Julia package for synthetic control methods
The package is currently in beta stage - check the documentation for the current implementation status of a variety of different synthetic control estimators and inference methods.
The package is registered in the general registry, installation therefore works through the Pkg REPL
pkg> add SynthControl
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 on the pre-treatment outcomes.
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)
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)
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])