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In recent years, goods' prices increased a lot. For example, food price went much higher most likely due to inflation. What cause house price increase? Inflation or its true value or both? To answer the question, let's look into real price (实际价格) and nominal price (名义价格) in Economics to reveal the return on a real estate investment after removing the effects of inflation and to see the true earning potential without external economic forces.

Inflation-adjusted value is historical data that has been adjusted to match the current value, and is also called real value. It enables comparison of quantities as if the prices of goods had not changed on average (用于比较在不同的时间点用同样的价格可以买到相似物品的数量). Changes in value in real terms therefore exclude the effect of inflation. In contrast with a real value, a nominal value has not been adjusted for inflation, and so changes in nominal value reflect at least in part the effect of inflation.

Inflation rate is needed to calculate real value from nominal value or to find the inflation rate during a time period (if a calculator is not used, such as BLS calculator). CPI charts by FRED (Federal Reserve Economic Data) make the calculation easier.

As an example, to calculate inflation rate in house price from January 2000 to September 2020 using CPI less Shelter (in Red line), I use equation "237.3 = 163.3 + 163.3 * IR", where 237.3 is the CPI less Shelter in September 2020 on red line and 163.3 is the CPI less Shelter in January 2000 (which is otside the range of above chart and so not shown on the chart), to get inflation rate IR = 237.3/163.3 - 1 = 45%. That matches the rate in article by Bill McBride.

Inflation-adjusted price in the past, which is adjusted to add inflation on top of it, is higher than its nominal price and is calculated by Real_Price = Nominal_Price * ( InflationIndexforCurrentPeriod / InflationIndexforPriorPeriod ). Below chart shows the nominal house price (in Blue) in Metro Phoenix and the "real" house price (in Red) , which is calculated from nominal price and 238.594, the CPI less Shelter at the end of Q4 2020 (or data point of January 2021) from above chart.

Real price at Q4 2006 peak is 365.4 on red line, meaning it costs 365.4 of January 2021's money on average to buy a house in Q4 2006. That is higher than Q4 2020 nominal price 335 on blue line. Conclusion from the chart: by the end of Q4 2020 Metro Phoenix house price after inflation-adjusted has NOT surpassed the peak price of 2006 housing bubble. Please note Metro Phoenix nominal house price in 2019 surpassed its nominal price of 2006 peak.
Another FRED chart gives "real" house prices in US Nation-wide. But the there are one or two quarters behind current date. In real terms, National house prices in late 2020 were at 2004 levels, not at peak yet.
More charts on education cost and stock price, showing inflation-adjusted data:
Tempe Town Lake, AZ. 2018
 
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  Delex Realty
6170 W Chandler Blvd #14
Chandler, AZ 85226