Correlation Between Stock Market Prices and GDP in England (1700 - 1900)
I. Introduction
An economy consists of many markets, one of the most important being the stock market. Historically, it has been one of the best places to accumulate wealth through investments. The stock market is also a good representation of the progress of the overall economy. It moves with economic growth since companies that do well receive high returns and their stock prices rise. Investments in these companies contribute to the productivity of the economy. However, the stock market is not perfectly correlated with GDP because the stock market operates based on predictions. The stock market is essentially acting ahead of the current state of the economy.
For the data analysis project, our group conducted an analysis of the English stock market from the years 1700 to 1900. The question we are looking to answer is if there is any correlation between English stock prices and English gross domestic product (GDP). We believe that stock market prices and GDP have a high correlation in the long run and a weaker correlation in the short run. Correlation in the short run can be low due to irrational behavior by investors, the unpredictability of future information, and economic shocks. Correlation is higher in the long run because it consists of a series of short-run price changes due to the availability of information. Over time these prices converge to the true value of the stock. One of the largest and oldest stock exchanges in the world is the London Stock Exchange (LSE). The LSE was founded in 1801 and is currently the third-largest stock exchange in the world with market capitalisation of $6.06 trillion. Our rational to examine the LSE is due to two reasons. The first is that England went through the industrial revolution during the eighteenth and nineteenth century. The second is that the dataset used is adequate to make inference on the correlation of the economy and the stock market because it contains reliable data from over two centuries.
II. Literature Review
There is extensive research on the prediction of the stock market and the GDP. The purpose of this section is to review the efficient market hypothesis and the long-term prediction of the stock market through multiple peer-reviewed sources.
In “The Efficient Market Hypothesis and Its Critics,” Burton Malkiel explains the efficient market hypothesis and how it is widely accepted by academic financial economists. The efficient market hypothesis is when the stock market reflects all relevant information in the world accurately. In other words, information gets speared quickly and is incorporated into the price of stocks without delay causing the “impossible to beat the market” effect. Malkiel also brought up the idea of random walk. The idea of random walk is that since information is incorporated into the stock price immediately, the stock price today is independent of the stock price yesterday. If stock prices reflects today’s news and news is unpredictable, the results of price changes must also be unpredictable.
It is important to note that we are not concluding that the market is efficient or not efficient. Our analysis serves as one of the possible explanations for Professor Benjamin Graham’s statement in “The Intelligent Investor: a Book of Practical Counsel” that the market is more likely to be efficient in the long run than in the short run. Malkiel believes that the market pricing is not always perfect. He does agree with Graham that “the stock market in the short run may be a voting mechanism, in the long run it is a weighing mechanism. True value will win out in the end.” Fama and French also agree with this in “Permanent and Temporary Components of Stock Prices.” Published in 1988, they found that negative correlations with past returns can be used as a tool to predict 25 to 40 percent of variation in long term holdings.
A common example of irrational behavior is when investors overvalue stocks without reason, which can lead to what is known as a bubble. Dr. Robert Shiller in his journal article “Speculative Asset Prices” describes the bubble phenomenon as “a situation in which news of price increases spurs investors enthusiasm which spreads by psychological contagion from person to person, in the process amplifying stories that might justify the price increase and bringing in a larger and larger class of investors, who, despite doubts about the real value of the investment, are drawn to it partly through envy of others’ successes and partly through a gambler’s excitement”. This behavioral aspect of investment contributes to low correlation in the short run.
Another author that has similar beliefs is Joshua Hausman. Hausman wrote about paying veterans two percent of the GDP, which would be forecasted by using the behavior of the stock market. He believes that overall expectations are already included in current stock market prices. This assumption allowed him to use the stock market to predict the expected increase in veteran income. Hausman concludes that “economic forecasters...expected future growth. A concrete measure of these expectations is the behavior of the stock market.” One example is if a country is expected to grow at a rapid rate in the future, that available information is already embedded in the current price of the stock market from investors. Therefore, countries with high economic growth do not always have high stock market growth, because that information is already embedded in the price of the stock. This argument is supported by Eugene Fama, where he states “a market in which prices always ‘fully reflect’ available information is called ‘efficient.’”
III. Data
The data used for this analysis is “A Millennium of Macroeconomic Data for the U.K.” using the years 1700 through 1900. This large dataset is a conglomeration of smaller datasets from various researchers, all compiled and made available by the Bank of England. Using this collection we selected the individual variables necessary for our analysis: English stock prices, English Real GDP at market prices, and English population.
The data for English stock market prices is courtesy of three different research papers. The first is from Philip Mirowski’s research on the functionality of the English stock market during the eighteenth century. He created a stock price index using the balance sheets from the Million Bank and Bank of England. He also gathered stock account balances from insurance companies such as Sun Fire Assurance and Hand-in-Hand Assurance. The most beneficial section of Mirowski’s paper is the data he collected from two different publications for investors, Collection and Course of the Exchange. Courses was a weekly article written by an investor by the name of “Houghten,” and Course of the Exchange was a bi-weekly report by John Castaing. Both publications listed stock prices and exchange rates throughout the eighteenth century and early nineteenth century.
The second source for stock price data, population, and the GDP of England is extracted from British Economic Growth, 1270-1870. The authors reconstruct Britain’s (England and Wales) national accounts to create a comprehensive study of its economic evolution during 1270 to 1870. Records from parishes that recorded baptisms, marriages, and burials were used as a baseline for population data. Another way population data was estimated was through back-projected censuses from nineteenth century. Back-projecting is when the differences between the most recent census and the one directly preceding it are analyzed to infer demographic changes. This method of working backwards through census data was proven to be robust by a sensitivity analysis conducted by bio-demographer and biostatistician Jim Oeppen. GDP data in this book was mostly gathered from previous research, but enhanced with new estimates of industry and service output.
The final paper used to track stock prices is from Richard Grossman’s New Indices of British Equity Prices 1870-1913. His research mainly uses the Investor’s Monthly Manual (IMM), a record of The London Exchange. This manual contained data from 507 companies in 1870 to 1,150 in 1901.
Table 1 shows the variables used in our analysis in 25-year increments. To have complete data on GDP for 1700-1900 we had the choice of using real GDP at market prices or GDP at factor cost. We chose real GDP at market prices since it is the gross value of all goods and services provided by England including taxes. This measure excludes subsidies on imports from the real GDP value. GDP, stock prices, and population all increased at an increasing rate starting at the nineteenth century. The population increase is identical to what we have learned in class regarding mortality decreasing around 1730, yet birth rates did not decrease for another 100-140 years. Regarding stock prices, there was an increase in the purchases of bonds during the late seventeenth century which could contribute to the large jump in stock prices from 1700 to 1725 before they remain stable for the rest of the century.
IV. Methodology
The first method used to measure the correlation is an ordinary least squares (OLS) regression. This allowed us to see the changes in price associated with changes in GDP. Equation (1) shows this regression in equation form, with price as the dependent variable, GDP as the independent variable of interest, and a random error term. Figure 1 shows how this linear regression fits through the data, with price on the y-axis and real GDP at market prices on the x-axis.
The next regression is identical to the first, but with the addition of population as a control variable. As shown in Table 1 population started to rapidly increase starting during the second half of the eighteenth century. The increase in population could be affecting the results, which can be countered by holding it constant as a control variable.
The final test we used was a simple correlation test. The coefficient from this test ranges from -1 to +1, with -1 being a perfectly negative correlation and +1 being a perfectly positive correlation.
V. Results and Limitations
The results for linear regressions (1) and (2) are found in Tables 2 and 3. The first notable result in table 2 is that a one-unit increase in GDP is associated with a .0001967-unit increase in English stock prices. The reported p-value is less than .01, meaning these results are statistically significant at the 1 percent level. Another way this can be interpreted that the probability of this result being generated by chance is less than 1 percent. The null hypothesis of that there is no correlation between stock prices and GDP is rejected. Additionally, the r-squared value reports that almost 94 percent of the variation in stock price is explained by GDP.
Table 3 shows the results for equation (2), the linear regression with population added as a control variable. The increase of stock prices correlated with GDP has increased to .0004589 in this regression, and is still significant at the 1 percent level. A notable change is the relationship between stock prices and population. A one-unit increase in population is correlated with a 1.3-unit decrease in stock prices.The r-squared value also increased to 99 percent in this regression.
The final part of our analysis was to run basic correlation tests. Table 4 shows the correlation coefficients for the entire span of our analysis and for three economic periods that experienced shocks. The first time period captures the South Sea Bubble, which is when the South Sea Company (SSC) bought large amounts of government debt in exchange for stock. This caused a chain of events where government debt holders saw their securities increase and the government saw their debt decrease. Eventually the SSC did not have enough funds to pay investors and their financial arm became insolvent. The shares of the SSC sharply declined in value, hurting investors and the economy. The correlation coefficient during period of the South Sea Bubble was .54, which is a moderate positive linear relationship.
The second time period encompasses the Seven Years’ War, and has the weakest correlation coefficient of -.07. This is between no linear relationship and an extremely weak negative relationship. Most of Britain’s income was used on financing the war, and their debt had almost doubled by the end of it. This damaged Britain politically and economically, and they pressured the colonies in the United States to increase revenue, while also raising their taxes. This disorder is reflected in the weak correlation we found, most likely due to changes in investment behavior and a drop in GDP. This allows us to make the inference that the market is not as correlated with GDP in the short-run, where collective judgment of investors sometimes can be “irrational.”
The last time period we looked at was the “Panic of 1825.” Around 1821 the Bank of England financed infrastructure and other projects in recently independent states in Latin America. English investors bid up prices of these stocks, until banks started to fail. Smaller banks went first, then more important banks in London as well. The collapse of banks started in 1825, and the recession officially began in 1826. The correlation coefficient for this time period was .82, where the relationship was strong positive linear relationship.
For the years 1700 to 1900, the correlation coefficient was .97. This indicates an almost perfect positive correlation between the variables real GDP at market prices and stock prices. This allows us to make the inference that the stock market prices and GDP have a higher correlation in the long run.
The results are aligned with our initial thoughts, but there were limitations to our analysis. The first is that our regression analysis lacked ideal control variables. For example, an indicator variable for years during economic shocks would have allowed us to hold those disturbances constant in our regressions. Educational attainment could have also been useful to see if perhaps an increase in the literacy rate affected investments. Another limitation was that we were unable to fully interpret a nonlinear regression of the data. Figure 2 shows the graph of our equation which fit the data more accurately, but the analysis was incomplete and could not be included.
VI. Conclusion
The observations that we can make from looking at the results of our analysis is that as the years increase, both real GDP at market prices and stock prices increase together with small fluctuations. Correlation in the long run is made up of small short run events with lower correlation due to irrational behavior by investors, unpredictability of future information, and economic shocks. From time to time, there exists a discontinuity, where GDP stays constant and the stock price indices fluctuate. This could illustrate “psychological contagion” in the market, where the collective judgement of market participants is irrational, like the behavior leading to the Panic of 1825. Concluded by Dr. Burton Malkiel in his journal article The Efficient Market Hypothesis, an alternative explanation could be that “as long as stock markets exist, the collective judgment of investors will sometimes make mistakes.” During these periods a plausible explanation could be that there is uncertainty about available information. Therefore, the expectation of market participant about the future is harder to forecast.
In the long run we can generalize that profitable companies retained a portion of their earnings to finance capital investment, research and development, and other core areas of the company. These investments increase their value, leading the stock price to rise with the expectations of market participants. Furthermore, companies retaining their earnings contribute to economic development and an increase in GDP over time.
In terms of market efficiency, there exists two sides: one is a believer of market efficiency and the other, a non-believer. There are Nobel prize winners on both. Robert J. Shiller is a behavioral economist who believes that the markets are not efficient, and Eugene G. Fama believes the markets are efficient. Our analysis does not conclude which side is correct or incorrect. Our analysis instead serves as possible evidence for Graham’s statement that markets are more likely to be efficient in the long run than in the short run.
Cordially,
Rojan Shrestha, Stephanie Stockton, and Emma Wu
December 6, 2017
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