# [R] dynlm and lm: should they give same estimates?

Werner Wernersen pensterfuzzer at yahoo.de
Thu Oct 16 00:10:09 CEST 2008

```Hi,

I was wondering why the results from lm and dynlm are not the same for what I think is the same model.
I have just modified example 4.2 from the Pfaff book, please see below for the code and results.

Can anyone tell my what I am doing wrongly?

Many thanks,
Werner

set.seed(123456)
e1 <- rnorm(100)
e2 <- rnorm(100)
y1 <- ts(cumsum(e1))
y2 <- ts(0.6*y1 + e2)
lr.reg <- lm(y2 ~ y1)
error <- ts(residuals(lr.reg))
error.lagged <- error[-c(99, 100)]

dy1 <- diff(y1)
dy2 <- diff(y2)
diff.dat <- data.frame(embed(cbind(dy1, dy2), 2))
colnames(diff.dat) <- c('dy1', 'dy2', 'dy1.1', 'dy2.1')
ecm.reg <- lm(dy2 ~ error.lagged + dy1.1 + dy2.1,
data=diff.dat)
ecm.dynreg <- dynlm(d(y2) ~ L(error) + L(d(y1),1) + L(d(y2),1))
summary(ecm.reg)
summary(ecm.dynreg)

> summary(ecm.reg)

Call:
lm(formula = dy2 ~ error.lagged + dy1.1 + dy2.1, data = diff.dat)

Residuals:
Min      1Q  Median      3Q     Max
-2.9588 -0.5439  0.1370  0.7114  2.3065

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)   0.003398   0.103611   0.033    0.974
error.lagged -0.968796   0.158554  -6.110 2.24e-08 ***
dy1.1         0.808633   0.112042   7.217 1.35e-10 ***
dy2.1        -1.058913   0.108375  -9.771 5.64e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.026 on 94 degrees of freedom
Multiple R-Squared: 0.5464,     Adjusted R-squared: 0.5319
F-statistic: 37.74 on 3 and 94 DF,  p-value: 4.243e-16

> summary(ecm.dynreg)

Time series regression with "ts" data:
Start = 3, End = 100

Call:
dynlm(formula = d(y2) ~ L(error) + L(d(y1), 1) + L(d(y2), 1))

Residuals:
Min      1Q  Median      3Q     Max
-2.9588 -0.5439  0.1370  0.7114  2.3065

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.003398   0.103611   0.033   0.9739
L(error)    -0.968796   0.158554  -6.110 2.24e-08 ***
L(d(y1), 1)  0.245649   0.126996   1.934   0.0561 .
L(d(y2), 1) -0.090117   0.105938  -0.851   0.3971
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.026 on 94 degrees of freedom
Multiple R-Squared: 0.5464,     Adjusted R-squared: 0.5319
F-statistic: 37.74 on 3 and 94 DF,  p-value: 4.243e-16

>

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