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The Interaction between the Stock Market and Consumption: A S tochastic Factor Model

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The Interaction between the Stock Market and Consumption: AStochastic Factor Model

Moawia Alghalith & Tracy Polius

- 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.

- 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

- 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

- 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.

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.

- 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

- 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%.

- 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

- 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.

- 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

- The risk free asset price process is given as;
- The risky asset price process is given as;
- The economic factor process is given as;

- 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.

- The value function satisfies the Hamilton-Jacobie-Bellman PDE;
- With optimal solution;

- 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.

- 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

We compute volatility of the index the correlation

factor between GDP and the JMSE as follows;

- We estimate the following non linear equations;

- Using the estimated parameters we obtain the following comparative statics;

- 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