Estimators

The function fit estimates models. It returns a model structure, which contains the estimation sample, the coefficients and their covariance matrix. For example, the output of fit(OLS, MD) has type OLS. Some have additional fields: e.g., two-stage models carry estimates from the first stage and GMM models carry the inverse of the weight matrix.

Model structures are subtypes of broader abstract types, such as MLE or GMM, which are ultimately instances of RegressionModel. The type hierarchy is:

RegressionModel
    ParModel
        GMM
        MLE
    TwoStageModel

Linear regression

Ordinary least squares

fit(OLS, MD::Microdata)

The Microdata must contain: response and control. See the documentation for linear IV if Microdata includes a treatment. OLS is a subtype of MLE.

Linear IV

fit(IV, MD::Microdata; method::String = "TSLS")

The following methods are currently implemented:

• method = "TSLS": two-stage least squares;
• method = "Two-step GMM": optimally weighted two-stage GMM with robust covariance matrix;
• method = "Optimal GMM": optimally weighted two-stage GMM with simplified covariance matrix.

Additional methods are available for convenience:

• method = "OLS": linear regression of the outcome on the treatment and controls;
• method = "First stage": linear regression of the treatment on the instruments and controls;
• method = "Reduced form": linear regression of the outcome on the instruments and controls.

The Microdata must contain: response, treatment, control and instrument. IV is a subtype of GMM.

Binary choice

fit(Logit, MD::Microdata)
fit(Probit, MD::Microdata)
fit(Cloglog, MD::Microdata)
fit(Gompit, MD::Microdata)

The Microdata must contain: response and control. The outcome should be binary. The model structures are subtypes of MLE.

Count data

fit(Poisson, MD::Microdata; novar::Bool = false)

The Microdata must contain: response and control. The Microdata may contain an offset. See the documentation for linear IV if Microdata includes a treatment. The outcome must be weakly positive. Poisson is a subtype of MLE.

fit(IVPoisson, MD::Microdata; novar::Bool = false, method::String = "One-step GMM")
fit(Mullahy, MD::Microdata; novar::Bool = false, method::String = "One-step GMM")

IVPoisson fits the exponential conditional mean model with additive errors. Mullahy fits the exponential conditional mean model with multiplicative errors (Mullahy, 1997).

The following methods are currently implemented:

• method = "One-step GMM": unweighted one-stage GMM;
• method = "TSLS": one-stage GMM with the average outer product of the instrument vector as weight matrix;
• method = "Two-step GMM": optimally weighted two-stage GMM with robust covariance matrix;
• method = "Optimal GMM": optimally weighted two-stage GMM with simplified covariance matrix.

The models are estimated with the Gauss–Newton algorithm. The first stage of the two-stage specifications is estimated with the average outer product of the instrument vector as weight matrix.

Additional methods are available for convenience:

• method = "Poisson": Poisson regression of the outcome on the treatment and controls;
• method = "Reduced form": Poisson regression of the outcome on the instruments and controls.

The Microdata must contain: response, treatment, control and instrument. The Microdata may contain an offset. The outcome must be weakly positive. IVPoisson and Mullahy are subtypes of GMM.

Reweighting methods

fit(IPW, M₁::Type{Micromodel}, MD::Microdata; trim::AbstractFloat = 0.0)
fit(IPW, M₁::Micromodel, MD::Microdata; trim::AbstractFloat = 0.0)

IPW estimates average treatment effects by inverse probability weighting. In a first stage, we use model M₁ to forecast the conditional probability of treatment take-up and construct estimation weights. In the second stage, we regress the outcome on the treatment and an intercept by weighted least squares. The intercept gives the mean outcome of the untreated. We ignore observations whose score is below trim or above 1 - trim (see Crump et al. (2009)).

The Microdata must contain: response, treatment and control. The treatment must be binary. IPW is a subtype of TwoStageModel.

fit(Abadie, M₂::Type{ParModel}, M₁::Type{Micromodel}, MD::Microdata; trim::AbstractFloat = 0.0, kwargs...)
fit(Abadie, M₂::Type{ParModel}, M₁::Micromodel, MD::Microdata; trim::AbstractFloat = 0.0 kwargs...)

Abadie estimates local average response functions according to Abadie (2003). In a first stage, we use model M₁ to forecast the conditional probability of instrument take-up and construct estimation weights. In the second stage, we fit M₂ with the weights from the first stage. Keywords customize the second-stage estimator. We ignore observations whose score is below trim or above 1 - trim (see Crump et al. (2009)).

The Microdata must contain: response, treatment, control and instrument. The treatment and the instrument must be binary. Abadie is a subtype of TwoStageModel.

fit(FrölichMelly, M₁::Type{Micromodel}, MD::Microdata; trim::AbstractFloat = 0.0)
fit(FrölichMelly, M₁::Micromodel, MD::Microdata; trim::AbstractFloat = 0.0)

This model estimates unconditional local average effects according to Frölich and Melly (2013). In a first stage, we use model M₁ to forecast the conditional probability of instrument take-up and construct estimation weights. In the second stage, we regress the outcome on the treatment and an intercept by weighted least squares. The intercept gives mean outcome of untreated compliers. We ignore observations whose score is below trim or above 1 - trim (see Crump et al. (2009)).

The Microdata must contain: response, treatment, control and instrument. The treatment and the instrument must be binary. FrölichMelly is a subtype of TwoStageModel.

fit(Tan, M₁::Type{Micromodel}, MD::Microdata; trim::AbstractFloat = 0.0)
fit(Tan, M₁::Micromodel, MD::Microdata; trim::AbstractFloat = 0.0)

This model estimates the unconditional local average treatment effects according to Tan (2006). In a first stage, we use model M₁ to forecast the conditional probability of instrument take-up and construct estimation weights. In the second stage, we regress the outcome on the treatment and an intercept by weighted two-stage least squares. The intercept gives mean outcome of untreated compliers. We ignore observations whose score is below trim or above 1 - trim (see Crump et al. (2009)).

The Microdata must contain: response, treatment, control and instrument. The treatment and the instrument must be binary. Tan is a subtype of TwoStageModel.