![Page 1: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/1.jpg)
Econ 240 C
Lecture 16
![Page 2: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/2.jpg)
2
Outline Project I ARCH-M Models Granger Causality Simultaneity VAR models
![Page 3: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/3.jpg)
3Project I Models for dduration Models for dlnduration Seasonality Conditional heteroskedasticity
![Page 4: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/4.jpg)
4
Models for ∆duration
Ufook Sahillioghlu• Ar(1) ar(2) ar(4) ar(5) ar(6) ma(7) ma(24) ma(36)
Tom Bruister• Ar(1) ar(2) ar(24) ma(1) ma(4)
Jesse Smith• Ar(1) ar(4) ar(24) ar(36)
![Page 5: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/5.jpg)
5Models for ∆lnduration Jonathan Hester
• Ar(1) ma(1) ma(2) ma(3) Ashley Hedberg
• Ar(1) ar(2) ma(1) ma(2) Jonathan Liu
• Ar(1) ar(2) ar(4) ar(5) ar(6) ma(7) ma(24) ma(36) Yana Ten
• Ma(1) ma(4) ar(24) ar(36) Jeff Ahlvin
• Ma(1) ma(2) ma(3) sma(24)
![Page 6: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/6.jpg)
6
![Page 7: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/7.jpg)
7
![Page 8: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/8.jpg)
8
![Page 9: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/9.jpg)
9
![Page 10: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/10.jpg)
10
![Page 11: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/11.jpg)
11
![Page 12: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/12.jpg)
12
Conditional Variance, h
![Page 13: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/13.jpg)
13
Part I. ARCH-M Modeks
In an ARCH-M model, the conditional variance is introduced into the equation for the mean as an explanatory variable.
ARCH-M is often used in financial models
![Page 14: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/14.jpg)
14Net return to an asset model Net return to an asset: y(t)
• y(t) = u(t) + e(t)• where u(t) is is the expected risk premium• e(t) is the asset specific shock
the expected risk premium: u(t)• u(t) = a + b*h(t)• h(t) is the conditional variance
Combining, we obtain:• y(t) = a + b*h(t) +e(t)
![Page 15: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/15.jpg)
15Northern Telecom And Toronto Stock Exchange
Nortel and TSE monthly rates of return on the stock and the market, respectively
Keller and Warrack, 6th ed. Xm 18-06 data file
We used a similar file for GE and S_P_Index01 last Fall in Lab 6 of Econ 240A
![Page 16: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/16.jpg)
16
![Page 17: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/17.jpg)
17Returns Generating Model, Variables Not Net of Risk Free
![Page 18: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/18.jpg)
18
![Page 19: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/19.jpg)
19Diagnostics: Correlogram of the Residuals
![Page 20: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/20.jpg)
20Diagnostics: Correlogram of Residuals Squared
![Page 21: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/21.jpg)
21
![Page 22: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/22.jpg)
22Try Estimating An ARCH-
GARCH Model
![Page 23: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/23.jpg)
23
![Page 24: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/24.jpg)
24Try Adding the Conditional Variance to the Returns Model PROCS: Make GARCH variance series:
GARCH01 series
![Page 25: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/25.jpg)
25Conditional Variance Does Not Explain Nortel Return
![Page 26: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/26.jpg)
26
![Page 27: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/27.jpg)
27OLS ARCH-M
![Page 28: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/28.jpg)
28
Estimate ARCH-M Model
![Page 29: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/29.jpg)
29Estimating Arch-M in Eviews with GARCH
![Page 30: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/30.jpg)
30
![Page 31: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/31.jpg)
31
![Page 32: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/32.jpg)
32Three-Mile Island
![Page 33: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/33.jpg)
33
![Page 34: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/34.jpg)
34
![Page 35: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/35.jpg)
35
![Page 36: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/36.jpg)
36
Event: March 28, 1979
![Page 37: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/37.jpg)
37
![Page 38: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/38.jpg)
38
![Page 39: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/39.jpg)
39Garch01 as a Geometric Lag of GPUnet
Garch01(t) = {b/[1-(1-b)z]} zm gpunet(t) Garch01(t) = (1-b) garch01(t-1) + b zm gpunet
![Page 40: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/40.jpg)
40
![Page 41: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/41.jpg)
41
Part II. Granger Causality
Granger causality is based on the notion of the past causing the present
example: Lab six, Index of Consumer Sentiment January 1978 - March 2003 and S&P500 total return, montly January 1970 - March 2003
![Page 42: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/42.jpg)
42Consumer Sentiment and SP 500 Total Return
![Page 43: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/43.jpg)
43
Time Series are Evolutionary
Take logarithms and first difference
![Page 44: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/44.jpg)
44
![Page 45: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/45.jpg)
45
![Page 46: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/46.jpg)
46
Dlncon’s dependence on its past
dlncon(t) = a + b*dlncon(t-1) + c*dlncon(t-2) + d*dlncon(t-3) + resid(t)
![Page 47: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/47.jpg)
47
![Page 48: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/48.jpg)
48Dlncon’s dependence on its past and dlnsp’s past
dlncon(t) = a + b*dlncon(t-1) + c*dlncon(t-2) + d*dlncon(t-3) + e*dlnsp(t-1) + f*dlnsp(t-2) + g* dlnsp(t-3) + resid(t)
![Page 49: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/49.jpg)
49
![Page 50: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/50.jpg)
Do lagged dlnsp terms add to the explained variance?
F3, 292 = {[ssr(eq. 1) - ssr(eq. 2)]/3}/[ssr(eq. 2)/n-7]
F3, 292 = {[0.642038 - 0.575445]/3}/0.575445/292
F3, 292 = 11.26
critical value at 5% level for F(3, infinity) = 2.60
![Page 51: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/51.jpg)
51
Causality goes from dlnsp to dlncon
EVIEWS Granger Causality Test• open dlncon and dlnsp• go to VIEW menu and select Granger Causality• choose the number of lags
![Page 52: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/52.jpg)
52
![Page 53: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/53.jpg)
53Does the causality go the other way, from dlncon to dlnsp? dlnsp(t) = a + b*dlnsp(t-1) + c*dlnsp(t-2) +
d* dlnsp(t-3) + resid(t)
![Page 54: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/54.jpg)
54
![Page 55: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/55.jpg)
55Dlnsp’s dependence on its past and dlncon’s past dlnsp(t) = a + b*dlnsp(t-1) + c*dlnsp(t-2) +
d* dlnsp(t-3) + e*dlncon(t-1) + f*dlncon(t-2) + g*dlncon(t-3) + resid(t)
![Page 56: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/56.jpg)
56
![Page 57: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/57.jpg)
Do lagged dlncon terms add to the explained variance?
F3, 292 = {[ssr(eq. 1) - ssr(eq. 2)]/3}/[ssr(eq. 2)/n-7]
F3, 292 = {[0.609075 - 0.606715]/3}/0.606715/292
F3, 292 = 0.379
critical value at 5% level for F(3, infinity) = 2.60
![Page 58: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/58.jpg)
58
![Page 59: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/59.jpg)
59Granger Causality and Cross-Correlation
One-way causality from dlnsp to dlncon reinforces the results inferred from the cross-correlation function
![Page 60: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/60.jpg)
60
![Page 61: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/61.jpg)
61Part III. Simultaneous Equations
and Identification Lecture 2, Section I Econ 240C Spring
2005 Sometimes in microeconomics it is possible
to identify, for example, supply and demand, if there are exogenous variables that cause the curves to shift, such as weather (rainfall) for supply and income for demand
![Page 62: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/62.jpg)
62
Demand: p = a - b*q +c*y + ep
![Page 63: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/63.jpg)
63
demand
price
quantity
Dependence of price on quantity and vice versa
![Page 64: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/64.jpg)
64
demand
price
quantity
Shift in demand with increased income
![Page 65: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/65.jpg)
65
Supply: q= d + e*p + f*w + eq
![Page 66: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/66.jpg)
66
price
quantity
supply
Dependence of price on quantity and vice versa
![Page 67: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/67.jpg)
67
Simultaneity
There are two relations that show the dependence of price on quantity and vice versa• demand: p = a - b*q +c*y + ep
• supply: q= d + e*p + f*w + eq
![Page 68: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/68.jpg)
68
Endogeneity
Price and quantity are mutually determined by demand and supply, i.e. determined internal to the model, hence the name endogenous variables
income and weather are presumed determined outside the model, hence the name exogenous variables
![Page 69: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/69.jpg)
69
price
quantity
supply
Shift in supply with increased rainfall
![Page 70: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/70.jpg)
70
Identification
Suppose income is increasing but weather is staying the same
![Page 71: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/71.jpg)
71
demand
price
quantity
Shift in demand with increased income, may trace outi.e. identify or reveal the demand curve
supply
![Page 72: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/72.jpg)
72
price
quantity
Shift in demand with increased income, may trace outi.e. identify or reveal the supply curve
supply
![Page 73: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/73.jpg)
73
Identification
Suppose rainfall is increasing but income is staying the same
![Page 74: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/74.jpg)
74
price
quantity
supply
Shift in supply with increased rainfall may trace out, i.e. identify or reveal the demand curve
demand
![Page 75: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/75.jpg)
75
price
quantity
Shift in supply with increased rainfall may trace out, i.e. identify or reveal the demand curve
demand
![Page 76: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/76.jpg)
76
Identification
Suppose both income and weather are changing
![Page 77: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/77.jpg)
77
price
quantity
supply
Shift in supply with increased rainfall and shift in demandwith increased income
demand
![Page 78: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/78.jpg)
78
price
quantity
Shift in supply with increased rainfall and shift in demandwith increased income. You observe price and quantity
![Page 79: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/79.jpg)
79
Identification
All may not be lost, if parameters of interest such as a and b can be determined from the dependence of price on income and weather and the dependence of quantity on income and weather then the demand model can be identified and so can supply
![Page 80: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/80.jpg)
The Reduced Form for p~(y,w)
demand: p = a - b*q +c*y + ep
supply: q= d + e*p + f*w + eq
Substitute expression for q into the demand equation and solve for p
p = a - b*[d + e*p + f*w + eq] +c*y + ep
p = a - b*d - b*e*p - b*f*w - b* eq + c*y + ep
p[1 + b*e] = [a - b*d ] - b*f*w + c*y + [ep - b* eq ]
divide through by [1 + b*e]
![Page 81: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/81.jpg)
The reduced form for q~y,w
demand: p = a - b*q +c*y + ep
supply: q= d + e*p + f*w + eq
Substitute expression for p into the supply equation and solve for q
supply: q= d + e*[a - b*q +c*y + ep] + f*w + eq
q = d + e*a - e*b*q + e*c*y +e* ep + f*w + eq
q[1 + e*b] = [d + e*a] + e*c*y + f*w + [eq + e* ep]
divide through by [1 + e*b]
![Page 82: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/82.jpg)
Working back to the structural parameters
Note: the coefficient on income, y, in the equation for q, divided by the coefficient on income in the equation for p equals e, the slope of the supply equation• e*c/[1+e*b]÷ c/[1+e*b] = e
Note: the coefficient on weather in the equation f for p, divided by the coefficient on weather in the equation for q equals -b, the slope of the demand equation
![Page 83: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/83.jpg)
This process is called identification
From these estimates of e and b we can calculate [1 +b*e] and obtain c from the coefficient on income in the price equation and obtain f from the coefficient on weather in the quantity equation
it is possible to obtain a and d as well
![Page 84: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/84.jpg)
84
Vector Autoregression (VAR)
Simultaneity is also a problem in macro economics and is often complicated by the fact that there are not obvious exogenous variables like income and weather to save the day
As John Muir said, “everything in the universe is connected to everything else”
![Page 85: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/85.jpg)
85VAR One possibility is to take advantage of the
dependence of a macro variable on its own past and the past of other endogenous variables. That is the approach of VAR, similar to the specification of Granger Causality tests
One difficulty is identification, working back from the equations we estimate, unlike the demand and supply example above
We miss our equation specific exogenous variables, income and weather
![Page 86: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/86.jpg)
Primitive VAR
(1)y(t) = w(t) + y(t-1) +
w(t-1) + x(t) + ey(t)
(2) w(t) = y(t) + y(t-1) +
w(t-1) + x(t) + ew(t)
![Page 87: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/87.jpg)
87
Standard VAR
Eliminate dependence of y(t) on contemporaneous w(t) by substituting for w(t) in equation (1) from its expression (RHS) in equation 2
![Page 88: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/88.jpg)
1. y(t) = w(t) + y(t-1) + w(t-1) + x(t) + ey(t)
1’. y(t) = y(t) + y(t-1) + w(t-1) + x(t) + ew(t)] + y(t-1) + w(t-1) + x(t) + ey(t)
1’. y(t) y(t) = [+ y(t-1) + w(t-1) + x(t) + ew(t)] + y(t-1) + w(t-1) + x(t) + ey(t)
![Page 89: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/89.jpg)
Standard VAR (1’) y(t) = (/(1- ) +[ (+
)/(1- )] y(t-1) + [ (+ )/(1- )] w(t-1) + [(+ (1- )] x(t) + (ey(t) + ew(t))/(1- )
in the this standard VAR, y(t) depends only on lagged y(t-1) and w(t-1), called predetermined variables, i.e. determined in the past
Note: the error term in Eq. 1’, (ey(t) + ew(t))/(1- ), depends upon both the pure shock to y, ey(t) , and the pure shock to w, ew
![Page 90: Econ 240 C Lecture 16. 2 Outline w Project I w ARCH-M Models w Granger Causality w Simultaneity w VAR models](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d785503460f94a5aa72/html5/thumbnails/90.jpg)
Standard VAR (1’) y(t) = (/(1- ) +[ (+ )/(1-
)] y(t-1) + [ (+ )/(1- )] w(t-1) + [(+ (1- )] x(t) + (ey(t) + ew(t))/(1- )
(2’) w(t) = (/(1- ) +[(+ )/(1- )] y(t-1) + [ (+ )/(1- )] w(t-1) + [(+ (1- )] x(t) + (ey(t) + ew(t))/(1- )
Note: it is not possible to go from the standard VAR to the primitive VAR by taking ratios of estimated parameters in the standard VAR