The Relationship Between Stock Performance and Money Supply Based on VAR Model in the Context of E-commerce

3.1 Variables

There are three variables used by the research: oil price indicated by the monthly average price of WTI, stock performance reflected by the monthly average of S&P 500 index, and money supply of the United States. The range of the data for the variables is from June 2012 to June 2022, and the frequency of the data is monthly.

The monthly average of WTI is chosen to reflect oil price, given its importance as a major oil price index. Rather than daily data, the monthly average of WTI is used in the model because the relatively long duration of a month could dampen temporary fluctuations in daily oil price to provide a more reliable representation of the oil market in a given period of time, which would be conducive to construction of VAR model. The monthly average of WTI is computed from the daily average of WTI extracted from Federal Reserve Economic Data. While the research could benefit from incorporating other indicators of oil prices, WTI is an authentic measure of oil price that is used under many professional circumstances, so it is selected as the measure for oil price in this research.

The stock performance is represented by the monthly average of S&P 500 index. Since the stock market is highly sensitive to shifts in oil prices, the inclusion of a stock index in the model can contribute to an accurate forecast of oil prices. S&P 500 is chosen to represent the stock market because it is a portfolio tracing the performance of 500 large companies listed on the stock exchange in the United States, so the inclusion of the index in model can reflect the relationship between oil price and stock performance of major companies in the United States. Similar to the oil market, the stock market often experiences significant fluctuations in the short run, affecting the reliability of analysis based on daily data. Therefore, the monthly average of S&P 500 is computed from daily historic data of S&P 500, which is extracted from the historic database of investing.com. While investing.com is an authentic source of information, there may be minor errors due to the fact that it is a secondary data source.

The third variable in the model is money supply. Money supply is incorporated in the model because it can reflect the role played by the central bank in the economy. Money supply is often changed by the central bank as part of monetary policies that serve as an official response to economic fluctuations caused by changes in oil price or stock market performance. Therefore, it would be meaningful to include money supply in the model and analyze its interaction with the two other variables. In this research, money supply is reflected by M2 of the United States. The source of the data is Federal Reserve Economic Data, and the frequency of the data is monthly.

3.2 Linearization of Data

As indicated in Table 1, the data for stock performance and money supply are substantially greater in value than those in oil price. To facilitate the creation of VAR model, the research would take the natural log of monthly average of S&P 500 and money supply and use them to represent oil price and money supply. Without taking natural log and linearization, the data would not be stationary, and a VAR model can only be created with stationary data. The list of variables is presented in Table 1.

3.3 Stationarity Test

In order to employ the data to establish VAR model and perform relevant analysis, the stationarity of the variables needs to be tested; otherwise, the results yielded by the model would be inaccurate. The p-value of the variables would be derived to shed light on their stability as part of the stability test. If the p-value of a variable is smaller than 0.8, it is stationary and is thus appropriate to be used in the model. If not, first-degree differentiation would be applied to the variable to facilitate its stationarity.

The results of the stationarity test show that the natural logarithm of stock price passed the test without having to undergo differentiation. However, due to yielding a p-value greater than 0.8, variables oil price and money supply fail the stationarity test, facilitating the need to take their first difference and use the resulted data to represent the variables in the model. Ultimately, the process of the stationarity test examines if the variables are adequate to serve as inputs for the VAR model and modifies them if they fail to qualify, as shown in Table 2.

4.1 Establishment of Model

Since data for the dependent and independent variables of the VAR model have been tested and processed, a VAR model can be established to capture the relationship between the difference in oil price, the natural logarithm of the monthly average of S&P 500 index, and the difference in natural logarithm of money supply.

4.2 Determination of Lag

After establishing the basic parameters of the VAR model, the optimal number of lags of the VAR model should be determined. If the lag is too great, then the degree of freedom would be reduced to the extent that the effectiveness of the estimation of the model would be hampered. If the lag is too small, the autocorrection of the error term would be too significant. Therefore, the essay would run the VAR model using five different lags from lag 2 to lag 3, then select the optimum lag via examination of the Schwarz information criterion (SIC) (Schwarz,1978) and Akaike information criterion (AIC) (Akaike,1998) of the models. Theoretically, the lag that yields the model with the least SIC and AIC should be applied.

Table 3 indicates that the VAR model with three lags has the least SIC and AIC. Therefore, it is the optimal model for this research.

4.3 Results of Model

After lag 3 is chosen to be the lag of the model, the research applies STATA to solve the model. The result is as follows:

d_WTI = 0.452d_WTI(−1) + 0.109d_WTI(−2) + 0.112d_WTI(−3) – 15.882 lnSP (−1) + 6.914 lnSP(−2) + 5.429lnSP(−3) − 174.311d_lnMS(−1) + 452.115d_lnMS(−2) + 5.43 d_lnMS(−3) + 14.004

lnSP = 0.013d_WTI(−1) + 0.003d_WTI(−2) + 0.002d_WTI(−3) + 0.503lnSP(−1) + 0.214lnSP(−2) + 0.224lnSP(−3) – 4.705d_lnMS(−1) + 13.250d_lnMS(−2) – 5.597d_lnMS(−3) + 0.223

d_lnMS = 0.000184d_WTI(−1) – 0.000025d_WTI(−2) – 0.000145d_WTI(−3) − 0.031lnSP(−1) + 0.033lnSP(−2) – 0.003lnSP(−3) + 0.745d_lnMS(−1) – 0.252d_lnMS(−2) + 0.164d_lnMS(−3) + 0.005

As shown in Table 4, the relatively small r ² value of 0.247 proved the difficulty of forecasting future oil prices by simply using historic oil prices because a relatively low proportion of variance in future oil prices can be attributed to past oil prices. Indeed, based on the coefficient derived in the model, past lags of oil price have a relatively small impact on future oil prices, making it difficult to use past oil prices as the sole indication for future oil price. With the addition of other explanatory variables, the model should have more significant predictive power. From the relatively more significant coefficients of −15.882, 6.914, and 5.429, it can be inferred that the relationship between the oil price and stock performance indicated by lnSP is comparatively more salient because the model shows that a unit change in lnSP leads to the greatest change in oil price, making it possible to forecast oil price with stock performance. This is understandable because changes in the stock market would impact the speculator’s forecast of economic outlook and oil demand, resulting in changes in oil prices. For example, when stock market performance worsens, speculators may speculate about the arrival of an impending economic crisis, which changes their position in oil futures because futures can be used to hedge stock performance. The coefficients between oil price and stock performance are also significant, highlighting the interactions between the two variables. Changes in oil prices can alter the overall economic performance, inviting monetary agencies to change money supply as part of monetary tools that serve to dampen adverse economic fluctuations. For example, if there is an economic downturn, the central bank can increase money supply to decrease the interest rate and stimulate the economy. On the other hand, monetary policies enacted by central banks could send a strong signal to speculators of oil futures regarding the upcoming economic situation, causing them to change their speculation of future oil demand and affect future oil prices. For example, if the central bank changes the target interest rate through monetary policies, speculators should change their position in oil futures to respond to the potential change in economic performance. Therefore, the interactive relationship between oil price and money supply is reasonable.

The high r ² value of 0.935 indicates the strong relationship between stock performance measured by lnSP and the other two variables in the model. Although the coefficients of three lags of oil price are not significant enough to justify their ability to forecast future stock prices, the coefficients of three lags of money supply (−4.705, 13.250, −5.597) show the impact of monetary policies on stock market performance, which is reasonable as investors often make investment decisions based on economic policies and the current economic environment. For example, expansionary monetary policy often results in the recovery of the economy from downturns, inviting investors in the stock market to grasp the opportunity and invest in stocks that are promising to increase in value. This would cause stock performance to overall increase.

The variable of money supply has an r ² value of 0.717, indicating that, to some extent, it can be inferred based on data of the oil price and stock performance. Indeed, central banks often respond to changes in economy caused by oil and stock market fluctuations. When there is economic downturn caused by oil price and stock market fluctuations, the central bank can alter the money supply to mitigate negative economic impact. However, since the policies of central banks are independent of public opinion and tend to focus on the long run, it might be difficult to use oil price and stock price in a comparatively short time frame to estimate money supply.

4.4 Granger Causality Test

Although the VAR model establishes the relationship between oil price, stock performance, and money supply, it does not necessarily warrant causality between the variables. To examine causality, the Granger causality test is applied to show whether one variable in the VAR model can be forecasted by other variables. Devised by Granger (1969), the Granger causality test has turned out to be a useful notion in characterizing dependent relations between time series in econometrics (Diks & Panchenko, 2006). Although there are debates regarding its reliability, it is a widely used method to examine the forecast capability of variables in the VAR model.

The criterion for Granger causality test is simple. If the significance value of a variable is smaller than 0.1, then it passes the Granger causality test, and it can be generalized that the variable can be used to forecast the variable concerned.

Based on the results of Granger causality test (Tables 5–7), it can be inferred that oil price reflected by d_WTI can be explained by money supply, stock performance can be explained by oil price and money supply, and money supply can only be explained by stock performance.

The results of Granger causality test are overall consistent with the results indicated by the VAR model despite the presence of some discrepancies. Although the r ² of oil price is low, the Granger causality test shows that it can be explained by changes in money supply, despite not being significant enough to be revealed in the VAR model. Such discrepancy is caused by differences in the fundamental mechanisms of the two methods. This also follows economic reasoning, because changes in monetary policy suggested by a shift in money supply would send signals to investors of oil futures, who make predictions of future oil demand and prices based on the current economic situations. They may be incentivized to change their speculation of future oil demand based on changes in current monetary policies, resulting in a change in oil prices. For example, if the central bank changes the target interest rate through monetary policies, speculators should change their position in oil futures to respond to the potential change in economic performance. Therefore, the explanatory role played by money supply in WTI oil prices suggested by Granger causality test seems valid.

On the variables that can explain fluctuations in stock performance measured by lnSP, the results yielded from Granger causality test matched those indicated by the VAR model: both indicate that stock performance is responsive to changes in oil price and money supply. This result is reasonable because investors in the stock market respond sensitively to changes in macroeconomy to yield profits. Changes in oil price and monetary policies indicated by shift in money supply all send signals to stock investors that their investment decisions might need to be changed, resulting in changes in stock prices. Moreover, changes in oil price and economic policy would influence the performance of major enterprises included in the S&P 500 index, causing their investors to change the amount of investment in the enterprises and resulting in changes in stock prices. Changes in oil price would also impact the stock performance of oil companies, affecting stock indices in the process. For these reasons, it is understandable that stock performance can be reflected by oil price and money supply.

On money supply, the Granger causality test indicates that the difference in natural logarithm of money supply in the United States can be explained by stock performance. Although not revealed by the r ² of money supply in the VAR model, this result is understandable because monetary policies respond to changes in macroeconomy that can be caused by stock market fluctuation and the speculation resulting from it. Despite its independence from government and public opinion, central banks do have the obligation to maintain the normal functioning of macroeconomy, so its monetary policies should be responsive to stock market fluctuations and dampen the potential adverse effects of such fluctuation, causing money supply to be affected by changes in stock market performance.

4.5 IRF Analysis

To understand how the impact of the variables on each other changes across time lags, IRF analysis is conducted. The IRF can describe the responsiveness of endogenous variables in the VAR model to changes in error, which is the impact resulting from an impulse with the size of one standard deviation. The model is selected to capture how the impact of independent variables on dependent variables changes across various lags. To show the respective impacts on other variables caused by impulses with the size of one standard deviation originated from differences in oil price, stock performance, and money supply, this research uses STATA software to generate IRFs. The results are shown in Figures 1–3.

Figure 1

The graphs show the impact on oil price caused, by oil price (a), stock performance (b), and money supply (c). The shaded region represents 95% confidence interval.

Figure 2

The graphs show the impact on stock performance caused, by oil price (a), stock performance (b), and money supply (c). The shaded region represents 95% confidence interval.

Figure 3

The graphs show the impact on money supply caused, by oil price (a), stock performance (b), and money supply (c). The shaded region represents 95% confidence interval.

The results of IRF analysis shed light on the interaction between the variables. The analysis shows that oil price responds to both stock performance and money supply. In the first five steps of IRF, the oil price would respond to a positive signal caused by stock performance, and the effect of the impulse gradually dampens after step 7. The fluctuation in oil price responding to stock price fluctuation shows that speculations play a role in the determination of future oil prices, which is supported by the work of Fawley et al. (2021). Although Granger causality test fails to identify stock performance as an explanatory factor of oil price, this does not interfere with the results yielded from IRF analysis due to the presence of inherent shortcomings of the test (Maziarz, 2015). Similarly, oil price responds strongly to an impulse of money supply. In the first five steps, oil price rises sharply to a positive impulse of money supply before dampening after step 7. This shows how oil price responds to expansionary monetary policy. Since expansionary monetary policies can cause economic boom and increase demand for oil, oil investors would invest more in oil future and cause oil price to rise, resulting in the IRF shown in Figure 1(c).

The IRF of stock performance shows the factors that affect the variable. In the first five steps, a positive impulse of oil price would cause a minor increase in stock performance before its effects dampen after step 5. This is somewhat different from the results from Granger causality test because the effects of oil price fluctuation on stock performance are not reflected by IRF analysis. However, money supply does have significant impact: In the first five steps, a positive impulse of money supply would result in an increase in stock performance. Since expansionary monetary policy would often result in economic recovery and expansion, the stock market would naturally react positively to the change.

Finally, the results of money supply to impulses show that money supply is overall independent from oil price fluctuation and is slightly influenced by stock market performance. As shown in Figure 3(a), a positive impulse in oil price fails to result in a significant change in the money supply. However, a positive impulse in stock performance does cause money supply to drop slightly in the first three steps. Money supply drops because of contractionary monetary policies, which are usually used by the central bank to slow down the overheating economy that can be signaled by rising stock prices. Overall, results from IRF analysis on money supply match those yielded by Granger causality test.

4.6 Variance Decomposition Analysis

The variance decomposition analysis of VAR model can reveal important information regarding the relative importance of random information. The key process is to decompose the variance of endogenous variables in the model into components that can be explained by other variables in the model and therefore substantiate the extent of impact on endogenous variables caused by other variables in the model (Omisakin, 2008). This research utilizes STATA to complete the variance decomposition analysis for oil price, stock performance, and money supply with a total of five steps.

As shown in Tables 8–10, the variance decomposition analysis provides new insights into factors that can explain the variance of the variables in the VAR model and is overall consistent with results yielded from previous analysis.

First, the results of variance decomposition of oil price show that in the first five steps, the majority of the variance in oil price can be accounted for by oil price itself, but the other two variables still account for almost 10% of the variance of oil price, substantiating their impact on oil prices. This is consistent with the results from Granger causality test and IRF analysis that stock price and money supply have noticeable influence on oil price, although the intensity and duration of such impact are not persistent. Combined, the results indicate that oil price is influenced not only by its own supply–demand interaction but also by macroeconomic changes indicated by other economic variables.

Second, the variance decomposition of stock performance indicates the role played by oil price in inducing variance in stock prices. In the first five steps, oil price accounts for more than 80% of the variance in stock performance, while money supply plays a relatively minor role. This is different from outcomes in IRF, where money supply is identified as a greater impacting factor on stock performance. Still, both tests show that stock prices are somewhat correlated and influenced by oil price and money supply changes. An increase in the money supply will affect stock prices through a series of economic variables. Initially, it caused a temporary negative impact on the stock price, causing the stock price to decline, and then a strong positive impact, driving the stock price to rise. Subsequently, the impact decreased, or even decreased to a negative value, indicating that the stock market would fluctuate under the impact of the money supply. An increase in the price level will also cause the stock price to rise first and then fall. Theoretically, rising price levels, i.e., increasing inflation, will lead to the devaluation of the currency held by residents. The awareness of maintaining value will encourage people to spend more money to purchase financial assets and real estate, thereby driving up stock prices. However, as inflation continues to increase, the currency continues to depreciate, resulting in a large amount of currency issuance, leading to excess liquidity. At this time, inflation has a greater inhibitory effect on stock prices than a stimulating effect, leading to a decline in stock prices. An increase in interest rates will have a negative impact on stock prices, which will briefly raise stock prices, followed by a negative impact on stock prices. This is basically consistent with the trend of increasing the money supply’s impact on stock prices and is inconsistent with practical experience. The main reason for this phenomenon is that in the past interest rate, marketization was low. Only when economic development deviated from the normal track, the central bank would adjust and control the economy by changing interest rates, and there was a significant time lag in this regulation.

Lastly, the variance decomposition of money supply confirmed the impact of stock performance variation on money supply. In the first five lags, the percentage of variance of money supply that can be accounted for stock performance first increases from 0.395 to 0.476 before gradually decreasing. This corresponds to the results of both Granger causality test and IRF analysis, which both indicate stock performance as a factor that has a significant impact on money supply. The major difference between variance decomposition and IRF on money supply is the role played by oil price. While the IRF function suggests that oil price has a weak impact on money supply, variance decomposition suggests that the influence of oil price on money supply was significant, although not as substantial as stock performance and money supply itself. Such difference stems from the fact that the fundamental mechanisms of the models are different, which naturally lead to some discrepancies in the results generated. This would invite a combined analysis of results yielded from Granger causality test, IRF, and variance decomposition analysis, which should be presented in the conclusion.