Believe those who are seeking the truth. Doubt those who find it. Andre Gide


Thursday, April 11, 2013

Monetary policy in a liquidity trap

Krugman has an interesting article today, Monetary Policy in a Liquidity Trap. I (sort of) agree with much of it. But I believe that a few comments are in order.

Consider this statement:
So, at this point America and Japan (and core Europe) are all in liquidity traps: private demand is so weak that even at a zero short-term interest rate spending falls far short of what would be needed for full employment. And interest rates can’t go below zero (except trivially for very short periods), because investors always have the option of simply holding cash.
This statement is, in varying degrees: [1] interpretative, [2] assertive, [3] misleading, and [4] wrong.

First, the quoted passage above suggests that a liquidity trap is the byproduct of "insufficient private demand," with the implication, of course, that more "public demand" is needed to rectify the situation. This may or may not be true. Regardless, the statement is [1], [2], and [3] above. Beware of economists making bald assertions.

Second, the statement is wrong in suggesting that our current liquidity trap is associated with zero nominal interest rates. Liquidity trap phenomena are much more general than this. And if you really want to further your understanding on this matter, please go read this piece by Steve Williamson: Liquidity Traps, Money, Inflation, and Bond Yields. As Steve says: this is not your grandma's liquidity trap.

In grandma's liquidity trap, the real interest rate is too high because of the zero lower bound. Steve argues that in our current liquidity trap, the real interest rate is too low, reflecting the huge world appetite for relatively safe assets like U.S. treasuries.

If this latter view is correct, then "corrective" measures like expanding G or increasing the inflation target are not addressing the fundamental economic problem: low real interest rates as the byproduct of real economic/political/financial factors.

Given these "real" problems, Steve's view is that the Fed is largely irrelevant. But he does assign hope to the Treasury: increase the supply of its securities to meet the world demand for them. I've been making similar arguments for some time now; for example, here.

Apart from all this, it will be interesting to see how the experiment in Japan plays out. Most of the massive purchases announced by the BOJ are for JGBs -- I'm really skeptical what sort of effect this should have (since the operation constitutes swaps of two assets that are close to perfect substitutes--although some purchases will take the form of higher risk assets--see Noah Smith on this). But what I think really does not matter--it is what market participants think--and the program does appear to be having some effect in financial markets.

Thank you, Japan, for this interesting experiment. Domo arigato, gozaimasu!

56 comments:

  1. In the post you linked to Steve wrote,

    "For now, the Fed can only monitor the economy for signs of a more serious inflation. Some of those signs may already be there, for example in currency growth, though it is hard to tell what is driving that."

    That was 2011. I guess the Fed's monitoring paid off since the serious inflation of the last few years hasn't worsened, though the signs remain ominous.

    If there's a shortage of U.S. treasuries (whatever that means), why doesn't the Fed sell some that it's hoarding? In fact, it could even sell more than it owns - short selling treasuries should present no difficulty for the Fed, right?

    ReplyDelete
    Replies
    1. There is something to be said wrt whether the Fed is helping matters by sucking highly-valued treasuries out of the economy. To the extent that interest-bearing reserves are close substitutes, however, it really doesn't matter.

      Delete
  2. Hi David,

    "the real interest rate is too low..."

    Too low relative to what? Relative to the natural rate of interest? Relative to the the internal rate of return on projects that the US government might invest in? Something else?

    ReplyDelete
    Replies
    1. Hi JP,

      I would say relative to the "natural" rate of interest. Take a look at Steve's recent AER piece:
      http://www.artsci.wustl.edu/~swilliam/papers/web%20page%20paper.pdf

      Delete
    2. No mention of the natural rate of interest in Steve's paper. Do you mean the rate of time preference?

      Steve doesn't like the natural rate of interest. Neither do you? You're embedding it in scare quotes.

      Delete
    3. I put the term in quotes because it seems to mean different things to different people.

      Yes, I meant the rate of time-preference. See Case (3) in his paper, page 8.

      Delete
    4. To add to the confusion, Brad DeLong is saying that the real interest rate is above the natural rate, opposite of you and Steve.

      Delete
    5. JP, let me tell you something that is different between me and that blowhard DeLong.

      I never said that the interest rate is below the natural rate. What I said was that if Steve's argument is correct, then...

      I have no friggin' idea where the "natural" rate of interest is. But DeLong, apparently, does. Good on him. There is an insatiable appetite for religion out there. Let DeLong supply it, and let the ignorant be comforted by it.

      Delete
    6. Point taken. We had this conversation a few years back. The natural rate is a theoretical object, not an empirical object.

      Delete
    7. This simply makes no sense. If, as you claim, the natural interest rate would indeed be above the actual one we wouldn't be in a depression. We'd be in a boom and the CB would have to lower interest rates to cool down the economy.

      Strange that academic economists can get something so very basic wrong.

      Delete
    8. "Natural rate" has a clear meaning. It's the equilibrium rate of interest if policy is optimal, within the class of feasible policies. That's exactly what it is in Woodford's world, for example. For him, the inefficiency is sticky prices, and monetary policy corrects that inefficiency (except a the zero lower bound, of course). For me, and I think David is more or less sympathetic, the inefficiency is due to something else.

      Delete
    9. Anonymous @ 9:23AM,

      Yes, it does make sense depending on the nature of the shock hitting the economy. A collapse in investment spending owing to binding credit constraints, for example, would produce said result.

      Delete
  3. David,
    Since Williamson believes QE has no influence on Treasury yields, then the low observed negative real rate must reflect the market's demand for "safe" assets. I'm not sure this view is compatible with other asset price movements. For instance, since 2010, the real rate has continued to decline even as the stock market has rallied to new highs. This implies that either 1) markets are segmented due to some inefficiency; or 2) the Fed, through QE and forward guidance, has reduced real Treasury rates. Since there is no evidence of 1), I'd say 2) has a good shot at being true. The mechanism at work may be any number of market inefficiencies (agency effects, mostly).

    I agree that the real rate may be "too low", but not because of a shortage of safe assets. Instead, the low real rate prevents structural adjustment necessary for the economy to experience a robust recovery.

    ReplyDelete
    Replies
    1. The Fed has probably contributed to lower Treasury yields, but keep in mind that the Fed only owns about 15% of outstanding Treasuries--to the majority of the demand is coming from somewhere else.

      As for your last point, I think I know what you mean. My colleague, Bill Gavin, argues basically that. There is a corresponding phenoemonon in the labor market, if the real wage does not adjust. Of course, wages and rental (interest) rates are related in a GE model. So if real wage is fixed, so is the rental (interest) rate. And vice-versa.

      On this latter point, see: http://andolfatto.blogspot.com/2010/11/wage-rigidities-and-jobless-recoveries.html

      Delete
  4. David,
    I'm curious why theory would point to a market-determined negative real rate caused by risk-aversion. Financial crises have been followed by: highly positive (Great Depression); modestly positive (Japan); modestly negative (U.S.) and highly negative (Latam) real rates. The independent variable in all cases was monetary policy, not risk tolerance.

    The question is important as its quite possible negative real rates will persist for years under current policy and assuming a continued weak recovery. To the extent this is a policy outcome, it may create significant distortions in the economy.

    ReplyDelete
    Replies
    1. Diego,

      I don't think that in any of those episodes there was such a huge international demand for the debt of a particular sovereign. Moreover, that same debt has served an exponentially increasing role as collateral in the rapidly growing repo and credit derivatives markets. US treasuries are king like never before. I'm not sure how swapping treasuries for interest-bearing reserves is supposed to do much of anything--you tell me.

      But I do, nevertheless, agree with your concluding paragraph. The issue definitely deserves further study.

      Delete
    2. I agree -- asset swaps for like assets do little. The question is whether QE/Forward guidance influences the real term premium in other ways besides expectations and the portfolio balances effects (both of which I mistrust). One answer is agency issues: money managers have an incentive to frontrun Fed QE. Additionally, the Fed is telling investors to put on duration bets as rate volatility is likely to stay low. All of these help depress nominal yields even as the Fed succeeds in creating inflation expectations. The result is a negative real term rate.

      Of course the above is hard to prove. However, no market-based explanation of the real rate can explain the divergence between Treasury and risk asset prices. So its a question of which thesis can have explanatory power. I maintain the "risk aversion" thesis cannot.

      Delete
    3. Diego,

      I am sympathetic to your comments. One thing to keep in mind, however, is that the term "safe asset" is not entirely descriptive of the role it plays in many models (and perhaps even in reality). More precisely, I like to think of these assets as "good collateral assets." Even in a world of no uncertainty, there can be a scarcity of such assets. Risk aversion does not play a role in generating low yields here.

      Delete
    4. David,
      Collateral is used by holders of s.t. liquid assets to disintermediate banks. Saying there is a "collateral shortage" is the same as saying "something is impeding bank maturity transformation". Whether that something is structural or cyclical is open to debate. A thought experiment: If bank capital ratios were raised to 20% immediately, and concurrently banks were forced to recognize losses on underwater mortgages, would there be a "collateral shortage"? Perhaps we should call it instead a "shortage of bank CEO's willing to dilute their shareholders"

      Delete
    5. Diego,

      Yes, exactly: "collateral shortage" = "something impeding bank maturity transformation" (or lending, in general). In the field, this something is a friction we call a "lack of commitment." I've wrote something on this here: http://andolfatto.blogspot.com/2010/08/asset-shortages-and-price-bubbles-new.html

      Yes, whether cyclical or structural, I'm not sure. Trust is a funny thing, it can come and go.

      In fact, we have the real world experiment of private label ABS disappearing altogether from the repo market in the crisis. Yes, this would exacerbate the shortage. Steve talks a bit about this too, see here: http://newmonetarism.blogspot.com/2013/04/liquidity-traps-and-low-real-rates.html

      Delete
    6. David,
      As I read your asset shortage piece, it struck me that it is nonbank-centric. We need collateral for payments. Except we don't, because banks traditionally intermediate between credit extension and liquidity provision. The problem is deposit "information sensitivity". This specific problem has existed in the past concurrent with highly positive real rates (Gorton himself gives the GD example).

      Delete
    7. Diego,

      That's right, the general argument applies more broadly to banks (narrowly defined) -- for example, the repo market. You say that the problem is "deposit information insensitivity." That is correct, except, I include the "deposit" of MBS as collateral for an overnight loan something analogous to a bank deposit. I think that Gary Gorton does too, if I am reading him correctly.

      In any case, I don't want to give the impression that I believe that this "asset scarcity" problem is the only or even main problem out there!

      Delete
  5. Silly me. I thought that people would want safe assets when economic conditions were so bad we were at the zero bound.

    You seem to be (maybe not) asserting that people started moving toward safe assets before we went to ground zero.

    Is that what you are asserting? If true, what was the time horizon for the movement. Did people start worrying about drone attacks, losing their guns, and losing their jobs to robots or some combination?

    And, you say nothing about the role of information, the fourth and most important factor or production.

    What are the time horizons of investors who start buying safe assets. And, how to we know?

    ReplyDelete
  6. Yesterday was a great day for the home team.

    First, the answer to our woes is Hamilton's Mercantilism.

    For countries following an innovative leader, the path is clear. Mercantilist policies of protection and subsidy have been effective instruments of an economically active state. In the US, the first profitable textile mills blatantly violated British patents. And ferociously entrepreneurial private enterprise was supported by a broad array of state investments, guarantees, and protective tariffs, in accordance with the “American System” inspired by Alexander Hamilton

    Read more at http://www.project-syndicate.org/commentary/china-and-the-frontiers-of-innovation-by-william-janeway#57ps8xkwWklxJ8tu.99

    Second, no doubt inspired by reading by comments above, Prof. Brad Delong delivers a knock out blow of ages, decking Williamson, Andolfatto, and Cowen with one simple swing.

    http://delong.typepad.com/sdj/2013/04/i-believe-tyler-cowen-is-simply-wrong.html

    There is some anon. troll here who always complains when I have to teach him (and other readers) economics. Add this to you to-do list: Resign.

    ReplyDelete
    Replies
    1. Random crank assertion =/= teaching, John. Maybe after you read some economics you can also consult a dictionary. Your arrogance is frankly astonishing.

      Delete
    2. My arrogance is well earned.

      Mercantilism drives the World baby. I started commenting as Hamilton when it became crystal clear that 97% of macro economists are wrong and fundamentally do not understand that it is a Hamilton/Keynes/Soros/Munger world.

      Even Cowen now admits China's Mercantilism has destroyed incomes here and in Europe.

      http://marginalrevolution.com/marginalrevolution/2013/04/another-way-of-thinking-about-the-european-economic-collapse.html

      Delete
  7. A further comment is necessary.

    The demand for safe assets is declining, for the price of Gold, of which the little three dream as the sole bench mark or standard, is down, well past a "correction."

    There is a developing bubble in tin foil

    ReplyDelete
    Replies
    1. "There is a developing bubble in tin foil"

      Well then your supply of hats should be quite valuable, John.

      Delete
    2. The reduced demand for gold does seem to indicate a reduced demand for safe assets. I would like to see an explanation for this contradiction.

      Delete
    3. My comment was intended to be ironic, as a pimp of the Gold Bugs Williamson, Cowen, and DA.

      My POV is that gold is not a save asset and is not an asset at all. Buying Gold is speculation, to the extent one can draw a line between investing and speculation.

      Zero Hedge says that is is market manipulation by Goldman Sachs (this would signal a rise in tin foil)

      You won't get an answer from David.

      My own explanation is that markets are irrational as explained by Soros and that when you have a President as bad as Obama, irrationality just boils over. It seems to me that when you have a President stupid enough to propose what he did on social security then it is time to really get scared about this ship going down for a second time.

      The confirming single is the consumer confidence and employment numbers.

      Williamson and DA need to re-read Keynes. In the long run we are all dead. What answers they discovery then will be wholly meaningless.

      Delete
    4. Steve J,

      First of all, the price of gold varies tremendously--it is not a safe asset.

      Second, gold is not widely used as collateral in support of credit arrangements, say, in the way that UST are.
      In this sense, UST are more "liquid" than gold. If really does not have much to do with riskiness.

      Delete
    5. David,

      Thanks for the reply. And that makes sense that gold might not be considered safe. I guess some people are learning that right now. I am still not sure about this idea that the interest rate is too low. Obviously the Fed has some impact on the rate but there are still a bunch of other buyers as well. Regardless it is an interesting idea to consider.

      Delete
  8. So increase the supply of USTs and then do what with the money? Maybe increase G? I don't see how what you wrote is an argument against fiscal stimulus.

    ReplyDelete
    Replies
    1. JS, cutting taxes is also an option. But I'm with Krugman, Kimball, and others, that now is a good time to invest in public infrastructure.

      Delete
    2. David, what if the Treasury just keeps the money under its pillow? Is the solution to too-low interest rates contingent on the Treasury doing something with the proceeds of newly issued Treasury bills? Does it have to reduce taxes and/or spend on infrastructure?

      Delete
    3. JP, great question.

      To be honest, I am not 100% sure. As always, I'd want to first study an explicit model to make sure I can keep the logic straight.

      But my intuition is that in some cases, the effect would work in the same way even if the Treasury simply held on to the cash. The general idea is, I think, that the additional supply of UST (or good collateral objects in general) somehow expands spending (for credit constrained agents).

      Let me work on trying to formalize this idea in a simple way.

      Delete
    4. Look forward to it. My intuition is the same. If Microsoft bonds gained a liquidity premium and Microsoft issued a bunch of bonds to satisfy that demand, the liquidity premium would shrink, even if it only kept the bonds at the bank.

      Delete
    5. ... even if it only kept the bond proceeds at the bank.

      Delete
  9. So I'm still confused. Sell more treasuries to drive the interest rate up and do what with the receipts? Spend it on infrustructure? And wouldn't that be classic fiscal stimulas?

    ReplyDelete
    Replies
    1. Melanie,

      There are many things that might be done with the revenues received via additional bond sales, including tax cuts or additional spending.

      But the additional Treasury supply might have an additional effect of stimulating investment demand. I know this sounds counterintuitive, but the basic idea is that with the availability of more good collateral assets (UST), credit constraints can be made to slacken, and this would have the effect of increasing spending together with real interest rates.

      I will try to follow up on this idea soon.

      Delete
    2. Melanie, I see that Steve Williamson has posted something that may be of some help:

      http://newmonetarism.blogspot.com/2013/04/liquidity-traps-and-low-real-rates.html

      Delete
  10. David,
    I am a biomedical research scientist and I must say your original comments were specious. You list 4 possible problems with Dr. Krugman's quote. As a scientist, I was expecting a list of reasons why you felt that. But then you provided nothing to support those claims. I am a smart, educated individual, who is good with numbers, data, etc., due to my training and my daily life, and am trying to find someone else who explains economics as well as Dr. Krugman. Saying something is wrong, interpretive or whatever, without clearly explaining why is unhelpful, at best, and intellectually misleading to those of us who want to hear well-reasoned debates on economic subjects.

    ReplyDelete
    Replies
    1. Anonymous,

      Thank you for stating your credentials.

      [1] Interpretive. All theories are interpretations. So there is nothing "wrong" with this. What I find wrong is the manner in which he presents his theory as if it is "the truth." I do not think we can afford to be so presumptive in economics. Perhaps things are different in the biomedical field, but strangely, I do not feel qualified to comment.

      [2] Assertive. Again, he is making unqualified claims. I've talked about this before. Things are not as simple as he is making them out to be. As a biomedical researcher, you might have some sympathy for why I feel this way.

      [3] Misleading. He is suggesting that the easy solution to the problems we face is more government spending. As I said above, this may or may not be true. Here is an example of what he suggests is false: http://ideas.repec.org/a/ime/imemes/v21y2003i4p1-20.html

      [4] Wrong. I linked to a supporting paper, published in the American Economic Review, one of the leading journals of the profession. What more do you want, man?

      Delete
    2. Noah Smith, Noah Opinion and George Soros and, if you have time, Pettis on China.

      It is all about China

      Delete
    3. You're welcome. The reason I stated my credentials is solely to let you know that a would not be scared off by numbers, or data, or something concrete to back up your claims.

      As for my comments:
      Explain why his interpretation is different from yours, if you have an interpretation worth sharing, and why. If someone has an interpretation, and says why they believe such, it is much stronger to weigh one vs. another.

      If one's position is correct and you are assertive, then you're right. If one's position is incorrect, and you are assertive about it, shame on you. But being assertive is not a problem of fact. If you disagree, you need to say why; you did not. If you don't like his tone, that's fair, but just say it. However, if he is correct, and your only problem is his tone, that seems trite.

      Again, if he is misleading, explain why you think so. Just saying he is misleading and not explaining why is intellectually dishonest. If you wish to refer to another's work, published in a respectable journal, then at least say why you support that data and feel Dr. Krugman's interpretation was misleading.

      Lastly, if I try and publish something that suggests someone else's position is wrong, I will try to convince you of it point by point by point. I would not say someone is wrong and then refer to another publication. If you really want to know what I would expect, it would be to add to the intellectual discourse. Just saying you agree with one side and don't with the other, just doesn't cut it, man.

      Joseph L. Messina, Ph.D.

      Delete
    4. Joseph,

      If you read my post carefully, which I doubt very much that you did, you'll see that I made the *conditional* statement "IF this latter view is correct, then..."

      I also said that what Krugman asserts "may or may not be true" (I can write down models where it is, and I can write down equally plausible models where it is not.)

      So your claim that "Just saying you agree with one side and don't with the other.." is just plain wrong. I hope that I have explain why it is wrong clearly enough for you.

      I think you do make a substantive point, however. I certainly could have explained myself much better. But you know, this is a blog, a part time activity, I've explained these things so many times in the past, and it's hard sometimes to realize that new readers are not familiar with the long history of the debate. I will try to do better on this front.

      Delete
  11. Andolfatto wrote:

    "I also said that what Krugman asserts "may or may not be true" (I can write down models where it is, and I can write down equally plausible models where it is not.)"

    And the academics wonder why the public is outraged by macro. These silly exercises where academics just keep changing such-and-such assumption in their models, arriving at different conclusions to never-ending back-and-forth avail, is madness. McCloskey is right: we need more inductive reasoning in macro, rather than these stupid deductive experiments, which only serve to cloud the discussion and prevent policy action.

    ReplyDelete
    Replies
    1. only serve to cloud the discussion

      1) this is intentional, but worse than you state. the intent is to hide root incompetence, which was revealed when none saw this Depression coming.

      2) there is a second reason. it is widely known in economics that only one national economic model creates jobs: mercantilism.

      however, none will admit such because they are all interested in lifting China from poverty rather than in what is best for the U.S. That, and they all are so dumb they think that Ricardo said something useful when he talked about comparative advantage, forgetting to mention that the U.S. is large enough that we do not need to trade to gain any benefit from the principle.

      Cowen, who is an implicit gold bug, alone with DA estimates that US income is down 8/10% due to China, since 2009

      http://marginalrevolution.com/marginalrevolution/2013/04/another-way-of-thinking-about-the-european-economic-collapse.html

      Keynes was emphatic that recovery by deficit spending by a country running a current account deficit was impossible; at best, what you do is tread water.

      economists know what to do:tariffs and other trade barriers here, deficit spending in China. They just will not admit that Hamilton's world economic view was right.

      http://www.project-syndicate.org/commentary/china-and-the-frontiers-of-innovation-by-william-janeway

      To the point, Hamilton was the Issac Newton of economics but economists will not admit what a Giant he truly was.

      Delete
    2. JSeydl:

      I think you have a fundamental misunderstanding of the philosophy of science. We take (imperfect) measurements and we offer interpretations (theories) of the data. Frequently, there are several equally plausible interpretations of the facts. More data is needed to weed out theories (or models) that make predictions inconsistent with the evidence. It is a slow go, given the limitations of data. If you think you can do better, you are welcome to join in the endeavor.

      @Alexander Hamilton: the intent is to hide root incompetence? This from a person who chooses to remain anonymous, critiquing a person who lays his ideas and opinions bare for public scrutiny? Sweet.

      Delete
    3. My identity doesn't matter, for my points are fundamental.

      My principle contribution is a theory of knowledge as the forth factor of production. Frankly, it is beyond your comprehension.

      You just made the argument that the real interest rate is too low.

      In making that argument did you consider, at all, that information is a substitute for capital.

      Consequently, interest rates are being driven down by knowledge. Did you consider that. Did you consider that their is no barrier to how low knowledge can drive interest rates?

      Look at the chart on Zero Hedge for the correlation between processor speed, since 1982, and interest rates. Or read Cowen on incomes falling 10% due to tech. If incomes fall 10% due to tech, how much does such imply that interest rates will fall? You have no answer. You never saw the question until I posed such, for you do not think in terms of information as a forth factor of production.

      What matters are a few very hard facts.

      1. Macro economists are incompetent, being wholly unable to foresee the coming of the present Depression.

      2. Macro economic policy is hard, much harder than people here will admit, for economic life is a confidence game. We just played a few quarters proving Obama, Summers, et al totally incompetent. Bernanke is also incompetent. People are people. The first book anyone should read on economics is La Russa's new book on coaching baseball, which is all about building confidence in the players. A macro model has to include confidence, but yours doesn't.

      3. There are only a few people to whom attention needs to be paid. Smith, Hamilton, Keynes, and Soros/Munger/Buffett.

      4. Hamilton and Keynes are the two that matter now. Hamilton accepted that only Mercantilism produces jobs and laid the conditions and foundations for a nation being successful at Mercantilism. Keynes (best explained by Pettis) was very plain that once you enter a Depression there is no way out---you can tread water---until you establish a current account surplus. That's what is confusing about WWII---it masks the current account surplus factor, but it is there.

      5. 97% of economists don't have the guts to propose Mercantilism because it doesn't promote harmony and peace. Sorry, but the Real World is brutally competitive and conflict is the permanent fact of life. Read. Col. John Boyd.

      Delete
  12. I just hope I never end up in Grandma's liquidity trap.

    ReplyDelete
  13. David,

    As I said, the alternative approach is in inductive reasoning. This means, among other things, that economists need to make better use of natural experiments and need a better grasp of economic history. It's a shame that we only have non-experimental data in macro, but we can do our best to tease out causality from natural experiments. For example, what was the affect on demand from austerity in 1937? How about on the east Asian economies in the late-1990s? Or what about on Europe today? Many economists are examining such developments for clues about fiscal policy, but we need more economists doing this type of work. If just half the macro guys who spend their time tweaking assumptions in thus-and-such DSGE model paid more attention to history, then the world would be in a better place.

    ReplyDelete
    Replies
    1. JSeydl,

      I agree that economists need to make better use of "natural" experiments. These are few and far between, however. And I do think the deductive approach is useful for exploring the likely properties of untried policies. So I think there is room for both approaches. And yes, I agree, I don't think most macroeconomists (including myself) have a sufficiently good grasp of economic history.

      Having said this, I'm not sure what motivated you to label what we are doing as "silly" exercises. This is the way science works--it's all part of the package. Thanks.

      Delete
  14. Have just encountered your page and I guess you should be complimented for this piece. More power to you!

    ReplyDelete
  15. make $19,659.60 per month
    don't miss this opportunity
    join now and get your free mastercard

    http://penny-matrix-system.blogspot.com

    For more information, contact me :

    Website : http://www.makemoneyleaders.com
    E-Mail : makemoneyleaders@hotmail.com
    Skype : makemoneyleaders

    ReplyDelete