Multiplier Effect - some results

My previous post, "Multiplier Effect," outlined the economic impact of various possible stimulus packages. On the top of the list -- those stimuli that provide the greatest productivity improvement per dollar spent -- were capital infrastructure improvements.

President-elect Obama's new plans include:

Save one million jobs through immediate investments to rebuild America's roads and bridges and repair our schools: The Obama-Biden emergency plan would make $25 billion immediately available in a Jobs and Growth Fund to help ensure that in-progress and fast-tracked infrastructure projects are not sidelined, and to ensure that schools can meet their energy costs and undertake key repairs starting this fall.

and...

Create a National Infrastructure Reinvestment Bank: Barack Obama and Joe Biden will address the infrastructure challenge by creating a National Infrastructure Reinvestment Bank to expand and enhance, not supplant, existing federal transportation investments.

It sounds promising, but of course the devil is in the details. As this Washington Post article points out, many of the actual projects will be more maintenance-type activities, rather than huge monorail systems. But if the goal is to improve the job situation at the same time as improving national infrastructure, these types of projects will certainly help. The big risk, when spending large amounts of money quickly, is of fraud, theft and corruption. In that case, the money will still have a stimulative effect -- even the thief spends his swag -- but the national will not get the full benefit.

Multiplier Effect

Because of the developing economic crisis, I've been reading more economics blogs. My favorites are Econbrowser, hosted by Profs. Hamilton and Chinn; Macro-Man an anonymous but extremely incisive and hilarious day-trader^*; and Follow the Money by Brad Setser. Any other reader favorites?

One excellent post by Prof. Chinn has direct relevance to governmental policy initiatives to deal with the economic problems. Her post is based on work by Mark Zandi of Economy.com. The question is: given that the economy needs to be stimulated, what method of stimulation yields the largest economic benefit. The benefit here is expressed as the stimulus multiplier, which is the amount of increase in GDP per unit of stimulus. For example, if we simply gave every person in the country $1, each could go out and buy a McDonald's value menu item. But the benefit doesn't stop there because with the increased consumption, McDonald's has to hire more workers, who in turn consume more; purchase more supplies from its suppliers, who in turn hire more workers, etc. So in principle, a $1 stimulus package can have more than $1 benefit to overall production.

So which economic stimuli had the greatest benefit? The top three were:

• Temporarily Increase Food-stamps (multiplier 1.73)
• Extend Unemployment Insurance Benefits (multiplier 1.64)
• Increase Infrastructure Spending (multiplier 1.59)

The first two items have the obvious benefits of keeping people on their feet, but also provide an extra 64-73% advantage beyond the direct stimulus. Of course these benefits can only be temporary. On the other hand, the third item has the advantage of improving neglected infrastructure -- a long term "capital gain" -- while at the same time providing an extra 60% bang for our buck.

Now for the worst stimulus concepts:

• Make Bush Tax Cuts Permanent (multiplier 0.29)
• Cut Corporate Tax Rate (multiplier 0.30)
• Make Dividend Tax Cuts Permanent (multiplier 0.37)

Since these multipliers are less than unity, it means that for every dollar of tax break, the country's production actually goes down. Of course some small segment of the population may benefit from such tax cuts, but in hard economic times, it's not clear why they would deserve a benefit when the broad population and the overall economy do not. To be fair, a few of the tax cut concepts do a little bit better, most most are break-even at best.

Note that these tax cuts that are discussed most readily as the solution to the economic problems have some of the worst possible effects on the economy. In fact, a tax cut actually hinders production, compared to other stimuli. Dr. Chinn discusses some reasons this may be true.

What fascinates me is the question of whether the multipliers work in reverse. If reducing corporate taxes by $1.00 hobbles the economy by $0.70, then would raising taxes by $1.00 improve the economy by $0.30? As heretical as that sounds, it seems that while raising taxes will withdraw $1.00 from corporate coffers and hence from the economy, it enables the government to spend $1.00 on more needful and worthy areas (say, on stimuli that have a large multiplier!).

The situation is somewhat more complicated because each of the stimulus concepts have different time scales, so it would require a more delicate touch than brute force. But it would be nice if, in the political dialog about what to do next, actual economic data would be used rather than mindless rhetoric with zero substantiation.

The Thermodynamics of Heating a House

Follow along as I explore trying to make my house a little more energy efficient, look at my energy usage history, and do a little thermodynamics. There will be some small equations, but I'll explain them in words as well. At the end, I discover something about the insulation efficiency of my house.

I live in a region which is heating-challenged. Every house or apartment I've lived in has had issues with heating in the winter and cooling in the summer. Builders in this area just don't seem to get that a little insulation goes a long way. For my current house, the homeowner's association also decided in its infinite wisdom that it would rip out all the old oil-fired boilers because they were too expensive, and replace them with electric baseboard heaters, because they are more economical. Whatever insane reasoning that led to that decision is now negated, especially since electricity has doubled in price over the past two years here. While it is true that electric heaters themselves are 100% efficient, the power plant and transmission lines are not. Furthermore, baseboard heaters tend to be mounted on outer walls below windows, so much of the heat can be conducted through the wall and escape the house.

I'm trying a few new strategies to try to make my house more comfortable, given its current limitations. First, I added transparent window films to almost all of the windows. The idea is that they hold an still pocket of air against the window, which adds an extra insulation factor. They also can contain small drafts so that cold air can't get in. It does take some work to install them, which basically involves stretching a huge sheet of saran wrap onto double stick tape mounted on each window frame, but eventually I developed a pretty efficient method (especially for smoothing the wrinkles).



A second thing I did was install curtains in the living room doorways, in order to keep the heat from escaping to colder parts of the house from the room I use most. These are cheap but heavy curtains I got on sale at Wal-Mart, hung from an expandable shower curtain rod across two doorways. Finally, I put some foam-board over my back door. It's a thin wooden door that conducts a lot of heat out.

I think these efforts have helped in a very qualitative sense. The living room is much less drafty, especially near the windows. Before installing the films, a cold down-draft from the windows would collide from an up-draft from the heaters to make chilly turbulent zone right where I was sitting. These drafts are gone now. The curtains also definitely help keep the heat where I appreciate it most.

Comfort is good, but I'd also like to know if this is saving energy and money.

PEPCO kindly puts my energy usage history on each bill, so it was a matter of collecting a few old bills and entering them in the computer. That's shown in black below (click for larger image).



The plot shows the number of kiloWatt-hours I use each month (ignore the red and blue curves for the moment). Unfortunately, I don't have data yet for December, the first month that I installed the window films or curtains, so I have to put the efficiency question on hold for now.

I decided to check out this plot a little more carefully. I use the greatest energy in the winter, obviously for heating. There are also small bumps in the summer, corresponding to cooling. Up until recently, I had a very old air conditioner which I rarely used, so my cooling expenses have never been large.

What to compare this with? Well, the there is a nifty number called a heating degree day used for heating calculations. Basically, any day that the mean temperature dips below 65 degrees Fahrenheit is considered a "heating day," and for that matter when the mean temperature is above 65 it is a "cooling day." The number of heating degree days is the number of degrees the mean temperature is below 65. The US National Climatic Data Center (not to be confused with the Climactic Data Center! Ooo la lah!) provides tabulated historical heating and cooling degree day data. The monthly total heating and cooling degree days are shown in the above plot (red=heating; blue=cooling; averaged over Maryland & Washington DC).

It's no big surprise that the heating and cooling curves match up with my energy usage pretty well. It's physics after all.

In fact, the Mr. Quantitative in me wants to do more. I decided to perform a linear regression between these quantities, with energy usage per day as the dependent variable, and heating/cooling degree days per day as the two independent variables. The simple function I tried was:

E = Constant + H(T_h) + C(T_c)

where H(T_h) is some function of heating degree days (per day), and C(T_c) is another function of cooling degree days (per day), both of which describe power usage versus temperature. This equation has the interpretation that I use some constant electric power all the time (for lights, water heater, etc.), plus the amount I use for heating and cooling, which depend on temperature.

The obvious choice is to make the two electric heating functions, H and C, proportional to temperature. However, I found that wasn't a good fit, as you will see below. Instead, there is an activation threshold. For small temperature excursions, no heating or cooling is required, and I don't use energy. This would be my comfort zone, the temperature range I'm willing to tolerate. I imagine I have a larger comfort zone than many people. As the outside temperature gets more extreme, then I use energy to maintain the inside house temperature within the comfort range. This function can be written as a constant when the heating/cooling temperature is within the comfort threshold, and a linear function outside of that. The linear coefficient of the function describes the number of kiloWatt-hours per day needed to heat (or cool) the house one extra degree Fahrenheit.

The fit works quite well, and here is how the results look. On the heating side, the function H(T) looks like this:

This means that I am willing to tolerate mean outside temperature drops of about 6.5 degrees (F) below the baseline temperature of 65 degrees before turning on the heat, and then I use about 0.84 kWh of energy per day for each degree (F) that it gets colder. At the current PEPCO price of 10.96 cents/per kWh, I pay an extra 10 cents per day for each degree colder that the outside temperature goes below about 59 degrees.

On the cooling side, the curve looks like this:

I'm apparently willing to tolerate large excursions before turning on the air conditioner (up to 10 degrees above the 65 degree baseline), and then I use 1.31 kWh of energy per day for each degree above that (for a cost of about 14 cents per day for each degree).

Finally, it's worth noting that I use 9.7 kWh of energy every day, no matter what the outside temperature is, just keeping the house going. I know for a fact that my refrigerator uses about 3.8 kWh every day on average, or about 40% of the total. It's a very old refrigerator from 1982 (!) which needs to be replaced. I used my handy Kill-a-Watt energy meter to measure this and other devices in the house. The refrigerator is by far the largest constant energy user.

Interestingly, last winter I changed from incandescent and halogen lamps to compact fluorescent bulbs. I predict this should save me between 1-2 kWh per day. A change such as this is barely detectable on the graphs, given the season and monthly fluctuations.

As one final exercise, I can estimate the overall efficiency my house, the effective "R-value". This quantity is defined as the reciprocal of the amount of heat lost per unit time per exposed area per degree temperature change, and has units of ft² per (BTU/hour/Fahrenheit). I already know the second quantity, since it's the linear heating coefficient I found above (0.845 kWh/day/F = 120 BTU/hour/F). The exposed area of my house is about 2000 ft², giving an effective R-value of 17. (NOTE 14 Jan: my original value of R-0.7 was had a unit conversion error and was incorrect).

An overall insulation efficiency of R-17 is okay but not great. As pointed out here, a house in my region (zone 2) demands an R value in the range of 18 (walls) to 49 (attic). However, as one of my commenters notes, there are other factors to consider, like how much air circulates through the building.

Remember that this data is all based on my house before I made the few changes above. Neither my usage data nor the climate data for the winter heating season are available yet. I hope to see improved efficiency!

Update (14 Jan): Oops! I made a unit error when converting from kWh/day to BTU/hr (missed a factor of 24). After the correction, the overall insulation efficiency of R-17 is more reasonable.