The Interaction between the Stock
Market and Consumption: A
Stochastic Factor Model
Moawia Alghalith & Tracy Polius
Introduction
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The relationship between the financial sector and the real sector has
been the subject of great discussion in economics
While the literature has largely agreed that the financial sector does
impact on the real sector; there is less agreement on the direction
of causality
Moreover, the literature has concluded that not all financial services
are created equal; and therefore all sub sectors within the financial
sector do not interact with the real sector in the same manner.
The most recent global financial crisis has prompted some analysts
to conclude that some financial innovations may be too risky and
there may be a need to revert to simpler bank centric models.
Objectives of Paper
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
The paper investigates the relationship between real private
consumption and the return/value of the Jamaica Securities
Exchange
The paper also seeks to determine whether the “wealth
effect” is validated in the context of Jamaica
Literature Review
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Some aspects of the literature focus on the channels
of linkage between equity markets and economic
growth.
Other aspects of the literature deal with the wealth
effect associated with price developments on equity
markets
The literature also covers what is termed
“uncertainty hypothesis” – associated with the impact
of high volatility of private consumption
Literature Review:
Stock Markets and Economic
Growth
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
Levine (1991) derived an endogenous growth model
which demonstrates that stock markets can promote
economic growth through a process where they
facilitate trading of “ownership” of firms without
allowing for disruptions in the productive process.
Bencivenga, Smith, and Starr (1996) develop a model
which predicts that as capital markets become more
efficient, transaction costs fall leading to a higher rate
of return on investments in equity.
Literature Review:
Stock Markets and Economic Growth
Developing country studies
 Osinubi (2004) utilized data for the period 1980 to
2000 for Nigeria. His results suggested a positive
relationship between stock market size, stock market
liquidity and economic growth
 In a similar study, Nowbutsing and Odit (2009) using
data for Mauritius for the period 1989 to 2007, found
stock market size and liquidity to be both positively
related to economic growth.
Literature Review;
Stock Market Wealth Effect
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
A “Wealth Effect” can be defined as an increase in
spending which occurs as a result of real or perceived
increases in wealth
The existence of a wealth effect presupposes that
when security prices are rising, economic agents
would perceive that their portfolios are valued more
and therefore increase their consumption
Literature Review;
Stock Market Wealth Effect


Starr-Mc Cluer (2002)examined the impact of stock
market wealth on consumer spending in the USA. The
results were broadly consistent with the life cycle
savings view that increases in wealth will result in
small to modest increases in current consumption, as
wealth gains are spread over the lifetime horizon.
Funke (2002) undertook an empirical analysis of
stock markets and private consumer spending in 16
emerging economies. The study concluded that in the
short run a 10 % fall in real stock market returns
could be linked to a decline in private consumption of
average magnitude 0.1-0.3%.
Literature Review;
Stock Market Wealth Effect


He and Mcgarrity (2005) in a modification and
extension of the Romer(1990) model sought to verify
the existence of the uncertainty effect and the wealth
effect in the USA. Their conclusions suggest that the
wealth effect is important in determining consumer
durable production.
Results point to decreasing size of the wealth effect
over time
Literature Review;
The Uncertainty Hypothesis
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The Uncertainty Hypothesis asserts that during periods
of high stock market volatility people become uncertain
about future economic prospects and therefore they alter
or postpone consumption expenditure on durable goods
Romer (1990) sought to test the existence of the
“Uncertainty Hypothesis” using data from the 1930’s and
post great depression period. His empirical results show a
negative and significant relationship between output of
consumer durables and stock market volatility which
lends support to the existence of the uncertainty
hypothesis. The results also pointed to the non existence
of a wealth effect.
Theoretical Framework
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We consider a standard investment-consumption
model, which includes a risky asset, a risk-free asset
and a random external economic factor
This implies a two dimensional standard Brownian
motion on a probability space (Ω, Fs, P), where
is the augmentation of filtration
Model is based on Alghalith (2009) who derived
explicit solutions for the investment consumption
model while relaxing the assumption of exponential
utility
Theoretical Framework
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The risk free asset price process is given as;
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The risky asset price process is given as;

The economic factor process is given as;
Theoretical Framework
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The wealth process is given as follows;
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The investor’s objective is to maximize the expected
utility of terminal wealth and consumption
Where the value function V(.) is smooth and the utility function u(.) is
bounded and strictly concave.
Theoretical Framework
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The value function satisfies the Hamilton-Jacobie-Bellman
PDE;
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With optimal solution;
Theoretical Framework
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Alghalith (2011) shows that the optimal portfolio can be
expressed as follows;
The partial impact of changes in the portfolio on
consumption can therefore be estimated.
Estimation and Results
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We use quarterly data for Jamaica for the period March
1998 to June 2010 for the following;
- real private aggregate consumption
- the Jamaica Securities Exchange
- the treasury bill rate
- real gross domestic product
Estimation and Results
We compute volatility of the index the correlation
factor between GDP and the JMSE as follows;
Estimation and Results
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We estimate the following non linear equations;
Estimation and Results
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Using the estimated parameters we obtain the following
comparative statics;
Estimation and Results
𝛽1
𝛽2
𝛽3
𝛽4
𝛽5
𝛽6
𝛽7
𝛽8
𝛽9
Parameter Estimates
3.66E+10
502072.4
1.89E+11
88519.04*
-72274.68
1.99E+10***
1.67E+12
29470778***
36904.06
Results;Comparative Statics
𝜕𝜋𝑡∗
𝜕𝑐𝑡∗
𝜕𝑐∗𝑡
𝜕𝜋∗𝑡
𝜕 𝑢(𝑦)
𝜕𝑐𝑡∗
Comparative
Statics
0.000883
Elasticity
0.0286
0.0401
3.78E-11
9.79E-6
0.001239
Results Summary
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Results support the existence of a very weak relationship
between private consumption, stock market return and
the level of the JMSE .
One percent increase in stock market return will increase
aggregate private consumption by $28,600- suggesting
very small wealth effect
Elasticity measures suggest that increases in private
consumption do not factor significantly in the
determination of returns for firms listed on the JMSE
The JMSE is not significantly influenced by changes in
private consumption