In xuyiqing/fect: Fixed Effects Counterfactual Estimators

Cheatsheet {#sec-cheatsheet}

In this chapter, we provide an overview of the main functionalities of the fect package, including the required inputs, available plot types, key options, and testing capabilities across various methods.

Methods

Inputs for fect(methods = "___")

| Method | Model for $\hat{Y}(0)$ | References | |--------------------|--------------------------------|--------------------| | fe | Standard two-way fixed effects model | Liu, Wang & Xu (2022), Borusyak, Jaravel & Spiess (2024) | | ife | Interactive fixed effects model | Gobillon & Magnac (2016), Xu (2017) | | mc | Matrix completion method | Athey et al. (2021) | | polynomial | Two-way fixed effects model with unit-specific trends | – | | cfe | "Complex" or multi-level fixed effects | – | | gsynth | Interactive fixed effects model | Xu (2017) |

Plot Types

Inputs for plot(fect_object, type = "___")

| Type | Description | Applicable Methods | |-------------------|------------------------------|-----------------------| | box | Box plot of ATT by period. | fe, ife, mc, gsynth, polynomial, cfe | | calendar | ATT by calendar time. | fe, ife, mc, gsynth, polynomial, cfe | | counterfactual | Observed vs. imputed outcome for treated units. | fe, ife, mc, gsynth | | equiv | Pretreatment residuals with equivalence intervals. | fe, ife, mc, gsynth, polynomial, cfe | | exit | Period-wise ATT relative to treatment exit. | fe, ife, mc, polynomial, cfe | | factors | Estimated factors (factor-based methods). | ife, gsynth | | gap | ATT by pre- and post-treatment periods. | fe, ife, mc, gsynth, polynomial, cfe | | loadings | Estimated factor loadings (factor-based methods). | ife, gsynth | | status | Treatment status by period for all units. | fe, ife, mc, gsynth, polynomial, cfe |

Tests as Options

Inputs for fect(...)

| Input | Description | Applicable Methods | |-------------------|---------------------------------|--------------------| | loo | Leave-one-period-out goodness-of-fit test (TRUE/FALSE). | fe, ife, mc, gsynth | | carryoverTest | Tests for carryover effects in post-treatment periods (TRUE/FALSE). | fe, ife, mc | | carryover.period | Range of post-treatment periods for the carryover test (vector). | fe, ife, mc | | permute | Permutation test (TRUE/FALSE). | fe, ife, mc, gsynth | | m | Block length for permutation test (m=2 by default). | fe, ife, mc, gsynth | | CV | Cross-validation for factor-based methods. | ife, mc, gsynth |

Required and Optional Inputs

A check mark (✓) indicates that the method requires or accepts the input.

Required Inputs

| Input | fe | ife | mc | gsynth | polynomial | cfe | |-----------|:---------:|:---------:|:---------:|:---------:|:---------:|:---------:| | Y (outcome) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | D (treatment) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | X (covariates) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | data | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | index (unit & time IDs) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | sfe (simple additive FEs) | – | – | – | – | – | ✓ | | cfe (complex FEs) | – | – | – | – | – | ✓ |

Optional Inputs

| Input | fe | ife | mc | gsynth | polynomial | cfe | |:----------|:----------|:---------:|:---------:|:---------:|:---------:|:---------:| | W (weight) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | se (uncertainty) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | nboots (# bootstrap reps) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | force (FE structure) | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | | lambda(Hyper-parameter sequence) | – | – | ✓ | ✓ | – | – | | nlambda(Length of hyper-parameter sequence) | – | – | ✓ | ✓ | – | – | | r (# factor) | – | ✓ | – | ✓ | – | – | | k ( # cross-validation rounds) | – | ✓ | ✓ | ✓ | – | – | | degree (degree of the interacted fixed effects) | – | – | – | – | ✓ | – |

Important Options

| Input | Options | Applicable Methods | |:-------------------------|:---------------------------|:------------------| | force | Fixed effects structure: "none", "unit", "time", "two-way" (default) | fe, ife, mc, poly, cfe, gsynth | | vartype (when method = "gsynth") | Uncertainty estimator: "parametric" (default), "bootstrap", "jackknife" | gsynth | | vartype (otherwise) | Uncertainty estimator: "bootstrap" (default), "jackknife" | fe, ife, mc, polynomial, cfe | | criterion | Model selection criterion: "mspe" (default), "gmspe", "moment", "pc". | ife, mc, polynomial, cfe, gsynth |

Notes

Most methods share core inputs (Y, D, X, data, index).
Method polynomial and cfe allow either "jackknife" or "bootstrap" for uncertainty estimates.
Factor-based methods (ife, gsynth) can use rand k for factor selection and cross validation. We can implement a similar process using mc or gsynth with lambda andnlambda.
carryoverTest and loo are available in fe, ife, mc, polynomial, and cfe but not in gsynth.
force allows various levels of fixed effects ("none", "unit", "time", "two-way").
fect includes several built-in values for optional arguments that often require an integer or boolean input. All boolean arguments (such as parallel, se, or CV) are set to FALSE by default to speed up computation. Below is a complementary table listing parameters that require numeric inputs.

| Inputs | Description | Default | |:-----------------:|:---------------------------------|:-----------------:| | degree | The degree of the interacted fixed effects(int) | 2 | | nboots | Number of bootstrap runs (int) | 200 | | k | Sets the number of cross-validation rounds(int) | 10 | | r | Sets the number of factors | 0; c(0,5) when CV | | m | Specifies the block length for the permutation test | 2 | | nlambda | Length of hyper-parameter sequence | 10 |