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This file contains supplementary material on the design of the study of the effects of early retirement on health reported in Ghasempour, Moosavi and de Luna (2023, Convolutional neural networks for valid and efficient causal inference; arXiv version). The study is an observational study using Swedish register data from Statistics Sweden and the Swedish Nationa Board of Health and Welfare, which were linked at the individual level at the Umeå SIMSAM Lab (https://www.umu.se/forskning/infrastruktur/umea-simsam-lab/), were the data is available.

To study the effects of early retirement we consider those who were still alive at age 62, and either retire at age 62 ($T=1$, treatment) or retire later ($T=0$, control group).

Retirement indicator

An individual alive at age 62 is considered as taking early retirement at that age if hers/his pension transfers become larger than income from work at that age for the first time (i.e., they were never so earlier).

Two income from work definition were used and both gave similar results (the second one below corresponds to the results reported in the paper):

First definition:

I1 = LoneInk+ArbLos+AmPol+Fortid+FInk+SjukSum_belop,

where the variables from the LISA register at Statistics Sweden:

  • LoneInk: Cash gross salary
  • ArbLos: Total income caused by unemployment
  • AmPol: Total income caused by labor market policy measures
  • Fortid: Total income caused by early retirement/sickness benefit
  • Fink: Surplus income from active business activities
  • SjukSum_belop: Sums the amount paid for types of compensation of illnesses during the year that has been transferred to sickness benefit, preventive sickness benefit, occupational injury benefit, and/or rehabilitation benefit.

Second definition:

In the second definition, the value CSFVI is considered, which corresponds to all recorded taxable incomes and is obtained from the Income and Taxation Register (IoT) register at Statistics Sweden.

Transfers from old-age pensions is obtained from the variable Aldpens (from LISA).

We then use the relative differences: P/ (I1 +1) and P/ (I2 +1), where P is the Aldpens and I2 is Max(0, CSFVI - P).

Finally, an individual is considered treated (retiree at age 62) if alive and P/ (I2 +1) was below one before that age and above one at age 62.

Pre-treatment covariates that are considered as potential confounders in the study are: Birthyear, Marriage status, Municipality, Education level, Spouse education level, and the number of biological children.

  • Birthyear: 1946 or 1947
  • Marriage status: Maried, Other(Single, Divorced, ...)
  • Municipality: Is it abig city(Stockholm, Gutenberg, Malmo), or not
  • Education level, and Spouse education level:
    • 0: Pre-secondary education shorter than 9 years, and Pre-secondary education 9 years
    • 1: Upper secondary education of a maximum of 2 years, and Secondary education 3 years
    • 2: Post-secondary education shorter than 3 years, Post-secondary education 3 years or longer, and Postgraduate education

Besides these scalar variables, we control for time series data:

  • Log of LoneInk: (10 years before treatment)
  • AldPens (10 years before treatment)
  • Unemployment = ArbLos+AmPol (10 years before treatment)
  • Fortid (10 years before treatment)
  • SjukSum_Belopp (10 years before treatment)
  • Par_SV (number of Inpatient care days per year, 10 years)
  • Par_OV (number of Specialized outpatient care dats per year, 10 years)
  • Spouse retirement (a time series that shows the state of the spouse’s retirement status using the above definition of retirement, 10 years)

The variables Par_SV and Par_OV were provided by the Swedish National Board of Health and Welfare.

CNN Architecture

The developed methods in the manuscript based on Convolutional Neural Networks are implemented in the R-package DNNCausal.

The code below was used for running CNN based AIPW estimator for the average treatment effect on the treated as described in the manuscript. One can define any arbitrary deep neural network architecture and pass it to the function. Models can be created using the Keras package. The outcome model and propensity score are estimated by two different models. The outcome model is a convolutional network with two layers with 128 and 16 filters in the layers respectively. For the propensity score, 32 and 8 filters were used in the two layers. Inputed time series can be centered either columnwise or rowwise by the package. In this case, we have used columnwise centering. For both cases, the mean and standard deviation of the vectors are kept as a new variable and are passed to the part of the architecture that handles scalars as inputs.

model_m = keras::keras_model_sequential()
model_m = keras::layer_conv_1d(model_m, 128,4, padding = 'valid' , activation = 'relu', input_shape = c(10,7))
model_m = keras::layer_conv_1d(model_m, 16,3, padding = 'same', activation = 'relu')
model_m = keras::layer_flatten(model_m)
model_p = keras::keras_model_sequential()
model_p = keras::layer_conv_1d(model_p, 32,4, padding = 'valid' , activation = 'relu', input_shape = c(10,7))
model_p = keras::layer_conv_1d(model_p, 8,3, padding = 'same', activation = 'relu')
model_p = keras::layer_flatten(model_p)


ATT = DNNCausal::aipw.att(Y=Observed_outcomes, T=Treatment, X_t=Timeseries_covariates,X = scalar_covariates, model = c(model_m, model_p), do_standardize = 'Column', verbose=FALSE, epochs = c(64,32), batch_size = 500)

For running this model the following hyperparameters have been chosen: batch size is 500 and the number of epochs is 64 for the fitting outcome model. The number of epochs for training the propensity score in this study is chosen to be 32.

For each group, men and women, and for each outcome years after treatment one to five, the same code has been utilized to estimate the causal parameter of interest.