | ldist | -1.119** | -1.119** | -1.119** | -1.119** | -1.119** | -1.119** | -1.119** | | | (0.006) | (0.006) | (0.022) | (0.051) | (0.050) | (0.051) | (0.078) | | lrgdp | 0.916** | 0.916** | 0.916** | 0.916** | 0.916** | 0.916** | 0.916** | | | (0.003) | (0.003) | (0.010) | (0.024) | (0.028) | (0.024) | (0.043) | | lrgdppc | 0.321** | 0.321** | 0.321** | 0.321** | 0.321** | 0.321** | 0.321** | | | (0.004) | (0.004) | (0.014) | (0.033) | (0.038) | (0.033) | (0.052) | | regional | 1.199** | 1.199** | 1.199** | 1.199** | 1.199** | 1.199** | 1.199** | | | (0.036) | (0.029) | (0.106) | (0.222) | (0.185) | (0.222) | (0.333) | | custrict | 1.118** | 1.118** | 1.118** | 1.118** | 1.118** | 1.118** | 1.118** | | | (0.037) | (0.035) | (0.122) | (0.165) | (0.176) | (0.165) | (0.235) | | comlang | 0.313** | 0.313** | 0.313** | 0.313** | 0.313** | 0.313** | 0.313** | | | (0.011) | (0.011) | (0.040) | (0.081) | (0.065) | (0.081) | (0.111) | | border | 0.526** | 0.526** | 0.526** | 0.526** | 0.526** | 0.526** | 0.526* | | | (0.027) | (0.026) | (0.111) | (0.148) | (0.150) | (0.148) | (0.207) | | landl | -0.271** | -0.271** | -0.271** | -0.271** | -0.271** | -0.271** | -0.271* | | | (0.009) | (0.010) | (0.031) | (0.069) | (0.079) | (0.069) | (0.110) | | island | 0.042** | 0.042** | 0.042 | 0.042 | 0.042 | 0.042 | 0.042 | | | (0.009) | (0.009) | (0.036) | (0.105) | (0.083) | (0.105) | (0.154) | | lareap | -0.097** | -0.097** | -0.097** | -0.097** | -0.097** | -0.097** | -0.097* | | | (0.002) | (0.002) | (0.008) | (0.025) | (0.025) | (0.025) | (0.043) | | comcol | 0.585** | 0.585** | 0.585** | 0.585** | 0.585** | 0.585** | 0.585** | | | (0.016) | (0.019) | (0.067) | (0.126) | (0.108) | (0.126) | (0.178) | | curcol | 1.075** | 1.075** | 1.075** | 1.075* | 1.075** | 1.075* | 1.075* | | | (0.107) | (0.070) | (0.235) | (0.462) | (0.256) | (0.462) | (0.480) | | colony | 1.164** | 1.164** | 1.164** | 1.164** | 1.164** | 1.164** | 1.164** | | | (0.031) | (0.023) | (0.117) | (0.193) | (0.115) | (0.193) | (0.209) | | comctry | -0.016 | -0.016 | -0.016 | -0.016 | -0.016 | -0.016 | -0.016 | | | (0.262) | (0.205) | (1.081) | (0.884) | (1.077) | (0.884) | (0.859) | | | | | | | | | | | Fixed effects | | | | | | | | | year | Yes | Yes | Yes | Yes | Yes | Yes | Yes | | | | | | | | | | | N | 234,597 | 234,597 | 234,597 | 234,597 | 234,597 | 234,597 | 234,597 | | R-squared | 0.648 | 0.648 | 0.648 | 0.648 | 0.648 | 0.648 | 0.648 | | SE type | IID | Heteroskedastic-robust | Cluster-robust | Cluster-robust | Cluster-robust | Cluster-robust | Dyadic-robust | Standard errors in parenthesis Significance levels: ** p < 0.01; * p < 0.05; + p < 0.10
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