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Time series data on US income and consumption expenditure, 1950–1993.

Usage

data("USConsump1993")

Format

An annual multiple time series from 1950 to 1993 with 2 variables.

income

Disposable personal income (in 1987 USD).

expenditure

Personal consumption expenditures (in 1987 USD).

Source

The data is from Baltagi (2002).

References

Baltagi, B.H. (2002). Econometrics, 3rd ed. Berlin, Springer.

Examples

## data from Baltagi (2002)
data("USConsump1993", package = "AER")
plot(USConsump1993, plot.type = "single", col = 1:2)


## Chapter 5 (p. 122-125)
fm <- lm(expenditure ~ income, data = USConsump1993)
summary(fm)
#> 
#> Call:
#> lm(formula = expenditure ~ income, data = USConsump1993)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -294.52  -67.02    4.64   90.02  325.84 
#> 
#> Coefficients:
#>               Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -65.795821  90.990824  -0.723    0.474    
#> income        0.915623   0.008648 105.874   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 153.6 on 42 degrees of freedom
#> Multiple R-squared:  0.9963,	Adjusted R-squared:  0.9962 
#> F-statistic: 1.121e+04 on 1 and 42 DF,  p-value: < 2.2e-16
#> 
## Durbin-Watson test (p. 122)
dwtest(fm)
#> 
#> 	Durbin-Watson test
#> 
#> data:  fm
#> DW = 0.46078, p-value = 3.274e-11
#> alternative hypothesis: true autocorrelation is greater than 0
#> 
## Breusch-Godfrey test (Table 5.4, p. 124)
bgtest(fm)
#> 
#> 	Breusch-Godfrey test for serial correlation of order up to 1
#> 
#> data:  fm
#> LM test = 24.901, df = 1, p-value = 6.034e-07
#> 
## Newey-West standard errors (Table 5.5, p. 125)
coeftest(fm, vcov = NeweyWest(fm, lag = 3, prewhite = FALSE, adjust = TRUE)) 
#> 
#> t test of coefficients:
#> 
#>               Estimate Std. Error t value Pr(>|t|)    
#> (Intercept) -65.795821 133.345400 -0.4934   0.6243    
#> income        0.915623   0.015458 59.2319   <2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 

## Chapter 8
library("strucchange")
## Recursive residuals
rr <- recresid(fm)
rr
#>  [1]   24.900681   30.354827   50.893291   63.260389  -49.805907  -28.404311
#>  [7]  -31.520559   53.194256   67.696114   -2.646556    9.679147   39.658827
#> [13]  -40.126557  -30.260756    2.605633  -78.941467   27.185066   64.363195
#> [19]  -64.906717  -71.641013   70.095867 -113.475323  -85.633171  -29.427630
#> [25]  128.328459  220.693133  126.591749   78.394247  -25.955574 -124.178686
#> [31]  -90.845193  127.830581  -30.794629  159.780872  201.707127  405.310561
#> [37]  390.953841  373.370919  316.431235  188.109683  134.461285  339.300414
## Recursive CUSUM test
rcus <- efp(expenditure ~ income, data = USConsump1993)
plot(rcus)

sctest(rcus)
#> 
#> 	Recursive CUSUM test
#> 
#> data:  rcus
#> S = 1.0267, p-value = 0.02707
#> 
## Harvey-Collier test
harvtest(fm)
#> 
#> 	Harvey-Collier test
#> 
#> data:  fm
#> HC = 3.0802, df = 41, p-value = 0.003685
#> 
## NOTE" Mistake in Baltagi (2002) who computes
## the t-statistic incorrectly as 0.0733 via
mean(rr)/sd(rr)/sqrt(length(rr))
#> [1] 0.07333754
## whereas it should be (as in harvtest)
mean(rr)/sd(rr) * sqrt(length(rr))
#> [1] 3.080177

## Rainbow test
raintest(fm, center = 23)
#> 
#> 	Rainbow test
#> 
#> data:  fm
#> Rain = 4.1448, df1 = 22, df2 = 20, p-value = 0.001116
#> 

## J test for non-nested models
library("dynlm")
fm1 <- dynlm(expenditure ~ income + L(income), data = USConsump1993)
fm2 <- dynlm(expenditure ~ income + L(expenditure), data = USConsump1993)
jtest(fm1, fm2)
#> J test
#> 
#> Model 1: expenditure ~ income + L(income)
#> Model 2: expenditure ~ income + L(expenditure)
#>                 Estimate Std. Error t value  Pr(>|t|)    
#> M1 + fitted(M2)   1.6378    0.20984  7.8051 1.726e-09 ***
#> M2 + fitted(M1)  -2.5419    0.61603 -4.1262 0.0001874 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

## Chapter 14
## ACF and PACF for expenditures and first differences
exps <- USConsump1993[, "expenditure"]
(acf(exps))

#> 
#> Autocorrelations of series ‘exps’, by lag
#> 
#>      0      1      2      3      4      5      6      7      8      9     10 
#>  1.000  0.941  0.880  0.820  0.753  0.683  0.614  0.547  0.479  0.412  0.348 
#>     11     12     13     14     15     16 
#>  0.288  0.230  0.171  0.110  0.049 -0.010 
(pacf(exps))

#> 
#> Partial autocorrelations of series ‘exps’, by lag
#> 
#>      1      2      3      4      5      6      7      8      9     10     11 
#>  0.941 -0.045 -0.035 -0.083 -0.064 -0.034 -0.025 -0.049 -0.043 -0.011 -0.022 
#>     12     13     14     15     16 
#> -0.025 -0.061 -0.066 -0.071 -0.030 
(acf(diff(exps)))

#> 
#> Autocorrelations of series ‘diff(exps)’, by lag
#> 
#>      0      1      2      3      4      5      6      7      8      9     10 
#>  1.000  0.344 -0.067 -0.156 -0.105 -0.077 -0.072  0.026 -0.050  0.058  0.073 
#>     11     12     13     14     15     16 
#>  0.078 -0.033 -0.069 -0.158 -0.161  0.034 
(pacf(diff(exps)))

#> 
#> Partial autocorrelations of series ‘diff(exps)’, by lag
#> 
#>      1      2      3      4      5      6      7      8      9     10     11 
#>  0.344 -0.209 -0.066 -0.038 -0.065 -0.060  0.056 -0.133  0.133 -0.014  0.058 
#>     12     13     14     15     16 
#> -0.079  0.005 -0.175 -0.032  0.065 

## dynamic regressions, eq. (14.8)
fm <- dynlm(d(exps) ~ I(time(exps) - 1949) + L(exps))
summary(fm)
#> 
#> Time series regression with "ts" data:
#> Start = 1951, End = 1993
#> 
#> Call:
#> dynlm(formula = d(exps) ~ I(time(exps) - 1949) + L(exps))
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -357.76  -78.18   22.49  108.97  201.06 
#> 
#> Coefficients:
#>                        Estimate Std. Error t value Pr(>|t|)   
#> (Intercept)          1048.96039  353.81291   2.965  0.00509 **
#> I(time(exps) - 1949)   39.90164   14.31344   2.788  0.00808 **
#> L(exps)                -0.19561    0.07398  -2.644  0.01164 * 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 147.4 on 40 degrees of freedom
#> Multiple R-squared:  0.1784,	Adjusted R-squared:  0.1373 
#> F-statistic: 4.343 on 2 and 40 DF,  p-value: 0.01963
#>