Very preliminary

Uncertainty of the Keynesian Multiplier:Monte Carlo Simulation Evidence from Malaysia

November 2009

Shinji Yoshioka*

Abstract
From the fourth quarter of 2008, the world economy experienced a deep recession and many
governments of both developed and developing countries took fiscal measures to stimulate the economy.
Among these, the Government of Malaysia employed a sizable fiscal expansionary policy ahead of otherdeveloping countries. It is however absolutely essential to understand the size of the Keynesian multiplier
as well as the gross domestic product (GDP) gap when adopting fiscal measures to stabilize or boost theeconomy. Therefore, this paper focuses on Malaysia's expansionary fiscal policy implemented in 2008
and 2009 adopting concepts of the Keynesian multiplier and its uncertainty. Both deterministic andstochastic simulations based on a small-sized IS-LM model are performed in this study. The results of theformer reveal the essence of the multiplier and those of the latter based on Monte Carlo simulations
indicate the uncertainty of the size of multipliers; this finding supports the Lucas critique and requires amore precisely designed fiscal policy.

Key Words: Econometric Model, IS-LM Analysis, Fiscal Policy, KeynesianMultiplier, Monte Carlo Simulation, Lucas Critique
JEL Classification: C32, E17, O41* Shinji Yoshioka, Nagasaki University, s-ysk@nagasaki-u.ac.jp.

-1-Uncertainty of the Keynesian Multiplier:Monte Carlo Simulation Evidence from Malaysia
1. An Introduction

After late 2008, the world economy experienced a deep recession caused by the US subprime bubble
collapse and a financial crisis as its aftermath. In both developed and developing countries, strong fiscal
measures were taken to boost the economy and to cover the large negative gross domestic product (GDP)gap to a sizable extent. For example, IMF (2009a) estimates that the GDP gap in Asia will increase toaround two percent in 2010. 1 From the fourth quarter of 2008, fiscal measures aimed at economic
stabilization and stimulation were taken. According to the Budget Speech for the Lower House by the
Minister of Finance of Malaysia on November 4, 2008, the Government of Malaysia provided a package
amounting to nearly US$ 2 billion2 to boost the country's economy.

1) Upgrade of repair and maintenance for public amenities, including schools, hospitals, roads, etc.
(RM 1,500 million)2) Upgrade and maintenance of public transportation, including the extension of two existing LRTlines and the construction of one new line (RM 500 million)3) Construction of additional low- and medium-cost houses and improvement of housing programs(RM 1,200 million)4) Establishment of an investment fund to attract private investment (RM 1,200 million)5) Provision of additional business premises for small and medium entrepreneurs (RM 100 million)
6) Micro-financing to provide support such as additional soft loans to commercial banks (RM 200
million)As described by Vijayaledchumy (2003), the Malaysian fiscal policy played a direct and active role inthe country’s overall social and economic development process during the 1970s and expanded further in
1980–82 to pursue a countercyclical purpose and stimulate economic activity in order to tackle thenegative effects of the global recession. Subsequently, since the Government of Malaysia shifted its
policy to private-sector-driven growth and the fiscal policy receded into the background, the share of
public expenditure in the GDP declined to 21% in 1997 from a peak of 44% in 1982. As Baharumshah
and Lau (2007) points out, however, Malaysia's fiscal policy has begun to play a bigger role in smoothing
the business cycle after the 1997 Asian financial crisis, which appears to be natural. Furthermore, Mahani
et al. (2003) stresses that the expansionary policy facilitated the quick recovery in Malaysia. Thanoon etal. (2006) reveals the that fiscal constraint in Malaysia is considerably larger than the savings and foreign
gaps, according to their three-gap model,3 which may possibly suggest that fiscal resources are one of the
scarcest in Malaysia. The measurement of the effects of fiscal policy is therefore very important, and it isabsolutely essential to assess the size of the multiplier, as well as the GDP gap, when a fiscal policy aimed
at boosting the economy is adopted. For example, Romer and Bernstein (2009) suggests that the size ofthe fiscal multiplier is around 1.5–1.64. However, the stability or certainty of this figure is unkown. Hence,
this paper explores the Malaysian fiscal policy by estimating the size of the Keynesian multiplier,employing small-sized IS-LM model simulations. In particular, the paper focuses on the consumption-2-

function, which is a key factor for the multiplier. Both deterministic and stochastic simulations arecompleted to unveil the uncertainty of the size of the multipliers.
Initially, it seems helpful to confirm that simple and textbook-style Keynesian multipliers aredifferently calculated for the three types, regardless of whether it is a closed or open economy, or whether
the government sector that does or does not collect taxes is included. The model is described as follows:(EQ-1)

Closed economy excluding the government sector (both tax revenue and imports are
exogenous)

MULT =(EQ-2)

Closed economy including the government sector (tax revenue is endogenous)

MULT =(EQ-3)

11− c

1
1 − (1 − t )c

Open economy including the government sector (both tax revenue and imports areendogenous)

MULT =

1
1 − (1 − t )c + m

where

MULT

multipliercmarginal propensity to consumetmarginal tax ratemmarginal propensity to import

The multiplier in a closed and government-excluded5 economy seems to be the largest among thethree and its size declines as the model assumption is expanded to include the government sector and toopen the economy that introduces the foreign sector, particularly, imports. This paper then estimates thesize of the Malaysian multiplier by simulating three types of models based on (EQ-1), (EQ-2), and (EQ-3).
Finally, to reveal the uncertainty of the size of the Keynesian multiplier, three types of stochastic
simulations are performed on the basis of a Monte Carlo methodology.
The contents of the paper are as follows. The introduction overviews the main fiscal policy adopted
by the Malaysian government in late 2008 and some existing literature on the Malaysian fiscal policy, andpresents basic concepts of the Keynesian multiplier. The next chapter reveals the structure of asmall-sized IS-LM model of Malaysia, which includes five structural equations and a definition. The thirdchapter reports the deterministic, i.e., non-stochastic, simulation results of the model, which indicate atendency to decline the size of multipliers according to the expanding model sectors such as thegovernment and the foreign sectors. The fourth chapter shows the stochastic, i.e., Monte Carlo, simulation
results, including the uncertainty of the consumption function on both the disturbance term and theestimated parameter. The final chapter briefly concludes the paper and presents some remaining issues.
Further, EViews V6 is employed for estimations and simulations.

-3-2. Structure of the Small-Sized IS-LM Model

This paper employs a small-sized IS-LM Keynesian model where demand factors determine theoutput level. The following equations in (EQ-4) depict the structural functions, while (EQ-5) reports thedefinitions. All structural functions are estimated for the period 1983–2008 and the GMM is employed inorder to minimize the coincident equation bias, which is one of the most remarkable features of the model.
The data adopted in the model are at current prices on an annual basis, and are taken from IMF (2009b),
except for tax revenue, which is referred from ABD (2009). R2, SE, and J-stat denote the adjusted
R-square, standard error of the equation, and p-value of overidentification tests, respectively. The
numbers within parentheses under the equations indicate the standard errors of each parameter. Moreover,Table1 reports the list of model variables.

(EQ-4)

Structural equations(1) Consumption function
C = 12.335 + 0.199 ( GDP - TAX ) - 1.415 R + 0.654 C-1 + ERROR(6.707)(0.186)(1.391)(0.386)2

R = 0.995, SE = 5.977, J-stat = 0.151(2) Investment function
I = 18.581 + 0.627 GDP-1 - 0.621 GDP-2 - 1.627 R + 0.663 I-1 + ERROR(8.892)(0.143)(0.190)(1.054)(0.178)2

R = 0.890, SE = 14.120, J-stat = 0.104(3) Import function
M = -39.570 + 0.439 GDP + 12.336 TT + ERROR(12.724)(0.049)(1.441)

2

R = 0.984, SE = 23.830, J-stat = 0.119(4) Tax function
TAX = 3.972 + 0.146 GDP+ ERROR(0.800)(0.0016)

R2 = 0.980, SE = 4.069, J-stat = 0.143(5) Money demand function
R = 11.939 + 0.809 log(GDP) - 2.049 log(M3) + ERROR(8.637)(6.349)(4.880)2

R = 0.131, SE = 2.032, J-stat = 0.195(EQ-5) Definition(6) Gross domestic product
GDP = C + I + II + G + X – M

Before proceeding to the model’s final test results, we must focus on the following three points:-4-1) The money demand function of equation (5) in (EQ-4) is set to be solved for the interest rate as aninverse function.
2) Imports and money demand functions are estimated on the basis of a normal and well-known
assumption, while Yoshioka (2001) provides some background information for estimating theconsumption and investment function.
3) Since the Keynesian multiplier is defined in a short run, which means that the prices are constant,
all variables in the model are denoted as nominal.

A final test is completed, which reports that the RMSPE of the GDP is 2.67 percent. Fig. 1 depicts theboth actual and the simulated GDP. Considering the RMSPE, the GDP traceability of the model does notseem bad.

3. Deterministic or Non-Stochastic Simulation Results

Before proceeding to stochastic simulations, some deterministic simulations are performed. Here,"deterministic" means that neither the elements of uncertainty, nor, those of stochasticity are included inequations or parameters. According to (EQ-1), (EQ-2), and (EQ-3), three types of simulations are
performed to confirm the decline of multipliers when the sectors are included in a model. The model issimulated through its estimation period during 1983–2008 with constant terms adjusting to the actual
values of each variable for baseline simulations. The sustainable shock of 1 percent of the GDP is added
to government consumption for the final three years from 2006 to 2008 for an impact simulation.
Evidently, the multipliers are derived with the deviation between baseline and impact simulations. Table 2reports the details of the model assumptions for estimated functions. Therefore, the smaller the number ofcases the larger is the size of the multipliers in a macroeconomics textbook.
While the imports function is not included in the model for Cases 1 and 2, it is included for Case 3.
On the other hand, tax revenue is treated as exogenous at its value for Case 1 and endogenous for Cases 2
and 3. For all simulation cases, the money demand function6 is always treated as endogenous, whichmeans that the LM curve is not flat. According to Friedman (1973), the slope of the LM curve determines
the size of the multiplier, while Romer (2000) discusses the requirement of the LM curve in a Keynesianframework. Apparently, Case 1 corresponds to (EQ-1), which excludes the government tax revenue
function and assumes a closed economy, while Case 2 is equivalent to (EQ-2), where the closed economy
leaks some expanding fiscal policy effect to taxes. Case 3 of the open economy spills the stimulus to bothtaxes and the foreign sector through imports. Most economists seem to regard that the multiplier of Case
1 is the largest among three cases and that of Case 3 is the smallest, whereas that of Case 2 lies midway
between Cases 1 and 3. This argument is empirically proven in this paper. Figure 2 depicts the Malaysianfiscal multipliers of three cases at Table 2.
According to the tax and imports functions reported in (EQ-4), the marginal propensity to import of
0.44 is far larger than the marginal tax rate of 0.15. Hence, the leakage of fiscal stimulus to the foreign ismuch larger than that of government tax revenue. Thus, the degree of decline of the multiplier including-5-

government tax revenue function is smaller than that including the foreign sector, as reported by Figure 2.
This is partly owing to data definition, since this model considers only central government tax revenue,7and the local government is excluded because of data availability. The inclusion of the local government,
however, does not seem to raise the marginal tax rate significantly, since the decentralization of
government power does not proceed in many developing countries and Malaysia8 is not an exception.
Moreover, in general, the trade dependency is sizably high in a small country. Figure 2 reports the imports,
exports, and central tax revenue in Malaysia during the estimation period. In particular, Tang and Nair
(2002) reveals that import volume, income, and relative prices are cointegrated by adopting the bounds
test of unrestricted error correction model. The estimated long-run elasticity of import demand withrespect to income is around 1.5, and is larger than that to relative prices, i.e., 1.3. During the estimation
period of the paper, tax revenue roughly indicates a tendency to decline, which is consistent with theaffirmation of Vijayaledchumy (2003). In contrast, the share of imports to the GDP has increased
according to the extent of globalization across the world, including Malaysia. Therefore, the inclusion of
the imports function therefore causes further decline to the multipliers than the tax revenue function does.

4. Stochastic Simulation Results

In addition to the previous deterministic, i.e., non-stochastic, simulations of the model, a few Monte
Carlo simulations are performed for Case 3 at Table 2, where both imports and taxes are treated as
endogenous. As mentioned before, this paper focuses on the uncertainty of consumption function, so that
two types of stochastic elements are employed and three types of Monte Carlo simulations are executed
as follows:

1) Case A includes uncertainty in the entire consumption function, i.e., a disturbance term that is the
product of the equation standard error and a normal random number is added at the equation's error
term.
2) Case B includes uncertainty in the parameter for the disposable income at the consumptionfunction, i.e., a disturbance term that is the product of the parameter's standard error that is given
as SE2 in thefollowing equation in (EQ-6), and a normal random number is added at the parameterfor the disposable income.
3) Case C includes both uncertainties of the above simulations, i.e.,(EQ-6)

Consumption function including uncertainty

C = 12.335 + 0.199(1 + SE 2 × RAND 2 )* (GDP − TAX ) − 1.415R + 0.654C −1 + SE1× RAND1
where

SE1

standard error for whole consumption function

SE2

standard error for parameter of disposable income

Here, normal random numbers are calculated from uniform random numbers according to Box-Müller
transformation indicated in Box and Müller (1958), which generates two sets containing 1000 random-6-numbers that follow N.I.D.(0,1).9 These two sets of normal random numbers for the equation of theconsumption function and the parameter of disposable income are stored, and identical random numbers
are employed for all three cases, which is one of the most remarkable features of the Monte Carlosimulations in the paper.10 Figure 4 depicts the histograms of these two sets of normal random numbers.
The sample means are almost equal to zero, and the sample standard deviations are practically identical to1.
After performing 1000 Monte Carlo simulations for each case, the values of standard deviations forthe last three years for each simulation case are derived from the results and are compared withdeterministic simulation results of Case 3 at Table 2 and Figure 2. Figure 5 reports the multipliers
according to each case. The center bars of each year depict the multiplier derived from deterministic
simulation results of Case 3 at Table 2 and Figure 2, while the left-side and the right-side bars indicate
those that added and reduced a value of one unit of standard deviation derived from each Monte Carlosimulation case respectively.
At a glance, it is not difficult to detect that multiplier deviations of stochastic simulation from thedeterministic case increase over the time, i.e., from 2006 through 2008. Moreover, the deviations of Cases
A, B, and C increase in this order according to the amount of uncertainty included in the consumption
equation. One of the most impressive results should be that the deviation of the parameter uncertainty
case is far larger than that of the equation uncertainty case. This is partly owing to a small significance orlarge standard error of the parameter, but is reminiscent of the also reminds Lucas critique presented in
Lucas (1976), which emphasizes that the estimated parameters of the models are not necessarily structural,i.e., not policy-invariant or policy-variant, such that they may change whenever the policy is changed.
Further, it reveals that policy conclusions based on those models would therefore be potentiallymisleading. Since the model system of the paper reported at (EQ-4) does not adapt to the Lucas critique,the Monte Carlo simulation is employed for approximation. According to the estimation results reported
in Figure 5, it is revealed that the Keynesian fiscal multiplier may possibly decline largely in the negative
for the case including uncertainty in a consumption function, specifically, for the parameter with its
standard error.

5. Conclusion and Remaining Issues

Numerous economists regard that Romer and Bernstein (2009) was unveiled to provide an empiricalbasis to promote fiscal stimulus not only in the US, but also across the world, including Malaysia. In
contrast, some critical literature, including Cogan et al. (2009) and Davig and Leeper (2009), is alsopresented, while Smets and Wouters (2007) asserts that the multiplier is around 1.0–0.4 and is far smaller
than that of Romer and Bernstein (2009), adopting the Bayesian DSGE approach.
This paper is also inspired by Romer and Bernstein (2009), but it employs a different approach fromother literature adopting the stochastic Monte Carlo Simulation, which reveals that the Keynesian fiscal
multiplier may possibly become negative if a sizable uncertainty is included in the consumer's behavior,specifically, in the marginal propensity to consume. The uncertainty of the Keynesian multiplier emerges-7-both in deterministic and stochastic simulations. Even in deterministic simulations, the Keynesian
multiplier differs, regardless of whether the government and the foreign sectors are involved in a model ornot. Clearly, the stochastic simulation results reveal a large uncertainty of the size of multipliers. From
another perspective, the results of the paper support the Lucas critique and suggest that a more precise
design of the fiscal policy would be required in both developed and developing countries, sincedeveloping countries also utilize fiscal policy as an autonomous tool for stabilizing the national economy
after the recent recession. Further, this is very important for the development economics.
Furthermore, it is essential to present a few remaining issues. First, greater accuracy of equation
estimations is necessary. Partly because of data availability of the general government's tax revenue, theparameter for disposable income in the consumption function that defines the marginal propensity toconsume may contain a bias. Second, a more comprehensive model is required. The model constructed in
the paper comprises only six structural functions and a definition. On the other hand, a morecomprehensive model does not necessarily provide more precise simulation results. Third, including
Romer and Bernstein (2009), quarterly models are employed in most developed countries. In developing
economies, however, it is difficult to obtain seasonally adjusted quarterly data, while it is not easy toresolve these remaining issues promptly but further investigation efforts will certainly be made for thedevelopment economics.

(Endnote)
1

See Figure 1.9 on p.16 in IMF (2009a).
This was equivalent to around RM 7 billion. After this package, an additional fiscal plan was alsoannounced.
3
See Figure 2 on p.307 in Thanoon et al. (2006), which indicates that the fiscal gap curve is the steepest
among the three against capacity utilization.
4
This figure is reported in Appendix 1 on p.12 in Romer and Bernstein (2009). However, some literature
raises important questions. The conclusion of this paper will address this point.
5
In the government-excluded economy here, both government expenditure and tax revenue are treated as
exogenous, and the word 'government-excluded' does not mean the absence of the government withregard to its expenditure.
6
The money demand function in the model is solved for an interest rate function as a reverse function.
This seems to be the usual manner for econometric models.
7
Usually, the tax revenue of the central government is smaller than that of the general government, but it
is unclear as to which marginal tax rate of these two types of government is larger.
8
Jalil and Karim (2008) provides useful information on local government fiscal constraints based on
Article 111(2) of the Constitution of Malaysia.
9
EXCEL is employed for this calculation.
10
Hence, the Monte Carlo simulations performed in the paper are reproducible.
2-8-(References)

Baharumshah, Ahmad Zubaidi and Evan Lau 2007, "Regime changes and the sustainability of fiscal
imbalance in East Asian countries," Economic Modelling 24(6), November 2007, pp.878-894
Box, G. E. P. and Mervin E. Müller 1958, "A Note on the Generation of Random Normal Deviates,"
Annals of Mathematical Statistics 29(2), 1958, pp.610-611
ADB 2009, Key Indicators for Asia and the Pacific 2009, Asian Development Bank, 2009
Cogan John F., Tobias Cwik, John B. Taylor and Volker Wieland 2009, "New Keynesian versus Old
Keynesian Government Spending Multipliers," NBER Working Paper No.14782, March 2009Friedman, Benjamin M. 1978, "Crowding Out or Crowding In? The Economic Consequences ofFinancing Government Deficits," Brookings Papers on Economic Activity 3, 1978, pp.593-654
IMF (2009a) World Economic Outlook – Crisis and Recovery, International Monetary Fund, April 2009
IMF (2009b) International Financial Statistics, International Monetary Fund, August 2001, CD-ROM
edition
Davig, Troy and Eric M. Leeper 2009, "Monetary-Fiscal Policy Interactions and Fiscal Stimulus," NBER
Working Paper No.15133, July 2009
Jalil, Ahmad Zafarullah Abdul and Noor Al-Huda Abdul Karim 2008, "Constraining the Spending
Behavior of Subnational Governments Through Borrowing Limitation: The Case of Malaysia," The
Icfai University Journal of Public Finance VI(3), August 2008, pp.7-28
Lucas, Robert E. Jr. 1976, "Econometric policy evaluation: A critique," Carnegie-Rochester Conference
Series on Public Policy 1, 1976, New York: American Elsevier, pp.19-46
Mahani, Zainal-Abidin, Kwanho Shin and Yunjong Wang 2003, "Macroeconomic Adjustments and theReal Economy in Korea and Malaysia Since 1997," KIEP Working Paper 03-07, Korea Institute forInternational Economic Policy, June 2003
Romer, Christina and Jared Bernstein 2009, "The Job Impact of the American Recovery andReinvestment Plan," January 9, 2009http://otrans.3cdn.net/ee40602f9a7d8172b8_ozm6bt5oi.pdf (November 10, 2009)
Romer, David 2000, "Keynesian Macroeconomics without the LM Curve," Journal of Economic
Perspectives 14(2), Spring 2000, pp.149-169
Smets, Frank and Raf Wouters 2007, "Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE
Approach," American Economic Review 97(3), June 2007, pp.586-606
Tang, Tuck Cheong and Mahendhiran Nair 2002, "A cointegration analysis of Malaysian import demand
function: reassessment from the bounds test," Applied Economics Letters 9(5), April 2002,
pp.293-296
Thanoon, Marwan Abdul-Malik, Ahmad Zubaidi Baharumshah and Abd. Aziz Abd. Rahman 2006,"Malaysia: from economic recovery to sustained economic growth," Journal of Post Keynesian
Economics 28(2), Winter 2005-6, pp.295-315
Vijayaledchumy, V. 2003, "Fiscal policy in Malaysia," Fiscal issues and central banking in emerging-9-economies BIS Papers No.20, Bank for International Settlement, 2003, pp.173-179
Yoshioka, Shinji 2001, "Structure, Property, and Simulation Results of TSQ Model: New Version of TSQ
Model QM0111," TSQ Discussion Paper Series 2001/2002-No.6, December 2001
http://tsq.link.net.id/paper.htm (November 10, 2009)- 10 -

Table1: List of Model Variables in Alphabetical Order
Notations
Types
Definitions
C
endogenous
household consumption
I
endogenous
gross fixed capital formation
II
exogenouschanges in inventories
G
exogenous
government consumption
X
exogenous
exports of goods and services
M
endogenous
imports of goods and services
GDP
endogenous
gross domestic product
TAX
endogenous
central government tax revenue
R
endogenous
treasury bill rate
M2
exogenous
money supply, M2TT
exogenous
linear time trend
Sources: IMF (2009b), ADB (2009), and author- 11 -

Unit
billion ringgit
billion ringgit
billion ringgit
billion ringgit
billion ringgit
billion ringgit
billion ringgit
billion pesos
percent per annum
billion ringgit
none

Sources
IMF (2009b)
IMF (2009b)
IMF (2009b)
IMF (2009b)
IMF (2009b)
IMF (2009b)
IMF (2009b)
ADB (2009)
IMF (2009b)
IMF (2009b)
dummy

Fig. 1: Actual and simulated GDP at the final test of the model
800
700
600
500
400
300
200
100
0

ActualSimulation

Note: The unit of the vertical axis is RM billion.
Sources: IMF (2009b) and Author’s estimation- 12 -

Table 2: Model Assumptions
Functions

Case 1Case 2

Case 3

Consumption function

endogenous

endogenous

endogenous

Investment function

endogenous

endogenous

endogenous

Import function

exogenous

exogenous

endogenous

Tax revenue function

exogenous

endogenous

endogenous

Source: Author- 13 -

Fig. 2: Sizes of Multipliers for Cases 1–3
2.96

3.0
2.5

2.69

2.28

2.15

2.0
1.5

1.24

1.20

1.19

1.0

1.32

0.79

0.5
0.0
2006

2007

2008

Case 1

2006

2007
Case 2

2008

2006

2007

2008

Case 3

Note: The unit of vertical axis is an absolute number, since the values shown are of multipliers.
Source: Author’s estimation- 14 -

Fig. 3: Imports, Exports, and Central Government Tax Revenue in Malaysia
140
120
100
80
60
40
20
0

Imports

Exports

Tax

Note: The unit of vertical axis is the percent to GDP.
Sources: ADB (2009) and IMF (2009b)- 15 -

Fig. 4: Histograms of Normal Random Numbers(1) RAND1: Random Numbers for Entire Consumption Function
250
Sample mean: -0.00632
Sample std. dev.: 0.99876
200

150

100

50

0
-3

-2.5

-2

-1.5

-1

-0.5

0

- 16 -

0.5

1

1.5

2

2.5

3

over

(2) RAND2: Random Numbers for Parameter of Disposable Income
250
Sample mean: 0.00821
Sample std. dev.: 0.98729
200

150

100

50

0
-3

-2.5

-2

-1.5

-1

-0.5

0

Source: Author's transformation- 17 -

0.5

1

1.5

2

2.5

3

over

Figure 5: Multipliers Derived from Monte Carlo Simulations(1) Case A: Including uncertainty in whole consumption function
4

Case A

3.43

3
2.13
2
1.32

1.19
1

0.83 0.79 0.74
0.25

0
-1

-0.80
2006

2007
ave + stdave

- 18 -

2008
ave - std

(2) Case B: Including uncertainty in coefficient of disposable income at consumptionfunction

8

Case B

6.40

8.48

6
4
2

3.25
1.32

1.19

0.79

0
-2

-1.68

-4
-4.02
-6
2006

2007
ave + stdave

- 19 -

2008
ave - std

-5.84

(3) Case C: Including uncertainty both in whole consumption function and in coefficient ofdisposable income at consumption function
9
6.51

7
5

8.84

3.25

3
1

Case C

1.32

1.19

0.79

-1
-1.68

-3
-5

-4.13

-7

-6.21
2006

2007
ave + std

ave

Source: Author's estimation- 20 -

2008
ave - std