the interaction between the stock market and consumption: a stochastic factor model moawia alghalith...
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The Interaction between the Stock Market and Consumption:
AStochastic Factor Model
Moawia Alghalith & Tracy Polius
Introduction
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
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
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
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 GrowthDeveloping 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 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 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 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 The risk free asset price process is given as;
The risky asset price process is given as;
The economic factor process is given as;
Theoretical Framework The wealth process is given as follows;
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 The value function satisfies the Hamilton-
Jacobie-Bellman PDE;
With optimal solution;
Theoretical Framework Alghalith (2011) shows that the optimal
portfolio can be expressed as follows;
The partial impact of changes in the portfolio onconsumption can therefore be estimated.
Estimation and Results
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 correlationfactor between GDP and the JMSE as follows;
Estimation and Results We estimate the following non linear
equations;
Estimation and Results Using the estimated parameters we obtain the
following comparative statics;
Estimation and Results
Parameter Estimates 𝛽መ1 3.66E+10 𝛽መ2 502072.4 𝛽መ3 1.89E+11 𝛽መ4 88519.04* 𝛽መ5 -72274.68 𝛽መ6 1.99E+10*** 𝛽መ7 1.67E+12 𝛽መ8 29470778*** 𝛽መ9 36904.06
Results;Comparative Statics
Comparative Statics
Elasticity
𝜕𝜋𝑡∗𝜕𝑐𝑡∗ 0.000883 0.001239
𝜕𝑐𝑡∗𝜕𝜋𝑡∗ 0.0286 0.0401
𝜕 𝑢(𝑦)𝜕𝑐𝑡∗ 3.78E-11 9.79E-6
Results Summary
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
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