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

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

julia> using SynthControl

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 SynthControlModel 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 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 unit, single continuous treatment
    Treated unit: ["United Kingdom"]
    Number of untreated units: 22
    First treatment period: [Date("2016-07-01")]
    Number of pretreatment periods: [30]
    Number of treatment periods: [9]


julia> s = SynthControlModel(bp)

Synthetic Control Model

Treatment panel:
Balanced Panel - single unit, single continuous treatment
    Treated unit: ["United Kingdom"]
    Number of untreated units: 22
    First treatment period: [Date("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 SynthControlModel in place:

julia> fit!(s)

Synthetic Control Model

Treatment panel:
Balanced Panel - single unit, single continuous treatment
    Treated unit: ["United Kingdom"]
    Number of untreated units: 22
    First treatment period: [Date("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)