Determinants of current account in vietnam, an intertemporal approach

UNIVERSITY OF ECONOMICS
HO CHI MINH CITY
VIETNAM

INSTITUTE OF SOCIAL STUDIES
THE HAGUE
THE NETHERLANDS

VIETNAM - NETHERLANDS
PROGRAMME FOR M.A. IN DEVELOPMENT ECONOMICS

DETERMINANTS OF CURRENT ACCOUNT
IN VIETNAM:
AN INTERTEMPORAL APPROACH

BY

DO NGUYEN KHANH LINH

MASTER OF ARTS IN DEVELOPMENT ECONOMICS

HO CHI MINH CITY, DECEMBER 2013


UNIVERSITY OF ECONOMICS
HO CHI MINH CITY
VIETNAM

INSTITUTE OF SOCIAL STUDIES
THE HAGUE
THE NETHERLANDS

VIETNAM - NETHERLANDS
PROGRAMME FOR M.A. IN DEVELOPMENT ECONOMICS

DETERMINANTS OF CURRENT ACCOUNT
IN VIETNAM:
AN INTERTEMPORAL APPROACH
A thesis submitted in partial fulfilment of the requirements for the degree of
MASTER OF ARTS IN DEVELOPMENT ECONOMICS

BY

DO NGUYEN KHANH LINH

Academic Supervisor:
NGUYEN VAN NGAI

HO CHI MINH CITY, DECEMBER 2013


Acknowledgement
I would like to express sincere gratitude to my supervisor – Prof. Nguyen
Van Ngai for scientific guidance, patient encouragement and useful advices, which
he has provided throughout the time of preparation and accomplishment of this
paper.
I also would like to thank to Dr. Truong Dang Thuy who gave precious
comments on the draft.
Special thanks to Prof. Nguyen Trong Hoai, and Dr. Pham Khanh Nam for
guidance and support as our program administrators.
I also would like to give my deepest thanks to my parents, and my beloved

husband Thanh Binh for his brilliant advices, spiritual supports, and
encouragements.

i


Table of Contents

Acknowledgement................................................................................................................................. i
Table of Contents.................................................................................................................................. ii
List of tables.......................................................................................................................................... iv
List of figures........................................................................................................................................ iv
Abbreviations......................................................................................................................................... v
Abstract................................................................................................................................................... vi
CHAPTER 1:

INTRODUCTION.............................................................................................. 1

1.1 Problem Statement................................................................................................................... 1
1.2 Research objectives and questions..................................................................................... 3
1.3 Justification of the thesis........................................................................................................ 3
1.4 Organization of the research................................................................................................. 4
CHAPTER 2:

LITERATURE REVIEW................................................................................. 5

2.1 Introduction................................................................................................................................. 5
2.2 Definition of Current Account (CA).................................................................................. 5
2.3 Theoretical Literature Review............................................................................................. 5
2.3.1 The old approaches.......................................................................................................... 6

2.3.2 The intertemporal approach.......................................................................................... 8
2.3.3 Determinants of CA balance based on the intertemporal approach............23
2.4 Empirical researches............................................................................................................. 27
2.5 Conceptual framework......................................................................................................... 40
2.6 Chapter summary................................................................................................................... 41
CHAPTER 3:

DATA AND RESEARCH METHODOLOGY...................................... 42

3.1 Data............................................................................................................................................. 42
3.2 Research Methodology........................................................................................................ 43
3.2.1 Analytical Framework.................................................................................................. 43
3.2.2 Model Specification...................................................................................................... 44

ii


3.2.2.2 Cointegration Test ................................................................................. 45
CHAPTER 4: FINDINGS AND DISCUSSIONS ................................................ 50
4.1 Descriptive statistics ........................................................................................ 50
4.2 The dynamics of variables ............................................................................... 51
4.3 The correlation matrix ..................................................................................... 53
4.4 The regression result........................................................................................ 54
4.4.1 Unit Root Test ........................................................................................... 54
4.4.2 ARDL Test ................................................................................................ 55
CHAPTER 5: CONCLUSION AND POLICY IMPLICATION.......................... 59
5.1 Conclusion ....................................................................................................... 59
5.2 Policy implication ............................................................................................ 60
5.3 Limitations and directions for further studies ................................................. 60
5.3.1 Limitation.................................................................................................. 60

5.3.2 Further studies .......................................................................................... 61
REFERENCES.......................................................................................................... 62
APPENDICES........................................................................................................... 68

iii


List of tables
Table 2-1: Empirical studies about determinants of CA balance..................................... 33
Table 3-1: The measurements and expected signs of variables........................................ 43
Table 3-2: Critical values for Dickey Fuller test.................................................................... 45
Table 3-3: Critical values bounds for testing the hypothesis of no – cointegration
relationship........................................................................................................................................... 47
Table 4-1: Descriptive statistics.................................................................................................... 50
Table 4-2: The correlation matrix of variables........................................................................ 53
Table 4-3: The values of stationary tests of all variables.................................................... 54
Table 4-4: The summary of result................................................................................................ 55
Table 4-5: Results of cointegration (m = 1)............................................................................. 56
Table 4-6: ARDL equations chosen with lowest AIC and SIC’s values....................... 56
Table 4-7: Estimated long – run coefficients using the ARDL approach.................... 57

List of figures
Figure 1-1: Current account of Vietnam from 1999 to 2012................................................ 2
Figure 2-1: Temporary fall in income......................................................................................... 15
Figure 2-2: Current account acts like a shock absorber....................................................... 22
Figure 2-3: The conceptual framework...................................................................................... 41
Figure 3-1: The Analytical framework....................................................................................... 44
Figure 4-1: The dynamics of variables....................................................................................... 52

iv

Abbreviations
ARDL : Autoregressive Distributed Lag
CA

: Current Account

CPI

: Consumer Price Index

ECM : Error Correction Model
GMM : Generalized Method of Moments
GSO : General Statistics Office of Vietnam
IFS

: International Financial Statistics

IMF : International Monetary Finance
LDC : Least Developed Countries
NFA : Net Foreign Assets
OECD : Organization for Economic Co-operation and Development

REER : Real Effective Exchange Rate
USD : United States Dollar
VND : Vietnam Dong

v

Abstract
This study attempts to explain theoretically and examine empirically
influences of macroeconomics factors on the current account behavior in Vietnam
from 2000Q1 to 2010Q2. The study employs the intertemporal approach to build the
theory of Vietnam current account behavior’s determinants and applies
Autoregressive Distributed Lag method to estimate the model. Theoretically,
intertemporal approach was an approach broadly employed to decide determinants
of current account recently. It treats current account as an absorber for the economy
in facing a shock in income. The study discovers that initial net foreign assets, trade
openness, real effective exchange rate and inflation volatility have significant
relationships with current account in Vietnam.

vi


CHAPTER 1:

INTRODUCTION

This study attempts to explain theoretically and test empirically influences of
macroeconomics factors on the current account behavior in Vietnam. The study
employs the intertemporal approach to build the theory of Vietnam current account
behavior’s determinant and applies autoregressive distributed lag method to
estimate the model. Theoretically, intertemporal approach was an approach broadly
employed to decide determinants of current account recently. It treats current
account as an absorber for the economy in facing a shock in income. Determinants
of current account will be determined based on this idea.
1.1 Problem Statement
The current account is a crucial indicator of a country’s economic

performance (Knight and Scacciavillani 1998). Current account deficit could
damage the economy in many ways. First, current account deficit that accompanies
by budget deficit leads to the increasing of debts (Krugman, 1987). According to
Ministry of Finance, public debt reached 52.6% of GDP, foreign debt hit 38.8% of
GDP in 2010 and was equal 56.6% compared to GDP in 2011. Second, in an
economy that applies fixed exchange rate regime and has weak foreign reserve, a
prolonged current account deficit may raise the probability of a monetary crisis
(Edwards, 2002). The Asian financial crisis in 1997 is a good example for this
situation. Third, a serious current account deficit raises people’s expectation of
depreciation that increases the volatility of the foreign exchange market. Altogether,
maintaining the balance of current account at suitable level is one of the majority
missions of macroeconomics policymakers. Consequently, strong understanding
about the determinants of current account balance becomes an important subject that
requires careful researches (Yang 2011).
Like most developing countries in the world, Vietnam mostly suffers from
the current account deficit over the past 12 years. There are two deficit periods of

1


current account: the low deficit period in 2002-2006 and the high deficit period in
2006-2010. The first deficit period started in 2002 and reached the lowest value (1.93 billion USD) in the year 2003. After 2003, it turned to improve until getting the
balance in 2006. However, the situation became worse after 2006. It reached - 6.953
billion USD in the year 2007 and -10.823 billion USD in the year 2008. Current
account had improved and had an increasing tendency since 2008. It got the surplus
position in the year 2012 (see Figure 1-1). Altogether, the situation of current
account is still very unpredictable. As observations mentioned in the previous
paragraph, the erratic current account level could have a negative impact on the
stability of Vietnamese macroeconomic, which has become instability for long time
owing to the impact of global crisis and the products of many overlap policy.

Therefore, it is very essential to identify determinants of Vietnam’s current account
balance so that the country could restore external balance by controlling those
causal factors through suitable macroeconomic policy options. Hence, the aim of
this paper is to shed the light on finding the determinants of current account in
intertemporal approach perspective.
Figure 1-1: Current account of Vietnam from 1999 to 2012
15000
10000
5000

15.00%
6.66% 10.00%
3.55%

2.10%

0.19%

0

5.00%

0.00%

-5000

-1.72%
-2.11%
-4.89%

-10000
-15000
2000 2001

CA

2002 2003

-1.06%

-0.27%

-5.00%
-7.12%

-4.14%

-10.00%
-9.77%
-12.05%
-15.00%
2004 2005 2006 2007 2008 2009 2010 2011 2012

CA/GDP

2


1.2 Research objectives and questions
The study is attempted to accomplish two major objectives: (1) To find the

determining factors that theoretically influence the current account based on intertemporal
approach; and (2) To examine those factors statistically explaining the current account
behavior in Vietnam. The central question of the research is: “What are the determinants of
Vietnamese current account?” To give an answer, thi s question is divided in to two subquestions: (1) What is the factors theoretically influencing Vietnamese current account? (2)
Do these factors statistically explain the current account in Vietnam? By examining the
theoretical literature review and empirical studies this study will get the answer the first
one. The second one will be answer by employing econometric method to analyze the
determinants which obtained by the first sub-question.

1.3 Justification of the thesis
The study gives main contributions in two aspects as follows
First, there has been a numerous quantity of empirical researches on the
determinants of current account. Many of them work in the case of developing
countries. However, there are still no published researches about this topic in the
context of Vietnam. Thus, this field in Vietnam still continues being an unexploited
subject although the demand for strongly concentration on it is considerable. Hence,
this research contributes to the literature as the first comprehensive study about this
subject in the Vietnamese case.
Second, this research provides useful and reliable understanding of the nature
of the Vietnamese current account behavior according to intertemporal approach
during the past ten years empirically for macroeconomics policymaker.
Consequently, they have dependable evidences to propose and implement better
policies for current account.

3


1.4 Organization of the research
The reminder of the thesis research design is organized into four sections as
follows: after introduction in the first section 1, literature review is discussed in the

second section, the third section is about data and research methodology, the fourth
section points out the findings and discussions, and the final section contains the
conclusions and policy recommendations.

4


CHAPTER 2:

LITERATURE REVIEW

2.1 Introduction
In this chapter, theories and studies of current account behavior will be
reviewed. This chapter will particularly concern about intertemporal approach
theory due to its central role in this study. The determinants of Vietnamese current
account will be introduced after learning carefully intertemporal approach. In
addition, other empirical research will be concern to attain the general viewing.
Conceptual framework will be introduced in the last section of this chapter.
2.2 Definition of Current Account (CA)
The CA is one of the two main elements of the balance of payments.
According to Madura (2007), CA is the sum of the trade balances (exports value
minus imports value), factor income payments (earnings on foreign investments
minus payments for foreign investors).
CA = Trade Balance + Income Payment
2.3 Theoretical Literature Review
Finding determinants of CA balance has always been the attractive topic of
economist for a long time. Initially, many economists such as Caprio and Howard
(1984), Baxter and Crucini (1993) try to treat CA balance as a static factor. This
leads to the using of static approaches to determine what factors have impacts on
CA balance. Although those approaches have an advantage in providing a

straightforward and easy perspective, they were claimed to be not effective and not
reasonable in explaining CA balance behavior (Obstfeld and Rogoff, 1995; Yang,
2011). The newer approach is dynamic approach that was named intertemporal. The
intertemporal approach to the CA was initially recommended by Sachs (1981) and
further extended by Obstfeld and Rogoff (1995). This approach is still extended by
many researches such as Debelle and Faruqee (1996), Yang (2011) and Brissimis,

5


Hondroyiannis, Papazoglou, Tsaveas and Vasardani (2012). This approach is based
on the consideration that CA balance is a dynamic result that must be determined
not only by the recent events but also by the past and the future ones. Therefore,
solely concentrating on the recent events could fail to find the determinants of CA
balance. Instead, intertemporal approach try to decide the CA balance’s
determinants based on investigating effect factors in multiple periods. Hence,
Obstfeld and Rogoff (1995), Yang (2011) claim that the intertemporal approach is
suitable for deciding determinants of CA balance than the old others. Consequently,
this thesis tries this approach to find out the determinant of CA balance.
2.3.1 The old approaches
In the beginning of open economy macroeconomics, CA balance’s behavior
was recognized as the consequence of impacts of static determinants. Indeed, many
theories were developed to explain CA balance’s determinants in this viewpoint.
The most prominent of those are elasticity approach and absorption approach.
A concentrating on the CA balance as the net export balance guided many
economists to think that vital determinant of CA could be its relative international
prices. The "elasticity approach" to the current account was born based on this idea.
According to elasticity approach, static price elasticities of supply and demand
decide the net international flow of capital while the determinants of international
expenditure and incomes levels are held fixed in the background (Obstfeld and

Rogoff, 1995). This approach was chiefly built on the study of price elasticities of
demand for exports and import, with respect to changes in RER (Yang, 2011). This
approach typically states that the CA balance is mostly decided by RER, domestic
income and foreign income. It has the advantage in straightforward empirical
calculations, which are frequently found to be useful in investigating the short-run
implications of exchange rate changes on the CA balance. Nonetheless, the most
important weakness of elasticity approach is that it merely concentrates on the role
of RER and the trade flow (Goldstein and Khan, 1985). Moreover, this approach

6


only looks at the traded goods market and ignores the interaction of other various
markets in an economy (Yang, 2011).
The absorption approach treats the CA balance as the gap between savings
and investment. Hence, this approach is similarly recognized as the savinginvestment balance approach. It claims that if a country produces less than it spends
(i.e. investment exceeds saving), it must import from other economies for its
redundant consumption and spending. This country thus runs a CA deficit. Because
the sum of CA and capital account must equal zero in a flexible exchange rate
regime, shocks that happen first in capital account will evidently affect CA, and vice
versa. Hence, the absorption approach maintains that it is necessary to involve
determinants of capital account balance when constructing the CA model. This
approach also claims that the RER is unimportant in CA adjustments (Krugman,
1987). It has the advantage when concerning two side, saving and investment, of the
current account problem. However, the critical weakness of this theory was that its
analyze CA position based on the level of determinants in a given point of time.
Therefore, Sachs (1981) calls it one period theory. It means that the determinant’s
value before and after the time t has no role in adjustment CA. This obviously
makes no sense. As Sachs (1981, p.212) appropriately put it, “[a] one period theory
of the CA that describes a static balance of imports and exports makes as much

sense as a one-period theory of saving and investment”. As he mentioned in his
paper in 1981, saving is, by definition, an intertemporal choice whereby an agent is
willing to offer consumption today for larger future consumption. He conclude that
this one-period approach is not effective enough to adjust saving. Hence, a static
approach is thus primarily inaccurate in analyzing CA balance.
To conclude, the old static approaches’ techniques should bring the
inappropriate results in examining the CA behavior.

7


2.3.2 The intertemporal approach
In contrast with the standard static approach, the modern intertemporal
optimizing approach presents a framework appropriate for a positive and normative
examination of CA dynamics (Razin, 1995). According to Sachs (1982), a dynamic
approach seems to be the best theory to explain the movement of CA balance.
Intertemporal approach was born owing to this consideration.

2.3.2.1 Overview
This model shares the saving – investment theory wi th absorption approach.
However, intertemporal approach is a microeconomics-oriented approach. Different
from other macroeconomics-oriented approaches, it analyzes CA balance of an
economy by treating that economy as an agent and using mathematical modeling
with the utility function to analyze its behavior.
Consumption smoothing was the core theory of intertemporal approach.
According to Williamson (2005), consumption smoothing is a principle in the
response of consumption to changes in income. That is, there are natural forces that
induce consumers to maintain a stable consumption path over time in spite of the
path of income (Vegh, 2013). This principle comes to substitute the opinion that
consumer had a marginal propensity to consume and hence present consumption

was tied to present income. For instance, James, who is currently wins $1 million in
a lottery, could be an unambiguous example for consumption smoothing principle.
James could consume all of his lottery prizes on consumption within the present
period and save nothing. However, it would appear more sensible if he spent a small
part of his winning in the present period and saved a considerable fraction in order
to consume more in the future. Therefore, his consumption just change a small value
compare with the increase in his income. That behavior of agents was named
consumption smoothing. At all, consumption smoothing is the tendency of
consumers to maintain a consumption path over time that is smoother than income
(Friedman, 1957). This theory involves an economic trade-off decision between

8


current and future consumption and saving, which will be called intertemporal
decision (Williamson, 2005).
When an open economy is considered as an agent, consumption smoothing
principle is still appropriate for explaining its behavior. In fact, this principle insists
that because agents in an economy wish to smooth their consumption, this economy
has the same desire (Yang, 2011). Different from a closed economy, an open
economy can borrow from abroad during bad times and pay back in good times. By
lending and borrowing, that open economy can weaken the connection between
present consumption and present production. Hence, it has an ability to smooth
entirely its consumption despite a vacillating endowment path (Vegh, 2013). To
smooth its consumption, when shocks happen, agents in the economy have a
tendency to adjust their saving (Blanchard and Fisher, 1989). Hence, shocks will
affect CA owing to the fact that CA equals saving minus investment. This ability,
thus, leads the CA acts as a shock absorber, improving in good times and worsening
in bad times, to avoid consumption of that economy being affected by shocks (Vegh,
2013).

Lastly, this approach is suitable for the developing economies that are usually
experiencing high level of investment and running the CA deficit (Dumitru and
Dumitru, 2009). It is due to the fact that developing economies characteristically
face larger shocks, which suggests that they should rely more on CA imbalances to
smooth consumption over time. This offers a theoretical rationale for efforts
intended at ensuring that developing economies have admission to external finance
during bad times (Vegh, 2013).

2.3.2.2 Mathematical model
As mentioned above, the intertemporal approach for examining CA’s
determinants is based on microeconomics principles. Therefore, to build the model,
the research will starts from the basic microeconomics concepts.

9


a) The basic model
This research considers Vietnam as a small open economy inhabited by a
large number of identical infinitely lived households. We assume that there is no
uncertainty (households have perfect foresights), no investment and no government
in the economy. We also assume that there is only one good, tradable and nonstorable one. Because the economy is small, it takes the tradable good’s price that is
set by the rest of the world. Households assume to borrow/lend in international
capital markets as much as they want at an exogenously given real interest rate, r t. rt
is assume to be constant over time at the value r.
Utility
In basic microeconomic theory, the household utility function is . In which,
each consumption level at time t () results in the corresponding level of utility . This
instantaneous utility function is assumed continuously differentiable, strictly
increasing, and strictly concave. We have the discounted factor of the continuous
utility:

(1)

where > 0
is the subjective discount rate.

Therefore, the household’s lifetime utility is represented by a utility
functional, U, which assigns utility U(ct) to each consumption path ct according to:
=ﾤ

(2)
Households are assumed to maximize their lifetime utility

subject to

their budget constraint.
Household budget constraint
The budget constraint in a period t is the net foreign assets that household
ﾤ

accumulates in that period. Let ﾤ represent net foreign assets (NFA) denominated
ﾤ

in terms of the tradable good held by the household at time t, represent the
10


endowment flow received by the household at time

t, and

denotes taxes.

According to (Vegh, 2013), the household budget constraint is given by:
ﾤ ﾤ = ﾤﾤ + ﾤ −1 − ﾤ
Equation (3) implies that the change in NFA

(3)

equals his/her total income (interest

receipts and endowment) minus his/her consumption and taxes. Notice that the
stock of NFA, b, is a predetermined variable in the sense that, barring some
exogenous change, it is a continuous function of time. The household was start with
some NFAs (i.e., b0)
Household maximizing problem
As usual, households want to maximize their utility under their budget constraint.
max

=ﾤ ﾤ

-∈[,]

Subject to
ﾤ
ﾤ
ﾤ ′=ﾤ +

ﾤ

− −

ﾤ

≥0

b0 is given
ﾤ
lim→ ﾤ

(4)

(

typically mentions a “no-Ponzi games

ﾤ

The condition lim→ ﾤ
(

≥0

condition” and implies that the household not “end” with debt. Because the
instantaneous utility function is strictly increasing in consumption (i.e., there is no
satiation point), it will never be optimal for the agent to “die” with assets because
increasing consumption at some point in time would always produce higher lifetime
utility. It means that, at an optimum, lim*→
(

ﾤ ≤ 0. Linking this condition with the constraint, given by (4), that the household

will not “end” with assets yields the condition
.

.

.

ﾤ

∆- –Due to continuous characteristic, the household budget constraint will be calculated by

When
1

, we have

∆→0

lim∆→

∆0 ∆

=
lim

ﾤ

=ﾤ

∆

∆→

11

ﾤ–

ﾤ+ ∆ .
ﾤ


(5)

ﾤ

lim→ ﾤ
(

=0
The process is proceeded here is to convert the issue into one that can be
solved with standard Lagrange multiplier methods. To this end, we will reformulate
this maximization problem subject to an uncountable number of constraints (i.e.,
budget constraints in each point of time) into a maximization issue subject to one
constraint (i.e., an intertemporal budget constraint).
Intertemporal budget constraint
To derive the household’s intertemporal budget constraint, rewrite equation
(3) as

ﾤ

ﾤ

ﾤ −ﾤ =

ﾤ

ﾤ

(6)

ﾤ
= −

ﾤ

⇒ 2ﾤ − ﾤ 3
ﾤ

− −

ﾤ

−

(

(

Integrating forward:

ﾤ
ﾤ

ﾤ

2ﾤ

ﾤ

ﾤ
−ﾤ

(

ﾤ

3

(

=

ﾤ

ﾤ

ﾤ

→

4
=ﾤ
= lim
ﾤ2
−ﾤ 3
ﾤ
Substituting the (8) to (7), we obtain:
ﾤ

(7)

−−

.
4- 567

−ﾤ ﾤ = ﾤ

(

− −ﾤ

(

ﾤ

ﾤ

ﾤ

(8)

−ﾤ =−ﾤ

(

(9)
We can rewrite the household’s intertemporal budget constraint (9) as
ﾤ

ﾤ

⇒ﾤ +ﾤ −
(

=ﾤ

(10)

ﾤ
(

This intertemporal constraint is very intuitive since it maintains that the
present discounted value of consumptions (right-hand side) have to be equal to the
household’s wealth (left-hand side), presented by the initial stock of NFA plus the
present discounted value of his endowment minus taxes.


12

Solution for the maximization problem
The household’s issue can then be restated as taking ∈ [0, ∞]to maximize
(1) subject to (10). We can examine this problem by standard Lagrange-multiplier
method. The Lagrangean is given by:
ﾤ
ﾤ

ℒ=:
ﾤ

+ ; <ﾤ + :

ﾤ
(

+
(

=

−:

where ; is the Lagrange multiplier. It can be represented that the first order
ﾤ

condition with respect to

is given by2,3
ﾤ

=;
(

(11)

In the long run, households discount rate is similar the market discounts rate
= ) (Vegh, 2013).
First-order condition (11) implies that:
ﾤ = ;
(12) The condition (12) provides the strong inference that,
despite the swings of the path of income, the path of consumption will be smooth
over time. In other
words, consumption is not influenced by predicted income adjustments. This
concept, named perfect consumption smoothing, is the outcome of a preference for
consumption smoothing (due to the strictly concave utility function) combined with
the ability to borrowing and lending at a constant real interest rate.
2

Appendix 2 presents how to obtain this first order condition by a discrete time approximation named as

“pointwise optimization”. The “pointwise optimizati on” captures the concept that, instinctually, optim al
consumption was being chosen by households at each point of time. Practically, this concept allows us to
“ignore” the integral when differentiating. Because consumption was being chosen at each point of time, this
ﾤ
first-order condition holds for any ∈ [0, ∞.
It should be noticed that (11) cannot be acquired by taking the partial derivative of ℒ with respect to ct and
3
ﾤ

>

ﾤ

−;
(?

letting it equal to zero. Actually, the outcome of that work would be

=0
.


13


Interpretation of the Lagrange multiplier
To have insightful interpretation of Lagrange multiplier, we multiply both
sides of equation (12) by
(

4

and integrate forward to obtain :
@

ﾤ

(

(13)

(=ﾤ

The term λ/r can then be considered as the (relative) price of an asset that
would give the household a “dividend” of

’

at every point in time. λ would

imply the annuity value of the present discounted value of dividends. If
constant overtime ( = ,then λ would imply that it equals the dividend ’.

were

According to basic finance principle, a stock price λ/r will not be affected by
anticipated changes in dividend, but by “news”, tha t is unanticipated events.
Similarly, the multiplier λ will not be affected by anticipated fluctuations in income,
but by unanticipated changes in income.
Constant consumption
The first-order condition (12) suggests that consumption will be constant
along a perfect foresight path (at a level denoted by ̅). From (10), it follows that:
ﾤ

ﾤ

ﾤ +:
(

ﾤ

ﾤ

(

=:

+:
3

+ﾤ

⇒ = 2ﾤ

ﾤ(

ﾤ

(

−ﾤ

(

(14)

The right hand side of the equation is considered as the permanent income of
the household. The permanent income is defined as the annuity value of the present
discounted value of available resources. Equation (14) suggests that permanent

income can be maintained forever if household maintains that constant
consumption. This principle refers to Friedman permanent income hypothesis. In
(

have
4

Multiply

(

to

(

both sides of

@

=;

.

equation (12),

we have

(

(

. Integrate forward, we


ﾤ
;

=ﾤ

=

14