US Labor Productivity

Description

US labor productivity in the manufacturing/durables sector.

Usage

data("durab")

Format

durab is a multivariate monthly time series from 1947(3) to 2001(4) with variables

y
growth rate of the Industrial Production Index to average weekly labor hours in the manufacturing/durables sector,
lag
lag 1 of the series y,

Source

The data set is available from Bruce Hansen’s homepage https://www.ssc.wisc.edu/~bhansen/. For more information see Hansen (2001).

References

Hansen B. (2001), The New Econometrics of Structural Change: Dating Breaks in U.S. Labor Productivity, Journal of Economic Perspectives, 15, 117–128.

Zeileis A., Leisch F., Kleiber C., Hornik K. (2005), Monitoring Structural Change in Dynamic Econometric Models, Journal of Applied Econometrics, 20, 99–121.

Examples

library("strucchange")

data("durab")
## use AR(1) model as in Hansen (2001) and Zeileis et al. (2005)
durab.model <- y ~ lag

## historical tests
## OLS-based CUSUM process
ols <- efp(durab.model, data = durab, type = "OLS-CUSUM")
plot(ols)

## F statistics
fs <- Fstats(durab.model, data = durab, from = 0.1)
plot(fs)

## F statistics based on heteroskadisticy-consistent covariance matrix
fsHC <- Fstats(durab.model, data = durab, from = 0.1,
           vcov = function(x, ...) vcovHC(x, type = "HC", ...))
plot(fsHC)

## monitoring
Durab <- window(durab, start=1964, end = c(1979, 12))
ols.efp <- efp(durab.model, type = "OLS-CUSUM", data = Durab)
newborder <- function(k) 1.723 * k/192
ols.mefp <- mefp(ols.efp, period=2)
ols.mefp2 <- mefp(ols.efp, border=newborder)
Durab <- window(durab, start=1964)
ols.mon <- monitor(ols.mefp)
Break detected at observation # 437 
ols.mon2 <- monitor(ols.mefp2)
Break detected at observation # 416 
plot(ols.mon)
lines(boundary(ols.mon2), col = 2)

## Note: critical value for linear boundary taken from Table III
## in Zeileis et al. 2005: (1.568 + 1.896)/2 = 1.732 is a linear
## interpolation between the values for T = 2 and T = 3 at
## alpha = 0.05. A typo switched 1.732 to 1.723.


## dating
bp <- breakpoints(durab.model, data = durab)
summary(bp)

     Optimal (m+1)-segment partition: 

Call:
breakpoints.formula(formula = durab.model, data = durab)

Breakpoints at observation number:
                           
m = 1               418    
m = 2       221         530
m = 3   114 225         530
m = 4   114 221     418 531
m = 5   114 221 319 418 531

Corresponding to breakdates:
                                                 
m = 1                            1981(12)        
m = 2           1965(7)                   1991(4)
m = 3   1956(8) 1965(11)                  1991(4)
m = 4   1956(8) 1965(7)          1981(12) 1991(5)
m = 5   1956(8) 1965(7)  1973(9) 1981(12) 1991(5)

Fit:
                                                                     
m   0          1          2          3          4          5         
RSS  5.586e-02  5.431e-02  5.325e-02  5.220e-02  5.171e-02  5.157e-02
BIC -4.221e+03 -4.220e+03 -4.213e+03 -4.207e+03 -4.194e+03 -4.176e+03

plot(ols)
lines(breakpoints(bp, breaks = 1), col = 3)
lines(breakpoints(bp, breaks = 2), col = 4)

plot(fs)
lines(breakpoints(bp, breaks = 1), col = 3)
lines(breakpoints(bp, breaks = 2), col = 4)