- Time series models. Static models and models with lags
Содержание
- 2. 2 HOUS is aggregate consumer expenditure on housing services and DPI is aggregate disposable personal income.
- 3. 3 PRELHOUS is a relative price index for housing services constructed by dividing the nominal price
- 4. 4 Here is a plot of PRELHOUS for the sample period, 1959–2003. TIME SERIES MODELS: STATIC
- 5. ============================================================ Dependent Variable: HOUS Method: Least Squares Sample: 1959 2003 Included observations: 45 ============================================================ Variable Coefficient
- 6. ============================================================ Dependent Variable: HOUS Method: Least Squares Sample: 1959 2003 Included observations: 45 ============================================================ Variable Coefficient
- 7. 7 Possibly. It implies that 15 cents out of the marginal dollar are spent on housing.
- 8. 8 The coefficient of PRELHOUS indicates that a one-point increase in this price index causes expenditure
- 9. 9 The constant has no meaningful interpretation. (Literally, it indicates that $335 billion would be spent
- 10. ============================================================ Dependent Variable: HOUS Method: Least Squares Sample: 1959 2003 Included observations: 45 ============================================================ Variable Coefficient
- 11. 11 Constant elasticity functions are usually considered preferable to linear functions in models of consumer expenditure.
- 12. 12 We linearize the model by taking logarithms. We will regress LGHOUS, the logarithm of expenditure
- 13. ============================================================ Dependent Variable: LGHOUS Method: Least Squares Sample: 1959 2003 Included observations: 45 ============================================================ Variable Coefficient
- 14. 14 Probably. Housing is an essential category of consumer expenditure, and necessities generally have elasticities lower
- 15. 15 Thus an elasticity near 1 seems about right. The price elasticity is 0.48, suggesting that
- 16. 16 Again, the constant has no meaningful interpretation. TIME SERIES MODELS: STATIC MODELS AND MODELS WITH
- 17. 17 The explanatory power of the model appears to be excellent. TIME SERIES MODELS: STATIC MODELS
- 18. 18 Next, we will introduce some simple dynamics. Expenditure on housing is subject to inertia and
- 19. 19 A variable X lagged one time period has values that are simply the previous values
- 20. Current and lagged values of the logarithm of disposable personal income Year LGDPI LGDPI(–1) 1959 5.4914
- 21. Current and lagged values of the logarithm of disposable personal income Year LGDPI LGDPI(–1) LGDPI(–2) 1959
- 22. ============================================================ Dependent Variable: LGHOUS Method: Least Squares Sample(adjusted): 1960 2003 Included observations: 44 after adjusting endpoints
- 23. 23 The estimate of the lagged income and price elasticities are 1.01 and 0.43, respectively. TIME
- 24. 24 The regression results will be summarized in a table for comparison. The results of the
- 25. 25 So also are the results of regressing LGHOUS on LGDPI and LGPRHOUS lagged two years.
- 26. 26 One approach to discriminating between the effects of current and lagged income and price is
- 27. 27 With the current values of income and price, and their values lagged one year, we
- 28. 28 The price side of the model exhibits similar behavior. TIME SERIES MODELS: STATIC MODELS AND
- 29. 29 However there is a problem of multcollinearity caused by the high correlation between current and
- 30. Alternative dynamic specifications, housing services Variable (1) (2) (3) (4) LGDPI 1.03 — — 0.33 (0.01)
- 31. 31 Notice how the standard errors have increased. The fact that the coefficients seem plausible is
- 32. Alternative dynamic specifications, housing services Variable (1) (2) (3) (4) (5) LGDPI 1.03 — — 0.33
- 33. 33 Despite the problem of multicollinearity, we may be able to obtain relatively precise estimates of
- 34. 34 The usual way of investigating the long-run relationship between Y and X is to perform
- 35. 35 One then evaluates the effect of a change in equilibrium on equilibrium . TIME SERIES
- 36. 36 In the model with two lags shown, (β2 + β3 + β4) is a measure
- 37. 37 We can calculate the long-run effect from the point estimates of β2, β3, and β4
- 38. 38 The table presents an example of this. It gives the sum of the income and
- 39. 39 If we are estimating long-run effects, we need standard errors as well as point estimates.
- 40. 40 The point estimate of the coefficient of Xt will be the sum of the point
- 41. 41 Since Xt may well not be highly correlated with (Xt – Xt–1) or (Xt –
- 42. ============================================================ Dependent Variable: LGHOUS Method: Least Squares Sample(adjusted): 1961 2003 Included observations: 43 after adjusting endpoints
- 43. 43 As expected, the point estimates of the coefficients of LGDPI and LGPRHOUS, 1.00 and –0.43,
- 44. 44 Also as expected, the standard errors, 0.01 and 0.03, are much lower than those of
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2
HOUS is aggregate consumer expenditure on housing services and DPI is
2
HOUS is aggregate consumer expenditure on housing services and DPI is
3
PRELHOUS is a relative price index for housing services constructed by
3
PRELHOUS is a relative price index for housing services constructed by
4
Here is a plot of PRELHOUS for the sample period, 1959–2003.
TIME
4
Here is a plot of PRELHOUS for the sample period, 1959–2003.
TIME
============================================================
Dependent Variable: HOUS
Method: Least Squares
Sample: 1959 2003
Included observations:
============================================================
Dependent Variable: HOUS
Method: Least Squares
Sample: 1959 2003
Included observations:
============================================================
Dependent Variable: HOUS
Method: Least Squares
Sample: 1959 2003
Included observations:
============================================================
Dependent Variable: HOUS
Method: Least Squares
Sample: 1959 2003
Included observations:
7
Possibly. It implies that 15 cents out of the marginal dollar
7
Possibly. It implies that 15 cents out of the marginal dollar
8
The coefficient of PRELHOUS indicates that a one-point increase in this
8
The coefficient of PRELHOUS indicates that a one-point increase in this
9
The constant has no meaningful interpretation. (Literally, it indicates that $335
9
The constant has no meaningful interpretation. (Literally, it indicates that $335
============================================================
Dependent Variable: HOUS
Method: Least Squares
Sample: 1959 2003
Included observations:
============================================================
Dependent Variable: HOUS
Method: Least Squares
Sample: 1959 2003
Included observations:
11
Constant elasticity functions are usually considered preferable to linear functions in
11
Constant elasticity functions are usually considered preferable to linear functions in
12
We linearize the model by taking logarithms. We will regress LGHOUS,
12
We linearize the model by taking logarithms. We will regress LGHOUS,
============================================================
Dependent Variable: LGHOUS
Method: Least Squares
Sample: 1959 2003
Included observations:
============================================================
Dependent Variable: LGHOUS
Method: Least Squares
Sample: 1959 2003
Included observations:
14
Probably. Housing is an essential category of consumer expenditure, and necessities
14
Probably. Housing is an essential category of consumer expenditure, and necessities
15
Thus an elasticity near 1 seems about right. The price elasticity
15
Thus an elasticity near 1 seems about right. The price elasticity
16
Again, the constant has no meaningful interpretation.
TIME SERIES MODELS: STATIC MODELS
16
Again, the constant has no meaningful interpretation.
TIME SERIES MODELS: STATIC MODELS
17
The explanatory power of the model appears to be excellent.
TIME SERIES
17
The explanatory power of the model appears to be excellent.
TIME SERIES
18
Next, we will introduce some simple dynamics. Expenditure on housing is
18
Next, we will introduce some simple dynamics. Expenditure on housing is
19
A variable X lagged one time period has values that are
19
A variable X lagged one time period has values that are
Current and lagged values of the
logarithm of disposable personal income
Year
Current and lagged values of the
logarithm of disposable personal income
Year
Current and lagged values of the
logarithm of disposable personal income
Year
Current and lagged values of the
logarithm of disposable personal income
Year
============================================================
Dependent Variable: LGHOUS
Method: Least Squares
Sample(adjusted): 1960 2003
Included observations:
============================================================
Dependent Variable: LGHOUS
Method: Least Squares
Sample(adjusted): 1960 2003
Included observations:
23
The estimate of the lagged income and price elasticities are 1.01
23
The estimate of the lagged income and price elasticities are 1.01
24
The regression results will be summarized in a table for comparison.
24
The regression results will be summarized in a table for comparison.
25
So also are the results of regressing LGHOUS on LGDPI and
25
So also are the results of regressing LGHOUS on LGDPI and
26
One approach to discriminating between the effects of current and lagged
26
One approach to discriminating between the effects of current and lagged
27
With the current values of income and price, and their values
27
With the current values of income and price, and their values
28
The price side of the model exhibits similar behavior.
TIME SERIES MODELS:
28
The price side of the model exhibits similar behavior.
TIME SERIES MODELS:
29
However there is a problem of multcollinearity caused by the high
29
However there is a problem of multcollinearity caused by the high
Alternative dynamic specifications, housing services
Variable (1) (2) (3) (4)
LGDPI 1.03 — — 0.33
(0.01) (0.15)
LGDPI(–1) — 1.01 — 0.68
(0.01) (0.15)
LGDPI(–2) — — 0.98 —
(0.01)
LGPRHOUS –0.48 — — –0.09
(0.04) (0.17)
LGPRHOUS(–1) — –0.43 — –0.36
(0.04) (0.17)
LGPRHOUS(–2) — — –0.38 —
(0.04)
R2 0.9985
Variable (1) (2) (3) (4)
LGDPI 1.03 — — 0.33
(0.01) (0.15)
LGDPI(–1) — 1.01 — 0.68
(0.01) (0.15)
LGDPI(–2) — — 0.98 —
(0.01)
LGPRHOUS –0.48 — — –0.09
(0.04) (0.17)
LGPRHOUS(–1) — –0.43 — –0.36
(0.04) (0.17)
LGPRHOUS(–2) — — –0.38 —
(0.04)
R2 0.9985
31
Notice how the standard errors have increased. The fact that the
31
Notice how the standard errors have increased. The fact that the
Alternative dynamic specifications, housing services
Variable (1) (2) (3) (4) (5)
LGDPI 1.03 — — 0.33 0.29
(0.01) (0.15) (0.14)
LGDPI(–1) — 1.01 — 0.68 0.22
(0.01) (0.15) (0.20)
LGDPI(–2) — — 0.98 — 0.49
(0.01) (0.13)
LGPRHOUS –0.48 — — –0.09 –0.28
(0.04) (0.17) (0.17)
LGPRHOUS(–1) — –0.43 — –0.36 0.23
(0.04) (0.17) (0.30)
LGPRHOUS(–2) — — –0.38 — –0.38
(0.04) (0.18)
R2 0.9985
Variable (1) (2) (3) (4) (5)
LGDPI 1.03 — — 0.33 0.29
(0.01) (0.15) (0.14)
LGDPI(–1) — 1.01 — 0.68 0.22
(0.01) (0.15) (0.20)
LGDPI(–2) — — 0.98 — 0.49
(0.01) (0.13)
LGPRHOUS –0.48 — — –0.09 –0.28
(0.04) (0.17) (0.17)
LGPRHOUS(–1) — –0.43 — –0.36 0.23
(0.04) (0.17) (0.30)
LGPRHOUS(–2) — — –0.38 — –0.38
(0.04) (0.18)
R2 0.9985
33
Despite the problem of multicollinearity, we may be able to obtain
33
Despite the problem of multicollinearity, we may be able to obtain
34
The usual way of investigating the long-run relationship between Y and
34
The usual way of investigating the long-run relationship between Y and
35
One then evaluates the effect of a change in equilibrium on
35
One then evaluates the effect of a change in equilibrium on
36
In the model with two lags shown, (β2 + β3 +
36
In the model with two lags shown, (β2 + β3 +
37
We can calculate the long-run effect from the point estimates of
37
We can calculate the long-run effect from the point estimates of
38
The table presents an example of this. It gives the sum
38
The table presents an example of this. It gives the sum
39
If we are estimating long-run effects, we need standard errors as
39
If we are estimating long-run effects, we need standard errors as
40
The point estimate of the coefficient of Xt will be the
40
The point estimate of the coefficient of Xt will be the
41
Since Xt may well not be highly correlated with (Xt –
41
Since Xt may well not be highly correlated with (Xt –
============================================================
Dependent Variable: LGHOUS
Method: Least Squares
Sample(adjusted): 1961 2003
Included observations:
============================================================
Dependent Variable: LGHOUS
Method: Least Squares
Sample(adjusted): 1961 2003
Included observations:
43
As expected, the point estimates of the coefficients of LGDPI and
43
As expected, the point estimates of the coefficients of LGDPI and
44
Also as expected, the standard errors, 0.01 and 0.03, are much
44
Also as expected, the standard errors, 0.01 and 0.03, are much
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