Replicating the Basque Study

Causal inferences with difference-in-differences and synthetic control methods.

Abstract : This study illustrates the effect of terrorism on GDP in Spanish areas between 1955 and 1997. We use difference-in-differences to examine causal impact and sensitivity to external influences post-intervention using a dataset from Abadie and Gardeazabal (2003). We find the impact of terrorist conflict on Basque country’s economy to be a GDP reduction of 0.57 units using the synthetic control method.

License: MIT License. \(~\)

knitr::opts_chunk$set(echo = TRUE)
rm(list=ls())

---

Workstation Setup

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library(SCtools)

## Loading required package: future

library(Synth)

## ##
## ## Synth Package: Implements Synthetic Control Methods.

## ## See http://www.mit.edu/~jhainm/software.htm for additional information.

library(rvest)

## Loading required package: xml2

library(tidyverse)

## ── Attaching packages ─────────────────────────────────────────────────────────── tidyverse 1.3.0 ──

## ✓ ggplot2 3.3.0     ✓ purrr   0.3.4
## ✓ tibble  3.0.1     ✓ dplyr   0.8.5
## ✓ tidyr   1.0.3     ✓ stringr 1.4.0
## ✓ readr   1.3.1     ✓ forcats 0.5.0

## ── Conflicts ────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter()         masks stats::filter()
## x readr::guess_encoding() masks rvest::guess_encoding()
## x dplyr::lag()            masks stats::lag()
## x purrr::pluck()          masks rvest::pluck()

library(dplyr)
library(ggplot2)
library(viridis)

## Loading required package: viridisLite

library(hrbrthemes)

## NOTE: Either Arial Narrow or Roboto Condensed fonts are required to use these themes.

##       Please use hrbrthemes::import_roboto_condensed() to install Roboto Condensed and

##       if Arial Narrow is not on your system, please see https://bit.ly/arialnarrow

library(skimr)
library(kableExtra)

## 
## Attaching package: 'kableExtra'

## The following object is masked from 'package:dplyr':
## 
##     group_rows

library(ggthemes)
library(stargazer)

## 
## Please cite as:

##  Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.

##  R package version 5.2.2. https://CRAN.R-project.org/package=stargazer

library(kableExtra)

---

Section 1: Get Basque Dataset

Load Basque Dataset from the Package

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data(basque)

---

Quick Information about the Package

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basque%>%
  glimpse()

## Rows: 774
## Columns: 17
## $ regionno              <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
## $ regionname            <chr> "Spain (Espana)", "Spain (Espana)", "Spain (Esp…
## $ year                  <dbl> 1955, 1956, 1957, 1958, 1959, 1960, 1961, 1962,…
## $ gdpcap                <dbl> 2.354542, 2.480149, 2.603613, 2.637104, 2.66988…
## $ sec.agriculture       <dbl> NA, NA, NA, NA, NA, NA, 19.54, NA, 19.05, NA, 1…
## $ sec.energy            <dbl> NA, NA, NA, NA, NA, NA, 4.71, NA, 4.31, NA, 4.3…
## $ sec.industry          <dbl> NA, NA, NA, NA, NA, NA, 26.42, NA, 26.05, NA, 2…
## $ sec.construction      <dbl> NA, NA, NA, NA, NA, NA, 6.27, NA, 6.83, NA, 7.6…
## $ sec.services.venta    <dbl> NA, NA, NA, NA, NA, NA, 36.62, NA, 38.00, NA, 3…
## $ sec.services.nonventa <dbl> NA, NA, NA, NA, NA, NA, 6.44, NA, 5.77, NA, 6.4…
## $ school.illit          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 2863.278, 2…
## $ school.prim           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 18679.10, 1…
## $ school.med            <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 1064.246, 1…
## $ school.high           <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 359.7457, 3…
## $ school.post.high      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 212.1434, 2…
## $ popdens               <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,…
## $ invest                <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, 18.36018, 2…

---

Idea of Database - Details in EDA

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summary(basque)

##     regionno     regionname             year          gdpcap      
##  Min.   : 1.0   Length:774         Min.   :1955   Min.   : 1.243  
##  1st Qu.: 5.0   Class :character   1st Qu.:1965   1st Qu.: 3.693  
##  Median : 9.5   Mode  :character   Median :1976   Median : 5.336  
##  Mean   : 9.5                      Mean   :1976   Mean   : 5.395  
##  3rd Qu.:14.0                      3rd Qu.:1987   3rd Qu.: 6.869  
##  Max.   :18.0                      Max.   :1997   Max.   :12.350  
##                                                                   
##  sec.agriculture   sec.energy      sec.industry   sec.construction
##  Min.   : 1.32   Min.   : 1.600   Min.   : 9.56   Min.   : 4.340  
##  1st Qu.:13.54   1st Qu.: 2.697   1st Qu.:17.81   1st Qu.: 6.240  
##  Median :19.24   Median : 3.675   Median :23.14   Median : 7.135  
##  Mean   :20.27   Mean   : 5.189   Mean   :23.92   Mean   : 7.212  
##  3rd Qu.:27.48   3rd Qu.: 6.080   3rd Qu.:27.48   3rd Qu.: 8.178  
##  Max.   :46.50   Max.   :21.360   Max.   :46.22   Max.   :11.280  
##  NA's   :684     NA's   :684      NA's   :684     NA's   :684     
##  sec.services.venta sec.services.nonventa  school.illit       school.prim     
##  Min.   :26.23      Min.   : 3.430        Min.   :   8.098   Min.   :  151.3  
##  1st Qu.:31.25      1st Qu.: 5.497        1st Qu.:  40.291   1st Qu.:  432.3  
##  Median :34.75      Median : 6.680        Median : 116.232   Median :  852.1  
##  Mean   :36.49      Mean   : 6.935        Mean   : 308.051   Mean   : 2118.5  
##  3rd Qu.:39.19      3rd Qu.: 7.928        3rd Qu.: 252.270   3rd Qu.: 1763.3  
##  Max.   :58.21      Max.   :13.110        Max.   :2863.278   Max.   :19459.6  
##  NA's   :684        NA's   :684           NA's   :666        NA's   :666      
##    school.med       school.high      school.post.high     popdens      
##  Min.   :   8.61   Min.   :  3.063   Min.   :  1.660   Min.   : 22.38  
##  1st Qu.:  26.51   1st Qu.:  9.132   1st Qu.:  4.407   1st Qu.: 44.77  
##  Median :  47.75   Median : 16.696   Median :  7.713   Median : 80.38  
##  Mean   : 145.61   Mean   : 45.944   Mean   : 25.458   Mean   :105.77  
##  3rd Qu.: 119.04   3rd Qu.: 38.758   3rd Qu.: 19.059   3rd Qu.:122.57  
##  Max.   :1696.15   Max.   :474.941   Max.   :252.250   Max.   :442.45  
##  NA's   :666       NA's   :666       NA's   :666       NA's   :756     
##      invest      
##  Min.   : 9.332  
##  1st Qu.:18.742  
##  Median :21.351  
##  Mean   :21.396  
##  3rd Qu.:23.751  
##  Max.   :39.410  
##  NA's   :198

---

Section 2: Clean Data from Basque Dataset

This study makes use of package “Synth”. Load basque dataset from the package

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data(basque)

---

Data Format

1. A panel dataframe made up of 18 units: 1 treated (no 17; the Basque country) and 16 control regions (no. 2-16,18).
2. Region no. 1 is the average for the whole country of Spain.
3. 1 outcome variable (gdpcap).
4. 13 predictor variables (6 sectoral production shares, 6 highest educational attainment categories, population density, and the investment rate).
5. Region names and numbers are stored in regionno and regionname.
6. 42 time periods (1955 - 1997).
7. All columns have self-explanatory column names. \(~\)

---

Clean data

Check for Missing Value

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str(basque)

## 'data.frame':    774 obs. of  17 variables:
##  $ regionno             : num  1 1 1 1 1 1 1 1 1 1 ...
##  $ regionname           : chr  "Spain (Espana)" "Spain (Espana)" "Spain (Espana)" "Spain (Espana)" ...
##  $ year                 : num  1955 1956 1957 1958 1959 ...
##  $ gdpcap               : num  2.35 2.48 2.6 2.64 2.67 ...
##  $ sec.agriculture      : num  NA NA NA NA NA ...
##  $ sec.energy           : num  NA NA NA NA NA ...
##  $ sec.industry         : num  NA NA NA NA NA ...
##  $ sec.construction     : num  NA NA NA NA NA ...
##  $ sec.services.venta   : num  NA NA NA NA NA ...
##  $ sec.services.nonventa: num  NA NA NA NA NA ...
##  $ school.illit         : num  NA NA NA NA NA ...
##  $ school.prim          : num  NA NA NA NA NA ...
##  $ school.med           : num  NA NA NA NA NA ...
##  $ school.high          : num  NA NA NA NA NA ...
##  $ school.post.high     : num  NA NA NA NA NA ...
##  $ popdens              : num  NA NA NA NA NA NA NA NA NA NA ...
##  $ invest               : num  NA NA NA NA NA ...
##  - attr(*, "datalabel")= chr ""
##  - attr(*, "time.stamp")= chr "23 Jan 2007 10:13"
##  - attr(*, "formats")= chr [1:17] "%8.0g" "%28s" "%9.0g" "%9.0g" ...
##  - attr(*, "types")= int [1:17] 254 28 254 254 254 254 254 254 254 254 ...
##  - attr(*, "val.labels")= chr [1:17] "" "" "" "" ...
##  - attr(*, "var.labels")= chr [1:17] "" "" "" "" ...
##  - attr(*, "version")= int -8
##  - attr(*, "label.table")=List of 17
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL
##   ..$ : NULL

# which(is.na(basque))
sum(is.na(basque))

## [1] 8388

There are 8388 missing value from the dataset.

---

Section 3: EDA

Study Data- General Idea

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summary(basque$year)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1955    1965    1976    1976    1987    1997

---

Use Skim to Understand the Databse

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basque%>% 
  skim() %>% 
  kable()

skim_type	skim_variable	n_missing	complete_rate	character.min	character.max	character.empty	character.n_unique	character.whitespace	numeric.mean	numeric.sd	numeric.p0	numeric.p25	numeric.p50	numeric.p75	numeric.p100	numeric.hist
character	regionname	0	1.0000000	6	28	0	18	0	NA	NA	NA	NA	NA	NA	NA	NA
numeric	regionno	0	1.0000000	NA	NA	NA	NA	NA	9.500000	5.191482	1.000000	5.000000	9.500000	14.000000	18.00000	▇▆▇▆▇
numeric	year	0	1.0000000	NA	NA	NA	NA	NA	1976.000000	12.417698	1955.000000	1965.000000	1976.000000	1987.000000	1997.00000	▇▇▇▇▇
numeric	gdpcap	0	1.0000000	NA	NA	NA	NA	NA	5.394987	2.242637	1.243431	3.693034	5.335690	6.869091	12.35004	▅▇▇▂▁
numeric	sec.agriculture	684	0.1162791	NA	NA	NA	NA	NA	20.268445	10.376150	1.320000	13.542499	19.240000	27.482500	46.50000	▅▇▇▅▂
numeric	sec.energy	684	0.1162791	NA	NA	NA	NA	NA	5.188556	4.035458	1.600000	2.697500	3.675000	6.080000	21.36000	▇▂▁▁▁
numeric	sec.industry	684	0.1162791	NA	NA	NA	NA	NA	23.915333	9.281848	9.560000	17.809999	23.135000	27.480000	46.22000	▅▇▆▂▂
numeric	sec.construction	684	0.1162791	NA	NA	NA	NA	NA	7.211556	1.361570	4.340000	6.240000	7.135000	8.177500	11.28000	▃▇▆▅▁
numeric	sec.services.venta	684	0.1162791	NA	NA	NA	NA	NA	36.485222	7.261439	26.230000	31.247500	34.750000	39.192500	58.21000	▇▇▃▁▂
numeric	sec.services.nonventa	684	0.1162791	NA	NA	NA	NA	NA	6.934556	1.978371	3.430000	5.497500	6.680000	7.927500	13.11000	▃▇▃▂▁
numeric	school.illit	666	0.1395349	NA	NA	NA	NA	NA	308.051261	630.842242	8.097660	40.290497	116.232128	252.270393	2863.27832	▇▁▁▁▁
numeric	school.prim	666	0.1395349	NA	NA	NA	NA	NA	2118.524959	4216.779749	151.320892	432.293228	852.125793	1763.311645	19459.55859	▇▁▁▁▁
numeric	school.med	666	0.1395349	NA	NA	NA	NA	NA	145.613775	297.452345	8.609827	26.513481	47.752241	119.039047	1696.14685	▇▁▁▁▁
numeric	school.high	666	0.1395349	NA	NA	NA	NA	NA	45.943488	92.106997	3.063398	9.131781	16.696211	38.758285	474.94116	▇▁▁▁▁
numeric	school.post.high	666	0.1395349	NA	NA	NA	NA	NA	25.458404	51.579575	1.660274	4.407411	7.712549	19.058688	252.25000	▇▁▁▁▁
numeric	popdens	756	0.0232558	NA	NA	NA	NA	NA	105.769444	101.518005	22.379999	44.772499	80.375000	122.567497	442.45001	▇▂▁▁▁
numeric	invest	198	0.7441860	NA	NA	NA	NA	NA	21.395883	4.111414	9.331671	18.742375	21.350711	23.750510	39.40980	▁▇▇▁▁

---

Create a databse with only contains Years (1955-1997), 17 Spanish Regions with no.1 (average) and GDP.

Unused Varibles

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Delete_Varibles_Table <- c("sec.agriculture", "sec.energy" , "sec.industry" , "sec.construction" , 
                     "sec.services.venta" , "sec.services.nonventa", "school.illit", "school.prim", 
                     "school.med", "school.high", "school.post.high", "popdens","invest","regionno")

---

Database for DD

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Basque_Table <- basque[,!(names(basque) %in% Delete_Varibles_Table)]

---

Plot

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Basque_Table %>%
  ggplot( aes(x=year, y=gdpcap , group=regionname, color=regionname)) +
  geom_line() +
  scale_color_viridis(discrete = TRUE) +
  theme(
    legend.position="none",
    plot.title = element_text(size=14)
  ) +
  ggtitle("GDPCAP from 1955-1997 on 18 Spanish Regions") +
  xlab("YEAR") + ylab("GDPCAP")+
  theme_ipsum()

Section 4: Difference in Differences of Basque Dataset

Create a databse with only contains Years (1955-1997), 17 Spanish Regions with no.1 (average) and GDP.

Unused Varibles

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Delete_Varibles <- c("sec.agriculture", "sec.energy" , "sec.industry" , "sec.construction" , 
                     "sec.services.venta" , "sec.services.nonventa", "school.illit", "school.prim", 
                     "school.med", "school.high", "school.post.high", "popdens")

---

Database for DD

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Basque_DD <- basque[,!(names(basque) %in% Delete_Varibles)]

---

Clean the Dataset

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basq_Clean <- Basque_DD %>%
  mutate(post = ifelse(year > 1975, 1, 0),
         treat = ifelse(regionname == "Basque Country (Pais Vasco)", 1, 0),
         regionname = as.factor(regionname)) %>%
  filter(regionno != 1)

---

First Differences

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basq_first_differences <- basq_Clean %>%
  filter(treat == 1)
ggplot(basq_first_differences, aes(x=year, y=gdpcap)) +
  geom_line(color = "blue") +  theme_economist() +
  geom_vline(xintercept=1975, color = "steelblue", linetype = "dashed") +
  labs(title="GDP Trend from 1955–1997 for Basque", 
       y="GDP per capita",x="Years", color = "Region") +
  annotate("text", x = 1970, y = 9, label = "Pre-period", size  =5, color = "Red") +
  annotate("text", x = 1980, y = 9, label = "Post-period", size  =5, color = "Red") 

Calculating First Differences

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f_did <- lm(data = basq_first_differences, gdpcap ~ post)
stargazer(f_did, type="text")

## 
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                               gdpcap           
## -----------------------------------------------
## post                         2.484***          
##                               (0.352)          
##                                                
## Constant                     5.382***          
##                               (0.252)          
##                                                
## -----------------------------------------------
## Observations                    43             
## R2                             0.549           
## Adjusted R2                    0.538           
## Residual Std. Error       1.153 (df = 41)      
## F Statistic           49.921*** (df = 1; 41)   
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

---

DiD Method

Codes From Synth: An R Package for Synthetic Control Methods in Comparative Case Studies - https://cran.r-project.org/web/packages/Synth/Synth.pdf \(~\)

dataprep.out <- dataprep(
  foo = basque,
  predictors = c("school.illit", "school.prim", "school.med",
                 "school.high", "school.post.high", "invest"),
  predictors.op = "mean",
  time.predictors.prior = 1964:1969,
  special.predictors = list(
    list("gdpcap", 1960:1969 ,"mean"),
    list("sec.agriculture", seq(1961, 1969, 2), "mean"),
    list("sec.energy", seq(1961, 1969, 2), "mean"),
    list("sec.industry", seq(1961, 1969, 2), "mean"),
    list("sec.construction", seq(1961, 1969, 2), "mean"),
    list("sec.services.venta", seq(1961, 1969, 2), "mean"),
    list("sec.services.nonventa", seq(1961, 1969, 2), "mean"),
    list("popdens",               1969,               "mean")),
  dependent = "gdpcap",
  unit.variable = "regionno",
  unit.names.variable = "regionname",
  time.variable = "year",
  treatment.identifier = 17,
  controls.identifier = c(2:16, 18),
  time.optimize.ssr = 1960:1969,
  time.plot = 1955:1997)

basq_synth <- basq_Clean %>%
  rename(Y = gdpcap) %>%
  mutate(regionname = as.character(regionname))
ggplot(basq_synth, aes(x=year,y=Y,group=regionno)) +
  geom_line(aes(color=as.factor(treat), size=as.factor(treat))) + 
  geom_vline(xintercept=1975,linetype="dashed", color = "steelblue") + theme_classic() + 
  labs(title="GDP Trend from 1955 to 1997 for All Regions", 
       y="GDP per Capita",x="Years", color = "Treatment group") +
  scale_color_manual(labels = c("Control", "Treated"), values = c("Red", "Blue")) +
  scale_size_manual(values = c(0.5,1), guide = 'none') +
  annotate("text", x = 1970, y = 11, label = "Pre-period", size  =5, color = "Red") +
  annotate("text", x = 1980, y = 11, label = "Post-period", size  =5, color = "Red") +
  theme_economist() 

Cataluna Region as Control Region

\(~\)

Selection <- basq_Clean %>%
  filter(post == 0) %>%
  left_join(dplyr::select(basq_Clean[basq_Clean$post==0 & basq_Clean$treat == 1, ], gdpcap, year),
            by = c("year"= 'year')) %>%
  mutate(perc_diff = (gdpcap.y - gdpcap.x) / gdpcap.y) %>%
  group_by(regionname) %>%
  summarise(gdp_var = abs(var(perc_diff))) %>%
  arrange(gdp_var)

---

Validating Assumption

\(~\)

did_data <- basq_Clean %>%
  filter(regionname %in% c("Basque Country (Pais Vasco)", "Cataluna"))
ggplot(did_data, aes(x=year, y=gdpcap, group = regionname)) +
  geom_line(aes(color = regionname)) + 
  theme_economist() + 
  geom_vline(xintercept=1975, color = "steelblue", linetype = "dashed") +
  labs(title="GDP Trend from 1955-1997 for Different Regions", 
       y="GDP per Capita",x="Years", color = "Region") +
  scale_color_manual(labels = c("Basque (Treated)", "Cataluna (Control)"), values = c("Blue", "Red"))+
  annotate("text", x = 1970, y = 11, label = "Pre-period", size  =5, color = "Red") +
  annotate("text", x = 1980, y = 11, label = "Post-period", size  =5, color = "Red")

Calculating DiD

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did <- lm(data = did_data, gdpcap ~ treat*post)
stargazer(did, type="text")

## 
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                               gdpcap           
## -----------------------------------------------
## treat                          0.139           
##                               (0.376)          
##                                                
## post                         3.339***          
##                               (0.371)          
##                                                
## treat:post                    -0.855           
##                               (0.525)          
##                                                
## Constant                     5.244***          
##                               (0.266)          
##                                                
## -----------------------------------------------
## Observations                    86             
## R2                             0.607           
## Adjusted R2                    0.593           
## Residual Std. Error       1.218 (df = 82)      
## F Statistic           42.279*** (df = 3; 82)   
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

---

Synthetic Control Methods

Codes From Synth: An R Package for Synthetic Control Methods in Comparative Case Studies - https://cran.r-project.org/web/packages/Synth/Synth.pdf \(~\)

dataprep.out <- dataprep(
  foo = basque,
  predictors = c("school.illit", "school.prim", "school.med",
                 "school.high", "school.post.high", "invest"),
  predictors.op = "mean",
  time.predictors.prior = 1964:1969,
  special.predictors = list(
    list("gdpcap", 1960:1969 ,"mean"),
    list("sec.agriculture", seq(1961, 1969, 2), "mean"),
    list("sec.energy", seq(1961, 1969, 2), "mean"),
    list("sec.industry", seq(1961, 1969, 2), "mean"),
    list("sec.construction", seq(1961, 1969, 2), "mean"),
    list("sec.services.venta", seq(1961, 1969, 2), "mean"),
    list("sec.services.nonventa", seq(1961, 1969, 2), "mean"),
    list("popdens",               1969,               "mean")),
  dependent = "gdpcap",
  unit.variable = "regionno",
  unit.names.variable = "regionname",
  time.variable = "year",
  treatment.identifier = 17,
  controls.identifier = c(2:16, 18),
  time.optimize.ssr = 1960:1969,
  time.plot = 1955:1997)

synth.out = synth(dataprep.out)

## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.008864606 
## 
## solution.v:
##  0.02773094 1.194e-07 1.60609e-05 0.0007163836 1.486e-07 0.002423908 0.0587055 0.2651997 0.02851006 0.291276 0.007994382 0.004053188 0.009398579 0.303975 
## 
## solution.w:
##  2.53e-08 4.63e-08 6.44e-08 2.81e-08 3.37e-08 4.844e-07 4.2e-08 4.69e-08 0.8508145 9.75e-08 3.2e-08 5.54e-08 0.1491843 4.86e-08 9.89e-08 1.162e-07

path.plot(dataprep.res = dataprep.out, synth.res = synth.out,Xlab="Year",Ylab="GDP Per Capita")
abline(v=1975,lty=2,col="steelblue")
title("Actual vs Synthetic GDP for Basque")

Placebo Tests

\(~\)

placebo <- generate.placebos(dataprep.out = dataprep.out,synth.out = synth.out, strategy = "multiprocess")

## Warning: [ONE-TIME WARNING] Forked processing ('multicore') is disabled
## in future (>= 1.13.0) when running R from RStudio, because it is
## considered unstable. Because of this, plan("multicore") will fall
## back to plan("sequential"), and plan("multiprocess") will fall back to
## plan("multisession") - not plan("multicore") as in the past. For more details,
## how to control forked processing or not, and how to silence this warning in
## future R sessions, see ?future::supportsMulticore

## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.001123037 
## 
## solution.v:
##  0.241915 0.004561014 0.0005982158 0.0004798842 0.001241421 0.01513177 0.3234859 0.01630921 0.02052098 0.1785447 0.00422904 0.006081587 0.09511713 0.09178419 
## 
## solution.w:
##  3.1e-09 1.9e-09 3e-09 5.1e-09 1.4e-09 3.6e-09 0.4744106 6.396e-07 0.1323778 0 0.3932067 4.3205e-06 3.9e-09 2.1e-09 2.1e-09 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.0005042449 
## 
## solution.v:
##  0.007951046 0.005383677 0.00339887 0.01137706 0.00460769 0.001229192 0.00942928 0.3711191 0.07144081 0.2706073 0.0009782796 0.2245375 0.01746217 0.0004780441 
## 
## solution.w:
##  0.01895674 0.1598039 0.04920978 0.1000861 0.01720838 0.09270212 0.002315982 0.0114126 0.007351221 0.06490908 0.008642634 0.03648222 0.01175011 0.4191682 8.657e-07 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 9.150192e-05 
## 
## solution.v:
##  0.007306654 0.03508239 0.02403886 0.04107291 0.02845283 0.01600231 0.03689203 0.2648573 0.08663512 0.003754926 0.144038 3.1e-09 0.2267502 0.08511643 
## 
## solution.w:
##  1.3e-09 0.1811191 8.428e-07 0.5491962 6.242e-07 5.4e-09 2.11e-08 0.2696795 4.32e-08 8e-10 1.24e-08 0 3.5521e-06 2.87e-08 2.73e-08 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.121049 
## 
## solution.v:
##  0.002617738 0.0002791556 2.57468e-05 0.000137047 0.00097715 0.008678213 0.5666581 0.05034707 0.2251532 9.92001e-05 0.01279458 0.02488051 0.07979401 0.0275582 
## 
## solution.w:
##  4.14567e-05 0.0002089316 1.5421e-06 0.004351484 0.0003378521 4.2789e-06 3.2254e-06 0.5733009 0.0004280817 0.0004464912 5.8471e-06 0.2508225 3.2848e-06 0.1700441 7.3e-09 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.001322934 
## 
## solution.v:
##  8.488e-07 0.01904002 0.02959735 0.03582989 0.0346101 0.1146028 0.06955046 0.01739945 0.1487795 0.1122417 0.0009692388 0.000475205 0.4166301 0.0002732522 
## 
## solution.w:
##  2.127e-07 2.18e-08 4.37e-08 0.1713031 1.071e-07 1.498e-07 4.6e-09 1.01e-08 2.41e-08 0.2497729 4.43e-08 2.86e-07 0.5789231 4.2e-09 2.8e-09 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 6.71562e-05 
## 
## solution.v:
##  0.09936656 0.03044294 0.02972727 0.05003989 0.01908395 0.07927748 0.1458313 0.2134485 0.007984265 0.03630765 0.08577594 0.194891 0.005290142 0.002533157 
## 
## solution.w:
##  7.2e-09 1.373e-07 0.2463714 0.03016985 8.263e-07 3.86e-08 6.49e-08 2.64e-08 0.5327529 5.04e-08 4.73e-08 3.2e-09 1.3424e-06 0.1076988 0.08300449 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.0003285848 
## 
## solution.v:
##  0.02044489 0.04385717 0.06860424 7.70025e-05 9.93798e-05 0.0007090437 0.02125673 0.0003438331 0.2376439 0.001942309 0.08550463 0.03828685 0.431263 0.049967 
## 
## solution.w:
##  0.2405035 0.02499768 0.06589436 7.7222e-06 4.1037e-06 1.86488e-05 5.34252e-05 5.9741e-05 1.20499e-05 0.007073272 0.2371783 0.003946094 0.4199905 0.0001347198 0.0001258654 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.004925438 
## 
## solution.v:
##  0.0640751 0.08790118 0.001980309 0.0003909784 0.001042542 0.009779076 0.06046502 0.3617145 0.1614419 0.004088867 0.002717818 0.2082107 0.002001196 0.03419076 
## 
## solution.w:
##  0.001196807 2.3356e-06 6.8792e-05 2.04e-07 3.601e-07 1.7593e-06 0.3517978 1.1187e-06 1.5301e-06 0.6414476 9.8923e-06 1.533e-07 3.784e-06 6.1336e-06 0.005461752 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.01361662 
## 
## solution.v:
##  0.001433952 0.03871014 0.1084723 0.06228383 0.009103274 0.0398204 0.04808129 0.4397184 0.04134378 0.1485366 0.005719523 0.04843611 0.00131105 0.007029396 
## 
## solution.w:
##  8.635e-07 2.1e-09 1.1e-09 1e-10 2e-10 0.3980367 1.09e-08 2.6e-09 1.07918e-05 7e-10 6.2e-09 0.6019516 7e-10 3.2e-09 2.9e-09 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.001117842 
## 
## solution.v:
##  0.0248724 5.94756e-05 0.1038749 0.001693213 0.0546291 0.1669822 0.2045931 0.0009081238 0.06845943 0.01931348 0.01832864 0.01195384 3.0517e-06 0.324329 
## 
## solution.w:
##  0.194387 7.6484e-06 1.5136e-06 0.0004885163 1.77094e-05 0.4662803 5.0585e-06 0.1050862 0.1032154 4.6847e-06 3.644e-07 0.1251891 2.04468e-05 1.11538e-05 0.005284934 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.1146391 
## 
## solution.v:
##  0.03571533 0.06494282 0.09362483 0.07491658 0.07469396 1.37939e-05 0.04935978 0.349576 0.1030824 0.08247467 0.001718186 0.0001076685 0.006958453 0.06281548 
## 
## solution.w:
##  1e-09 6.3e-09 9e-10 6.83e-08 1.731e-07 4e-09 1.5e-09 0.9999997 6e-10 2.5e-09 4.6e-09 3.1e-09 5.5e-09 1.53e-08 4.3e-08 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.0004963764 
## 
## solution.v:
##  0.0009361261 0.1333922 0.02525684 0.1227094 0.05640474 0.0004846876 0.419331 9.00574e-05 0.01196674 0.05946839 0.1680857 1.42442e-05 0.001858875 1.0247e-06 
## 
## solution.w:
##  0.286836 0.003897055 0.05920034 0.001340042 0.002269029 0.007676064 0.09404751 0.4512099 0.005251879 0.007917988 0.07104263 0.000415688 0.002069254 0.003351204 0.003475416 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.7209181 
## 
## solution.v:
##  0.05343497 0.0121308 0.08151981 0.05309881 0.06651345 0.07808911 0.261331 0.09139274 0.03624163 0.03912748 0.01813165 0.08133689 0.02373037 0.1039213 
## 
## solution.w:
##  5.929e-07 1.123e-07 1.222e-07 0.04087338 1.0595e-06 2.69e-08 1.823e-07 7.34e-08 0.9591236 1.817e-07 8.57e-08 1.869e-07 2.062e-07 1.018e-07 1.011e-07 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.001775702 
## 
## solution.v:
##  0.0001311986 0.002637929 0.1641209 0.08811159 0.004142852 0.07747617 0.3947256 0.00124808 0.04052377 0.0001841404 0.06422426 0.05199957 0.07180447 0.03866944 
## 
## solution.w:
##  1.9427e-06 1.1112e-06 0.02391781 1.25e-07 0.3687398 3.1e-09 0.01449668 0.3780162 4.957e-07 5.086e-07 0 1.8853e-06 2.81679e-05 2.478e-07 0.214795 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.0002705289 
## 
## solution.v:
##  0.01972369 0.0005686467 0.001710033 8.41935e-05 5.4099e-05 0.1506841 0.2549567 0.2465513 0.1368061 0.03261514 0.002974493 0.1309928 0.000170366 0.02210827 
## 
## solution.w:
##  0.0003172171 0.05824001 6.6413e-05 0.01134615 9.8315e-05 0.09664233 0.0001627458 9.64939e-05 0.1327023 0.0001892526 0.004009706 0.0002083849 0.001109842 0.0001280464 0.6946828 
## 
## 
## X1, X0, Z1, Z0 all come directly from dataprep object.
## 
## 
## **************** 
##  searching for synthetic control unit  
##  
## 
## **************** 
## **************** 
## **************** 
## 
## MSPE (LOSS V): 0.0004131752 
## 
## solution.v:
##  0.1276 0.2059267 0.02060637 0.1085751 0.01427578 0.002102533 0.0835427 0.009201901 0.00282947 0.3837883 0.0110102 6.9e-07 0.02223868 0.008301534 
## 
## solution.w:
##  1.38e-08 2.58e-08 1.9e-08 0 6.7e-09 1.46788e-05 2.98e-08 1.0763e-06 8.4e-09 3.43e-08 2.49e-08 4.17e-08 8.5e-09 0.1709315 0.8290525

plot_placebos(placebo)

Post/Pre MPSE Test

\(~\)

mspe_plot(placebo)

*** ### Calculatating root mean squared error between actual and synthetic \(~\)

round(sqrt(mean((dataprep.out$Y1plot - (dataprep.out$Y0plot %*% synth.out$solution.w))^2)), 2)

## [1] 0.57

---

Comparison of results from difference-in-differences and synthetic control methods

\(~\)

labels <- c("DiD","Synthetic Control")
Changes <- c(-0.85, -0.57)
Changes_df <- data.frame(labels,Changes)
names(Changes_df ) <- c("Method", "Change in GDP per Captial")
kable(Changes_df )

Method	Change in GDP per Captial
DiD	-0.85
Synthetic Control	-0.57

---

Reference

Alberto Abadie, Alexis Diamond, Jens Hainmueller (2011). Synth: An R Package for Synthetic Control Methods in Comparative Case Studies. Journal of Statistical Software, 42(13), 1-17. URL http://www.jstatsoft.org/v42/i13/.

Bruno Castanho Silva and Michael DeWitt (2019). SCtools: Extensions for Synthetic Controls Analysis. R package version 0.3.0. https://CRAN.R-project.org/package=SCtools

H. Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2016.

Hadley Wickham (2019). rvest: Easily Harvest (Scrape) Web Pages. R package version 0.3.5. https://CRAN.R-project.org/package=rvest

Hadley Wickham, Romain François, Lionel Henry and Kirill Müller (2020). dplyr: A Grammar of Data Manipulation. R package version 0.8.4. https://CRAN.R-project.org/package=dplyr

Hao Zhu (2019). kableExtra: Construct Complex Table with ‘kable’ and Pipe Syntax. R package version 1.1.0. https://CRAN.R-project.org/package=kableExtra

Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables. R package version 5.2.1. https://CRAN.R-project.org/package=stargazer

Jeffrey B. Arnold (2019). ggthemes: Extra Themes, Scales and Geoms for ‘ggplot2’. R package version 4.2.0. https://CRAN.R-project.org/package=ggthemes

Lüdecke D (2018). “sjmisc: Data and Variable Transformation Functions.” Journal of Open Source Software, 3(26), 754. doi: 10.21105/joss.00754 (URL: https://doi.org/10.21105/joss.00754).

Lüdecke D (2020). sjlabelled: Labelled Data Utility Functions (Version 1.1.3). doi: 10.5281/zenodo.1249215 (URL: https://doi.org/10.5281/zenodo.1249215), <URL: https://CRAN.R-project.org/package=sjlabelled>.

Lüdecke D (2020). sjPlot: Data Visualization for Statistics in Social Science. doi: 10.5281/zenodo.1308157 (URL: https://doi.org/10.5281/zenodo.1308157), R package version 2.8.3, <URL: https://CRAN.R-project.org/package=sjPlot>.

Simon Garnier (2018). viridis: Default Color Maps from ‘matplotlib’. R package version 0.5.1. https://CRAN.R-project.org/package=viridis

Wickham et al., (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686, https://doi.org/10.21105/joss.01686