SynthControl.jl

Julia package for synthetic control methods

The package is currently at alpha stage - it currently offers a basic SyntheticControlModel implementation which uses all pre-treatment periods and no other covariates in constructing the control unit.

Installation

The package is registered in the general registry, installation therefore works through the Pkg REPL

pkg> add SynthControl

Usage

Fitting a SimpleSCM model

The package includes example data borrowed from the CER Brexit study:

julia> using SynthControl, Dates

julia> df = load_brexit()
897×3 DataFrame
│ Row │ country        │ quarter    │ realgdp │
│     │ String         │ Date       │ Float64 │
├─────┼────────────────┼────────────┼─────────┤
│ 1   │ Australia      │ 2009-01-01 │ 1.04    │
│ 2   │ Austria        │ 2009-01-01 │ -1.53   │
│ 3   │ Belgium        │ 2009-01-01 │ -1.15   │
⋮
│ 894 │ Sweden         │ 2018-07-01 │ 22.48   │
│ 895 │ Switzerland    │ 2018-07-01 │ 14.35   │
│ 896 │ United Kingdom │ 2018-07-01 │ 15.72   │
│ 897 │ United States  │ 2018-07-01 │ 19.32   │

The package defines a SimpleSCM type, instances of which can be constructed from a TreatmentPanel object from the package TreatmentPanels. The TreatmentPanel is constructed from a DataFrame and a specification of treatment assignment. The SimpleSCM model constructs a synthetic control unit based only

The example data set includes quarterly GDP for a number of OECD countries, and we are interested in estimating the impact of the Brexit vote in Q2 2016 on GDP in the UK:

julia> bp = BalancedPanel(df, "United Kingdom" => Date(2016, 7, 1); id_var = :country, t_var = :quarter, outcome_var = :realgdp)
Balanced Panel - single treated unit, continuous treatment
    Treated unit: United Kingdom
    Number of untreated units: 22
    First treatment period: 2016-07-01
    Number of pretreatment periods: 30
    Number of treatment periods: 9


julia> s = SimpleSCM(bp)

Synthetic Control Model

Treatment panel:
Balanced Panel - single treated unit, continuous treatment
    Treated unit: United Kingdom
    Number of untreated units: 22
    First treatment period: 2016-07-01
    Number of pretreatment periods: 30
    Number of treatment periods: 9

Model is not fitted

The output indicates that the model is not fitted, that is we have at this stage only defined the basic model structure. We can fit the model using the fit! function, which will modify our SimpleSCM in place:

julia> fit!(s)

Synthetic Control Model

Treatment panel:
Balanced Panel - single treated unit, continuous treatment
    Treated unit: United Kingdom
    Number of untreated units: 22
    First treatment period: 2016-07-01
    Number of pretreatment periods: 30
    Number of treatment periods: 9

        Model is fitted
        Impact estimates: [-0.54, -0.31, -0.206, -0.732, -1.241, -1.482, -1.818, -2.327, -1.994]

The reported impact estimates are the difference between observed outcome variable and estimated outcome in the absence of treatment - a negative value therefore means the treatment is expected to have reduced the outcome variable compared to the counterfactual.

The package also defines a plot recipe which allows to visualise the estimated impact:

julia> using Plots

julia> plot(s_model)

Fitting a SyntheticDiD model

The package also implements a the synthetic differences-in-differences estimator of Arkhangelsky et al. (2021) with the SyntheticDiD type. An example using data on California's ban of tobacco advertising:

julia> sp = load_smoking_panel()
Balanced Panel - single treated unit, continuous treatment
    Treated unit: 3
    Number of untreated units: 38
    First treatment period: 1989
    Number of pretreatment periods: 19
    Number of treatment periods: 12

Here we are using the load_*_panel() family of functions rather than the load_*() family of functions used above - when using the panel version of the load functions, a BalancedPanel object is returned which obviates the need for creating this from the raw data.

Fitting the model:

julia> sdid_model = SyntheticDiD(sp)
Synthetic Difference-in-Differences Model

Model is not fitted

As before, the fit! function is used to fit the model:

julia> fit!(sdid_model)
Synthetic Difference-in-Differences Model
        Model is fitted
        Impact estimate: -15.604

The model estimate can also be accessed as sdid_model.τ̂, and the standard error as sdid_model.se_τ̂. The only algorithm for estimation of standard errors currently implemented is the placebo algorithm, in which the estimator is sequentially applied to each control unit. By default, standard errors are not estimated, the se keyword can be used to do so:

julia> fit!(sdid_model; se = :placebo)
Synthetic Difference-in-Differences Model
        Model is fitted
        Impact estimate: -15.604
                          (9.31)

Fitting a MC-NNM model (experimental)

The package includes an experimental implementation of the Matrix Completion with Nuclear Norm Minimization (MC-NNM) estimator (Athey et al., 2021). Due to its experimental nature it is currently not exported and has to be accessed through the internal fect_default function:

julia> SynthControl.fect_default(sp)
[ Info: Cross-validating...
        λ_norm = 1.0; MSPE = 184.11
        λ_norm = 0.4217; MSPE = 97.12
        λ_norm = 0.17783; MSPE = 60.18
        λ_norm = 0.07499; MSPE = 55.38
        λ_norm = 0.03162; MSPE = 83.68
        λ_norm = 0.01334; MSPE = 133.34
        λ_norm = 0.00562; MSPE = 176.03
        λ_norm = 0.00237; MSPE = 180.63
        λ_norm = 0.001; MSPE = 182.63
        λ_norm = 0.0; MSPE = 184.11

        λ_norm* = 0.07499
(τ̂ᵃᵗᵗ = -25.90741309106447, eff = [-3.777787420126515 -2.1951292344078013 … 2.8272388331494795 1.7451236037973956; -2.225234537444024 -0.6429018374729338 … -0.5174054676892013 -0.35710884584517544; … ; 2.3972577740355073 1.5448822989699096 … -1.6290392876871636 2.093390785866191; 1.1496735178409807 -1.3143906741400713 … -1.1176962789642886 -4.041039492499593])