How Many Hours Does It Take To Buy A House

A Special Kaleberg Report

I can't stand it any more. There are too many inconsistent facts and numbers being bandied about, and an awful lot of claims being made. I really had to find out if houses less affordable or more affordable than ever. Thanks to Google, the government, the realtors, the economics data providers and a host of other folks, including Microsoft who put the PMT function for computing mortgage payments into Excel, I figured I'd compute a Fermi Solution to clarify things.

Fermi Solution

What is a Fermi Solution? A Fermi solution is a solution that is based on facts that one knows or that one can easily find. It uses all too many simplifying assumptions and uses estimates to avoid hard calculations in the hopes that all the errors will balance out and give one a reasonable answer. This method of analysis was named for Enrico Fermi, one of the great atomic pioneers and a certified genius. He taught his method in his physics classes, presenting his students with questions like:

• How many piano tuners are there in Chicago?
• How many miles does it take the wear the tread off a tire?
• What is the capture cross section of a neutron?

Enrico Fermi was the guy at the first atomic bomb test dropping bits of paper and timing them so he could compute the dynamite equivalent energy release of the bomb. His estimate was surprisingly good.

So, having made my methodological apology, I am not going to defend every number or calculation point by point, though I will try to give some backing to my assertions. If this kind of half baked calculation worked for a guy a hundred times brighter than me, then it should work for me too, though probably not as well.

The Problem

The affordability index most commonly used compares the price of buying a home, usually the median price, with the median family income, on the theory that most single family homes have a single family living in them. This is a useful index, but it ignores the mutability of the family. The current model of the nuclear family with the mother and father both working is a relatively new model. Older versions of the nuclear family had only one wage earner, and even older ones included elderly parents and unmarried, but adult, children. It would be nice to have an affordability index that reflected how hard it is to buy a house, if only to shed light on the adjustments to the family structure that housing prices entail.

During the Cold War, there was a common chart presented to show how much better life was in the United States as opposed to in the Soviet Union. It ignored the issues of religious freedom, a free press, the renunciation of torture, checks and balances in government, and freedom from unwarranted wiretapping, and concentrated on the economic benefits. Needless to say, the American worker came out far ahead.

I haven't seen this kind of chart lately. This is probably because hourly income was rising back during the Cold War, particularly during the 1950s and 1960s, but much less so since the 1980s. I should look around for such a chart on eBay. It would be interesting to see some of the numbers updated. Some things have gotten much cheaper.

A 10 cent phone call took 4 minutes to earn at the $1.50 minimum wage I earned at my first job in a machine shop making rocket fuse parts. Nowadays, phone calls are too cheap to meter. In the 1930s, at 50 cents an hour, it took 550 hours to buy a round trip air ticket from New York to Los Angeles. The train wasn't much cheaper. Today, even at $6 an hour, it only takes 50 hours to buy a $300 round trip on a jet.

While travel and communications are cheaper, cooperative apartments are more expensive. My parents bought a two bedroom cooperative apartment in Queens for $800. Even at 50 cents an hour, that's 1,600 hours, less than a year's work for an apartment. When my father died, the apartment was appraised at about $60,000 dollars, or about 20,000 hours of work at the $3 an hour minimum wage. The neighborhood had not really improved much, and Public School 148 was still standing next door. From the point of view of a minimum wage worker, the price had gone up more than ten-fold.

If I had three time series, for hourly wages, interest rates and house prices, running from 1946 to today, I could compute a useful affordability index. Unfortunately, such time series are hard to find, and those that do exist require some qualification. This is where I have to appeal to Enrico Fermi. It is hard to get the actual numbers one wants. For example, the Bureau of Labor Statistics gives average hourly wages, not median hourly wages, and I presume that they are mathematically and politically astute enough to know the difference.

Despite this, I plunged ahead. I tried to use as few sources of data as I could. If nothing else, the Frankenstein stitches holding the time series together would be less visible if they had been massaged by a trained statistician working for the government or some think tank.

What I Found On The Web

There was no reason I was going to get up out of my chair. In the old days, all you had was the World Almanac, the CRC Handbook and Ripley's Believe It Or Not. Nowadays, the resources of the world are at one's fingertips, and it makes one appreciate the up and coming resource crisis.

I wanted to find three time series:

• The Median Hourly Wage
• The Median Price of a Single Family House
• The Median Mortgage Rate

Any skilled statistician could tell you that piling together three medians doesn't get you a fourth median, but I figured that the median makes a good bet when one is not sure of the distribution of the data. What I wanted to compute was something approximating the median number of hours an individual has to work in a year to pay for one year of a mortgage on a house purchased that year.

Median Hourly Wage

I Googled™ around a bit on this one, since I really wanted the MEDIAN hourly wage, but I wound up settling for the AVERAGE hourly wage provided by the Bureau of Labor Statistics. Since these statistics are for private, non-supervisory, non-farm workers, it doesn't include Bill Gates to screw up the average. Still, if low end wages follow a power law distribution, rather than a Gaussian distribution, the median is overstated. On the other hand, it omits government workers, which would skew wages downward. This is a good sign. Enrico Fermi relied on the errors balancing out.

I was pleased to find that the BLS had a series that ran from 1964 into late 2005, so I used it. If you want to check my numbers, it is at ftp://ftp.bls.gov/pub/suppl/empsit.ceseeb2.txt . Obviously, the 2005 figure isn't completely right; I got lazy and just used the December number.

Median Price of a Single Family House

I always hate it when people talk about single family homes when they mean single family houses. A single family home can be a wagon under the stars, a palace on the Nile or a nice three bedroom, two bath split level ranch in a subdivision. Home is where the heart is. Houses are much easier to measure without an MRI.

My hourly wage data is probably better than my house price data. Median or average, the basic length of time in an hour has not changed much in the last 50 years, though I am sure that even now, some genius at Walmart is working on a 65 minute hour. In contrast, houses have changed. They are much larger, they have better insulation, more wall outlets, central air conditioning, and they are wrapped in Tyvek. Let us all hope that Tyvek is as safe and inert as we all think.

I did find some house value data at the Census site, but house values are like potential energy. They measure the price of the house if it were to be sold. House prices reflect the price that houses actually sell for. Too many investors and economists do not draw this distinction. Since houses are quantized, the median house price is probably as good a measure as I am likely to find. My source was HUD User which seems to be the research and analysis branch of the Department of Housing and Urban Development. (If you are a policy wonk and familiar with HUD User, let me know if I've guessed wrong here).

My numbers for 1964 to 2000 come from http://www.huduser.org/periodicals/USHMC/fall2001/histdat08.htm and my numbers from 2000 to 2005 come from http://www.huduser.org/periodicals/ushmc/fall05/USHMC_05Q3.pdf. Obviously, my number for 2005 is approximate.

Median Mortgage Rate

One would think that this would be the easiest number to get a usable time series for. It turned out the be the trickiest. There are all sorts of metrics for the price of renting money, depending on how it is leased. The number I wound up using was the average contract rate. The contract rate should reflect actual mix or mortgage terms and types being used to purchase houses. Contract rates are likely to have a Gaussian distribution, so here it is likely that the average is close to the median.

My first source was Mortgage X, a mysteriously named "independent information service", "not affiliated with any lending institution". They are aimed at mortgage professionals, and they have a lot of data that does not appear to be aggregated anywhere else. Unfortunately, everything was in little pieces, so I had to get out my Frankenstein needle and thread and do some stitching.

First I found http://mortgage-x.com/ general/ indexes/ contract_rate_history.asp which provides the national average contract rate from 1980 to 1990. Some of the interest rates remind me of the mad bicycle races around downtown Boston trying to lock in a interest rates, even as the available rates soared. My mortgage was at 12.25%. The was at peak at 15.8% in November 1981. A friend of mine wound up paying 19.2%. Those were scary times for first time home buyers, and there were lots of us.

Then I found http://mortgage-x.com/general/indexes/default.asp and got the contractual rates from 1990 to the present.

Unfortunately, this left me in the dark from the 1964 to 1979, a rather critical period.

Via Google, I found EconStats which took me back another decade. They seem to be a commercial economic data provider with a fairly useful website. The file http://www.econstats.com/r/r_am18.htm took me back to 1971, but not into the 1960s. This data was not heavily qualified. It was merely labeled Conventional Mortgages - US Int Rates - Average Over Month. I used the data for December of each year.

Then I found the Financial Forecast Center, another economic data provider. They had FHA data for mortgages rates on 30 year mortgages at http://www.forecasts.org/ data/ data/ FHA30.htm. Interestingly, the dataset is marked as DISCONTINUED, though I am sure that people can still get 30 year mortgages and that the FHA is still around. Maybe they just aren't interesting enough. This dataset also aligns with the Econstats dataset, so they are both for 30 year mortgages. Luckily, these are the most common types of mortgages, and their rates reflect interest rates overall.

The four datasets I found stitched together fairly well. You might almost suppose that my Frankenstein monster was born that way. The series seemed to match to within at tenth of a percentage point. They also made sense historically, with rates rising in the late 1960s in response to the Vietnam War deficits.

My Analysis

Having managed to eke out three time series, I could now compute the cost of a house in wage hours. I fired up Excel which has a neat function called PMT to compute the payment on a fixed rate, fixed term loan given the principal, the rate and the time period. Given the, shall we say, informal nature of this analysis and my blind faith in Saint Fermi that all my errors would cancel out somehow, I simply assumed one payment per year and a 30 year term.

Then, I had Excel divide the annual payment by the hourly wage, and presto, the number of hours Joe Median had to work each year to pay for his house in Medianville. Ignoring all the errors and approximations and special pleadings, the number of hours ranged from 556 in 1968 to 1,406 in 1981. From my years pricing software projects I remember that there are about 1,920 man hours, mythical or real, in a year. Home buyers were bleeding in the early 1980s.

Here is what the chart looks like:

Back in the 1960s, one had to work about 30% of a year to pay your mortgage. This went up in the mid-1970s, but didn't approach 50% until 1978. Then the cost really soared, nearing three quarters of a work year in 1981. You really could not afford a home without two full time workers then. The cost didn't get back down to 50% until 1985. The cost was stable through the 1990s and into the new century, hovering around 40% . In 2005, the number of hours began to rise again, nearly reaching 50%, as in the late 1970s.

Of course, this 2005 effect could be an artifact of my numbers. House prices jumped $15,000 from 2003 to 2004, but $30,000 from 2004 to 2005. Are my numbers garbage here? Wages went up a bit too, as did interest rates, but most of the change seems based on the house price. I didn't index for inflation, since we are comparing hours to houses here. Money is just an intermediate unit.

You could use this data a number of ways. You could pick 1981 as your base year and show how much better things are, or you could choose 1968 as your base year and show how much worse off we are. You could also use this chart to show why the two worker family replaced the one worker family in the early 1980s.

Conclusions

1. Compared to the early 1980s, houses are cheap. The highest housing prices in the 20th century were in the early 1980s.
2. Compared to the 1960s, houses are expensive. The old "one third of your income pays for housing" rule worked for single breadwinner families in the early 1960s. In the 1990s, the typical family needed to have about 1.33 breadwinners to buy a house. From this, one would expect that about half of all married women would have to work to afford housing.
3. Getting historical time series is a lot of work, and I'm probably not the only one cutting some corners stitching it together. If you have some more data I could use, let me know, and we'll see just how the 1940s and 1950s really stacked up.
4. Enrico Fermi was a genius.

The Time Series

For those who would care to grovel over the numbers I used, I have provided them below:

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