1

แบบฝกหดท 1.1: แบบจำลองตลาด (ILS)

Demand Function:

�

Qt = 0 + 1Pt + 2Xt + u1t

Supply Function:

�

Qt = 0 + 1Pt + u2t

โดยท Q = Index of Crop Production, 1977=100

P = Index of Crop Prices Received by Farmers, 1977=100

X = Real Per Capita Personal Consumption Expenditure, 1982 $

ทมา: ตารางท 20.1 Gujarati p.767

File: Simultaneous.xls Sheet: EX1

2

แบบฝกหดท 1.2: แบบจำลองสำหรบการประมาณการดวยวธ TSLS

Income Function: Y1t = 10 + 11Y2t + 11X1t + 12X2t + u1t

Money Supply Function: Y2t = 20 + 21Y1t + u2t

โดยท Y1 (GDP) = Gross Domestic Product, Billions of $

Y2 (M2) = Money Supply, Billions of $

X1 (GPDI) = Gross Private Domestic Investment, Billions of $

X2 (FEDEXP) = Federal Government Expenditure, Billions of $

X3 (TB6) = Interest Rate on 6-Month Treasury Bills, Percent

ทมา: ตารางท 20.2 Gujarati p.775

File: Simultaneous.xls Sheet: EX2

Identification

Income Function is under-identified

Money supply function is over-identified

Estimation

Estimate money supply function with Two Stage Least Square (TSLS)

Process of Estimation with TSLS

Step I: กำจด correlation ระหวาง

�

u2t กบ

�

Y1t โดยการประมาณการสมการถดถอยของ

�

Y1t

ทถกกำหนดจาก predeterminedvariables ทงหมดในแบบจำลอง ดงน

Y1t = 0 + 1X1t + 2X2t + ut

จะได Y1t= ˆ

0+ ˆ

1X

1t+ ˆ

2X

2t

และ Y1t= Y

1t+ u

t

3

Step II: แทนคา

�

Y1t = � Y 1t + �

u t ใน money supply equation

�

Y2t = 20 + 21 [� Y 1t + �

u t ] + 2t

�

Y2t = 20 + 21� Y 1t + [21

� u t + 2t ]

�

Y2t = 20 + 21� Y 1t + 2t

โดยท

�

e2t = [21

� u t + 2t ]

4

LS Result

Two Stage Least Square

5

6

ตวอยางท 1.3: Klein’s Model

Consumption Function:

�

CONSt = 10 + 11P2t + 12 [Wt + W1t ] + 13Pt1 + 1t

Investment Function:

�

It = 20 + 21Pt + 22Pt1 + 23Kt1 + 2t

Demand for Labor:

�

Wt = 30 + 31 [Yt Tt W1t ] + 32 [Yt1 Tt1 W1t1 ] + 33t + 3t

Identities:

�

Yt + Tt = CONSt + It + Gt

�

Yt = Wt + W1t + Pt

�

Kt = Kt1 + It

โดยท

�

CONSt is consumption,

�

It is investment,

�

Wt is private wage,

�

W1t is

government wage,

�

Pt is profit,

�

Gt is government spending,

�

Kt is capital stock,

�

Yt is

national income และ is indirect taxes and is time trend (year)

(Gujarati P779 Example 20.2 or Pindyck 363)

7

ตวอยาง 1.4: Small Linear Macroeconomic Model Pindyck p.396, p.390

Consumption: cn = f [gnp, cn(-1)]

Investment: i = f [(gnp-gnp(-1)), gnp, r(-4)]

Interest Rate: r = f [gnp, (gnp-gnp(-1)), (m-m(-1))]

Income Determination: gnp = cn + i + g

Endogenous Variable: cn, i, r, gnp

Exogenous Variable: g, m

Estimation : Least Square Method

Smpl 1950 .1 1985 .4

ls cn c gnp cn(-1 )

8

ls i c gnp(-1 ) -gnp(-2 ) gnp r(-4 )

ls r c gnp gnp-gnp(-1 ) m-m(-1 ) r ( -1 )+r(-2 )

9

Model

10

11

Simulation : Ex post (1950 .1 -1985 .4 )

12

13

14

Simulation

Ex post (1986 .1 1988 .4 )

15

16

Simulation

Ex ante Forecast : 1988 . 2 -1989 .4 (Baseline)

17

18

19

20

Policy Simulation :

Scenario1: G increases 10% from baseline

Scenario2: M increases 10% from baseline

Scenario3: G and M increase 10% from baseline

Scenario4: G increases 20% from baseline

Scenario5: M increases 20% from baseline

Scenario6: G and M increase 20% from baseline

Scenario1 : G increases 10% from baseline

21

22

23

24

25

Scenario2 : M increases 10% from baseline

Scenario3 : G and M increase 10% from baseline

26

ตวอยางท 1.5: Gujarati Example 19.16 p.760 data Table 19.4

Demand for Money Function:

�

Mtd = 10 + 11Yt + 12R + 13Pt + 1t

Supply of Money Function:

�

Mts = 20 + 21Yt + 2t

where

�

Mt is money,

�

Yt is income,

�

Rt is interest rate and

�

Pt is price

27

ตวอยางท 1.6: Demand and Supply of oats

Qd = a + bP + cYD + e1

Qs = f + gP + hW + e2

Qd = Qs

ตวอยางท 1.7: Selected Macroeconomic Data, United States, 1970-1999

แบบจำลองท 1: Rt = b0 + b1 Mt + b2 Yt + u1t

Yt = c0 + c1 Rt + u2t

แบบจำลองท 2: Rt = b0 + b1 Mt + b2 Yt + b3 Yt-1 + u1t

Yt = c0 + c1 Rt + u2t

แบบจำลองท 3: Rt = b0 + b1 Mt + b2 Yt + u1t

Yt = c0 + c1 Rt + c2 It + u2t

แบบจำลองท 4: Rt = b0 + b1 Mt + b2 Yt + u1t

Yt = c0 + c1 Rt + c2 It + u2t

It = d0 + d1 Rt + u3t

โดยท Y = Gross Domestic Product, Billions of $

M = Money Supply, Billions of $

I = Gross Private Domestic Investment, Billions of $

G = Federal Government Expenditure, Billions of $

R = Interest Rate on 6-Month Treasury Bills, Percent

Gujarati Example 20.8 p.788 data Table 20.2

ตวอยางท 1.8: Naïve Linear Keynesian Macroeconomic Model

Yt = COt + It + Gt + NXt

COt = a0 + a1 YDt + a2 COt-1 + u1t

YDt = Yt – Tt

It = a3 + a4 Yt + a5 rt-1 + u2t

ทมา: S p.489 (ยงไมมขอมล)

ตวอยางท 1.9: Public Spending

EXPt = a1 + a2 AIDt + a3 INCt + a4 POPt + u1t

AIDt = b1 + b2 EXPt + b3 PSt + u2t

ทมา: Pindyck p.354