Package 'ablasso'

AB-LASSO Estimator with Random Sample Splitting for Multivariate Models

Description

Implements the AB-LASSO estimation method for the multivariate model $Y_{it} = \alpha_{i} + \gamma_{t} + \sum_{j=1}^{L} \beta_{j} Y_{i,t-j} + \theta_{0} D_{it} + \theta_{1} C_{i,t-1} + \varepsilon_{it}$, with random sample splitting. Note that $D_{it}$ and $C_{it}$ are predetermined with respect to $\varepsilon_{it}$.

Usage

ablasso_mv_ss(Y, D, C, lag = 1, Kf = 2, nboot = 100, seed = 202302)

Arguments

Y	A P x N (number of time periods x number of individuals) matrix containing the outcome/response variable Y.
D	A P x N (number of time periods x number of individuals) matrix containing the policy variable/treatment D.
C	A list of P x N matrices containing other treatments and control variables.
lag	The lag order of $Y_{it}$ included in the covariates, default is 1.
Kf	The number of folds for K-fold cross-validation, with options being 2 or 5, default is 2.
nboot	The number of random sample splits, default is 100.
seed	Seed for random number generation, default 202302.

Value

A dataframe that includes the estimated coefficients ($\beta_{j}, \theta_{0}, \theta_{1}$), their standard errors, and T-statistics.

Examples

# Use the Covid data
N = length(unique(covid_data$fips))
P = length(unique(covid_data$week))
Y = matrix(covid_data$logdc, nrow = P, ncol = N)
D = matrix(covid_data$dlogtests, nrow = P, ncol = N)
C = list()
C[[1]] = matrix(covid_data$school, nrow = P, ncol = N)
C[[2]] = matrix(covid_data$college, nrow = P, ncol = N)
C[[3]] = matrix(covid_data$pmask, nrow = P, ncol = N)
C[[4]] = matrix(covid_data$pshelter, nrow = P, ncol = N)
C[[5]] = matrix(covid_data$pgather50, nrow = P, ncol = N)

results.kf2 <- ablasso_mv_ss(Y = Y, D = D, C = C, lag = 4, nboot = 2)
print(results.kf2)
results.kf5 <- ablasso_mv_ss(Y = Y, D = D, C = C, lag = 4, Kf = 5, nboot = 2)
print(results.kf5)

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AB-LASSO Estimator Without Sample Splitting

Description

Implements the AB-LASSO estimation method for the univariate model $Y_{it} = \alpha_{i} + \gamma_{t} + \theta_{1} Y_{i,t-1} + \theta_{2} D_{it} + \varepsilon_{it}$, without sample splitting. Note that $D_{it}$ is predetermined with respect to $\varepsilon_{it}$.

Usage

ablasso_uv(Y, D)

Arguments

Y	A P x N (number of time periods x number of individuals) matrix containing the outcome/response variable Y.
D	A P x N (number of time periods x number of individuals) matrix containing the policy variable/treatment D.

Value

A list with three elements:

• theta.hat: Estimated coefficients.

• std.hat: Estimated Standard errors.

• stat: T-Statistics.

Examples

# Generate data
data1 <- generate_data(N = 300, P = 40)

# You can use your own data by providing matrices `Y` and `D`
results <- ablasso_uv(Y = data1$Y, D = data1$D)
print(results)

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AB-LASSO Estimator with Random Sample Splitting

Description

Implements the AB-LASSO estimation method for the univariate model $Y_{it} = \alpha_{i} + \gamma_{t} + \theta_{1} Y_{i,t-1} + \theta_{2} D_{it} + \varepsilon_{it}$, incorporating random sample splitting. Note that $D_{it}$ is predetermined with respect to $\varepsilon_{it}$.

Usage

ablasso_uv_ss(Y, D, nboot = 100, Kf = 2, seed = 202304)

Arguments

Y	A P x N (number of time periods x number of individuals) matrix containing the outcome/response variable variable Y.
D	A P x N (number of time periods x number of individuals) matrix containing the policy variable/treatment D.
nboot	The number of random sample splits, default is 100.
Kf	The number of folds for K-fold cross-validation, with options being 2 or 5, default is 2.
seed	Seed for random number generation, default 202304.

Value

A list with three elements:

• theta.hat: Estimated coefficients.

• std.hat: Estimated Standard errors.

• stat: T-Statistics.

Examples

# Generate data
data1 <- generate_data(N = 300, P = 40)

# You can use your own data by providing matrices `Y` and `D`
results.ss <- ablasso_uv_ss(Y = data1$Y, D = data1$D, nboot = 2)
print(results.ss)

results.ss2 <- ablasso_uv_ss(Y = data1$Y, D = data1$D, nboot = 2, Kf = 5)
print(results.ss2)

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COVID-19 Spread and School Policy Effects Data

Description

A balanced panel data set analyzing the impact of K-12 school openings and other policy measures on the spread of COVID-19 across U.S. counties. The data spans 32 weeks from April 1st to December 2nd, 2020, and covers 2510 counties.

Usage

covid_data

Format

A data frame with 80320 (2510 counties times 32 weeks) rows and 9 columns. Each column represents a variable:

fips

County FIPS

week

Week

school

A measure of visits to K-12 schools from SafeGraph foot traffic data

logdc

Logarithm of the number of reported COVID-19 cases

pmask

Policy indicators on mask mandates

pgather50

Policy indicators on ban on gatherings of more than 50 persons

college

Measure of visits to colleges

pshelter

Policy indicators on stay-at-home orders

dlogtests

A measure of the weekly growth rate in the number of tests

Source

Data initially provided by Victor Chernozhukov, Hiroyuki Kasahara, and Paul Schrimpf on the GitHub repository https://github.com/ubcecon/covid-schools. Counties with missing values are dropped to obtain a balanced panel dataset.

Examples

data(covid_data) # Access the dataset

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Generate a Dataset for Simulations

Description

Generates data according to the following process: $Y_{it} = \alpha_{i} + \gamma_{t} + \theta_{1} Y_{i,t-1} + \theta_{2} D_{it} + \varepsilon_{it}$ and $D_{it} = \rho D_{i,t-1} + v_{i,t}$. Note that $D_{it}$ is predetermined with respect to $\varepsilon_{it}$.

Usage

generate_data(
  N,
  P,
  sigma_alpha = 1,
  sigma_gamma = 1,
  sigma_eps.d = 1,
  sigma_eps.y = 1,
  cov_eps = 0.5,
  rho = 0.5,
  theta = c(0.8, 1),
  seed = 202304
)

Arguments

N	An integer specifying the number of individuals.
P	An integer specifying the number of time periods.
sigma_alpha	Standard deviation for the normal distribution from which the individual effect alpha is drawn; default is 1.
sigma_gamma	Standard deviation for the normal distribution from which the time effect gamma is drawn; default is 1.
sigma_eps.d	Standard deviation for the error term associated with the policy variable/treatment (D); default is 1.
sigma_eps.y	Standard deviation for the error term associated with the outcome/response variable (Y); default is 1.
cov_eps	Covariance between error terms of Y and D, default 0.5.
rho	Autocorrelation coefficient for D across time, default 0.5.
theta	Regression Coefficients for univariate AR(1) dynamic panal, default c(0.8, 1).
seed	Seed for random number generation, default 202304.

Value

A list of two P x N matrices named Y (outcome/response variable) and D (policy variable/treatment).

Examples

# Generate data using default parameters
data1 <- generate_data(N = 300, P = 40)
str(data1)

data2 <- generate_data(N = 500, P = 20)
str(data2)

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