# Term paper - Part 4

### 4. Housing Affordability and Inventory

Now that we have determined the affordability of housing there are several directions we can go. For example we could relate housing costs to the business cycle, to rental value, to quality (e.g., square footage), and other variables. For this part of the term paper we will look at the inventory of houses available for sale measured as "months supply".

Let's define inventory months supply. Assume on January 1 we have 1,000 houses on the market for sale. Each month an average of 200 houses are sold. This implies that on January 1 the number of houses available for sale would satisfy 5 months of demand. The number of houses available for sale on January 1 (actually December 31 in the Census Bureau numbers) and the number of houses sold during the year are available from the Census Bureau on their new residential sales page at:

http://www.census.gov/const/www/newressalesindex.html

Consider this sample calculation. At the end of 1963 there were 265,000 houses for sale. During 1964 there were 565,000 houses sold. At the end of 1963 the number of houses available for sale represented 5.63 months of supply (12 x 265,000 / 565,000). We could have calculated a simple index (e.g., 265,000/565,000) but by multiplying by 12 months to create a months supply index we get a more intuitively appealing measure of housing supply (5.63 months rather than 0.47 years). Note that we use houses for sale at the end of 1963 and houses sold in 1964 to calculate our index.

Presenting inventory as days, months, or even years of supply is a common method of eliminating the effect of changing sales rates over time. For example, over the last 40 years the number of households in the U.S. has almost doubled. With a growing population we should probably expect an increasing number of new home sales every year. We might also expect the number of houses available for sale at any point time to also increase. If we were to look at a time series of just inventories this trend of steadily increasing market activity would overwhelm and hide the market influences we are actually looking for. Dividing the level of inventory by expected sales provides a better picture of the inventory situation, i.e. whether inventories are low or high relative to sales.

Now the question is how should the affordability index you calculated in Part 3 relate to the inventory months supply index? Caution! Do not confuse our inventory months supply index with the economic term "supply". The economic term supply refers to the production or output of goods or services at a given price. That is not what we are measuring. So, don't discuss the inventory months supply index as if were simply a measure of production, which increases when prices increase and declines when prices decline. Our inventory months supply index reflects the balance between supply and demand. When the affordability index is low (i.e., mortgage payments take up a smaller portion of income) is the months supply index high or low? Why would you expect a positive (low affordability and low inventory) or negative (low affordability and high inventory) relationship between affordability and months supply? Can you discuss it clearly in words that would not give the reader a headache?