Inference for Synthetic Control Estimators

Overview

This vignette walks through inference for the synthetic control method as implemented in the Synth package, using the canonical example from Abadie, Diamond, and Hainmueller (2010): California’s Proposition 99 cigarette tax of 1988. For the basic dataprep() → synth() → path.plot() flow, see vignette("synth-quickstart", package = "Synth").

Which inference method should I use?

Question	Method	Function
How surprising is the effect vs. other units?	placebo MSPE-ratio rank	`mspe_test()`
Lightweight prediction band around the counterfactual	split-conformal	`synth_inference(method = "conformal")`
Same, with i.i.d. Gaussian residuals	parametric	`synth_inference(method = "parametric")`
Period-varying intervals decomposing in/out-of-sample uncertainty	CFPT	`scpi::scpi()` (separate package)

It covers:

Building the synthetic control with the new synth_data() wrapper.
Computing prediction intervals with synth_inference() (split-conformal and Gaussian-residual methods).
Running an in-space placebo test with generate_placebos(), mspe_test(), mspe_plot(), and plot_placebos().

For background on the method itself, see ?synth and the references at the end. For methods that further decompose in-sample and out-of-sample uncertainty (period-varying prediction intervals), see the scpi package on CRAN.

library(Synth)
#> ##
#> ## Synth Package: Implements Synthetic Control Methods.
#> ## See https://web.stanford.edu/~jhain/synthpage.html for additional information.
data(smoking)

1. Build the synthetic control

The smoking dataset (new in Synth 1.2-0) is the canonical state-level panel from Abadie, Diamond, and Hainmueller (2010): 39 US states from 1970 through 2000, with annual per-capita cigarette sales as the outcome and four covariates (log income, beer consumption, the share of the population aged 15-24, and the retail price of cigarettes). California raised its cigarette tax via Proposition 99 in late 1988, so 1989 is the first post-treatment year and the donor pool is the 38 other states.

ca_id <- unique(smoking$state_id[smoking$state_name == "California"])

dp <- synth_data(
  panel              = smoking,
  outcome            = "cigsale",
  unit_col           = "state_id",
  time_col           = "year",
  treated            = ca_id,
  treatment_time     = 1989,
  predictors         = c("lnincome", "age15to24", "retprice", "beer"),
  special_predictors = list(
    list("cigsale", 1988, "mean"),
    list("cigsale", 1980, "mean"),
    list("cigsale", 1975, "mean")
  ),
  unit_names_col     = "state_name"
)
#> 
#>  Missing data- treated unit; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data- treated unit; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data- treated unit; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data- treated unit; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data- treated unit; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 1 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 1 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 6 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 6 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 7 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 7 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 8 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 8 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 9 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 9 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 10 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 11 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 12 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 12 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 13 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 13 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 14 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 14 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 15 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 15 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 16 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 17 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 20 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 23 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 24 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 25 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 25 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 26 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 26 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 27 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 27 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 28 ; predictor: lnincome ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 28 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 30 ; predictor: lnincome ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 1 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 2 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 4 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 5 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
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#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 6 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 7 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 8 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 9 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 10 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 11 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 12 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 13 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 14 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 15 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 16 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 17 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 18 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 19 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 20 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 21 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 22 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 23 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 24 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 25 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 26 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 27 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 28 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 29 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 30 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 31 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 32 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 33 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 34 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 35 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 36 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 37 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 38 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1970 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1971 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1972 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1973 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1974 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1975 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1976 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1977 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1978 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1979 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1980 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1981 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1982 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.
#> 
#>  Missing data - control unit: 39 ; predictor: beer ; for period: 1983 
#>  We ignore (na.rm = TRUE) all missing values for predictors.op.

fit <- synth(dp, verbose = FALSE)

The fitted weights match the published Proposition 99 paper closely:

top <- sort(fit$solution.w[, 1], decreasing = TRUE)
head(top, 5)
#>         34         21         19          5          4 
#> 0.34103519 0.24884085 0.20471615 0.11062154 0.09383158

Synthetic California is roughly Utah + Nevada + Montana + Connecticut — a convex combination of states that, in the pre-period, smoked at similar rates and had similar demographics.

path.plot(synth.res = fit, dataprep.res = dp,
          Ylab = "Cigarette sales per capita (packs)",
          Xlab = "Year",
          Legend = c("California", "Synthetic California"),
          tr.intake = 1989)

2. Prediction intervals: `synth_inference()`

synth_inference() returns a prediction band around the synthetic counterfactual. Two methods are available.

Split-conformal (default)

The half-width is the order statistic at rank \(k = \lceil (n+1)(1-\alpha) \rceil\) of the absolute pre-treatment residuals (Chernozhukov, Wuthrich, and Zhu 2021):

inf_conf <- synth_inference(fit, dp,
                            method = "conformal", alpha = 0.10)
inf_conf
#> Synthetic control inference (split-conformal)
#> Pre-treatment periods (SSR window): 19
#> Post-treatment periods (>= 1989): 12
#> alpha = 0.100, conformal q = 2.8662
#> Pre-period MSPE  = 3.0693
#> Post-period MSPE = 391.8716
#> Post/Pre MSPE ratio = 127.6762
#> Post-period points outside (1-alpha) band: 12 / 12
#> 
#> Note: validity assumes pre-period residuals are exchangeable.
#> With autocorrelated outcomes the nominal coverage is approximate.
#> See ?synth_inference, the SCtools package for placebo-based
#> inference, and the scpi package for methods that decompose
#> in-sample and out-of-sample uncertainty.

plot(inf_conf,
     Ylab = "Cigarette sales per capita (packs)",
     Xlab = "Year",
     Main = "California: 90% conformal band")

Split-conformal 90% band around the synthetic counterfactual.

The band is constant in width by construction. It is finite-sample valid when pre-treatment residuals are exchangeable; with autocorrelated outcomes the nominal coverage is approximate.

Parametric (Gaussian residuals)

The half-width is qnorm(1 - alpha/2) * sd(gap_pre):

inf_par <- synth_inference(fit, dp,
                           method = "parametric", alpha = 0.10)
inf_par$sigma_pre
#> [1] 1.790587

plot(inf_par,
     Ylab = "Cigarette sales per capita (packs)",
     Xlab = "Year",
     Main = "California: 90% parametric band")

Parametric Gaussian 90% band.

When to use which

Method	Validity	Width
`conformal`	Exact under exchangeability of pre-period residuals	order statistic of \(\|gap_{pre}\|\)
`parametric`	Exact under i.i.d. Gaussian residuals	`qnorm(1 - α/2) * sd(gap_pre)`

Both produce constant-width bands. They do not separately quantify uncertainty about the synthetic weights. For period-varying intervals that decompose in-sample and out-of-sample uncertainty, see the scpi package.

3. Placebo inference

The classical Abadie-Diamond-Hainmueller approach treats each donor state as if it had received the intervention, refits synth(), and ranks the treated unit’s post/pre MSPE ratio against the placebo distribution.

Generate the placebos

generate_placebos() runs one refit per donor. With 38 donor states this takes about a minute on a laptop.

placebos <- generate_placebos(fit, dp, verbose = FALSE)
placebos
#> Synth placebos
#> Donors:           38
#> Successful refits:38
#> Failed refits:    0
#> Pre-treatment periods : 19
#> Post-treatment periods: 12
#> Treated post/pre MSPE ratio: 127.6762
#> One-sided placebo p-value:   0.0256  (n_valid = 38)

Test

mspe_test() returns a one-sided p-value via the empirical rank of the treated unit’s post/pre MSPE ratio:

test <- mspe_test(placebos)
test$mspe_ratio_treated
#> [1] 127.6762
test$pvalue
#> [1] 0.02564103
test$n_valid_placebos
#> [1] 38

California’s post/pre MSPE ratio is far in the right tail of the placebo distribution: only one or two of the 38 placebo states have ratios as extreme as California’s, so the one-sided p-value is small.

Plot the placebo distribution

mspe_plot(placebos)

Distribution of post/pre MSPE ratios across placebos. California is highlighted.

Plot the placebo gaps

plot_placebos(placebos,
              Ylab = "Gap in cigarette sales per capita (packs)",
              Xlab = "Year",
              Main = "California and placebo gaps")
abline(v = 1989, lty = 3)

Treated gap (black) overlaid on placebo gaps (grey).

For interpretability, ADH 2010 recommend dropping placebos whose pre-period MSPE is much worse than the treated unit’s (their synthetic controls couldn’t fit them well in the first place):

plot_placebos(placebos,
              mspe_threshold = 5,
              Ylab = "Gap in cigarette sales per capita (packs)",
              Xlab = "Year",
              Main = "California and placebo gaps (pre-MSPE <= 5x California)")
abline(v = 1989, lty = 3)

Same plot, restricted to placebos with reasonable pre-period fit.

4. Combining prediction intervals and placebos

The two inference modes are orthogonal. A typical Proposition 99 results section would include both: a prediction band on the path plot to show the size of the post-period drop, and a placebo p-value to show that the drop is unusual relative to other states.

data.frame(
  method                = c("conformal 90%", "parametric 90%", "placebo p-value"),
  width_or_pvalue       = c(2 * inf_conf$conformal_q,
                            2 * stats::qnorm(0.95) * inf_par$sigma_pre,
                            test$pvalue),
  notes                 = c("constant-width band",
                            "constant-width Gaussian band",
                            "one-sided MSPE-ratio rank")
)
#>            method width_or_pvalue                        notes
#> 1   conformal 90%      5.73245891          constant-width band
#> 2  parametric 90%      5.89050649 constant-width Gaussian band
#> 3 placebo p-value      0.02564103    one-sided MSPE-ratio rank

Alternative QP backends

By default, synth() solves the inner simplex-constrained QP for the unit weights via kernlab::ipop. As of Synth 1.2-0, two opt-in backends are also available:

# Convex-optimization backend (CVXR; default solver is OSQP)
fit_cvxr  <- synth(dp, quadopt = "cvxr",  verbose = FALSE)

# Autodiff/GPU backend (Frank-Wolfe simplex LS via torch)
fit_torch <- synth(dp, quadopt = "torch", verbose = FALSE)

Both are in Suggests: and only loaded when requested. The CVXR backend is a drop-in alternative useful when ipop converges slowly or you want a different solver pool (OSQP by default; SCS, ECOS, or MOSEK selectable via cvxr_pars = list(solver = ...)). The torch backend supports CPU, CUDA, and Apple MPS via torch_pars = list(device = "cuda") and is most useful on large panels. The first torch call in a session may require torch::install_torch() to download libtorch (~600MB).

For Python users with very large panels or who want autodiff at the estimator level, see Apoorva Lal’s trex package — a PyTorch-native implementation of the synthetic control family (SC, synthdid, matrix completion).

References

Abadie, A., Diamond, A., and Hainmueller, J. (2010). Synthetic control methods for comparative case studies. Journal of the American Statistical Association, 105(490), 493-505.
Chernozhukov, V., Wuthrich, K., and Zhu, Y. (2021). An exact and robust conformal inference method for counterfactual and synthetic controls. Journal of the American Statistical Association, 116(536), 1849-1864.
Cattaneo, M. D., Feng, Y., Palomba, F., and Titiunik, R. (2025). Uncertainty quantification in synthetic controls with staggered treatment adoption. Review of Economics and Statistics.