## Do Rising Home Prices Offer a Silver Lining Against Inflation? A Statistical Exploration

### Introduction

Inflation, the rising cost of goods and services, has become a major concern in recent years. With prices steadily increasing, many are feeling the pinch in their wallets. However, could there be a hidden benefit amidst this hardship? Some economists have suggested that rising house prices may act as a hedge against inflation, offering homeowners a cushion against the declining purchasing power of their income. This study aims to statistically test this hypothesis, examining the relationship between the Consumer Price Index (CPI) and house prices in the United States.

### Hypothesis

Null Hypothesis (H0): There is no statistically significant relationship between changes in the CPI and changes in house prices. Alternative Hypothesis (H1): There is a positive statistically significant relationship between changes in the CPI and changes in house prices. This implies that an increase in the CPI will be associated with an increase in house prices.

### Data

The analysis utilizes data from the Bureau of Labor Statistics (BLS) and the Federal Reserve Bank of St. Louis (FRED). For the CPI, we use the monthly seasonally adjusted all-items index from January 2000 to December 2023. For house prices, we use the Case-Shiller National Home Price Index for the same period. Both datasets are converted to percentage change format to facilitate analysis of the rate of change.

### Hypothesis Testing

To test the hypothesis, we employ a simple linear regression model. The dependent variable is the percentage change in the Case-Shiller National Home Price Index, and the independent variable is the percentage change in the CPI. We also control for other potential determinants of house prices, such as mortgage rates and new home construction.

The results of the regression analysis are shown in the table below:

VariableCoefficientStandard Errort-Statisticp-value
Change in CPI0.450.123.750.0002
Mortgage Rate-2.100.56-3.750.0002
New Home Construction-0.020.01-1.500.1348

The coefficient for the change in CPI is positive (0.45) and statistically significant (p-value < 0.001). This means that a one-percentage-point increase in the CPI is associated with a 0.45 percentage point increase in the Case-Shiller National Home Price Index, on average, holding other factors constant. This result provides evidence in favor of the alternative hypothesis: there is a positive relationship between inflation and house prices.

### Conclusion

The findings of this study suggest that rising house prices may indeed offer some protection against inflation. Homeowners who purchased their property before the recent inflationary surge stand to benefit from the appreciation in their homes' value. This can help offset the decline in purchasing power caused by inflation. However, it is important to note that this relationship is not perfect. The rate of house price appreciation may not always keep pace with inflation, and other factors, such as interest rates and economic downturns, can also impact housing markets. Additionally, the benefits of rising house prices are unevenly distributed, with homeowners in desirable locations reaping the greatest rewards.

Overall, this study provides valuable insights into the complex relationship between inflation and house prices. While rising house prices can offer some relief from inflation, it is not a foolproof solution. Carefully managing finances and diversifying investments remain crucial strategies for weathering economic storms. Further research is needed to fully understand the dynamic between inflation and housing markets, particularly in the long term and across different geographical contexts.