getspanel: Getting Started

The getspanel package can be downloaded and installed from CRAN here by simply using:

install.packages("getspanel")

The source code of the package is on GitHub and the development version can be installed using:

# install.packages("devtools")
devtools::install_github("moritzpschwarz/getspanel", ref = "devel")

Once installed we need to load the library:

library(getspanel)

Currently the package is called getspanel to align with the gets package, but it’s main function of course remains the isatpanel function.

The isatpanel function implements the empirical break detection algorithm that is described in a paper by Felix Pretis and Moritz Schwarz and was applied to a study by Nico Koch and colleagues on EU Road CO2 emissions, which was published in Nature Energy in 2022.

A quick overview over what has changed:

The isatpanel function

We first load some data of EU CO2 Emissions in the housing sector.

data("EUCO2residential")
head(EUCO2residential)
# A tibble: 6 × 9
  country  year  lgdp  lhdd  lcdd urban av.rate     pop agg.directem
  <chr>   <dbl> <dbl> <dbl> <dbl> <dbl>   <dbl>   <dbl>        <dbl>
1 Austria  1969  25.6    NA    NA  65.2      NA      NA           NA
2 Austria  1970  25.7    NA    NA  65.3      NA      NA           NA
3 Austria  1971  25.8    NA    NA  65.3      NA 7500482           NA
4 Austria  1972  25.8    NA    NA  65.3      NA 7544201           NA
5 Austria  1973  25.9    NA    NA  65.3      NA 7586115           NA
6 Austria  1974  25.9    NA    NA  65.3      NA 7599038           NA

# let's subset this a little bit to speed this up
EUCO2residential <- EUCO2residential[EUCO2residential$year > 2000 & 
                                       EUCO2residential$country %in% c("Germany", "Austria",
                                                                       "Belgium", "Italy", 
                                                                       "Sweden", "Denmark"),]

# let's create a log emissions per capita variable
EUCO2residential$lagg.directem_pc <- log(EUCO2residential$agg.directem/EUCO2residential$pop)

# and let's also turn off printing the intermediate output from isatpanel
options(print.searchoutput = FALSE)

Let’s look at how we input what we want to model. Each isatpanel command takes:

Basics

  1. In the gets package style i.e. using vectors and matrices to specify y, mxreg, time and id

  2. But also in a form that resembles the lm and plm specification i.e. inputting a data.frame (or matrix or tibble), a formula argument as well as character vectors for index (in the form c("group_variable_name", "time_variable_name"))

This already means that the following two commands will give the same result:

Using the new method

is_lm <- isatpanel(data = EUCO2residential,
                   formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                   index = c("country","year"),
                   
                   effect = "twoways",
                   
                   fesis = TRUE)

Using the traditional method

is_gets <- isatpanel(y = EUCO2residential$lagg.directem_pc,
                     mxreg = EUCO2residential$lgdp,
                     time = EUCO2residential$year,
                     id = EUCO2residential$country,

                     effect = "twoways",

                     fesis = TRUE)

From here onwards, I will use the lm notation.

Plotting

We can plot these simply using the default plotting methods (rely on the ggplot2 package):

plot(is_lm)

plot_grid(is_lm)

plot_counterfactual(is_lm)

Saturation Methods

Impulse Indicator Saturation

This argument works just as in the gets package. The method simply adds a 0 and 1 dummy for each observation.

Simply set iis = TRUE.

iis_example <- isatpanel(data = EUCO2residential,
                         formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                         index = c("country","year"),

                         effect = "twoways",

                         iis = TRUE,
                         fesis = TRUE)
plot(iis_example)

Step Indicator Saturation

Traditional Step Indicator Saturation does not make sense in a panel setting. Therefore, the gets function of sis is disabled.

Joint Step Indicator Saturation

It is possible, however, to consider Step Indicator Saturation with common breaks across individuals. Such indicators would be collinear, if effects = c("twoways") or effects = c("time") i.e. if Time Fixed Effects are included.

If, however, effect = "individual" then we can use jsis = TRUE to select over all individual time fixed effects.

jsis_example <- isatpanel(data = EUCO2residential,
                          formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                          index = c("country","year"),

                          effect = "individual",

                          jsis = TRUE)
plot(jsis_example)

Coefficient Step Indicator Saturation

Note: This method has only been tested using the lm implementation (using data, formula, and index).

This method allows detection of coefficient breaks that are common across all groups. It is the interaction between jsis and the relevant coefficient.

To illustrate this, as well as the advantages of using the lm approach, we include a non-linear term of the lgdp variable using I(lgdp^2):

csis_example <- isatpanel(data = EUCO2residential,
                          formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                          index = c("country","year"),

                          effect = "twoways",

                          csis = TRUE)
plot(csis_example)

By default, all coefficients will be interacted and added to the indicator list - but his can be controlled using the csis_var, which takes a character vector of column names i.e. csis_var = "lgdp".

csis_example2 <- isatpanel(data = EUCO2residential,
                           formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                           index = c("country","year"),

                           effect = "twoways",

                           csis = TRUE,
                           csis_var = "lgdp")

Fixed Effect Step Indicator Saturation

This is equivalent to supplying a constant to the mxbreak argument in the old method. This essentially breaks the group-specific intercept i.e. the individual fixed effect.

fesis_example <- isatpanel(data = EUCO2residential,
                           formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                           index = c("country","year"),

                           effect = "twoways",

                           fesis = TRUE)
plot(fesis_example)

Similar to the csis_var idea, we can specify the fesis method for a subset of individuals as well using the fesis_id variable, which takes a character vector of individuals. In this case we can use e.g. fesis_id = c("Austria","Denmark").

fesis_example2 <- isatpanel(data = EUCO2residential,
                           formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                           index = c("country","year"),

                           effect = "twoways",

                           fesis = TRUE,
                           fesis_id = c("Austria","Denmark"))
plot(fesis_example2)

Coefficient Fixed Effect Step Indicator Saturation

This method combines the csis and the fesis approach and detects whether coefficients for individual units break over time.

This means we can also combine the subsetting in both the variable and in the individual units using cfesis_id and cfesis_var.

cfesis_example <- isatpanel(data = EUCO2residential,
                            formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                            index = c("country","year"),

                            effect = "twoways",

                            cfesis = TRUE,
                            cfesis_id = c("Belgium","Germany"),
                            cfesis_var = "lgdp",
                            t.pval = 0.001)
plot(cfesis_example)

The ar argument

It is now possible to specify an argument to include autoregressive coefficients, using the ar argument.

fesis_ar1_example <- isatpanel(data = EUCO2residential,
                               formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                               index = c("country","year"),

                               effect = "twoways",

                               fesis = TRUE,

                               ar = 1)

Post-selection robustness

The options for the robust_isatpanel are to use HAC Standard Errors, use a standard White Standard Error Correction (with the option of clustering the S.E. within groups or time):

robust_isatpanel(fesis_ar1_example, HAC = TRUE, robust = TRUE, cluster = "group")
$plm_object

Model Formula: y ~ ar1 + lgdp + I.lgdp.2. + pop + indicators
<environment: 0x000001887980b6b0>

Coefficients:
       ar1 indicators 
   0.79587   -0.18504 


$robust

t test of coefficients:

            Estimate Std. Error t value  Pr(>|t|)    
ar1         0.795872   0.011568  68.801 < 2.2e-16 ***
indicators -0.185045   0.015963 -11.592 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1


$HAC

t test of coefficients:

              Estimate  Std. Error t value  Pr(>|t|)    
idAustria  -1.5389e+03  1.1792e+03 -1.3050   0.19522    
idBelgium  -1.5386e+03  1.1792e+03 -1.3048   0.19528    
idDenmark  -1.5390e+03  1.1792e+03 -1.3052   0.19517    
idGermany  -1.5387e+03  1.1792e+03 -1.3049   0.19526    
idItaly    -1.5388e+03  1.1792e+03 -1.3050   0.19522    
idSweden   -1.5391e+03  1.1792e+03 -1.3052   0.19514    
time       -1.7146e-02  8.3591e-03 -2.0512   0.04315 *  
ar1         6.9527e-01  5.4987e-02 12.6443 < 2.2e-16 ***
lgdp        1.1814e+02  8.8929e+01  1.3285   0.18737    
I.lgdp.2.  -2.2249e+00  1.6687e+00 -1.3333   0.18578    
pop         3.5077e-07  1.6777e-07  2.0908   0.03937 *  
indicators -2.5696e-01  4.0278e-02 -6.3797 7.509e-09 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

The engine argument

Another new argument is also the engine argument. This allows us to use an external package to estimate our models. At this stage, the fixest package can be used.

This also means that we can now use an argument to cluster Standard Errors using cluster.

fixest_example <- isatpanel(data = EUCO2residential,
                            formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                            index = c("country","year"),

                            effect = "twoways",

                            fesis = TRUE,

                            engine = "fixest",
                            cluster = "none")

We can verify that, using no clustering of Standard Errors at all, using the fixest package does not change our estimates:

head(fixest_example$isatpanel.result$mean.results)
                           coef    std.error      t-stat      p-value
lgdp              -2.371189e+01 2.914939e+00 -8.13461036 6.615453e-12
I(lgdp^2)          4.088169e-01 5.271872e-02  7.75468191 3.491379e-11
pop               -1.300282e-09 1.461405e-08 -0.08897482 9.293391e-01
fesisAustria.2004  4.972763e-02 4.597850e-02  1.08154087 2.829219e-01
fesisBelgium.2004  1.232366e-01 4.756271e-02  2.59103348 1.149348e-02
fesisBelgium.2009  1.010547e-01 5.105385e-02  1.97937523 5.144411e-02

Compared to the default estimator:

head(is_lm$isatpanel.result$mean.results)
                   coef    std.error       t-stat      p-value
lgdp      -2.371189e+01 2.914939e+00  -8.13461036 6.615453e-12
I(lgdp^2)  4.088169e-01 5.271872e-02   7.75468191 3.491379e-11
pop       -1.300282e-09 1.461405e-08  -0.08897482 9.293391e-01
idBelgium  8.715540e-01 9.241906e-02   9.43045775 2.269246e-14
idDenmark -8.793057e-01 8.029376e-02 -10.95110838 3.232923e-17
idGermany  2.730805e+00 1.614286e+00   1.69164900 9.486428e-02

However, changing the cluster specification of course does. The Standard Error correction with it’s current implementation is not valid, so allows for many more indicators than true - clustering is therefore currently not recommended.

fixest_example_cluster <- isatpanel(data = EUCO2residential,
                                    formula = lagg.directem_pc ~ lgdp + I(lgdp^2) + pop,
                                    index = c("country","year"),

                                    effect = "twoways",

                                    fesis = TRUE,

                                    engine = "fixest",
                                    cluster = "individual")
plot(fixest_example_cluster)