The labor incentive effects of raising income taxes--a personal view

I like the stuff I buy.  If you raise my taxes, I will probably consult a little more so I can keep buying that stuff. This is the income effect being more important than the substitution effect.  I know that it is for me, and I am pretty sure it is for lots of others, as well.

"We are all in it together," and benefits taxes.

Tyler Cowen says that the Republican Party should propose raising taxes on everyone because, "we are all in it together."

To some extent, this is a benefits tax view--a view that we should pay to society our fair share of what we get from society.  But the implication of this is not necessarily that everyone should sacrifice in order to put us all on a sustainable fiscal path.

With Ronald Reagan's election in 1980, the US saw a sea change in tax and regulatory policy.  While the policy was suppose to benefit everyone, it clearly hasn't.  For the bottom quintile of the income distribution, income has risen about 5 percent since 1982 (the first year in which Reagan's policies bit); for the next quintile, it has risen 8 percent; for the next, 11 percent, for the next, 20 percent, and for the highest, 45 percent.  But most of the highest quintile didn't do so well--the top 5 percent has seen average household income rise by 68 percent.

These data are before tax, and come from the US Census, Table H-3.  Before anyone suggests that this means that everyone has benefited, I should point out that average income in the lowest quintile of the income distribution is $11,239, which is right at the Federal Poverty Level for a single person household.  In a benefits tax view of the world, people who haven't sufficient income to live should not be taxed (they are living at subsistence levels as it is, and taxing them makes thing worse).

So let's begin by holding the bottom quintile harmless in doing any kind of deficit reduction.  But what of the remaining quintiles?  If we look at the share of income growth by quintile (excluding the meager income growth of the bottom quintile), we find that 3 percent went to the second quintile from the bottom; 7 percent to the next; 18 percent to the next, and 73 percent to the top quintile.  So little has gone to the second and third quintile from the bottom that one could make a case that they should be left along as well.

The fourth quintile, though, has seen a material improvement in incomes, so it is probably OK to ask this group for something--this includes people who nearly everyone would consider middle class.  Nevertheless, the lion's share of the benefits of the policy changes of the early 1980s has appeared to go to the top quintile, and so the top quntile should pay the most to put us on a sustainable fiscal path.

One last calculation--the top 5 percent got 57 percent of the income growth within its quintile.

It is true that households move in and out of quintiles, but as Dalton Conley shows, not as much as we would like to think,  In any event, we have not been all in it together when it has come to benefitting from the policies of the past 30 years.

California leads

From California's Legislative Analyst's Office:

The 18th annual edition of the LAO's Fiscal Outlook--a forecast of the state's budget condition over the next five years--shows that California's budget situation has improved sharply. The state's economic recovery, prior budget cuts, and the additional, temporary taxes provided by Proposition 30 have combined to bring California to a promising moment: the possible end of a decade of acute state budget challenges. Our economic and budgetary forecast indicates that California's leaders face a dramatically smaller budget problem in 2013-14 compared to recent years. Furthermore, assuming steady economic growth and restraint in augmenting current program funding levels, there is a strong possibility of multibillion-dollar operating surpluses within a few years.

The voters of California raised taxes on themselves. Most of the revenue will come from income taxes on the top 3 percent of the income distribution; there is also a small hike in the sales tax.

Will Google, Apple, Intel, Disney, etc. run away because of this?  I rather doubt it.  And comparisons to Greece now look particularly ridiculous.

John Griffith on why Gretchen Morgenson should not trust Edward Pinto

He writes in American Banker:

The onslaught began last month after the agency released a sobering financial report, then accelerated last week when the New York Times reported on an alleged "pattern of risky lending" in the agency's mortgage insurance program.

The Times piece, penned by columnist Gretchen Morgenson, relays the findings of a controversial new report from Edward Pinto of the conservative American Enterprise Institute. Pinto's study takes on an important issue—the performance of FHA-insured home loans—but draws conclusions based on ideology rather than a cold appraisal of the facts. By relying entirely on one man's misleading data and unfounded opinions, Morgenson has done a grave disservice to a critical federal program.

The report in question argues that the FHA is "financing failure" for working-class families by peddling high-risk loans to unworthy borrowers, based on an analysis of loans insured in 2009 and 2010. Pinto concludes that the agency's basic business model—insuring long-term, low-down-payment loans to borrowers with less-than-perfect credit—puts homeowners at an unacceptably high risk of default with negative consequences for communities.

Nothing could be further from the truth....

.... Pinto focuses on the cost of foreclosure without considering the FHA's contribution to these neighborhoods since the crisis began. If FHA insurance weren't available under reasonable terms, it would have been much more difficult for low- and moderate-income families to get mortgage credit since the crisis began. As a result, home prices would have declined precipitously beyond already-depressed levels – by as much as 25%,according to one estimate from Moody’s Analytics – leading to far more foreclosures on all homes, not to mention additional job loss, lost household wealth and a far deeper or more prolonged recession.

That counter-cyclical support is a key part of the agency's mission, and it understandably comes with some costs. If the foreclosure crisis were a fire, Pinto would be blaming the firefighters for getting the house wet.

In the coming months, we hope there is a serious debate about the FHA's role in the housing market and the overall role of the government in housing finance. That will require us to sort facts from partisan nonsense, and here's hoping this report doesn't make the cut.

Matthew Yglesias says weather doesn't matter

I just caught up with his Valentine to Minneapolis:

People appear to be deterred from moving to Minneapolis on the grounds that it's very cold, but David Schkade and Daniel Kahneman have found that people's thinking about weather and happiness is dominated by "focusing illusion" in which "easily observed and distinctive differences between locations are given more weight in such judgments than they will have in reality." They specifically looked at the weather gap between California and the Midwest and found that while Midwesterners thought the good weather in California would make a huge difference in people's lives, it doesn't in reality.

OK, maybe I am idiosyncratic.  But as a person who lived most of his life in Wisconsin (not as cold as Minnesota), and who now lives in California, I can tell you the three reasons I will most likely never leave this place:

(1) My wife does cool and useful things here.
(2) I like the people I work with very much.
(3) Weather.

George Bittlingmayer on Buffet v Asness

From comments:

Under this theory, if gross-of-tax discount rates are 10% and an investment promises $10 per year, I'll plunk down $100 for it if tax rates are zero, and $100 if tax rates are 50% and I get only $5 per year. "To be tested." Recall also, if tax rates are on nominal returns, with even moderate inflation, the tax falls on what is a compensation for inflation. The effect of higher taxes seems like an empirical question, with all due respect to both Buffett & Asness, and Richard.

I agree, it is testable.  One thing that makes testing tough, though, is trying to figure out how the market discount rate change as a result of tax policy.  IN any event my principal criticism of Asness is that if you are going to change the numerator, you also need to change the denominator.

Hannah Green in Think Progress on trash

She writes:

In India, there is a thriving market for trash. People make lives for themselves collecting it, sorting it, buying it, selling it: making it useful once again.

While the community of trash workers occasionally gets attention from the American media, the focus often revolves around the initial realization that people can earn a living from garbage piles, and what this says about poverty levels.

Katherine Boo’s recent book related to the subject, Behind the Beautiful Forevers, went deeper, exploring the mechanisms of entrepreneurship and exploitation in India. However, there is also a more positive side to this story that often goes uncommented on. An efficient recycling system has a long-term positive effect on society as a whole, and is also something that North America and Europe generally lack. That is a significant part of what the trash economy in India is- an informal recycling system.

Who is right: Clifford Asness or Warren Buffet?

In a Wall Street Journal piece this morning, a man named Clifford Asness says that Warren Buffet is wrong when he says the impact of taxes on investment decisions is very small.  His argument:

Consider how every business-school student, investment banker and investment analyst on Earth has been taught to choose whether to invest in a specific project or company. You make a spreadsheet (a napkin will do sometimes). You put in your best guess of the future cash flows, and you discount those cash flows back to the present at some required rate of return you believe reflects the risk entailed. Of course, opinions about the future cash flows and the proper discount rate can vary widely, but the essential methodology is ubiquitous.

Now here's the kicker: Nobody who pays taxes and has ever done this exercise has failed (while sober) to use after-tax cash flows in this calculation. Somewhere in the spreadsheet there is a number, say 20%, or 28%, or a Gallic 75%, representing the taxes you'll pay on the assumed cash flow—and you only count the amount you'll get after paying this tax. If you turn the tax rate up high enough, projects or companies that looked like good investments become much less attractive and vice versa.

Here is the problem with this argument--it focuses on the numerator of the discounted cash flow calculation, but not the denominator.  The denominator contains the discount rate, which is the opportunity cost of capital.  One can do an analysis based on before tax cash flows, in which case the denominator is the before tax OCC.  The formula for before tax cash flow valuation is

Where CF is cash flow subscripted by time t,  r is the discount rate, and E is the expectations operator.

But if one is going to take taxes out of the denominator, he must also take it out of the numerator.  This means the ATDCF formula needs to be

The greek letter τ is the marginal income tax rate.  If we examine this formula, we see that for small t, value does in fact decline with an increase in taxes.  But now let us approximate a long term investment by looking at the perpetual annuity formula--one that has a constant cash flow for infinite t.

Now the formula for before tax valuation becomes:

Analogously, the formula for after tax valuation becomes:

Of course, the (1-τ) divides through, so the after tax and before tax values are the same.

But here is where I will add a kicker of my own: if it is really true that fiscal issues as creating uncertainty, resolving those issues should reduce the discount rate, and thus encourage investment.  People such as Mr. Asness should welcome greater certainty, and the investment opportunities it will doubtless induce.

Hannah Green in Thinkprogress on Renewable Energy in India

She writes:

This August, power shortages in India that left 300 million in the dark made it very clear that one of the world’s fastest growing economies was facing an energy crisis. Less clear is how realistically to solve it. Many firms are looking for new sources of oil to fulfill India’s growing energy demands, but this could prove to be painfully expensive.  On the brighter side, solar energy and other renewable resources are already being rapidly harnessed in the non-Western world, and they are becoming cheaper and cheaper.
As of June 2012, 31 percent of India’s energy came from renewable resources, including hydroelectric power, while only 9 percent of the United States’ did as of the end of 2011. In a 2009 McKinsey & Company survey, India was rated the top producer of solar energy in the world, just above the United States, with an annual yield of 1,700 to 1,900 kilowatt hours per kilowatt peak (kWh/KWp). However, demand for energy in India will only continue to grow, and the question is whether energy will continue to come mainly from fossil fuels or from renewable energy sources...

The housing cycle is the business cycle--again

Ed Leamer said so.  I said so.  And I continue to think it so.

Run a simple bi-directional Granger Causality model of change in residential investment and GDP.  It turns out a model with one and three lags best fits the data going back to 1969.  That model's four quarter forecast for GDP growth is 2.6, 2.5, 2.1 and 2.5 percent; for residential investment growth is 6.2, 5.0, 4.9 and 4.9 percent.  (BTW, the model passes the stationarity test).

But residential investment has grown by between 8.5 and 20 percent over the past four quarters.  Let's say that an exogenous shock (kids moving out of their parents' houses) leads residential investment to grow by 10 percent.  The forecast for GDP growth now increases to 2.6, 2.9, 2.6 and 2.9, or about .4 percentage points higher than the baseline case.  This increase in GDP reflects more than the direct impact of residential investment on GDP.

What is Apple's objective function?

Walter Isaacson's biography of Steve Jobs is a lot of fun--at least in part because it is not a hagiography.

One of the most striking things about the book is that Jobs never pushed profit maximization per se--he pushed "great products."  When John Scully pushed out Jobs and ran the company, he did push profit maximization--and Apple nearly went out of business.  Re-enter Jobs with his products-first philosophy, and Apple eventually becomes the most valuable company in history.

When economists model firms, we inevitably assume profit maximization, and then allow firms to compete either through price or quality.  The exception to this is a principal-agent set-up, where managers are seeking to maximize their own compensation.  But this doesn't really work for Apple, where Jobs was both a principal and an agent.

Maybe none of this matters--that making great products is a sufficiently strong proxy for profit maximization.  But Job's desire to make great products led him to care a lot less about cost minimization than, say, Dell--the chapter on how fanatical Jobs was about the plastic case molding for the original Macintosh underscores how Jobs tended not to think about marginal revenue and marginal cost when making decisions.

It turns out Harry Hopkins didn't say it

After Mitt Romney's "gifts" comments, I couldn't help but remember that I thought FDR advisor and WPA director Harry Hopkins said "we shall tax and tax, and spend and spend, and elect and elect."  But it turns out this is likely apocryphal--indeed, Hopkins denied having said any such thing.

Here is a nice chronology from Bartleby:

AUTHOR:	Harry Lloyd Hopkins (1890–1946)
QUOTATION:	We shall tax and tax, and spend and spend, and elect and elect.
ATTRIBUTION:	Attributed to HARRY L. HOPKINS, administrator of the Works Progress Administration.   Although Frank R. Kent mentioned the subject of “spending, taxes, and election” in reference to Hopkins in his column, “The Great Game of Politics” (Baltimore, Maryland, Sun, September 25, 1938, pp. 1, 16) he first attributed “we are going to spend and spend and spend, and tax and tax and tax, and elect and elect and elect” to Hopkins in the Sun, October 14, 1938, p. 15.   Joseph Alsop and Robert Kintner in their column, “The Capital Parade” (Washington, D.C., Evening Star, November 9, 1938, p. A–11), elaborated Hopkins’s “probably apocryphal” words to: “Now, get this through your head. We’re going to spend and spend and spend, and tax and tax and tax, and re-elect and re-elect and re-elect, until you’re dead or forgotten.”   Arthur Krock, in his column, “In the Nation” (The New York Times,November 10, 1938, p. 26), reported the wording as “we will spend and spend, and tax and tax, and elect and elect.” He also repeated this wording in an article in The New York Times, November 13, 1938, sec. 4, p. E–3. A letter by Hopkins denying this attributed quotation and a response by Krock were published in The New York Times, November 24, 1938, p. 26.   Over the years the quotation attributed to Hopkins has evolved into the wording above.

Karen Chapple on the most reasonable way to create affordable housing

Housers need to listen to this:

The myth that taxes are too complicated for the typical American

I was listening to David Walker on the radio this morning, and he was going on about how tax preparation is too complicated for the vast majority of Americans.  This didn't seem right to me, so I went to the IRS SOI data Table 1.2 to see how many American's qualified for the 1040A return (a two-page form) or the 1040EZ return (a one page form).

The answer: of the 140 million tax returns filed in 2009, 90 million were filed by taxpayers that had adjusted gross income of less than $100,000 and that used the standard deduction.  These taxpayers qualify for using the 1040A or1040EZ.  So for more than 3/5 of US taxpayers, filing is not complicated at all.

Is the tax code too complicated for the other 50 million and for corporations?  Almost certainly.  But it is not a problem that afflicts the "vast majority" of Americans.

[update: according to this source, 32 percent of filers use 1040A or 1040EZ]

Mark Thoma suggests that Sheila Bair could be the next Treasury Secretary

He talks about the Fed and Treasury here.  Bair would be a superb choice.

Coastlines and votes

President Obama did better on the coasts and the Great Lakes states than elsewhere.  I thought it would be fun to plot coastline/shoreline miles by state against Obama vote percentage in 2012.  Here is what I got:

The data on coastline/shoreline come from http://www.michigan.gov/deq/0,4561,7-135-3313_3677-15959--,00.html and The Statistical Abstract of the United States, Table 364.  Vote totals come from Dave Leip's Atlas of Presidential Elections.  The correlation is .22, so not huge, but not nothing either.

If one adds Alaska, with its 6000+ miles of coastline and support of Romney, the correlation goes to zero.

Who is doing the shopping?

I was listening to a retailer last week discuss the interaction between housewives and grocery stores.  The tone of his remarks suggested that he thought housewives were grocery stores' principal customers.

This didn't seem right to me, so I tabulated the Family Type and Employment variable in the 2006-2010 sample of the American Community Sample (having a laptop with flash memory is pretty awesome--it allowed me to do it in about five minutes).

Here are the results:


Household Type                                           # of Households         % 0f Households

Married Couple, both in labor force|           22,309,285                           41.16      
Married Couple, only man in labor force      8,792,744                           16.22      
Married Couple, only woman in labor force 2,933,758                            5.41      
Married Couple, neither in labor force          6,473,742                          11.94      
Male only, in labor force                               2,848,830                            5.26      
Male only, not in labor force                            720,066                            1.33      
Female only, in labor force                            7,230,003                          13.34      
Female only, not in labor force                       2,890,776                           5.33    

I am guessing that most retailers know and understand the implications of a country where only 16 percent of households have housewives (in the traditional sense of the word), but perhaps they are not.

I am not thrilled...

..that President Obama has made Tim Geithner the point person for budget negotiations. I very much hope he doesn't negotiate away the President's strong position.

Remarks to USC Alumni Association

Another thought on Nate Silver

If poll errors are randomly distributed across states, then Obama has it won.  But if they are not, Romney still had a chance.   If how voters break is one state relative to polls is correlated with how they break in others, then if they break toward Obama, it makes no difference to the ultimate win-lose outcome; but if they break toward Romney, it does make a difference.

So statistical independence in errors across polls is good for Obama; correlation is bad for him.

I was wondering about Nate Silver's confidence intervals.

There is a nice discussion here.

More detail on the MID and House Prices (long and wonky)

Capozza, Hendershott and Green (1997) developed a model of determining whether federal tax policy would be capitalized into house prices.  The foundation for their analysis was an estimating of the user cost model of housing.  In the user cost model, in equilibrium, the costs of owning and renting the same house must be the same.  This means that:

Rent = Value*(after tax cost of capital + property tax rate + maintenance rate – expected house price growth).

After tax cost of capital is a blend of return on equity and the cost of debt, taking into account tax preferences.  The equity return to homeowner is imputed rent (i.e., the rent the homeowner pays herself).  Because imputed rent is not taxed, it receives a tax preference.  The return to debt—mortgage interest—also receives a tax preference in the tax code, at least for homeowners who itemize their deductions (only about half of homeowners are itemizers).

The effective property tax rate facing owners is the ad valorem rate less the tax preference.  Expected house price growth and maintenance are difficult to observe, but we will model them using a method described below.

We may rewrite the equation above to produce the foundation for an estimating equation:

Rent/Price = R*(1-ty)+PT*(1-ty)+M-π.

We estimate

R/P = α + β1*R*(1-ty) + β2*)T(1-ty) + MSAi + T + ε

Where R/P is the rent to price ratio, the α soaks up maintenance costs, R is an interest rate, ty is the marginal tax rate for those taking the mortage interest deduction, PT is the ad valorem property tax rate, MSAi are MSA fixed effects, which proxies for price expectations, T is a time fixed effect, and ε is a residual.

When Capozza, Green and Hendershott estimated an equation similar to (X), they found B1 and B2 were not statistically different from one, which is the prediction of the model.  From this, they concluded that taxes do get capitalized into house prices, and ran simulations based on that conclusion.

The most recent data available in CGH was the 1990 census.  The American Community Survey will allow us to do a much more timely estimate.

Data

We use the most recent-five year American Community Survey to find mean rents and mean house prices for 255 metropolitan areas in the United States.  The smallest sample we have among these MSAs is 1912 observations over five years, so we have sufficiently large samples to draw inferences about mean values and prices.

For the before tax cost of capital, we use the Freddie Mac 30-year fixed interest rate series.  For average marginal tax rates by state, we use the results produced by the NBER TAXSIM web site, which gives the average marginal rate of those who use the mortgage interest deduction and the average marginal rate of those who use the property tax deduction.  NBER TAXSIM gives estimates by state and by year; for those MSAs in more than one state, we take the population weighted average of the TAXSIM rates.

It is worth spending a little time discussing the TAXSIM data.  It contains a number of surprising, including the fact that the average total state and federal marginal tax rate for California among those taking the deduction was only slightly higher than for Texas.  This is surprising because (1) California has a state marginal top tax bracket of xx percent, while Texas has no state income taxes and (2) nominal incomes in California are on average higher than in Texas.

I conferred with Dan Feenberg, who runs the NBER model, to make sure I was interpreting the data correctly, and be confirmed that I was.  The following might explain why we see the peculiar data phenomenon.

California relied very heavily on subprime lending, while Texas, owing to its heavily regulated mortgage market, did not.  Subprime lenders specifically targeted minority borrower and lower income borrowers—they also originated loans for borrowers who self reported their incomes.  Because California has a high state income tax, and because mortgages were large, borrowers in low tax Federal brackets in California had an incentive to itemize; those in Texas did not.   

As we shall see below, we have difficulty finding a relationship between the after tax cost of capital and house prices.  We present our regression results below.

Regressions

We begin by presenting rent-to-price ratios.  

We will show four sets of regressions: simple linear regressions with year fixed effects that are both population weighted and non-population weighted; linear regressions for each year individually, and panel regressions.  Let us begin with a set of “base” regressions, where the rent-to-value ratio is explained by the after tax cost of capital (atcc1) and the “after-tax” property tax rate (ptrate1). 

Specifications (1) and (3) include dummy variables for years; (1) and (2) treats each MSA as an equal observation, while (3) and (4) weight MSAs by population.

	(1)	(2)	(3)	(4)
	Unweighted	Unweighted	Weighted	Weighted
atcc1	-0.190***	0.266	-0.226***	1.191***
	(-3.60)	(1.30)	(-4.12)	(4.73)
ptrate1	0.965***	0.954***	1.018***	0.985***
	(13.75)	(13.58)	(13.0)	(12.7)
y1		-0.00584*		-0.0195***
		(-2.02)		(-5.59)
y2		-0.00708*		-0.0196***
		(-2.53)		(-5.79)
y3		-0.00636**		-0.0161***
		(-2.68)		(-5.66)
y4		-0.00227*		-0.00500***
		(-1.99)		(-4.06)
_cons	0.0488***	0.0325***	0.0430***	-0.00917
	(19.02)	(4.21)	(15.7)	(-0.97)
N	1275	1275	1275	1275

t statistics in parentheses

·      p < 0.05, ^** p < 0.01, ^*** p < 0.001

In equilibrium, the signs on both coefficients should be positive, and the magnitude of the coefficient should be one.  The property tax coefficient works quite nicely across all four specifications—it is statistically different from zero at the 99.9 percent level of confidence, and is quite close to zero.  The coefficients on after-tax cost of capital are another matter, however.  They are in two instances negative, and in one instance not different from zero.  The predicted result only occurs in specification (4).  While one might argue that this is the best specification, it also would amount to cherry picking to rely on it when the three others are so different.  It is thus worth investigating other regression techniques.

We next turn to panel techniques, where we allow the intercept of the regression to vary with MSA; this could reflect differences in expectations about house prices from one MSA to the next.  Now our after tax cost of capital is either not different from zero, or has the wrong sign.  Interestingly, property taxes now become even more important, and their magnitude is too large—it suggests full capitalization and then some.  This also does not comport with economic theory.

	(1)	(2)	(3)	(4)
	rvratio1	rvratio1	rvratio1	rvratio1
atcc1	-0.0618**	0.143	-0.144***	0.128
	(-3.07)	(1.25)	(-7.48)	(1.09)
ptrate	2.632***	2.713***	1.720***	1.782***
	(21.14)	(22.30)	(18.54)	(19.33)
y1		-0.00191		-0.00290
		(-1.23)		(-1.83)
y2		-0.00326*		-0.00422**
		(-2.17)		(-2.75)
y3		-0.00361**		-0.00418**
		(-2.88)		(-3.26)
y4		-0.00128**		-0.00151**
		(-2.77)		(-3.17)
_cons	0.0227***	0.0145**	0.0366***	0.0260***
	(11.10)	(3.17)	(20.95)	(5.67)
N	1275	1275	1275	1275

t statistics in parentheses

^* p < 0.05, ^** p < 0.01, ^*** p < 0.001

Finally, we run regressions separately for each year (both weighted and unweighted). 

Unweighted

	(2006)	(2007)	(2008)	(2009)	(2010)
	rvratio1	rvratio1	rvratio1	rvratio1	rvratio1
atcc1	-0.319	-0.992*	0.951	2.090***	1.529*
	(-0.87)	(-2.20)	(1.91)	(4.18)	(2.42)
ptrate1	1.322***	1.288***	1.006***	0.679***	0.590***
	(7.61)	(7.95)	(6.62)	(4.87)	(4.02)
_cons	0.0532**	0.0859***	-0.00737	-0.0415*	-0.0113
	(2.85)	(3.83)	(-0.31)	(-2.03)	(-0.48)
N	255	255	255	255	255

t statistics in parentheses

^* p < 0.05, ^** p < 0.01, ^*** p < 0.001

Weighted by Population

	(2006)	(2007)	(2008)	(2009)	(2010)
	rvratio1	rvratio1	rvratio1	rvratio1	rvratio1
atcc1	0.355	-0.967	2.045***	4.137***	4.145***
	(0.81)	(-1.79)	(3.34)	(6.70)	(5.38)
ptrate1	1.423***	1.343***	0.998***	0.643***	0.604***
	(7.62)	(7.76)	(5.88)	(4.11)	(3.80)
_cons	0.00997	0.0769**	-0.0666*	-0.131***	-0.116***
	(0.45)	(2.84)	(-2.25)	(-5.18)	(-4.01)
N	255	255	255	255	255

t statistics in parentheses

^* p < 0.05, ^** p < 0.01, ^*** p < 0.001

To say the coefficient on the after tax cost of capital are unstable is an understatement.  The series of regressions listed above suggest that we cannot currently reliably estimate the impact of changing the tax treatment of mortgage interest on house prices.