R Fixest Package: IV Estimation Without Further Exogenous Variables - r

Question

I intend to run instrumental variable regressions with fixed effects using the fixest package's feols function. However, I am having issues with the syntax specifying an estimation without further exogenous controls.
Consider the following example:
# Load package
require("fixest")
# Load data
df <- airquality
I would like to something like the following, i.e. explaining the outcome via the instrumented endogenous variable and fixed effects:
feols(Temp | Month + Day | Ozone ~ Wind, df)
This, however, produces an error:
The dependent variable is a constant. Estimation cannot be done.
It only works, when I add further exogenous covariates (as in the documentation's examples):
feols(Temp ~ Solar.R | Month + Day | Ozone ~ Wind, df)
How do I fix this? How do I run the estimation without further controls, such as Solar.R in this case?
Note: I post this on Stack Overflow rather than Cross Validated because the question relates to a coding syntax issue, and not to the econometric techniques underlying the estimations.

Answer 1

actually there seems to be a misunderstanding on how to write the formula.
The syntax is: Dep_var ~ Exo_vars | Fixed-effects | Endo_vars ~ Instruments.
The parts Fixed-effects and Endo_vars ~ Instruments are optional. On the other hand, the part with Exo_vars must always be there, be it with only the intercept.
Knowing that, the following works:
base = iris
names(base) = c("y", "x1", "x_endo", "x_inst", "fe")
feols(y ~ 1 | x_endo ~ x_inst, base)
#> TSLS estimation, Dep. Var.: y, Endo.: x_endo, Instr.: x_inst
#> Second stage: Dep. Var.: y
#> Observations: 150
#> Standard-errors: Standard
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 4.345900 0.08096 53.679 < 2.2e-16 ***
#> fit_x_endo 0.398477 0.01964 20.289 < 2.2e-16 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 0.404769 Adj. R2: 0.757834
#> F-test (1st stage): stat = 1,882.45 , p < 2.2e-16 , on 1 and 148 DoF.
#> Wu-Hausman: stat = 3.9663, p = 0.048272, on 1 and 147 DoF.
# Same with fixed-effect
feols(y ~ 1 | fe | x_endo ~ x_inst, base)
#> TSLS estimation, Dep. Var.: y, Endo.: x_endo, Instr.: x_inst
#> Second stage: Dep. Var.: y
#> Observations: 150
#> Fixed-effects: fe: 3
#> Standard-errors: Clustered (fe)
#> Estimate Std. Error t value Pr(>|t|)
#> fit_x_endo 0.900061 0.117798 7.6407 0.016701 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> RMSE: 0.333489 Adj. R2: 0.833363
#> Within R2: 0.57177
#> F-test (1st stage): stat = 44.77 , p = 4.409e-10, on 1 and 146 DoF.
#> Wu-Hausman: stat = 0.001472, p = 0.969447 , on 1 and 145 DoF.
Getting back to the original example:
feols(Temp | Month + Day | Ozone ~ Wind, df) means that the dependent variable will be Temp | Month + Day | Ozone with the pipe here meaning the logical OR, leading to a 1 for all observations. Hence the error message.
To fix it and obtain an appropriate behavior, use feols(Temp ~ 1 | Month + Day | Ozone ~ Wind, df).