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

Wednesday, November 23, 2011

Not enough U.S. debt?

One way to measure the ability to service debt is to compute a debt-to-income ratio. Suppose, for example, that your income is \$50K per year, that your home is worth \$200K, and that you have a \$150K mortgage. Then your debt-to-income ratio is 150/50 = 3; or 300%.

Similarly, one way to measure the ability of a country to service its national debt is to compute debt-to-GDP (a measure of domestic income) ratio. The ratio of U.S. federal debt to GDP is currently close to 100%.

Of course, what has a lot of people worried is not the level, but the trajectory, of this ratio. Clearly, the debt-to-GDP ratio cannot rise forever.

No, but on the other hand, there is some evidence to suggest that it can feasibly go much higher. (Whether it should be permitted to do so is a different question, of course.)

Before I go on, I want to clear up a misguided analogy that I frequently hear repeated. The misguided analogy is the idea of the government behaving like a household running up a massive amount of credit card debt.

If this is the way you like to think about things, let me ask you this: Which of your credit cards charge you 0% interest? I ask because that is the interest rate creditors around the world are willing to lend to the U.S. federal government. And what sort of credit card company starts to reduce the interest it charges on your debt as you become progressively more indebted (see the figure above)?

In fact, the terms are even much better than 0%. The real cost of borrowing is measured by the real (inflation adjusted) interest rate. As the figure above shows, the real cost of borrowing has plummeted over the last decade for the U.S. government. As the following figure shows, the U.S. government can now borrow funds for 10 years at close to zero real interest. It can borrow funds for 5 years at a negative real interest.

Now, a negative real rate of interest is a pretty cool deal. Imagine importing 100 bottles of beer from China today, and having to return only 99 bottles next year. If the interest rate remains unchanged one year from now, you can rollover your debt and make a profit. For example, you could borrow another 100 bottles of beer from China, use 99 of these bottles to pay off your maturing obligation, and then drink the remaining beer for free. (Of course, domestic beer brewers would become upset at the lack of demand for their own product, but maybe they can be bribed with free Chinese beer?)

Before we get too carried away, however, I explain here why these very low real rates constitute bad news.

Why are real rates so low?

My own view is that this phenomenon, at its root, has little to do with Federal Reserve or Treasury policy. I believe that the decline in real rates on U.S. treasuries reflects a steady change in how agents and agencies around the world want to structure their wealth portfolios. There has been a massive substitution away from many asset classes into U.S. treasuries; and it is this fundamental market force that is driving real interest rates lower.

The phenomenon began in the early 1990s, with the collapse of the Japanese stock market. Then Mexico in 1994, the Asian crisis 1997-98, Russia in 1998, and Brazil in 1999; see Bernanke (2005). Investors became rationally pessimistic about the returns to investing in these countries, as well as similar countries that had not yet experienced crisis. The natural effect of this would be capital outflows from these countries into relative safe havens, like the United States.

The basic thesis here is very much related to what Ricardo Caballero calls a "global asset shortage." See his discussion here and here; and my own discussion here and here.

The global investment collapse associated with the recent recession has pushed already low real rates lower still. There has been a flight to U.S. treasuries not only by foreigners, but this time by Americans too. Evidently, the perceived return to domestic capital spending remains low. (Some basic theory available here.)

Policy

Given this pessimistic outlook, it seems unclear what monetary policy can do (the Fed is largely limited to swapping low interest currency for low interest treasuries).

I do, however, believe that there may be a role for the U.S. treasury (in principle, at least). In particular, given the huge worldwide appetite for U.S. treasury debt (as reflected by absurdly low yields), this is the time to start accommodating this demand. Failure to do so at this time will only drive real rates lower. For a world economy that is reasonably expected to grow, negative real interest rates imply a dynamic inefficiency. In short, this is the time to start raising real rates, not lowering them (real rates theoretically rise when new debt crowds out private capital, but note that new debt can also be used to finance corporate tax cuts to stimulate investment, if so desired).

Of course, what theory also tells us is that the government should also be prepared to reverse this recommended debt expansion (assuming that tax rates remain unchanged) once the domestic and world economy return to normal. One may legitimately question whether the government can be expected to make these cuts at the appropriate time. If the government lacks credibility along this dimension (or if future governments cannot be expected to abide by policies put in place by previous governments), then political forces may emerge to block an otherwise socially desirable debt expansion. Perhaps this is one way to interpret recent events.

1. I don't think you need to encourage politicians to borrow. They can do that just fine all by themselves.

Btw, does the gross debt in the top graph include entitlement debts (e.g. social security)?

2. Prof J: Ha ha, yeah, I guess not. But then, what is your explanation for the 40 year long decline in the debt/GDP ratio? (I don't think this debt measure includes SS obligations.)

3. David,

I'm going to get back to you on your question. A quick graph of GDP and gross federal debt together, rather than as a ratio, indicates that GDP growth leads federal debt growth. But GDP includes government spending... so what's the right way to look at this? My initial thought is that government spending has been leading government borrowing, and that translates pretty much into a 1-to-1 relationship, although it would be a lagged relationship.

So... gotta do some serious drinking. I mean thinking.

4. "But then, what is your explanation for the 40 year long decline in the debt/GDP ratio?"

Invert the ratio and it gives you a measure of credit efficiency. The "bowl" shape of 1947-1980, inverted, becomes declining efficiency of credit.

Others observe that the a dollar of GDP increase requires N dollars of debt increase, where N is a growing number. They examine only *additions* to debt.

But all debt is credit-in-use.

5. I think I'm right in saying that the dynamic inefficiency argument only applies if the real interest rate is *permanently* below the real growth rate (Samuelson 195x)? Is that right? Because only if it's permanent can you run a stable Ponzi scheme.

For example, a temporary negative real interest rate because of baby boom demographics doesn't seem to imply dynamic inefficiency. The boomers in an OLG model want to lend to their kids, even at a negative r, but it's not obvious how an infinitely-lived government can solve this problem.

6. Shaka, when the walls fell.

7. Nick:

I'm not sure that the definition of dynamic inefficiency requires r < n permanently. If it does, then I have used language incorrectly.

In any case, the claim I want to make is that even if r < n is temporary, then the equilibrium is not Pareto optimal. The market rate of return is lower than the social rate of return. A temporary intervention by the government can (theoretically, at least) improve efficiency (by borrowing at the low rate, and investing at the high rate).

Your last paragraph is correct in the sense that if the negative interest is caused by a decline in n, then there is no dynamic inefficiency (as long as r >= n).

Personally, I find it hard to swallow than n = 0 ten years out for the USA. Surely, there are infrastructure projects that can yield in excess of zero percent? If not, then we're all in big trouble.

8. David: "In any case, the claim I want to make is that even if r < n is temporary, then the equilibrium is not Pareto optimal."

I'm not sure that's correct. Assume a stationary consumption economy. Assume monthly output of food is constant, the food is non-storeable, but people get hungrier in the Winter because of cold weather. So the 6 month real rate of interest could be negative in the Summer. People want to lend food so they can eat more in the Winter and less in the Summer.

Now, if the government had a storage technology, and people didn't, then sure it would be Pareto Improving for the government to use it, to buy food in the Summer and store it for the Winter. But that's what Steve Williamson would call a "chicken model" ;-)

9. "Personally, I find it hard to swallow than n = 0 ten years out for the USA. Surely, there are infrastructure projects that can yield in excess of zero percent? If not, then we're all in big trouble."

Yep. Agreed. You and Brad DeLong should pal up on this one ;-). He argues the same.

10. Positive NPV infrastructure projects probably won't help. But this fellow says it more eloquently than I do:

http://www.thefreemanonline.org/featured/the-infrastructure-delusion-getting-nowhere-faster/

11. I wouldn't argue with any of this post, but you should say something about what Treasury does with the dough. I suspect you intend for the them to hold dollars or a portfolio of currencies, as opposed to fiscal stimulus.

12. Its surprising to me to hear economists argue that negative real rates are a market outcome. The Fed controls inflation AND short term nominal rates. Right now, markets are predicting that the Fed will leave the overnight rate near zero for years (hence low nominal rates); and that it will continue to create inflation for years (hence low real rates).

In Japan, the same conditions that you argue are producing negative real rates produced consistently positive real rates. The difference was that the BOJ was willing to live with modest deflation.

The attempt to describe negative real rates as market outcomes stems, I think, from the desire to brand monetary policy today as being "too tight". The fact is, we have 3%+ inflation in much of the developed world, and this is why real rates are negative.

13. Nick:

The example you gave was of a preference shock driving the real rate negative. Fine, this is similar to the demographic shock you described earlier. But now imagine the same economy with a private storage technology. Imagine that the expected return to private storage drops temporarily (all sorts of reasons why). But suppose that population growth remains constant. Then intergenerational transfers may be Pareto improving (have to be careful here). And yes, I am assuming a chicken model in the sense that the government is assumed to have powers that the private sector does not (like taxation, for example). As for DeLong, my beef with him is not necessarily with his ideas; rather, it is with the certainty with which he holds them.

ProfJ: How does he know that there has been "overinvestment" in infrastructure? What supports his claim that a \$ spent on infrastructure crowds out \$ spent elsewhere? I can certainly write down *neoclassical* models where this is not the case. Having said this, the guy has a point. But we know (or are supposed to know) this. I provided a caveat at the end of this piece to this effect (i.e., that my recommended policy prescription depended on a level of commitment that may not exist).

Anonymous @ 6.59AM:

You are right. Implicitly I was assuming (I have an explicit mathematical model written down) that the treasury is gathering or rebating revenue via lump-sum taxes/transfers. In reality, of course, the treasury is charged with financing the program spending coming out of Congress and hence, may not have the control that I have assumed in my model.

14. Anonymous @7.15AM:

Its surprising to me to hear economists argue that negative real rates are a market outcome. The Fed controls inflation AND short term nominal rates.

You should not be so surprised.

The Fed may (under normal conditions) have influence on inflation over the medium to long term. But what is critical here are inflation expectations; and these expectations come from the market. While the Fed may control short term nominal rates, it has much less control over longer rates.

I am not sure why you believe that low real interest rates cannot be a market outcome. Certainly, we have plenty of models that can deliver this result. I like to think of fundamental market forces driving real interest rates lower, and policy as accommodating (more or less) what the market wants.

The motive you (implicitly) ascribe to me in your concluding paragraph is incorrect.

15. Inflation expectations are a market outcome based on predictions of what the Fed will do.

The Fed usually has less control over longer term rates. The exception is financial repression across the curve, which is occurring now.

Low real interest rates can be a market outcome; negative real interest rates are an artifact of policy. This is because the condition that would result in a market outcome of zero rates are also ones that would naturally result in deflation in the absence of central bank intervention. Examples: Japan and the 1930's.

A model that produces market-derived negative real rates must somehow ascribe to market participants expectations of future inflation, which the Fed controls. Perhaps a supply shock (oil) might otherwise produce this effect, but even then, the pass-through to general prices would have to be accommodated by the Fed.

16. "we have plenty of models that can deliver this result"

To be clear: models can produce equilibrium negative real rates. Getting to that equilibrium necessitates that market actors believe that the Fed can produce inflation. Is this a "market outcome", or a "policy outcome"? Perhaps its in the eye of the beholder.

17. I'm not convinced that you can use the yield, or own rate, on TIPS as an indication of what the economy-wide real rate of interest is.

Yes, the TIPS own-rate is currently negative. But there are all sorts of other potentially pecuniary and non-pecuniary yields provided by holding TIPS, including a liquidity yield and a prospective rental yield. Add these to the observed TIPS own-rate, and the expected return on holding TIPS could very well be positive. So why are observed TIPS own-rates so low? Perhaps because the other returns provided by TIPS are so high. But these are unobservable, which means we can't determine what the economy wide real rate of return is.

18. Anonymous (why can't people adopt handles?) @ 8.50AM:

Inflation expectations are a market outcome based on predictions of what the Fed will do.

You mean, based on the predictions of what the Fed is expected to do. But the Fed has a policy function that reacts to the way the economy unfolds. And so people will have to forecast how things unfold in general, and how the Fed may react to these developments, etc. It's a little more complicated than what you are suggesting.

Low real interest rates can be a market outcome; negative real interest rates are an artifact of policy. This is because the condition that would result in a market outcome of zero rates are also ones that would naturally result in deflation in the absence of central bank intervention. Examples: Japan and the 1930's.

OK, I think I know what you're saying (it is not a theoretical proposition, more like an empirical claim). But as for your example of Japan, I think you may have your facts wrong. Base money growth in Japan exploded in the 2000s, yet deflation persisted. See:

http://1.bp.blogspot.com/-Bl4XQnrc2c0/TdHo3r-rx1I/AAAAAAAAEj0/S9TjhU7rQMY/s400/Japan%2Bmonetary%2Bbase.PNG

19. David,

Enough economics for today - Happy Thanksgiving!

Jeff

20. Hi David,

It's hard to argue against undertaking projects with a positive NPV! But doing the C-BA gets us right back into current debates about macro. What discount rate should we use? Some of the textbooks say use the ROR of a project (with similar risk) that would be displaced. The question is: in the current circumstances, would any project be displaced?

Second question: if the project is undertaken, and if it doesn't displace other spending (investment or otherwise), should we count the net benefits that arise when the newly employed workers buy goods at prices that exceed the MC of production?

So, it seems that we're right back where we started: is there really any slack in the economy (I think there's a lot), and is there really a multiplier (I think there is)?

21. Greg:

Sure, those are always going to be difficult questions to answer. But for practical purposes, I would be happy with "second best" solutions. So, for example, conditional on the government supplying UI benefits to construction workers, why not have them rebuild something instead?

Jeff:

Yes, happy thanksgiving! Happy thanksgiving to all. I appreciate all the comments!

22. David, I don´t wnow if we can talk of negative interest rate using the Tb yields, because te private intereste rate show a huge gap compared to TB.
So, for example, in the graph below, where you can see that Baa private bonds yield is at 5%, at level more than 3 pp. above the 10 years TB, probably the higher gap since 1962. So the risk premia are in this case very much important that the level of TBy.
if Treasury rise the TBy, I suppose that private bonds yield will rise also.

23. Anonymous again. Really I'm asking how you get to equilibrium negative real rates without expectations of policy action. When there is no demand for marginal bank reserves and a large output gap exists, markets would not produce this result on their own. They would only do so if the Fed had credibility in raising the price level (which the BOJ did not).

BTW, I think you may be Canadian, but Happy Thanksgiving anyway, and thanks for a great blog.

24. The real question to ask is not whether domestic private borrowers are paying zero or near zero rates. (Actually some are, judging by the offers I receive.) Rather, it is whether they have a printing press in their basement that churns out dollars.

The US federal government is the monopoly provider of a non-convertible floating rate currency and is therefore not operationally constrained in creating the unit of account (although existing political restraints require issuance of Treasury securities in offset of deficits).

The federal government is the currency issuer and households, firms and US states are currency users. The federal government is not revenue constrained while all other users of dollars are revenue constrained. The relationship is inverse rather than direct. The government as big household analogy is just wrong.

The government fiscal balance, the domestic private balance, and the external balance sum to zero as a national accounting identity. If the domestic private sector and the external sector desire to save, then the government must run a corresponding deficit to accomodate this or the desired level of saving cannot be achieved. If the deficit is too small to accomodate the desire to save, then the sectoral balances will adjust by either forcing less saving and more indebtedness at the present output and investment, or less consumption and less output and investment. With consumer borrowing tapped out, the alternative is less consumption and lagging nominal aggregate demand relative to the performance ability of the economy.

Accordingly, the federal government therefore needs to run a larger deficit to offset saving desire by a mix of lowering taxes (extension of the payroll tax holiday) and increasing spending (infrastructure, extension of safety net) in order to stimulate NAD to close the output gap.

Given current rules, this would also result in an increase in the issuance of Treasury securities to supply market demand. But in your scenario, which only considers increased availability of Tsys, the Fed could simply sell some of its assets and reduce bank reserves. There is no longer an acute liquidity crisis preventing this course of action. However, the present stage of the crisis involves lagging demand, and that requires a fiscal remedy through increasing non-government net financial assets by adding to the deficit.

25. Ok. What are the possibilities that all of this changes if/when investors, fearing contagion, push the dollar over the cliff along with the Euro?

Unlikely yes, but some level of contagion from the EU is absolutely possible. That's a game changer.

26. What if net real global growth is from now on impossible, due to the fact of Peak Oil making the world economy energy constrained. Lack of growth makes debts more onerous with time, and is highly deflationary. Real interest rates should get more negative as the energy crunch worsens, since there will be a mad scramble for assets that provide a decent return OF capital (forget about a return on capital). Energy and food should get increasingly expensive with wild oscillations in price while everything else deflates. And this is exactly what has been happening.

27. Luis Arroyo: Good point. But still, the real borrowing cost for the US federal government remains very low. As for the private sector, you raise an excellent point. Let me reflect on this.

Anon@12.20PM: If you want, email me and I will send you a simple OLG model that I am currently working on. (And thanks for the compliment!)

Tom Hickey: I'm not sure I fully absorbed your argument. But let me say a few things. First, the US government is not the provider of currency; the Federal Reserve is. Second, while the Treasury may not be revenue constrained in a nominal sense, it is in a real sense (if inflation gets out of hand, they can print all the debt they want without being able to purchase anything with it--see Zimbabwe). Finally, I'm not sure that having the Fed sell of Treasuries will matter. This is because in doing so, they will effectively be purchasing interest-bearing money (reserves currently yield 25 basis points). This is just a swap of one form of debt for another that is a close substitute.

James Gilley: Push the USD and the Euro off a cliff...and where do investors turn to? Gold?

Anon@7.09AM: I have a hard time believing your opening conditioning statement. But if it is true, then what you describe subsequently is a plausible scenario.

28. David, have you read Warren Mosler's The Seven Deadly Innocent Fraud os Economic Policy? It would assist you in understanding what I am driving at about the need for a fiscal approach and why a fiscal approach in such circumstances is not at all likely to become inflationary.

BTW, the Fed creates bank reserves and distributes FRN to the banking system in exchange for reserves. As you know, reserves exist only no the FRS spreadsheet. Reserves created by the Fed do not directly affect the amount of non-government net financial assets and therefore do not directly affect NAD unless those reserves find their way into deposit accounts, either through bank loans or government expenditure. Only the Treasury acting on directives resulting from Congressional appropriations increases non-government NFA through deficit expenditure, since the deposits created by bank loans net to zero.

I really surprised to that you cite Zimbabwe. Surely you realize that the situation in Zimbabwe was nothing like the situation in the US, or anything the US or any developed country will ever experience. Weimar, too, was a special case. Both Weimar and Zimbabwe resulted from political issues affecting the economy. If you want to cite examples of inflation that might be relevant to the US, various Latin American inflations are more to the point. Inflation is a complex issue and Modern Monetary Theorists like Scott Fulwiller, Bill Mitchell, and Randy Wray have discussed it in detail. Basically, the quantity theory doesn't hold water. You might want to check out their work before citing Zimbabwe. See Bill Mitchell, Zimbabwe for hyperventilators 101. I think that before you dismiss fiscalism as potentially inflationary, you would serve yourself by examining what they have written in addressing such objections. It appears to me that you are being overly dismissive here.

However, I am happy to see that you seem to admit that the constraint in US policy is the availability of real resources and that inflation will occur if the US increases non-government NFA to the degree that effective demand grows beyond the ability of the economy to expand to meet it. Of course, supply constraints will produces a similar effect if they are broad and deep enough to result in a continuous rise in the price level.

29. Just to be clear, I am agreeing with the suggested policy to fund public infrastructure investment through deficit expenditure, which would under current rules involves issuance of Treasuries in offset, which seems in line with bond market appetite. What I am saying is that the operative reason has to do with fiscal policy, and neither "affordability" nor appetite for Tsys is the real issue.

Emphasizing affordability simply plays into the hands of the deficit-debt hawks by giving credence to the mistaken notion that the US is financially constrained when it is not. Accommodating the desire of the bond market is serving the wrong master.

The operative constraint, as David noted in his comment to me above, is potential inflation. With present level of idle resources that is not a problem and won't be for some time. But as the economy recovers tax revenue will increase, the automatic stabilization will decrease, and stimulus can be wound down as determined by the sectoral balances and iaw functional finance.

30. How big is the US public debt? 100 or 120 or 140 or more, taking into account State debt and Fannie and Agencies?

thank you

Mario

31. In a competitive economy, at least, dynamic efficiency can also be evaluated by comparing capital's share of output to the fraction of GDP used for capital formation. For the US, in the case of physical capital the numbers are roughly 30% and 15% respectively, implying dynamic efficiency. Given that much of what we call labor's share is really the share of human capital I'd guess that this condition also holds for human capital. I'm not sure how the failure of the competitive economy assumption would change things.

32. Mario: I'm afraid I don't have the numbers handy. But if one was to include state and local government debt, together with Fannie, Freddie, Social Security...I would not be surprised to see debt-GDP equal to 200.

Anon@8.10PM Dynamic inefficiency may or may not exist in economies without capital (so capital share is 0%). Are you reporting the result of a theorem? (I'm not aware of this result.)

33. Tom Hickey:

Well, I read over Bill Mitchell's piece. (How do you embed the link in a comment?)

I'm not sure what to make of the list of propositions he lists; for example:

1. The sovereign government, which is not revenue-constrained because it issues the currency, has a responsibility for seeing that the workforce is fully employed.

2. Full employment means less than 2 per cent unemployment, zero underemployment and zero hidden unemployment.

Are these logical conclusions to some theory? And if so, where might I find a succinct (mathematical) exposition of this theory?

I'm still not sure what this has to do with my reference to Zimbabwe. Are you suggesting that that government did not appeal excessively to the printing press to finance its expenditure needs? I simply meant to point out that there are constraints to raising seigniorage revenue, even for a monopoly issuer of currency.

34. Anon@8.10PM here. Yes, it is a theorem. Recall the Solow growth model. A closed, competitive economy that saves what would be capital's share of output in the golden rule steady state will attain that steady state. This follows from the fact that in the steady state the saving rate (I/Y) is equal to depreciation/Y = Î´K/Y which is equal to capital's share of output under the premise above. Thus Î´K/Y=MPk*K/Y or MPk=Î´ which is the condition for the golden rule capital stock. As the steady state capital stock is increasing in the saving rate, any economy with a lower saving rate will attain a steady state with a lower capital stock and hence be dynamically efficient (providing you'll grant me the luxury of thinking about efficiency in an economy without optimizing agents).

35. Anon@9.27PM: Ah yes, the Solow model. Sheesh, I do have a vague recollection...lol.

36. Glad to hear it! To continue the discussion, the r > growth rate condition for dynamic efficiency is a steady-state condition. I don't know that it is of much use for an economy like the US that is currently so far from its long-run growth path. I find it difficult to see how the US could have too much physical capital which is what dynamic inefficiency would imply. "Too much", of course, that we could make everyone (current and future generations) better by consuming some of the existing capital stock.

37. One could make the case, I think, that given the downward revision in the expected rental income from residential property, and given the massive build up in residential capital prior to the crisis, that we now have too much residential capital. MPK is low, and is expected to remain low until inventory is worked off.

38. No argument here on that but I'm not sure that it informs the issue of dynamic efficiency as we are currently so far from the steady-state growth path. That said, I'd suggest that along that path we do overinvest in housing due to the home mortgage interest deduction so I'm open to the idea that we have too much residential capital for that reason.

39. «What if net real global growth is from now on impossible, due to the fact of Peak Oil making the world economy energy constrained. [ ... ] mad scramble for assets that provide a decent return OF capital (forget about a return on capital).»

What if governments worldwide are well aware of this and they are deliberately keeping their economies in stagnation in order to avoid putting pressure on oil prices? Reckoning that if supply is limiting growth, owners of oil stocks will capture nearly all growth that does occur through higher oil prices?

What if some big interests have foreseen this for 2-3 decades and have pushed a policy which amounts to a highly leveraged buyout of the USA economy for the purpose of asset stripping? Blowing up debt levels as much as possible to pay themselves huge returns and using serial asset bubbles to pump up asset prices and dump them on the public?

40. And what sort of credit card company starts to reduce the interest it charges on your debt as you become progressively more indebted. China Direct

41. Amazing! With year-end promotion comes to its zenith. Diablohome is now giving a huge thanks to everyone who support us with extra free 10% bonus for?diablo 3 gold. You must be eager to know some details. Just let the following reveal the answer.
Free Extra 10% Bonus for Diablo 3 Gold Buying
You can get extra 10% bonus if buy diablo 3 gold for normal mode on our site, the more d3 gold you buy, the more bonus you get.
More tags: buy diablo 3 gold diablo gold

42. That's amazing, i like your article style, you really do me a favor on this issue.
d3 gold
runescape gold for sale
Diablo 3 Gold
cheap Diablo 3 Gold

43. Thanks. I always enjoy reading your posts - they are always humorous and intelligent. You can learn more: China tour packages | China travel packages | China Travel Agency

44. AllMandarin is the only company that can give you an excellent alternative to learn Mandarin Chinese that is not only better, but also more efficient in terms of cost, flexibility and learning methods.I am a Chinese teacher,you can learn more about Free Chinese language info: Learn mandarin online | Learn mandarin Chinese | Mandarin Teacher

45. Since our founding in 2002, Hanbridge Mandarin has provided thousands of learners with high-quality campus-based courses, online classes, and intensive cultural immersion programs. Utilizing?easy, fun and rewarding methods, we work hard to ensure our students can understand, use and ultimately master Mandarin communication skills.

More Chinese learning tags : study Chinese online | learning to speak Chinese | learn to speak Chinese