US Ex-post Real Interest Rate
Description
US ex-post real interest rate: the three-month treasury bill deflated by the CPI inflation rate.
References
Bai J., Perron P. (2003), Computation and Analysis of Multiple Structural Change Models, Journal of Applied Econometrics, 18, 1-22.
Zeileis A., Kleiber C. (2005), Validating Multiple Structural Change Models - A Case Study. Journal of Applied Econometrics, 20, 685-690.
Examples
## estimate breakpoints
bp.ri <- breakpoints(RealInt ~ 1, h = 15)
plot(bp.ri)
Optimal (m+1)-segment partition:
Call:
breakpoints.formula(formula = RealInt ~ 1, h = 15)
Breakpoints at observation number:
m = 1 79
m = 2 47 79
m = 3 24 47 79
m = 4 24 47 64 79
m = 5 16 31 47 64 79
Corresponding to breakdates:
m = 1 1980(3)
m = 2 1972(3) 1980(3)
m = 3 1966(4) 1972(3) 1980(3)
m = 4 1966(4) 1972(3) 1976(4) 1980(3)
m = 5 1964(4) 1968(3) 1972(3) 1976(4) 1980(3)
Fit:
m 0 1 2 3 4 5
RSS 1214.9 645.0 456.0 445.2 444.9 449.6
BIC 555.7 499.8 473.3 480.1 489.3 499.7
## fit segmented model with three breaks
fac.ri <- breakfactor(bp.ri, breaks = 3, label = "seg")
fm.ri <- lm(RealInt ~ 0 + fac.ri)
summary(fm.ri)
Call:
lm(formula = RealInt ~ 0 + fac.ri)
Residuals:
Min 1Q Median 3Q Max
-4.5157 -1.3674 -0.0578 1.3248 6.0990
Coefficients:
Estimate Std. Error t value Pr(>|t|)
fac.riseg1 1.8236 0.4329 4.213 5.57e-05 ***
fac.riseg2 0.8661 0.4422 1.959 0.053 .
fac.riseg3 -1.7961 0.3749 -4.791 5.83e-06 ***
fac.riseg4 5.6429 0.4329 13.036 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.121 on 99 degrees of freedom
Multiple R-squared: 0.6842, Adjusted R-squared: 0.6714
F-statistic: 53.62 on 4 and 99 DF, p-value: < 2.2e-16
## setup kernel HAC estimator
vcov.ri <- function(x, ...) kernHAC(x, kernel = "Quadratic Spectral",
prewhite = 1, approx = "AR(1)", ...)
## Results from Table 1 in Bai & Perron (2003):
## coefficient estimates
coef(bp.ri, breaks = 3)
(Intercept)
1961(1) - 1966(4) 1.8236167
1967(1) - 1972(3) 0.8660848
1972(4) - 1980(3) -1.7961384
1980(4) - 1986(3) 5.6428896
## corresponding standard errors
sapply(vcov(bp.ri, breaks = 3, vcov = vcov.ri), sqrt)
1961(1) - 1966(4) 1967(1) - 1972(3) 1972(4) - 1980(3) 1980(4) - 1986(3)
0.1857577 0.1499849 0.5026749 0.5887460
## breakpoints and confidence intervals
confint(bp.ri, breaks = 3, vcov = vcov.ri)
Confidence intervals for breakpoints
of optimal 4-segment partition:
Call:
confint.breakpointsfull(object = bp.ri, breaks = 3, vcov. = vcov.ri)
Breakpoints at observation number:
2.5 % breakpoints 97.5 %
1 18 24 35
2 33 47 48
3 77 79 81
Corresponding to breakdates:
2.5 % breakpoints 97.5 %
1 1965(2) 1966(4) 1969(3)
2 1969(1) 1972(3) 1972(4)
3 1980(1) 1980(3) 1981(1)
