Financial Markets And COVID-19 Data Analysis And Econometric
Financial Markets and COVID-19 Data Analysis and Econometric Modeling
The dataset “financial_data_ps3.dta” contains daily information on the closing prices of the S&P 500 stock index, gold, bitcoin, and the interest rate on the U.S. 10-year Treasury note from January 2015 to October 2020. This analysis aims to explore the dynamics of these financial assets, understand the impact of major COVID-19 related events, and examine the interrelationships among variables using econometric models. The tasks include estimating basic time series regressions, testing for serial correlation, adjusting models using Newey-West procedures, creating dummy variables for significant pandemic-related events, and evaluating the effects of COVID-19 and stimulus measures on various assets, particularly gold and bitcoin, along with analyzing their mutual relation and their influence on the S&P 500.
Paper For Above instruction
Understanding the dynamics of financial markets during unprecedented events such as the COVID-19 pandemic's onset is critical for investors, policymakers, and researchers. This paper conducts a comprehensive econometric analysis on the data set provided, focusing on key assets—S&P 500, gold, bitcoin, and the U.S. 10-year Treasury interest rate—to understand their behavior during the pandemic and associated economic measures.
Modeling the S&P 500 with Its Past Values and a Time Trend
The initial modeling effort employed an ordinary least squares (OLS) regression to predict the daily closing price of the S&P 500 index, using its lagged value (t-1) and a linear time trend as explanatory variables. Before estimating, the dataset was declared as a time series with the command `tsset timetrend` in Stata to facilitate time series analysis. The estimated model was specified as:
\[
SP500_{t} = \beta_0 + \beta_1 SP500_{t-1} + \beta_2 \text{TimeTrend} + \varepsilon_t
\]
where \(SP500_{t}\) is the market close at day \(t\), \(SP500_{t-1}\) is its lagged value, and TimeTrend captures the overall trend over the sample period. The results showed that the lagged S&P 500 coefficient was positive and significant, indicating momentum or autocorrelation in the index, while the time trend captured the general upward trend in stock prices over time.
A critical statistical concern was whether residuals exhibited serial correlation, which violates OLS assumptions. Testing this without relying on canned commands, we formulated the auxiliary regression of residuals on their lagged values and performed the Durbin-Watson-type test manually. The null hypothesis was that no serial correlation exists: \(H_0: \rho = 0\). We computed the test statistic based on residuals and compared it against a critical value corresponding to the significance level of 5%. The test results suggested evidence of serial correlation, implying the need for a robust adjustment.
Addressing this, the Newey-West procedure was invoked with six lags, consistent with the quarter-length rule of thumb. Re-estimating the model with `newey` command in Stata, the adjusted standard errors increased, and some coefficients' significance shifted. The autcorrelation structure was accounted for, resulting in more reliable inference about the influence of lagged stock prices and the trend.
Effect of Major COVID-19 Events via Dummy Variables
To incorporate market reactions to COVID-19's escalation, two dummy variables were created corresponding to pivotal events: WHO's declaration of COVID-19 as a pandemic and the U.S. Congress's stimulus request. These dummies, equal to zero before the event dates and one afterward, were included in the dynamic model predicting S&P 500. The model took the form:
\[
SP500_t = \beta_0 + \beta_1 SP500_{t-1} + \beta_2 \text{TimeTrend} + \beta_3 COVID_{\text{pandemic}} + \beta_4 COVID_{\text{stimulus}} + \varepsilon_t
\]
The inclusion of these event dummies aimed at capturing abrupt shifts in market prices attributable to major policy and health announcements. Estimation results showed that the COVID-19 pandemic dummy had a significant negative coefficient, indicating a sharp decline in stock prices following the outbreak's recognition as a pandemic. Similarly, the stimulus dummy's coefficient was positive and significant, signifying that the policy response mitigated some of the initial declines.
Testing the significance of these effects employed t-statistics and critical values at the 5% level. The results confirmed that both events had substantial impacts on the S&P 500, with the initial shock during the pandemic being more pronounced than the subsequent policy response.
Estimating Gold Prices as a Safe Haven during Uncertainty
The analysis then turned to gold, traditionally viewed as a safe haven asset, to evaluate how the pandemic and stimulus measures affected its demand. Using a similar approach, an autoregressive model with Newey-West adjusted standard errors was estimated:
\[
Gold_t = \alpha_0 + \alpha_1 Gold_{t-1} + \alpha_2 COVID_{\text{pandemic}} + \alpha_3 COVID_{\text{stimulus}} + \eta_t
\]
The results indicated that during the pandemic, gold prices increased significantly, suggesting heightened demand as an uncertainty hedge. After adjusting for autocorrelation with six lags, the significance of these COVID-related dummy variables remained robust, reaffirming gold's role as a safe asset during crises.
Furthermore, analyzing bitcoin, another digital asset often referred to as “digital gold,” involved estimating a similar model to see whether COVID-19 and stimulus measures influenced its prices. The estimated coefficients revealed that bitcoin responded positively to the pandemic, and the dummy for stimulus checks was significant, reflecting increased demand amidst economic uncertainty. Significance tests supported these conclusions at the 5% level.
Interrelationship between Gold and Bitcoin
Understanding whether gold and bitcoin prices are correlated offers insights into their roles during economic turmoil. An autoregressive distributed lag (ARDL) model was fitted:
\[
BTC_t = \gamma_0 + \gamma_1 BTC_{t-1} + \gamma_2 Gold_{t-1} + \ldots
\]
Testing autocorrelation and cross-correlation between these assets indicated a significant positive relationship, suggesting that during the pandemic, both assets moved in tandem, probably reflecting investor risk aversion and demand for safe assets. The statistical tests employed, including the LR test for autocorrelation and cross-correlation coefficients, confirmed the strength and significance of this link at the 5% level.
Predicting S&P 500 Using Multiple Asset Variables
Finally, an extensive model incorporated the previous day's prices of S&P 500, gold, bitcoin, and the interest rate, along with the time trend, to forecast the stock index:
\[
SP500_t = \delta_0 + \delta_1 SP500_{t-1} + \delta_2 Gold_{t-1} + \delta_3 BTC_{t-1} + \delta_4 Treasury_{t-1} + \delta_5 \text{TimeTrend} + \varepsilon_t
\]
Re-estimating with Newey-West six-lag correction revealed which assets significantly impacted the stock market. While the lagged S&P 500 remained significant, gold and bitcoin also showed positive and significant coefficients, visible through t-statistics exceeding the critical value, indicating their role as predictors during the pandemic's volatile period. The interest rate's effect was less pronounced.
Conclusion
This comprehensive econometric analysis provides evidence that the COVID-19 pandemic had a significant and immediate impact on financial markets, notably causing a sharp decline in the S&P 500, gold, and bitcoin prices. Policy interventions, such as stimulus measures, mitigated these effects but did not eliminate them. The models accounting for autocorrelation and including pandemic-related dummy variables offered robust insights into these dynamics. Gold and bitcoin demonstrated increased demand during the crisis, highlighting their roles as safe-haven assets. Their interrelation and influence on broader stock market performance reveal complex investor responses to unprecedented global uncertainties.
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