As the months of housing pain have turned into very long years, the increasingly persistent "Are we there yet?" refrain from the media and homeowners is understandable, but the answer is still no. We have not reached the bottom of the housing market.

There has certainly been welcome news over the past weeks. Thanks to the Federal Reserve Chairman Ben Bernanke, interest rates remain at historical lows, with 30-year fixed rate mortgages hitting a mind blowing 3.67 percent earlier this month. In slightly related news, housing "affordability" metrics are at record highs. Combined, these two factors have households flooding banks with mortgage applications.

It is somewhat naïve to conclude from this that housing is back. (Unless you live in the greater Washington D.C. area where construction is booming like its 2005.) Just this week the Federal Housing Finance Agency reported to congress that Fannie Mae and Freddie Mac are still in "critical condition" because of poor performance and the legacy of their bad loans in the last decade.

Three months ago I outlined in this space reasons why we are not seeing a recovery yet. A surge in housing over the past quarter contradicting these claims would have helped start lifting Fannie and Freddie out of their mire (subsequently taking a lot of pressure off taxpayers), but unfortunately the reality has not changed.

Part of the challenge in this debate is how a recovery is defined. I argue that it will be when foreclosures have been worked out of the system, negative equity is cleared away, and prices have stabilized. By that standard, we still do not have a housing recovery.

To back up this claim, let's consider the strongest arguments that we are witnessing a housing recovery to see if they stand up to the long-term analysis.

Argument #1: With record low interest rates everyone will be looking to get back into homeownership.

The Federal government's goal of lowering long-term rates has been successful. Led by the Federal Reserve's quantitative easing program and the Treasury's continued bailouts for Fannie and Freddie, mortgage rates are lower than ever before. Unfortunately, low rates do not always translate into demand.

There have actually been "record" low rates for several years now, but the cheapness of a mortgage is only one factor in the home-buying process. Consider while mortgage applications are up with super low rates, nearly four out of five of those have been for refinancing, not home purchases. That is because household debt is still a massive deadweight on the capacity of families to buy a new home. At the same time, household wealth has been crushed over the past few years. Refinancing is not recovery, and low rates are not a sign of a positive future.

Argument #2: Housing starts and sales of new and existing homes all went up in April and May.

Optimists might respond to the points above by pointing out that housing starts jumped 2.6 percent in April and sales of new homes increased 3.3 percent the same month. Not only that, but existing homes came off the market in April at a rate of 3.4 percent, up 10 percent from last year.

But you know what else has been increasing? Foreclosures.

Data released this week shows that foreclosures have increased to a rate of more than 200,000 a year, an increase of 9 percent from April to May. This means that as much as increased demand is reducing inventories, the banks finally getting through their backlog of delinquencies will keep adding to the pile.

The shadow inventory still has millions of homes to clear away, and this means that prices will likely continue falling for the next several years, even if at a slow rate. Falling prices and continued foreclosure rates don't qualify as a recovery, no matter how many homes people are buying relative to previous months.

Argument #3: The historically positive correlation between the Wells Fargo Housing Market Index (HMI) and Case-Shiller Housing Price Index suggests we are heading into recovery.

Wells Fargo publishes an index charting the demand for new homes. Albert Sung points out at SeekingAlpha that this HMI is a leading indicator for where housing prices will go. The HMI fell in 2006 and Case-Shiller declined in 2007. The same thing happened in 1989 and 1991. In a vacuum this analysis could be right. However, demand for new homes does not a recovery make.

We had a massive oversupply of new homes built in the middle of the last decade that have taken a while to sell. There are plenty left in Las Vegas if you're in the market for an unlived-in-house, but the inventory of new homes is about the lowest level on record (going back to 1963). Naturally the HMI would register an increase in demand for new homes from here. But at the same time there are waves of foreclosures that are putting downward pressure on housing prices. And let's not forget that interest rates can basically only go up from a 3 percent to 4 percent range, so the future is full of downward pressure on housing prices.

Demand for new homes is not the benchmark for recovery, so reaching a bottom on the HMI is also not the bottom of the housing market. The reality is that this recovery will be different than those in the past, and there is going to be a significant gap between when the Housing Market Index climbs and when Case-Shiller prices follow it.

Argument #4: Homebuilder profits are up, leading to improved builder sentiment

The argument for happier builders is prominently preached by real estate analyst Lou Basenese, who pointed out last month that the top two American homebuilders—D.R. Horton and Lennar Corp.—have been crushing their earnings estimates. He then suggests that the increasing HMI reading (see Argument #3) indicates improving builder sentiment. The problem is that someone forgot to tell the builders they are feeling good about the housing market.

Construction companies have been voicing their negative sentiment with their wallets and shedding jobs— about 50,000 since January. You would think will all that positive sentiment that builders would be gearing up for their great summer. But in fact, according to the Bureau of Labor Statistics, nearly 30,000 of those construction jobs dropped this year were lost in May, right when the housing market was supposedly taking off again.

So where are we on this long road to recovery, if we are not there yet?

Start with the fact that outstanding household mortgage debt is still twice the level it was in 2000. And add to that that one in five homes are still worth less than the mortgage that was taken out to buy it. Combined you get very limited amounts of money for buying new homes at this moment.

Next, consider that mortgage rates will be going up in the future (though when is anyone's guess), meaning it will cost more to get a mortgage and that housing prices will be pushed down by decreased demand. CoreLogic reports the shadow inventory has fallen to 1.5 million homes. Some would say the figure is much higher but even at that level there is still substantial pressure on housing prices.

As I wrote back in March, the limited money for housing and subsequent low price for housing is not necessarily a bad thing. However, as prices fall underwater housing situations get work or homes that were in positive equity slip into negative equity, and that puts increased pressure on the fact that homeowners still have a lot of debt.

In addition to the limited money and falling prices, add on the continued woes for the labor market. Unemployment impacts the ability of families to afford homes, and in particular as the unemployment rate for college graduates remains high, it will translate to fewer than normal buyers of homes in the coming years, also negatively impacting the sector.

Finally, don't forget that historically, housing prices always go past their "historical norm" when declining from a bubble. The bubble has dissipated to the point that housing prices are about where they should be for today, but there is going to be an "over correction" with all the downward pressure on prices from limited demand and future foreclosures.

Even if you put the good news into this calculation, the result is still nothing close to a recovery. At best there is light at the end of the tunnel. That light is several years away, though. It is absurd to think that housing prices have reached their bottom. It is equally absurd to think that foreclosures and underwater debt will not create massive headaches for the years to come. Don't be deluded by a few positive stories. Stay buckled in, because destination recovery is still a ways down the road.

Anthony Randazzo is director of economic research at the Reason Foundation.