Package 'sdpdth'

Title: M-Estimator for Threshold Spatial Dynamic Panel Data Model
Description: M-estimator for threshold and non-threshold spatial dynamic panel data model. Yang, Z (2018) <doi:10.1016/j.jeconom.2017.08.019>. Wu, J., Matsuda, Y (2021) <doi:10.1007/s43071-021-00008-1>.
Authors: Junyue Wu
Maintainer: Junyue Wu <[email protected]>
License: MIT + file LICENSE
Version: 0.2
Built: 2024-12-13 06:43:50 UTC
Source: CRAN

Help Index

sdpdth

Description

M-estimator for threshold and non-threshold spatial dynamic panel data model.

Author(s)

Junyue Wu <[email protected]>

A simulated data set for testing

Description

A simulated data set for testing

Usage

data_n

Format

An object of class list of length 4.

A simulated data set for testing

Description

A simulated data set for testing

Usage

data_nw

Format

An object of class matrix with 12 rows and 12 columns.

A simulated data set for testing

Description

A simulated data set for testing

Usage

data_th

Format

An object of class list of length 8.

A simulated data set for testing

Description

A simulated data set for testing

Usage

data_w

Format

An object of class matrix with 16 rows and 16 columns.

M-estimator for spatial dynamic panel data model

Description

Estimating the spatial dynamic panel data model with M-estimator

Usage

msdpd(
  y,
  x,
  w1,
  correction = TRUE,
  hessian_er = FALSE,
  true_range = FALSE,
  max_try = 5,
  w2 = w1,
  w3 = w1,
  no_tf = FALSE,
  model = "full",
  rcpp = TRUE,
  cma_pop_multi = 1
)

Arguments

y

matrix, containing regional index (first column), time index (second column, numeric) and dependent variable (third column, numeric).
x

matrix, containing regional index (first column), time index (second column, numeric) and regressors (numeric).
w1

matrix, the spatial weight matrix. If w2 and w3 are supplied, the spatial weight matrix for spatial lag.
correction

logical, whether to use adjusted score function. Default value is TRUE.
hessian_er

logical, whether to output hessian based se. Ignored if correction is set to False. Default value is FALSE.
true_range

logical, whether to used the accurate stationary check. Default value is FALSE due to performance reasons.
max_try

integer, maximum attempt for the solver. Default value is 5.
w2

matrix, the spatial weight matrix for spatio-temporal lag. Default value is the same as w1.
w3

matrix, the spatial weight matrix for spatial error. Default value is the same as w1.
no_tf

logical, whether to account for time effect. Default value is TRUE.
model

character, indicates the model used for estimation, can be "full", "slm", "sem", "sltl". See Details.
rcpp

logical, whether to use the rcpp implementation to calculate the score function. Default value is TRUE.
cma_pop_multi

integer, multiplier for the population size used in CMA-ES. Default value is 1.

Details

Estimating the spatial dynamic panel data model with Yang(2018)'s M-estimator

yti=μi+αt+xtiβ+ρyt−1,i+λ1∑j=1nw1,ijytj+λ2∑j=1nw2,ijyt−1,j+uti,uti=λ3∑j=1nw3,ijutj+vti,i=1,…,n,t=1,…,Ty_{ti} = \mu_{i}+\alpha_t + x_{ti}\beta + \rho y_{t-1,i} + \lambda_1 \sum_{j =1}^{n}w_{1,ij}y_{tj} + \lambda_2 \sum_{j =1}^{n}w_{2,ij}y_{t-1,j} + u_{ti},\\ u_{ti} = \lambda_3\sum_{j =1}^{n}w_{3,ij}u_{tj} + v_{ti}, i=1,\ldots,n,t=1,\ldots,T

The minimum number of time-periods is 4. Make sure the rows and columns of w1, w2, and w3 are lined up with the regional index. Sub-models can be specified by argument "model"

  • "full" Full model

  • "slm" λ2=λ3=0\lambda_2 = \lambda_3 = 0

  • "sem" λ1=λ2=0\lambda_1 = \lambda_2 = 0

  • "sltl" λ3=0\lambda_3 = 0

Some suggestions when the optimizer fails:

  • Increase max_try

  • Increase cma_pop_multi

  • try a different submodel

Value

A list of estimation results of S3 class "msdpd"

  • "coefficient" list, coefficients and standard errors

  • "model" character, model used for estimation

  • "vc_mat" matrix, variance-covariance matrix

  • "hessian" matrix, optional, hessian matrix

References

Yang, Z. (2018). Unified M-estimation of fixed-effects spatial dynamic models with short panels. Journal of Econometrics, 205(2), 423-447.

Examples

data(data_n, data_nw)
result <- msdpd(y = data_n$y, x = data_n$x, w1 = data_nw)

M-estimator for threshold spatial dynamic panel data model

Description

Estimating threshold spatial dynamic panel data model with M-estimator

Usage

msdpdth(
  y,
  x,
  w1,
  th,
  correction = TRUE,
  max_try = 5,
  all_er = FALSE,
  true_range = FALSE,
  residual = FALSE,
  w3 = w1,
  w2 = w1,
  no_tf = FALSE,
  model = "full",
  th_type = "row",
  ini_val = NULL,
  rcpp = TRUE,
  cma_pop_multi = 1
)

Arguments

y

matrix, containing regional index (first column), time index (second column) and dependent variable (third column).
x

matrix, containing regional index (first column), time index (second column) and regressors.
w1

matrix, the spatial weight matrix. If w2 and w3 are supplied, the spatial weight matrix for spatial lag.
th

data.frame, containing regional index (first column, numeric) and grouping indicator(second column, logical). The number of rows should be the same as the number of regions.
correction

logical, whether to use adjusted score function. Default value is TRUE.
max_try

integer, maximum attempt for the solver. Default value is 5.
all_er

logical, whether to output Hessian and Gamma matrix based se. Ignored if correction is set to FALSE. Default value is FALSE.
true_range

logical, whether to used the accurate stationary check. Default value is FALSE due to performance reasons.
residual

logical, whether to output the residual. Default value is FALSE.
w3

matrix, the spatial weight matrix for spatial error. Default value is the same as w1.
w2

matrix, the spatial weight matrix for spatio-temporal lag. Default value is the same as w1.
no_tf

logical, whether to account for time effect. Default value is TRUE.
model

character, indicates the model used for estimation, can be "full", "slm", "sem", "sltl". See Details.
th_type

character, "row" or "col". Indicates whether the threshold is applied to the columns or the rows of the weight matrix. Default value is "row".
ini_val

vector msdpd object. A length 4 vector of the initial values of lambda1, lambda2, lambda3, rho or an msdpd object that contain the non-threshold estimation result. If unsupplied msdpd() will be called.
rcpp

logical, whether to use the rcpp implementation to calculate the score function. Default value is TRUE.
cma_pop_multi

integer, multiplier for the population size used in CMA-ES. Default value is 1.

Details

Estimating threshold spatial dynamic panel data model with extended Yang(2018)'s M-estimator

yti=μi+αt+xtiβq+ρqyt−1,i+λ1q∑j=1nw1,ijytj+λ2q∑j=1nw2,ijyt−1,i+uti,uti=λ3q∑j=1nw3,ijutj+vti,i=1,…,n,t=1,…,T,q=1,2y_{ti} = \mu_{i} +\alpha_t+ x_{ti}\beta_{q} +\rho_{q} y_{t-1,i} + \lambda_{1q}\sum_{j=1}^{n}w_{1,ij}y_{tj} \\ \qquad + \lambda_{2q}\sum_{j=1}^{n}w_{2,ij}y_{t-1,i}+ u_{ti},\\ u_{ti} = \lambda_{3q}\sum_{j=1}^{n}w_{3,ij}u_{tj}+ v_{ti},i=1,\ldots,n,t=1,\ldots,T, q = 1,2

The minimum number of time-periods is 4. Make sure the rows and columns of w1, w2, and w3 are lined up with the regional index. Sub-models can be specified by argument "model"

  • "full" Full model

  • "slm" λ2q=λ3q=0\lambda_{2q} = \lambda_{3q} = 0

  • "sem" λ1q=λ2q=0\lambda_{1q} = \lambda_{2q} = 0

  • "sltl" λ3q=0\lambda_{3q} = 0

Some suggestions when the optimizer fails:

  • Increase max_try

  • Increase cma_pop_multi

  • try a different submodel

Value

A list of estimation results of S3 class "msdpdth"

  • "coefficient" list, coefficients and standard errors

  • "model" character, model used for estimation

  • "vc_mat" matrix, variance-covariance matrix

  • "hes_mat" matrix, optional, Hessian matrix

  • "gamma_mat" matrix, optional, Gamma matrix

  • "residual" numeric, optional, residuals

References

Wu, J and Matsuda, Y. (2021). A threshold extension of spatial dynamic panel model with fixed effects. Journal of Spatial Econometrics 2,3

Examples

data(data_th, data_w)
result <- msdpdth(y = data_th$y, x = data_th$x, w1 = data_w, th = data_th$th)

Print method for msdpd class

Description

Print method for msdpd class

Usage

## S3 method for class 'msdpd'
print(x, ...)

Arguments

x

msdpd class
...

other parameters

Details

Print method for msdpd class

Value

A data.frame containing the coefficients and the corresponding standard error.

Examples

data(data_n, data_nw)
result <- msdpd(y = data_n$y, x = data_n$x, w1 = data_nw)
result

Print method for msdpdth class

Description

Print method for msdpdth class

Usage

## S3 method for class 'msdpdth'
print(x, ...)

Arguments

x

msdpdth class
...

other parameters

Details

Print method for msdpdth class

Value

A data.frame containing the coefficients and the corresponding standard error.

Examples

data(data_th, data_w)
result <- msdpdth(y = data_th$y, x = data_th$x, w1 = data_w, th = data_th$th)
result

Wald test for threshold spatial dynamic panel data model

Description

Wald test for threshold spatial dynamic panel data model

Usage

wald_test(th_res)

Arguments

th_res

msdpdth class, generated by function msdpdth()

Details

Two sided Wald test for testing whether two estimated parameters for each group are equal

  • "h_0" θ1=θ2\theta_1 = \theta_2

  • "h_1" θ1≠θ2\theta_1 \neq \theta_2

Value

A list of p-values for each parameter.

Examples

data(data_th, data_w)
result <- msdpdth(y = data_th$y, x = data_th$x, w1 = data_w, th = data_th$th)
wald_test(result)