Went to a fairly interesting seminar last week. The presentation was on career switching, although it was really a career/job ladder model in which those who are more talented move up and those who are less talented move down. Matches the career switching data (at least in Denmark) although for me it raises the question of what the difference is between a job and a career. Successful engineers moving up to management (of other engineers) have switched careers in this model.
It seems to me that a model that is more successful in describing reality would have two dimensions. One dimension would be the "fit" of a job for a particular individual. That is, each individual has different interests and skills which will be matched differently by different (jobs? careers? occupations?) fields. Some will be math people, some medicine people, some construction people, etc. Young people just entering the labor force may have some idea what fits them best, but they learn a lot as they hold different jobs.
The second dimension would be a vertical dimension in which more capable people move up the ladder (in the field). The key would be that moving up the ladder would be a function both of overall ability (independent of field), but also the "fit" in the particular field.
If I went into the art field I might be allowed to clean the brushes, even if I have a reasonably high overall ability, because the field is such a bad fit for me. If I decided to teach math, I could probably rise to a semi-successful high school teacher. If I want to teach and research economics, perhaps I can rise a little higher because it's a better fit for me.
So how to do it? Well, each agent would have to have two describing statistics: field and ability. Let's say they're distributed between 0 and 1. The field could be a circle (i.e. it doesn't need to have a max and min). Say there are fields (each with one firm) distributed evenly around a Salope circle. Each has a ladder representing higher paying jobs in the field. The wage would then be a function both of the fit of the field and of ability.
Agents may or may not have any information about their field and ability when entering the labor market. After each job they learn more about each of those statistics, as do their employers. They (and their employers) have the option to move them up, move them down, keep them steady, or institute a search for a new field. If there's enough uncertainty and job search costs are high enough, most people will stay put. Those who have a good fit on the field but are on the margins in terms of ability will move up or down. Those who have a bad fit in the field will either quit or be fired.
This paper may have already been written. I feel like I've seen something like this, but I don't remember the model.
Wednesday, March 18, 2009
Tuesday, March 10, 2009
More on Housing
So apparently I'm not as original as I think. Nouriel Roubini has also suggested "breaking every mortgage contract."
Considering the fact that he's a lot smarter than I am, maybe we should take this idea seriously. But let's think about an asset other than houses to see if it clarifies the situation any.
Imagine that we all invest in gold. Whenever we want to save, we go to the goldsmith and buy a couple of nuggets. First, let's say we all pay cash for our gold. Now let's say there's a bubble in gold prices. I bought $50,000 worth of gold at the top of the bubble. But then the bubble burst, and now it's only worth $30,000.
There are really only two things that I can do. If I think the price is going to go back up, I can hold onto the gold and hope to sell it for more (than it's worth now) in the future. Or I can just sell it now and take the $20,000 loss. If it's clear that the gold only has an intrinsic value of $30,000, and I need the cash for whatever reason, then it makes sense to sell it now and realize I'm not the best precious metals investor in the world.
Now let's imagine that we all borrow the money to buy the gold. It's a loan backed by collateral, so that if we fail to make payments the bank comes and takes our nuggets. Maybe I bought the $50,000 worth of gold with $5,000 down and a $45,000 loan from my local bank. But now that gold is only worth $30,000 and I'm faced with a choice. I can keep paying the loan, or I can default. If I keep paying, then I will eventually pay much more for the gold than it is worth. If I default, the bank comes and takes my gold and I'm out $5,000. But in this case I'm out a lot less than if I had paid cash. The bank, on the other hand, now has $30,000 worth of gold that it can sell but faces a loss of $15,000 on the loan.
Now let's say the government steps in and "breaks every gold contract" so that the principal is reduced by however much the price has fallen. In our case, the price of gold has gone down by 40%. If the principal on the loan is reduced by this much, the new amount would be $27,000 and I would have $3,000 worth of "equity" in my gold. Now the bank will only go for this plan if the costs of seizing and selling the gold are larger than $3,000 ($30,000 - $27,000). Based on what I've read about the foreclosure process, it seems that costs are generally larger than 10% of the "true market value."
So as long as foreclosure costs are significant (larger than the average percent of the down payment), then the idea of reducing the principal on all mortgages will benefit everybody. Banks would prefer doing this only for mortgages with little to no equity on the original mortgage, but that doesn't seem like a politically feasible solution as it would benefit the least responsible borrowers.
The reason we need to do this is because we convinced ourselves that an asset that most people buy and all banks finance was worth more than it really was. The value was never there and now that we realize it, the only rational thing to do is rewrite all the loans that were based on the inflated value. The data to do this is out there. We can simply adjust every mortgage principal based on how much prices have fallen since the mortgage was written in that particular zip code.
Reducing the monthly payments for borrowers will only help people who plan on staying in their house for the entire length of the mortgage (then the difference between principal and interest is irrelevant). But for people who want or need to move, reducing the interest will have no effect. These people will still be faced with selling their house at some price less than their mortgage balance and either having to declare bankruptcy or coming up with the cash somehow.
The fact is, one of the main ways the country recovers from recession is for people who are unemployed or underemployed to move to areas that have jobs. If they are pinned to their house because they can't sell it for what they owe on their mortgage, then the recovery will take that much longer.
Remember, we had the same problem in the early stages of the Great Depression. In that case, the asset wasn't houses, but stocks. Individuals and banks were highly leveraged in their stock portfolios. When the stock market crashed and everybody received margin calls, the system blew up and thousands of banks went out of business over the next couple of years.
Considering the fact that he's a lot smarter than I am, maybe we should take this idea seriously. But let's think about an asset other than houses to see if it clarifies the situation any.
Imagine that we all invest in gold. Whenever we want to save, we go to the goldsmith and buy a couple of nuggets. First, let's say we all pay cash for our gold. Now let's say there's a bubble in gold prices. I bought $50,000 worth of gold at the top of the bubble. But then the bubble burst, and now it's only worth $30,000.
There are really only two things that I can do. If I think the price is going to go back up, I can hold onto the gold and hope to sell it for more (than it's worth now) in the future. Or I can just sell it now and take the $20,000 loss. If it's clear that the gold only has an intrinsic value of $30,000, and I need the cash for whatever reason, then it makes sense to sell it now and realize I'm not the best precious metals investor in the world.
Now let's imagine that we all borrow the money to buy the gold. It's a loan backed by collateral, so that if we fail to make payments the bank comes and takes our nuggets. Maybe I bought the $50,000 worth of gold with $5,000 down and a $45,000 loan from my local bank. But now that gold is only worth $30,000 and I'm faced with a choice. I can keep paying the loan, or I can default. If I keep paying, then I will eventually pay much more for the gold than it is worth. If I default, the bank comes and takes my gold and I'm out $5,000. But in this case I'm out a lot less than if I had paid cash. The bank, on the other hand, now has $30,000 worth of gold that it can sell but faces a loss of $15,000 on the loan.
Now let's say the government steps in and "breaks every gold contract" so that the principal is reduced by however much the price has fallen. In our case, the price of gold has gone down by 40%. If the principal on the loan is reduced by this much, the new amount would be $27,000 and I would have $3,000 worth of "equity" in my gold. Now the bank will only go for this plan if the costs of seizing and selling the gold are larger than $3,000 ($30,000 - $27,000). Based on what I've read about the foreclosure process, it seems that costs are generally larger than 10% of the "true market value."
So as long as foreclosure costs are significant (larger than the average percent of the down payment), then the idea of reducing the principal on all mortgages will benefit everybody. Banks would prefer doing this only for mortgages with little to no equity on the original mortgage, but that doesn't seem like a politically feasible solution as it would benefit the least responsible borrowers.
The reason we need to do this is because we convinced ourselves that an asset that most people buy and all banks finance was worth more than it really was. The value was never there and now that we realize it, the only rational thing to do is rewrite all the loans that were based on the inflated value. The data to do this is out there. We can simply adjust every mortgage principal based on how much prices have fallen since the mortgage was written in that particular zip code.
Reducing the monthly payments for borrowers will only help people who plan on staying in their house for the entire length of the mortgage (then the difference between principal and interest is irrelevant). But for people who want or need to move, reducing the interest will have no effect. These people will still be faced with selling their house at some price less than their mortgage balance and either having to declare bankruptcy or coming up with the cash somehow.
The fact is, one of the main ways the country recovers from recession is for people who are unemployed or underemployed to move to areas that have jobs. If they are pinned to their house because they can't sell it for what they owe on their mortgage, then the recovery will take that much longer.
Remember, we had the same problem in the early stages of the Great Depression. In that case, the asset wasn't houses, but stocks. Individuals and banks were highly leveraged in their stock portfolios. When the stock market crashed and everybody received margin calls, the system blew up and thousands of banks went out of business over the next couple of years.
Thursday, March 5, 2009
A Draft Solution to the Housing Crisis
The criticism leveled at the Obama administration's housing plan is that it does nothing to reduce the number of households that are (or will be) underwater (i.e. they owe more on their mortgage(s) then their houses are currently worth). It seems to me that there's an obvious reason that it doesn't do this. I can't see a lot of political support for reducing the principal owed by (especially subprime) many borrowers. I imagine there would be a lot of "Why should their mortgage principal be reduced because they paid too much for their house while mine stays the same because I (a) bought a smaller house and/or (b) put down a larger down payment so that even though my house has depreciated, I still have positive equity." And frankly, that's not a completely unreasonable opinion, right?
So what should we as a country do? What can we do? First, let's think about what happened during the housing bubble. Imagine there's a house with a true market value of $200,000 (i.e., the rent/buy ratio is around 1 at this price). Suppose it was bought 12 years ago at $200,000 by the Smiths. They lived in it for ten years and then sold it at the top of the market for $300,000 to the Johnsons. The Johnsons bought it with 5% down and a $285,000 mortgage. The mortgage was then packaged into a mortgage-backed security and sold to various investors.
The market has now corrected as the bubble has burst and the house is once again worth $200,000, leaving the Johnsons $85,000 under water. There's an $85,000 loss that has to be recognized by someone. It could be the Johnsons. The problem, of couse, is that most people who buy a $300,000 house don't have an extra $85,000 lying around. The only way they could end up paying the $85,000 is by paying off the mortgage, at least until the price got up to their mortgage balance. Another (market) option, is that the Johnsons walk away, mail the key to the bank who is then forced to foreclose and sell the house at a discount (probably significantly less than $200,000). The bond holders are then left holding the $85,000+ loss. We know they can swallow the loss because their asset simply has depreciated in value rather than creating a new liability (as it did for the Johnsons).
The problem with sticking the bond holders with the loss (as far as I understand it), is that most of these bond holders are large financial institutions. Reducing the value of their assets by a large amount (with lots of foreclosures) will put them under water (their assets will be less than their liabilities so that their capital will be negative or at least below the required amount for a bank to have) and they will be forced out of business or into receivership. If this happens to enough (or at least to large enough) banks, then the whole financial system seems likely to fail for the near future and we all lose. This is what happened in the Great Depression, combined with the fact that depositors lost their deposits when a bank closed.
So the losers are fairly clear: the Johnsons, the bond holders, and possibly everybody (represented here by the taxpayers).
The winners, in this case, are the Smiths, or are they? They received an extra $100,000 above the true market value when they sold their house. Of course, unless they were clever and decided to rent, they probably went and bought a $400,000 house that was really only worth $300,000 and have, therefore, lost that $100,000 they thought they made in the sale of their house.
When you look at it this way, you can see that there really are no winners here. Or if there are some, they are few and difficult to identify. For the most part our former selves were the winners and our current selves are the losers. The assets we thought we had have simply vanished because they were never truly there.
So what's the right policy? I have to agree with the critics of the Obama housing plan that point out that it doesn't do anything to solve the situation. The only way to truly solve the problem is to force the system to recognize all of the losses. The most fair way to do this is probably to write down ALL mortgages by however much real estate prices have fallen in that area (say by zip code) since the property was bought. This would involve trillions of dollars of loss for mortgage holders and MBS and derivative holders. However, for the most part, it's a loss that they've already recognized and may even be less. This would reduce foreclosures by getting everybody out from under water and would encourage investment in homes because people would no longer be facing losses. Reducing the principal and then allowing home owners to refinance at the current low rates would further help reduce foreclosures.
In our example, the Johnsons home depreciated by 1/3 from the time they bought it. Reducing their mortgage by 1/3 would drop it from $285,000 to $190,000. Their equity would have fallen from $15,000 to $10,000, but they would still have equity. Whoever owns the mortgage would face a loss of $95,000, but this is probably less than if the home went into foreclosure.
But what would happen for a "responsible" owner? Imagine the Miller family which bought a house for $250,000 with $50,000 down and a $200,000 mortgage. The house is now worth $220,000 meaning their equity has decreased from $50,000 to $30,000. In this case the value of their home has fallen by 12%. Reducing their mortgage principal by 12% would drop it to $176,000. Their equity would now be $44,000 (down $6,000 from the original but up $14,000 from current levels). The mortgage owner(s) would have seen its value drop $24,000.
There would be no direct cost to the taxpayer in this plan. The total cost to banks is hard for me to estimate. There's probably about $15 trillion worth of mortgage debt that would qualify. According to the Case-Shiller index, home prices are down almost 30% from their high, although they may have another 10-15 percentage points to go. That would mean that if everybody got their mortgage at the peak, the maximum write down of mortgage debt would be a little less than $5 trillion now or about $7 trillion if we wait for the bottom (we should probably only do this once). Of course, not everybody got their mortgage at the peak of the market, and regional markets have significant differences. The total write down would probably be between $3 and $5 trillion. It's a lot of money, but mortgage debt more than doubled between 2000 and 2007, so it's not a surprise.
Banks would probably fight this because it would reduce the value of the prime mortgages on their books that are unlikely to default. The question is, what would the net loss to banks be? They stand to gain something on subprime (and other) mortgages that will not now go into default. I would guess that the loss would be between $2 and $3 trillion. Unfortunately, that might put some of the larger banks under water (at least in terms of regulatory capital requirements). An injection of capital by the government for common shares would seem appropriate in this case as the government is forcing a reduction in the value of the banks assets.
Of course, that leaves the question of legality. This plan is probably not legal, and may even be unconstitutional. One option to force its acceptance would be to nationalize the major banks, take the write down, and then sell the banks to private investors. Hopefully, the banks would now be more attractive since the toxic assets currently on the books would have been mainly decontaminated.
Mortgage holders will be happy. Almost all will see an increase in their equity and a drop in the principal they owe on their mortgage. Renters will be pissed, so this would probably be a good time to eliminate the tax exemption for mortgage interest and give a one-time tax rebate to non-mortgage holders.
The plan should also help stabilize the real estate market by forcing home owners to recognize the fall in the value of their house. And it should help consumer spending by increasing the wealth of homeowners.
So what should we as a country do? What can we do? First, let's think about what happened during the housing bubble. Imagine there's a house with a true market value of $200,000 (i.e., the rent/buy ratio is around 1 at this price). Suppose it was bought 12 years ago at $200,000 by the Smiths. They lived in it for ten years and then sold it at the top of the market for $300,000 to the Johnsons. The Johnsons bought it with 5% down and a $285,000 mortgage. The mortgage was then packaged into a mortgage-backed security and sold to various investors.
The market has now corrected as the bubble has burst and the house is once again worth $200,000, leaving the Johnsons $85,000 under water. There's an $85,000 loss that has to be recognized by someone. It could be the Johnsons. The problem, of couse, is that most people who buy a $300,000 house don't have an extra $85,000 lying around. The only way they could end up paying the $85,000 is by paying off the mortgage, at least until the price got up to their mortgage balance. Another (market) option, is that the Johnsons walk away, mail the key to the bank who is then forced to foreclose and sell the house at a discount (probably significantly less than $200,000). The bond holders are then left holding the $85,000+ loss. We know they can swallow the loss because their asset simply has depreciated in value rather than creating a new liability (as it did for the Johnsons).
The problem with sticking the bond holders with the loss (as far as I understand it), is that most of these bond holders are large financial institutions. Reducing the value of their assets by a large amount (with lots of foreclosures) will put them under water (their assets will be less than their liabilities so that their capital will be negative or at least below the required amount for a bank to have) and they will be forced out of business or into receivership. If this happens to enough (or at least to large enough) banks, then the whole financial system seems likely to fail for the near future and we all lose. This is what happened in the Great Depression, combined with the fact that depositors lost their deposits when a bank closed.
So the losers are fairly clear: the Johnsons, the bond holders, and possibly everybody (represented here by the taxpayers).
The winners, in this case, are the Smiths, or are they? They received an extra $100,000 above the true market value when they sold their house. Of course, unless they were clever and decided to rent, they probably went and bought a $400,000 house that was really only worth $300,000 and have, therefore, lost that $100,000 they thought they made in the sale of their house.
When you look at it this way, you can see that there really are no winners here. Or if there are some, they are few and difficult to identify. For the most part our former selves were the winners and our current selves are the losers. The assets we thought we had have simply vanished because they were never truly there.
So what's the right policy? I have to agree with the critics of the Obama housing plan that point out that it doesn't do anything to solve the situation. The only way to truly solve the problem is to force the system to recognize all of the losses. The most fair way to do this is probably to write down ALL mortgages by however much real estate prices have fallen in that area (say by zip code) since the property was bought. This would involve trillions of dollars of loss for mortgage holders and MBS and derivative holders. However, for the most part, it's a loss that they've already recognized and may even be less. This would reduce foreclosures by getting everybody out from under water and would encourage investment in homes because people would no longer be facing losses. Reducing the principal and then allowing home owners to refinance at the current low rates would further help reduce foreclosures.
In our example, the Johnsons home depreciated by 1/3 from the time they bought it. Reducing their mortgage by 1/3 would drop it from $285,000 to $190,000. Their equity would have fallen from $15,000 to $10,000, but they would still have equity. Whoever owns the mortgage would face a loss of $95,000, but this is probably less than if the home went into foreclosure.
But what would happen for a "responsible" owner? Imagine the Miller family which bought a house for $250,000 with $50,000 down and a $200,000 mortgage. The house is now worth $220,000 meaning their equity has decreased from $50,000 to $30,000. In this case the value of their home has fallen by 12%. Reducing their mortgage principal by 12% would drop it to $176,000. Their equity would now be $44,000 (down $6,000 from the original but up $14,000 from current levels). The mortgage owner(s) would have seen its value drop $24,000.
There would be no direct cost to the taxpayer in this plan. The total cost to banks is hard for me to estimate. There's probably about $15 trillion worth of mortgage debt that would qualify. According to the Case-Shiller index, home prices are down almost 30% from their high, although they may have another 10-15 percentage points to go. That would mean that if everybody got their mortgage at the peak, the maximum write down of mortgage debt would be a little less than $5 trillion now or about $7 trillion if we wait for the bottom (we should probably only do this once). Of course, not everybody got their mortgage at the peak of the market, and regional markets have significant differences. The total write down would probably be between $3 and $5 trillion. It's a lot of money, but mortgage debt more than doubled between 2000 and 2007, so it's not a surprise.
Banks would probably fight this because it would reduce the value of the prime mortgages on their books that are unlikely to default. The question is, what would the net loss to banks be? They stand to gain something on subprime (and other) mortgages that will not now go into default. I would guess that the loss would be between $2 and $3 trillion. Unfortunately, that might put some of the larger banks under water (at least in terms of regulatory capital requirements). An injection of capital by the government for common shares would seem appropriate in this case as the government is forcing a reduction in the value of the banks assets.
Of course, that leaves the question of legality. This plan is probably not legal, and may even be unconstitutional. One option to force its acceptance would be to nationalize the major banks, take the write down, and then sell the banks to private investors. Hopefully, the banks would now be more attractive since the toxic assets currently on the books would have been mainly decontaminated.
Mortgage holders will be happy. Almost all will see an increase in their equity and a drop in the principal they owe on their mortgage. Renters will be pissed, so this would probably be a good time to eliminate the tax exemption for mortgage interest and give a one-time tax rebate to non-mortgage holders.
The plan should also help stabilize the real estate market by forcing home owners to recognize the fall in the value of their house. And it should help consumer spending by increasing the wealth of homeowners.
Endogenizing Sticky Prices in a Relationship Model
One of the main reasons that firms do not raise prices, according to survey data, is that they are worried about disrupting customer relationships. Yet I haven't seen a model that takes this seriously.
A successful model would have customers that buy one (or many goods) from a known retailer at some price p = (1+mu)*MC which is set by the retailer. The customers would have the option of buying from the retailer at price p or investing in a search at some some cost s to find a new retailer. The customer would have to form some expectation about the price other retailers are charging (some sort of information extraction problem).
The customer then is balancing the expected benefit of finding a lower price with the (known) cost of executing the search. The information available to the consumer might be some sort of productivity shock that affects the marginal cost for retailers in an idiosyncratic way.
The retailers, then, would face an idiosyncratic marginal cost (known only to them) and would choose the markup mu every period. The retailers would then balance the marginal benefit (or cost) from raising (or lowering) the price with the cost (or benefit) of losing (or gaining) customers. The intuition for sticky prices should be fairly clear. A small increase in marginal cost won't lead to a change in prices because it would lead to customers to leave and look for a new retailer. A small decrease in marginal cost won't lead to a drop in price because retailers would have nothing to gain.
There are other things that could (should) be considered in this type of model. Should retailers be able to advertise (gaining customers who are paying more) at some convex cost. This would add realism and would lead to price drops as well as price increases (I assume they wouldn't advertise price increases unless it represented a lower price compared to everybody else).
I could assume that customers have an idiosyncratic reservation price (i.e. they don't buy unless the price is less than their reservation price). Customers could only buy one unit so that retailers focus on gaining more customers rather than selling more to their current customers. The distribution of the reservation prices might be known so that retailers can form a conditional expectation of how much quantity would change if they changed their prices from p to p'.
A successful model would have customers that buy one (or many goods) from a known retailer at some price p = (1+mu)*MC which is set by the retailer. The customers would have the option of buying from the retailer at price p or investing in a search at some some cost s to find a new retailer. The customer would have to form some expectation about the price other retailers are charging (some sort of information extraction problem).
The customer then is balancing the expected benefit of finding a lower price with the (known) cost of executing the search. The information available to the consumer might be some sort of productivity shock that affects the marginal cost for retailers in an idiosyncratic way.
The retailers, then, would face an idiosyncratic marginal cost (known only to them) and would choose the markup mu every period. The retailers would then balance the marginal benefit (or cost) from raising (or lowering) the price with the cost (or benefit) of losing (or gaining) customers. The intuition for sticky prices should be fairly clear. A small increase in marginal cost won't lead to a change in prices because it would lead to customers to leave and look for a new retailer. A small decrease in marginal cost won't lead to a drop in price because retailers would have nothing to gain.
There are other things that could (should) be considered in this type of model. Should retailers be able to advertise (gaining customers who are paying more) at some convex cost. This would add realism and would lead to price drops as well as price increases (I assume they wouldn't advertise price increases unless it represented a lower price compared to everybody else).
I could assume that customers have an idiosyncratic reservation price (i.e. they don't buy unless the price is less than their reservation price). Customers could only buy one unit so that retailers focus on gaining more customers rather than selling more to their current customers. The distribution of the reservation prices might be known so that retailers can form a conditional expectation of how much quantity would change if they changed their prices from p to p'.
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