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What Factors Affect the Wilshire 5000 Index?
By
Faizan Qaiyum
Applied Econometrics
Professor Neil Alper
November 26, 2014
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I. Introduction
The Wilshire 5000 index (TMWX) measures the entire stock market of the United States. in
an index. The stocks are actively traded in the U.S. It represents over 6700 companies of diverse
backgrounds, from every industry based on a points system. The stocks have pricing information
that is available to the public. The index is one of the broadest stock indices in the U.S. Its
purpose is to track to the overall performance of the U.S. stock markets. In Chart 1 below, the
historical path of the Wilshire 5000 Index is shown over the years 1971-2013.
Chart. 1 Wilshire 5000 Index Historical Prices
The Wilshire 5000 has risen in value over the years and now has more competitive firms in
the index which has helped the increase. As shown in Chart 1, the maximum that the Wilshire
5000 Index has reached is 17073.76 in 2013, while the lowest being 713.14 in 1971.
Since it is a market capitalization-weighted index, the Wilshire 5000 index assigns
companies with a larger firm more weight than those firms with a lower firm value. Stock
markets like the Wilshire 5000 can be significantly affected by changes in economic policies—
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1971
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2013
Wilshire 5000 Index
Historical Points
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“strong economic ties and policy-making decisions in different markets can indirectly affect
stock price behavior over time” (Samitas et al). Therefore, this effect could manifest in many
ways. For example, if the performance of a foreign economy declines, this would impact the
success of the domestic stock market and vice versa. This paper will examine which
macroeconomic and other factors significantly affect the Wilshire 5000 index to determine which
variables have the greatest impact.
II. Literature Review
Research shows the Wilshire 5000 is one of the best representations of the total market for
stocks, even outdoing the S&P 500. The number of equity securities included are much higher
than that in the S&P 500 which only has the stock of 500 companies.
In a paper written by Nathan Taulbee, titled “An Examination of the Effect of Economic
Variables on the S&P 500,” the author uses a log-log generalized least squares model to explain
which economic variables have the most significant impact on the S&P 500. The author then
applies his model, which uses real GDP, the unemployment rate, and the Fisher equation,
accounting for the real interest rate with expected inflation rates factored in for his explanatory
variables. The author’s main findings are that GDP, unemployment, and inflation all have a
statistically significant impact on the S&P 500. These finding influenced my decision to add
these variables in my model.
Another paper by Michael Parker and Tamm Rapp discusses how the movement between
world markets is increasing influence on one another. They state that “a growing body of
literature suggests that the linkages between the world markets are increasing” (Parker, 1998).
The authors claim that the reason behind the co-movement is that the world stock markets are
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interconnected due to the similar fundamentals. The authors also claim that “the differences of
the logs of the stock market indices should not share a common feature if efficiency in the
markets exist” (Parker and Rapp, 1998). The data for their model is taken from the S&P 500,
NASDAQ, Wilshire, Footsie, Hang Seng, and Nikkei indices and the foreign markets were
selected “to proxy different aspects of the U.S. equities market” (Parker and Rapp, 1998).
Their model is highly advanced but in Parker and Rapp’s main findings they discuss the joint
efficiency between the United States’ stock market indices and foreign indices. The authors write
that “there was inefficiency between the Footsie and S&P 500, the Footsie and the Wilshire, the
Footsie and the NASDAQ” (Parker and Rapp, 1998). The authors also note that the consistent
inefficiency between the United States and British markets could potentially be explained by
further research in common business cycles between the two countries (Parker and Rapp, 1999).
This paper finds that all the stock markets move together. Because of this my results should
mirror other indices such as the S&P 500 and Dow Jones.
The purpose of this paper is to determine which macroeconomic and other factors will have
the most significant impact on the Wilshire 5000.
III. Model
The variables in the initial model are as follows: the unemployment rate, the inflation rate
(from the Consumer Price Index), real GDP per capita, the one-year Treasury bill rate and the
thirty-year conventional mortgage interest rates. The University of Michigan’s Consumer
Sentiment index is also used to measure of consumer confidence.
Macroeconomic factors may influence the Wilshire 5000 index. Unemployment rate was
chosen because lack of employment leads to a lack of investment from people having less
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money. If people have no money, they won’t be able to buy stocks. People often do their
investing through their employers. Hence people who are not working means that they are not
investing through their employers. As a result, I expect a higher unemployment rate to lead to a
lower Wilshire 5000 price index.
Higher inflation will lead to people buying fewer stocks since their purchasing power
decreases and more of their income goes towards necessities such as food and rent. Thus, this
will lead to a decrease in the Wilshire 5000 price index as people demand less stock. In addition,
an increase in real GDP per capita will allow consumers to have more money. This will lead to
higher purchasing power to buy stocks and will increase stock prices and the Wilshire 5000
index.
Treasury bills are a substitute to stocks. If the interest rates of treasury bills increase,
people will purchase less stocks and will switch to the bond market. Thus demand for bonds
increase and the Wilshire 5000 index prices will fall. Mortgage interest rates are also a substitute
to stocks. Hence the Wilshire 5000 index prices will rise when mortgage interest rates increase.
Consumer confidence is also a huge factor that affects the Wilshire 5000 index. If consumers are
expecting high stock prices, consumers will buy more stocks and thus will raise the Wilshire
5000 index.
IV. Data
The data collected for this research paper is time-series data from 1971 to 2013. The
dependent variable for the model is the Wilshire 5000 index. The independent variables are as
follows: unemployment rate, inflation from the CPI, GDP per capita, 1-year treasury bills,
University of Michigan’s Consumer sentiment index, and 30 Year Mortgage Interest rates. Data
for unemployment rate and inflation was collected from the Bureau of Labor Statistics website.
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The data for the U.S. GDP, 1 year treasury bills, University of Michigan’s Consumer Sentiment
index, the 30 year conventional Mortgage interest rate, and the Wilshire 5000 price index was
gathered from Federal Reserve Economic Data (FRED).
The following table (Table 1) lists the mean, standard deviation, and minimum
and maximum values for the independent variables and dependent variables:
Table 1. Descriptive Statistics
From the data in Table 1, the average of the Wilshire 5000 price index is 6117.33 points with a
standard deviation of 5127.47 points. The range of the Wilshire 5000 index is 16360.62 which
tells us that the Wilshire index over the years has been steadily rising.
The unemployment rate has an interesting pattern, with a mean of 6.44% and a standard
deviation of 1.54%. This tells us over the years the unemployment rate has been relatively steady
in spite of the recession periods of 2001 and 2008.
Real GDP per capita has a minimum of value of $5,623 per capita in 1971 and a
maximum of $52,985 per capita in 2013. The data for 1 year Treasury bill and Mortgage interest
rates have a lower bound – zero.
Wilshire
5000 Index
(Points)
Unemploy
ment rate
(%)
Inflation
(CPI)
(%)
GDP Per
Capita
($)
1 Year
Treasury
Bill
(%)
Mortgage
Interest
Rate
(%)
Consumer
Sentiment
(Points)
Mean 6117.33 6.44 134.44 27077.84 5.21 8.47 85.14
Std Dev 5127.47 1.54 58.46 14851.76 3.16 2.98 12.34
Min 713.14 4.00 39.90 5623 0.11 3.41 63.80
Max 17073.76 9.70 231.32 52985 12.77 17.40 107.60
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The Treasury bill has an interest rate range of 12.66 percentage points, while the
mortgage interest rate has a range of 13.99 percentage points. The maximum consumer sentiment
points was 107.6 points in 2000, right before the dot com bubble. While the lowest consumer
sentiment points was 63.8 points in 2008, during the great recession of 2008.
V. Estimation of the model
The three economic models below show the gradual adjustments made through
regression analysis:
Model 1: Wilshire 5000 = β0 + β1 (unemployment rate) + β2 ln(Real GDP per capita) + β3 (CPI
index) + β4 (1 year Treasury Bill) + β5 (consumer sentiment + β6 (Yearly Mortgage interest
rate) + ϵ
Model 2: Wilshire 5000 = β0 + β1 ln (Real GDP per capita) + β2 (Inflation) + β3 (1 year
Treasury bill) + β4 (consumer sentiment) + β5 (Yearly Mortgage interest rate) + ϵ
Model 3: ln Wilshere 5000 = β 0 + β 1 ln (Real GDP Per Capita) + β 2 (1 year Treasury bill)
+ β3 (Consumer sentiment) + β 4 (Yearly Mortgage interest rate) + ϵ
The initial model (Model 1) on the Wilshire 5000 index (see Table 2 in appendix), which
included all six explanatory variables have several significant results in the model and adjusted
R-squared statistic of 0.94. This means 94% of the variation in the Wilshire 5000 index is
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explained by the model. The significant variables are GDP per capita, One Year Treasury Bills,
and consumer sentiment index at 5% level of significance. Inflation and mortgage interest rates
are significant at the 10% level of significance. Unemployment was the only insignificant
variable of the initial model. All the significant coefficients were in the expected direction being
positive, except for treasury bills which was in the opposite direction being negative.
The final model had a log-log form. It had unemployment and inflation dropped since
both the variables were strongly correlated showing multicollinearity in the model. Log of
Wilshire and log of Real GDP per Capita was taken into consideration for the final model.
Therefore the log-log model is the most preferred model.
To address several problems such as multicollinearity, omitted variable bias and
autocorrelation on the model, I performed two test and ran the VIF. Looking at the high adjusted
high R-squared it seems that there is a high possibility of multi-collinearity. I ran the VIF for the
initial model. There was a Mean VIF of 46.29 with unemployment and inflation being strongly
correlated with each other. So I dropped the variable, unemployment, used log of real GDP per
capita as an explanatory variable and found a Mean VIF of 44.32 (Model 2). I created and
regressed a new model (Model 3) and found a Mean VIF of 6.17, which is less than 10 and
shows no sign of multicollinearity.
To test for autocorrelation, the Durbin-Watson test was used on the third model. The
Durbin-Watson statistic (d-stat) = 0.9101. The Durbin-Watson critical values, DL = 1.295 and
Du = 1.65, at n = 36 and k = 5 which mean the model does exhibit first degree positive
autocorrelation. It occurred since the dest < dcrit. In order to improve the final model a Newey-
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West standard errors was run. After that the standard errors in the model improved and the t-
statistic became more significant. There is also no time lag in the model now.
Lastly, I performed the RESET test which was run on each model to test for the possibility of
misspecification error through an omitted variable bias. In each of the models the test produced a
statistic capable of rejecting the null hypothesis of no omitted variables. The Ramsey reset
[F (3, 28)] for the third model is 0.0084 at the 5% level of significance.
As seen in Table 2, a one percentage point increase in real GDP per capita will lead to a 1.81%
increase in the Wilshire 5000 Index points, and also the t-statistic is very significant, 25.97. An
additional percent increase in Treasury bill will lead to an increase 6.29% increase in the
Wilshire 5000 index points. An additional percent increase in Mortgage interest rates will lead to
a reduction of the Wilshire 5000 Index by 8.39 points. A one point increase in consumer
sentiment will lead to a 0.76 percentage point increase in the Wilshire 5000 index.
VI. Conclusion
In conclusion, I have found that GDP has the largest impact on the Wilshire 5000 index.
Quantitative easing and zero interest rate policy may have contributed to increase in GDP in
recent times. Also, China recently announced they will lower their own interest rates which
increased the global stock markets and raised the Global Dow. Some policies, for instance to
increase the Wilshire 5000 index points can be by increasing productivity of workers; by
providing them with incentives such as tax-free holidays and tax-free gasoline, and reduced rent
for housing. These will as a result increase consumption, which would increase GDP, and keep
consumer confidence strong, and thus increase the Wilshire 5000 Index.
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Inflation was highly correlated with unemployment in my model which made sense
because of the theory of the Phillips curve. Both inflation and unemployment had to be dropped
out of the final model due to the disease of multicollinearity. In order to improve the final model
the sample size should be increased, meaning a longer time period should be accounted for in the
research. Adding higher order polynomials will further improve the model.
Overall, it was a very interesting research topic to work on and there is potential for more
research in the dynamic field of stock indices. Since there isn’t much literature published for the
Wilshire 5000 index, hence my research provided a unique insight.
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References –
1 Year Treasury Bills:
http://research.stlouisfed.org/fred2/series/TB1YR/downloaddata
Consumer Sentiment part 1:
http://research.stlouisfed.org/fred2/series/UMCSENT1/downloaddata
Consumer sentiment part 2: http://research.stlouisfed.org/fred2/series/UMCSENT/downloaddata
Inflation http://www.bls.gov/data/
Mortgage interest rate: http://research.stlouisfed.org/fred2/series/MORTG
Parker, M. (1998). An Empirical Investigation of the Comovement Between Stock Markets.
Studies in Economics and Finance. 19, Page 108.
Samitas, A., & Kenourgios, D. (n.d.). Macroeconomic factors' influence on 'new' European
countries' stock returns: The case of four transition economies. International Journal of
Financial Services Management, 34-34.
Taulbee '00, Nathan (2001) "Influences on the Stock Market: Examination of the Effect of
Economic Variables on S&P 500," The Park Place Economist: Vol. 9
US GDP: www.fred.gov
Unemployment http://www.bls.gov/data/#unemployment
Wilshire 5000 price index: www.fred.gov
