spsur (version 1.0.1.4)

lr_betas: Likelihood ratio for testing homogeneity constraints on beta coefficients of the SUR equations.

Description

Function lr_betas obtains a Likelihood Ratio test, LR in what follows, with the purpose of testing if some of the \(\beta\) coefficients in the G equations of the SUR model are equal. This function has a straightforward application, especially when \(G=1\), to the case of testing for the existence of structural breaks in the \(\beta\) parameters.

The function can test for the homogeneity of only one coefficient, of a few of them or even the homogeneity of all the slope terms. The testing procedure implies, first, the estimation of both a constrained and a unconstrained model and, second, the comparison of the log-likelihoods to compute the LR statistics.

@usage lr_betas (obj, R, b)

Usage

lr_betas(obj, R, b)

Arguments

obj

An spsur object created by spsurml, spsur3sls or spsurtime.

R

A row vector of order \((1xPr)\) showing the set of r linear constraints on the \(\beta\) parameters. The first restriction appears in the first K terms in R, the second restriction in the next K terms and so on.

b

A column vector of order (rx1) with the values of the linear restrictions on the \(\beta\) parameters.

Value

Object of htest including the LR statistic, the corresponding p-value, the degrees of freedom and the values of the sample estimates.

References

• Mur, J., L<U+00F3>pez, F., and Herrera, M. (2010). Testing for spatial effects in seemingly unrelated regressions. Spatial Economic Analysis, 5(4), 399-440.

See Also

spsurml, spsurtime, wald_betas

Examples

# NOT RUN {
## VIP: The output of the whole set of the examples can be examined 
## by executing demo(demo_lr_betas, package="spsur")

# }
# NOT RUN {
#' #################################################
######## CROSS SECTION DATA (G>1; Tm=1)  ########
#################################################

#### Example 1: Spatial Phillips-Curve. Anselin (1988, p. 203)
rm(list = ls()) # Clean memory
data(spc)
lwspc <- spdep::mat2listw(Wspc, style = "W")
Tformula <- WAGE83 | WAGE81 ~ UN83 + NMR83 + SMSA | UN80 + NMR80 + SMSA
### H0: equal beta for SMSA in both equations.
R <- matrix(c(0,0,0,1,0,0,0,-1), nrow=1)
b <- matrix(0, ncol=1)
spcsur.slm <- spsurml(formula = Tformula, data = spc, 
                      type = "slm", listw = lwspc)
summary(spcsur.slm)
lr_betas(spcsur.slm, R = R, b = b)

### Estimate restricted SUR-SLM model
spcsur.slmr <- spsurml(formula = Tformula, data = spc, 
                      type = "slm", listw = lwspc,
                      R = R, b = b)
summary(spcsur.slmr)
#################################################
######## PANEL DATA (G>1; Tm>1)          ########
#################################################

##### Example 2: Homicides + Socio-Economics (1960-90)
## Homicides and selected socio-economic characteristics for continental
## U.S. counties.
## Data for four decennial census years: 1960, 1970, 1980 and 1990.
## \url{https://geodacenter.github.io/data-and-lab/ncovr/}
rm(list = ls()) # Clean memory
data(NCOVR, package="spsur")
nbncovr <- spdep::poly2nb(NCOVR.sf, queen = TRUE)
### Some regions with no links...
lwncovr <- spdep::nb2listw(nbncovr, style = "W", zero.policy = TRUE)
Tformula <- HR80  | HR90 ~ PS80 + UE80 | PS90 + UE90
### H0: equal beta for PS80 and PS90 in both equations.
NCOVRSUR.slm <-spsurml(formula = Tformula, data = NCOVR.sf, 
                       type = "slm", listw = lwncovr,
                       method = "LU", zero.policy = TRUE, 
                       control = list(fdHess = TRUE))
summary(NCOVRSUR.slm)
R <- matrix(c(0, 1, 0, 0, -1, 0), nrow = 1)
b <- matrix(0, ncol = 1)
lr_betas(NCOVRSUR.slm, R = R, b = b)
### Restricted model
NCOVRSUR.slmr <-spsurml(formula = Tformula, data = NCOVR.sf, 
                       type = "slm", listw = lwncovr,
                       method = "LU", zero.policy = TRUE, 
                       control = list(fdHess = TRUE),
                       R = R, b = b)
summary(NCOVRSUR.slmr)                        
#################################################################
######### PANEL DATA: TEMPORAL CORRELATIONS (nG=1; nT>1) ########
#################################################################
### Example 3: with classical panel data set. Database is
###            a spatio-temporal panel

N <- nrow(NCOVR.sf)
Tm <- 4
index_time <- rep(1:Tm, each = N)
index_indiv <- rep(1:N, Tm)
pHR <- c(NCOVR.sf$HR60, NCOVR.sf$HR70, NCOVR.sf$HR80, NCOVR.sf$HR90)
pPS <- c(NCOVR.sf$PS60, NCOVR.sf$PS70, NCOVR.sf$PS80, NCOVR.sf$PS90)
pUE <- c(NCOVR.sf$UE60, NCOVR.sf$UE70, NCOVR.sf$UE80, NCOVR.sf$UE90)
pNCOVR <- data.frame(indiv = index_indiv, time = index_time,
                     HR = pHR, PS = pPS, UE = pUE)
form_pHR <- HR ~ PS + UE
## H0: equal PS beta coefficient in equations 1, 3, and 4
## Fit with spsurtime and fit_method = "ml"...
pHR.slm <-spsurtime(formula = form_pHR, data = pNCOVR,
                    time = pNCOVR$time, 
                    type = "slm", listw = lwncovr,
                    zero.policy = TRUE,
                    fit_method = "ml", method = "LU", 
                    control = list(fdHess = TRUE))
summary(pHR.slm)
### H0: equal betas for PS in equations 1, 3 and 4.
R <- matrix(0, nrow = 2, ncol = 12) 
## nrow = number of restrictions 
## ncol = number of beta parameters
R[1, 2] <- 1; R[1, 8] <- -1 # PS beta coefficient in equations 1 equal to 3
R[2, 2] <- 1; R[2, 11] <- -1 # PS beta coefficient in equations 1 equal to 4
b <- matrix(0, nrow = 2, ncol = 1)
lr_betas(pHR.slm, R = R, b = b)
# }