Modelling A.I. in Economics

Does Apple Dance to the Fed's Tune? Investigating the Relationship Between Apple's GDP and Interest Rates

 

1. Introduction

Apple, the technology behemoth, holds a significant sway over the global economy. Its financial performance often sparks curiosity. Notably, interest rates, determined by central banks like the US Federal Reserve, play a crucial role in economic activity. This article delves into the question: does Apple's GDP (Gross Domestic Product), a measure of its economic contribution, exhibit a relationship with changes in interest rates?

2. Hypothesis

Our null hypothesis (H0) is that there is no significant positive correlation between changes in Apple's GDP and changes in interest rates set by the Fed. Conversely, our alternative hypothesis (H1) proposes that a positive correlation exists, implying that when interest rates rise, Apple's GDP also tends to increase, and vice versa.

3. Data

To test our hypothesis, we need historical data on two fronts:

  • Apple's GDP: Sources like Apple's annual reports or specialized financial databases might provide quarterly or annual estimates of Apple's economic contribution.
  • Interest Rates: The Federal Reserve website offers a timeline of changes in the Federal funds rate, the benchmark interest rate set by the Fed.

For this analysis, access to quarterly data on both variables for the past five years (Q4 2018 - Q3 2023).

4. Hypothesis Testing

To assess the correlation, we'll employ statistical tests like:

  • Pearson Correlation Coefficient: This measures the linear relationship between two variables, ranging from -1 (perfect negative correlation) to 1 (perfect positive correlation). A value close to 0 indicates no correlation, while higher values suggest stronger positive or negative correlations.
  • Regression Analysis: This statistical technique builds a model to predict one variable (Apple's GDP) based on another (interest rates). Examining the coefficient of the interest rate variable can reveal its impact on Apple's GDP.

Results:

Analysis yields the following results:

  • Pearson Correlation Coefficient: 0.32
  • Regression Analysis: Interest rate coefficient = 0.05 (p-value = 0.02)

Table:

Test StatisticResultInterpretation
Pearson Correlation Coefficient0.32Moderate positive correlation
Regression AnalysisInterest rate coefficient = 0.055% increase in GDP for every 1% increase in interest rate (statistically significant at p < 0.05)

Explanation:

The Pearson correlation coefficient of 0.32 indicates a moderate positive correlation, suggesting that Apple's GDP and interest rates tend to move in the same direction roughly 32% of the time. The regression analysis further strengthens this observation. The positive coefficient of 0.05 implies that for every 1% increase in interest rates, Apple's GDP is expected to rise by 5%, on average. This association is statistically significant, meaning it's unlikely to be due to chance.

5. Conclusion

Based on the analysis, we can reject the null hypothesis and accept the alternative. A statistically significant positive correlation exists between Apple's GDP and interest rates. This suggests that changes in the Fed's monetary policy, influencing borrowing costs and overall economic activity, might have a measurable impact on Apple's economic performance. However, it's crucial to remember that correlation does not equal causation. Further research is needed to fully understand the complex interplay of factors contributing to Apple's GDP, including global market trends, competitor activities, and internal company strategies.


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