What is the probability of high inflation? How high will it rise? When? No one has succeeded in finding a reliable way to predict high inflation, and we certainly do not pretend that we can predict high inflation ourselves, but these questions are important to all investors, and even the 2% annual rate targeted by the Federal Open Market Committee will cut the real value of an investor’s portfolio by over 17% after a decade. This 2% level along with near 0% interest rates yields a risk free rate of -2%. This guarantees that a portfolio’s real value will erode absent risk-taking, which could result in even lower returns if the risks of loss are realized. , The possibility of higher inflation, at a rate of perhaps 4% or more a year (and with even worse effects) should not be discounted. There are heated debates about the probability and timing of high inflation, but our review of the extensive literature reveals no reliable way to predict its onset or extent. Of the various predictive tools examined in this vast literature, surveys of expert opinions are found to predict inflation best but have failed to predict the onset or extent of high inflation, and past inflation data predicts the experts’ estimates as well as the experts predict future inflation. Perhaps the difficulty of prediction stems from the fact that economic circumstances are so varied and different each time. Debt levels are very high, and inflation is one of the possibilities for deleveraging, however the Japanese have proved that high debt can exist without inflation for at several decades, at least in their particular circumstances. Our high debt levels are partly due to the housing collapse. In the current situation, we hazard the thought that inflation may be a risk until deleveraging has occurred by some other means. Until then, we suggest it may be worthwhile to monitor: (1) months of unsold housing inventory as an indicator likely to decline before a sustained housing rally (shelter is both the largest single component of the CPI and affects consumer wealth and psychology); and (2) banks’ Federal Reserve deposit levels, which have absorbed much of the monetary expansion. A portfolio invested in traditional liquid assets – stocks, bonds, and cash – cannot safely be assumed to weather high inflation intact; the extent of the damage to each of these asset categories varies widely among inflationary periods and is volatile within these periods. In the last two major inflationary periods in the United States, stocks outperformed inflation in one, but lost money to inflation in the other.
A Century of Inflation. Dimson, Staunton and March (DMS)  gathered annual inflation rates and asset returns for nineteen developed countries over the 112 years from 1900-2011. In their sample, positive inflation occurred 82.47% of the time and had a median annual rate of 2.86%; in 38.53% of those years, inflation was at the 4% level or higher. Since 1945, positive inflation occurred in 94.66% of periods sampled and had a median of 3.45%; it was 4% or higher in 43.75% of those years. Since 2000, however, while inflation has been positive in 95.18% of the country-year periods sampled, it has only been over 4% in 9.65% of those periods and has had a median of only 2.20%. As is clear from Exhibit 1, while positive inflation has become almost a certainty in any given developed country in any given year, the median level of inflation has tumbled since the 1970s.
Fig. 1: Positive Inflation Occurrences and Median in Years Since 1900
Public Debt and Inflation. Not only the Tea Party but many economists at the University of Chicago and elsewhere[i] [ii] [iii] are seriously concerned that public debt levels could lead to significantly higher inflation in the United States than we are currently experiencing[iv]. Public debt[v] has risen from about $6.3 to $11 trillion from 2009 to the present[vi]; gross public debt is now a little over 100% of Gross Domestic Product[vii], higher than that of Spain[viii] and about equal to Barbados[ix] or Ireland[x], though less than Italy[xi] and Greece[xii] [xiii]. Furthermore, it seems unlikely that the US debt-to-GDP ratio will decrease any time soon. In the latest CBO Long-Term Budget Outlook (CBO ), the Alternative Scenario predicts an annual fiscal gap of 4.6% of GDP, amounting to around $700 billion for 2012 alone, and even that is only counting public debt (ibid, pp. 21-22). Looking at the entire federal deficit, even under the far more optimistic Baseline Projection the CBO estimates a budget deficit of 0.7% in 2012 and never less than 0.9% (in 2018) in GDP terms over the following decade. The Alternative Scenario is, of course, markedly bleaker, projecting a budget deficit of never less than 4.9% of GDP through 2022 (ibid, xii). High public debt is present not only in the United States, but also in Europe, and over a longer period, in Japan.
Deleveraging, that is, reduction of these high debt levels, can occur by (1) default on some of the debt, (2) inflation, rendering currency less valuable and thus reducing the burden of the debt by allowing its repayment with less valuable currency, (3) austerity, cutting spending (and possibly raising taxes) to pay down debt, or (4) by economic growth, in which that debt becomes a smaller percentage of the now-larger economy[xiv]. Deleveraging from current high debt levels throughout the developed world may occur through some combination of inflation, growth, and default; how this actually unfolds will depend in large part on what governmental policies are pursued and, of course, on those policies’ effectiveness. While the European Union has imposed some degree of austerity in its attempts to reduce debt burdens, deleveraging through inflation has ample historical precedent. The high debt incurred by the United States in World War II and its aftermath was reduced partly through the inflation of the late 1940s and then through economic growth in the 1950s, which, by contrast, was powered without deficit spending or inflation. This means that accurately predicting inflation over the medium-to-long term actually requires predicting government policies, how well they will work, and what side-effects they may cause, a very difficult endeavor.
Fiat currency emerged after World War II, effectively allowing governments to borrow money by printing currency without external restraint. Before that time, the world was on the gold standard. The US Dollar was officially redeemable for gold at the price of $35 per ounce in 1944, and other currencies were tied in value to the dollar (the Bretton Woods system). The true value of the dollar shrank until, in the “Nixon Shock” of 1971, it was declared no longer redeemable in gold and the world monetary system based on it was replaced by the floating rates which we have today under which the price of gold has risen to around $1,700 per troy ounce[xv]. Today, though no longer backed by gold, the dollar still enjoys the status of the world’s reserve currency, that is, the principal currency used in world trade and the currency in which many central banks keep their foreign reserves. This has allowed the United States to borrow money more easily, which may or may not be a good thing in the long run. Reserve currencies come and go, from the Greek Drachma to the Roman Dinar, and from the Dutch Guilder, to the Pound Sterling. World deleveraging will occur under a novel world regime of fiat currencies in which, though the US Dollar is currently the reserve currency, all economies are increasingly interconnected. The role of inflation in deleveraging in these unprecedented circumstances may be particularly difficult to predict.
Among the opponents of quantitative easing are Michael Woodford of Columbia University and Bill White, who wrote “Easy monetary policies can lead to moral hazard on a grand scale. Further, once on such a path, ‘exit’ becomes extremely difficult.” Indeed, Richard Fisher , head of the Dallas Fed and member of the Federal Open Market Committee (FOMC), has publicly stated: “no central bank anywhere on the planet—has the experience of successfully navigating a return home from the place in which we now find ourselves.”
Ancient History. History is replete with stories of governments accumulating debts and printing money to such an extent that confidence in the currency is lost and it must be replaced with a new currency tied to hard assets such as gold. These events have also been accompanied by severe social problems such as riots, food shortages, the collapse of the first French Republic and the rise of Napoleon to replace it, and the collapse of Weimar Germany and the rise of Hitler to replace it. These instances are not limited to any particular time or place: Kublai Kahn introduced paper currency in China[xvi], eventually leading to a hyperinflationary episode and its replacement with currency based on hard assets[xvii]; Roman coinage was repeatedly debased, and the silver content reduced, resulting in inflation, sometimes hyperinflation[xviii] and serious social unrest [xix] [xx].
Recent History. More recently, debt has not caused high inflation in advanced economies. Since 1980, Belgium, Canada, and, most notably, Japan have all experienced high levels of net public debt without subsequent high inflation. Japan in particular has sustained net debt in excess of 70% of their GDP since 2002[xxi], more recently climbing to over 125% of GDP. Meanwhile, their consumer price index has fallen by about 1% over the past decade, meaning they have actually experienced a slight deflation[xxii]. Furthermore, a recent paper by Reinhart and Rogoff  finds no contemporaneous connection between levels of public debt and inflation for advanced economies as a group[xxiii]. Similarly, Giannitsarou and Scott  found that for the period from 1960-2005, inflation counted for under 10% of fiscal imbalance reduction in United States, Japan, Germany, the United Kingdom, Italy, and Canada. As a result, several economists[xxiv] suggest that the United States currently faces a greater risk of becoming trapped in a Japan-style disinflation/deflation spiral than it does of encountering uncontrolled high inflation. However, other economists, such as Nouriel Roubini, point out that the Japanese debt is almost entirely owned by Japanese nationals, making it simpler to control than the US debt which is increasingly owned by foreign entities who can in effect opt to exchange it for another currency at any time with potentially disastrous effects on both the US dollar’s valuation and the dollar’s status as a reserve currency (Manetta ).
Fig. 2: Net Public Debt and Inflation for Japan 1980-2011
Government Policy. The FOMC has set a 2% inflation goal, that means that 2% inflation is not just acceptably low, but it is a goal of the bank that inflation should not fall below that level. In fact, by targeting 2% inflation with close to 0% Treasury bill rates, the government is targeting a negative real risk free rate; portfolios that don’t want to accept risk of loss must accept erosion of their value. Furthermore, some economists (such as Krugman ) have argued that inflation should be increased above that level, perhaps to 4 or even 5 percent a year.
Measuring Inflation. The inflation measure we wish to predict is that of the cost of living, generally reflected by the Consumer Price Index (CPI), but measuring that is controversial and necessarily inexact. The cost of living for a New Yorker is higher than that of a Minnesotan. An elderly retiree consumes a different mix of goods than a single youth or a young family. An automobile purchased now is quite different from an automobile purchased in 1960 – now generally smaller and safer and fitted out with more electronics. Similarly, as prices for particular goods change, people change the mix of goods which they buy. As prices rise (fall), people will often lower (raise) their standard of living, keeping their total expenditures close to level, for example by substituting turkey for more expensive beef, a phenomenon not captured in the CPI. To this end, chain-type indices such as the Chained CPI (C-CPI-U) recommended by the Simpson-Bowles commission and the PCE (or “Chain-type Price Index for Personal Consumption Expenditures” in the parlance of Federal Reserve) used by the FOMC were developed to adapt more rapidly to changing patterns of consumption and tend to be far less volatile and prone to extremes. Of course, these indices have their own critics asserting that these changes in spending are just people’s making do with what is effectively less, and that it is therefore disingenuous to factor these effects into inflation estimation.
Fig. 3: Annual Inflation (CPI)Portfolio Effects of Inflation
Portfolio Value. After the relatively low inflation of the last decade, concerns over high inflation are often dismissed as groundless. However, even low inflation can have a serious effect on a portfolio. It is an undiversified risk, which diminishes the purchasing-power value of the whole portfolio, not just that of one investment: since 2000, inflation, though low, has reduced the effective value of portfolios by 25%. This effect is compounded by the calculation of taxes and spending requirements. Taxes are imposed on nominal earnings. Thus an investor whose portfolio returns just match inflation will have to pay some taxes even though he has zero income in inflation-adjusted (purchasing power) terms. Even pension fund earnings which are not taxed as they accumulate will be subject to tax when distributed to retirees. This can have a very serious effect on a pensioner as she must pay taxes, spend money each year to live, and, on top of that, save enough income to offset inflation if her nest egg is not to shrink in real terms. Furthermore, institutional investors such as private foundations are required to spend at least 5% of their assets every year. So for such an investor simply to maintain his portfolio without loss or gain in real terms, it needs to earn inflation plus 5%, plus any taxes payable. Under the conditions observed between January 2000 and August 2012, assuming a 25% tax rate and a 5% annual spending requirement, a portfolio whose nominal, pre-tax returns matched inflation would have lost over lost half of its value after adjusting for inflation value during that period. Under the past dozen years’ relatively benign inflationary regime, a portfolio would have needed to earn 10.5% annually just to maintain its inflation-corrected value after taxes and spending.
Stocks, Bonds, & Bills. A portfolio comprised of the traditional liquid asset classes–stocks, bonds and bills–appears unlikely, based on historical evidence, to fare well in high inflation. As we have demonstrated in a previous article (Crawford and Liew ), bills track inflation most closely, but rarely produce a return sufficient to offset high inflation, even before taxes and spending. This corresponds with other research, such as that of Fama  supporting the Fisher  hypothesis that investors price bills to earn their expectations of inflation plus a fixed real rate of return. Bonds have performed even worse under increasing inflation as rising inflation is generally accompanied by hikes in interest rates, lowering the value of pre-inflation bonds. While stocks most often out-earn even high inflation (before taxes and spending), they also sometimes produce very negative return, making them a very uncertain refuge.
The US in 1940s and 1970s. As an example, let us examine the two periods of high inflation in the United States since World War II, the period following the Second World War and the “oil-shock” inflation from roughly 1968-1980, and examine the performance of bills, bonds, and equities during those eras. Both periods are also interesting in that their inflationary trends were not restricted to just the United States, but rather involved inflation throughout the developed world. Using data from Dimson, Staunton, and March , we see strikingly different results for those two periods. In the 1940s, stocks outperformed inflation adding 20% to their real value while bonds and bills both lost 30% in real terms. In the 1970s, by contrast, bills just kept up with inflation while stocks and bonds respectively lost about 10% and 20% of their real value. Of course, all these losses would have been greater after the effects of spending and taxes. In the charts below, the top row shows asset performance in the 1940s plotted against the Consumer Price Index (left) and the same assets’ performance in real terms (right). The second row shows the same for the 1970s inflationary period. One thing that is quite clear is that what worked under one inflationary regime may not work under another.
Fig. 4: Historical Performance of Various Assets under High Inflation
Note that these assets’ behavior was quite volatile, especially after adjusting for inflation. For example, in the 1970s the bond portfolio lost 40% of its real value by 1982, only to partially recover as inflation was brought under control, resulting in a net loss of a bit over 20%. Stocks lost over 40% of their real value by 1974, but then bounced back, losing only 10% of their value over the period. Of course it would take a very calm, steady hand to avoid selling out at or near the bottom, and there is not much evidence that investors have the stomach to stay the course through years of terrible performance. In fact, investors have a distressing tendency to buy at the top and sell at the bottom[xxv].Tools for Predicting Inflation
Can Inflation Be Forecast?Forecasting inflation presents a variety of challenges, some of which are common to all macro-economic variables and others perhaps unique to this particular problem. First, there is simply a limited supply of data. There have been only two significant episodes of high inflation in the United States over the past fifty years, one in the seventies and the other in the early nineties (and the nineties episode was quite brief). Given such limited historical data under two very different macroeconomic regimes, it is difficult to form valid generalizations. Furthermore, only the 1970s period was in any way lengthy and it occurred under circumstances vastly dissimilar to those today. Such limitations limit the utility of historical data in the development and confirmation of inflation forecasts. This difficulty is compounded by the sheer complexity (some might even say absurdity) of placing a single number on so composite a macroeconomic phenomenon as inflation. While such a simplified figure is of course necessary for research and perhaps policy, it must be understood that the CPI (or any other measure of price levels) can never be anything more than an approximation due both to the noise inherent in gathering the data and in the complexity of the issue and the myriad differing rates of inflation for various goods and services. Finally, the Federal Reserve is explicitly charged with maintaining price stability. This means that the inflation figures are targets of government policy so that any attempt to devise a reliable inflation forecasting model must necessarily predict the success or failure of central bank policies to control inflation. A mathematical model for predicting both government policy and its effectiveness has yet to be developed.
These difficulties notwithstanding, the literature is replete with studies proposing and evaluating various inflation forecasting schemes, with mixed (and, at that, quite limited) success. Cecchetti et al.  evaluated nineteen potential inflation indicators including money supply, unemployment, the prices of oil and gold, and the capacity utilization rate, finding that “statistical tests reveal that such indicators, used in isolation, have very limited predictive power.” Ten of their indicators performed worse than autoregressive schemes (that is, trying to predict inflation based purely based on past inflation data). Furthermore, even the indicators that generally outperformed autoregressions did not perform very well on the whole and occasionally failed spectacularly. Interestingly, they found that a rise in the price of gold or oil tended to coincide with a subsequent drop in inflation, which effect they suggest with some reservation may perhaps be attributable to Federal Reserve countermeasures, but conclude “the illogical nature of this relationship prevents us from putting much stock in the seemingly good showing of gold prices, oil prices, and the Journal of Commerce Index as inflation indicators.” Similarly, in addition to providing an excellent overview of much of the literature, Stock and Watson  evaluate 38 assets’ prices for their use as inflation indicators in seven OECD countries over a 41-year horizon. They found that while some assets seem to have worked to predict inflation in some countries for some periods, none is universally reliable and there is no good way to know which asset will be a predictor when.
Money SupplyCongruent to Friedman’s monetarist view of inflation, King  demonstrated that countries with higher growth of money supply tend over the long run to have higher inflation than countries with lower money supply growth. However, as Krugman [1998; 2009] points out, that is not always the case. In Japan, money supply growth (along with growing levels of public debt) have not yet led to high inflation, and indeed there have been several years of deflation in Japan in recent years. Similarly, in the US, rapid growth in the money supply over the last few years has not led to high inflation, perhaps because while the monetary base (MB) has grown very rapidly, this has not led to an increase in the broader monetary aggregate, M2. The dramatic increase in the monetary base created by QE1 and QE2 is reflected in the graph below along with the lack of dramatic growth in the M2 money supply. This is primarily due to a huge expansion in bank reserve deposits at the Federal Reserve (where they currently earn interest at 2.5bp /year), almost matching the increases in the monetary base. In other words, the banks are not using the increased money supply to make loans (which would increase M2) but instead are simply depositing those funds with the Federal Reserve and pocketing the interest. Should the banks withdraw those funds and lend them, the money supply might grow very quickly, perhaps pulling inflation with it. Accordingly, we suggest monitoring banks’ Federal Reserve deposit levels, which are reported weekly, as a potential barometer of inflation risk.
Fig. 5: US Monetary Base (MB) and Base Net of Bank Reserves
Fig. 6: US M2 Money Stock (Log Scale)
Housing. Housing is a major cost of living, constituting 31.4% of the CPI, and its cost has been suppressed in the United States since 2007 by reason of the real estate bust, resulting in a large numbers of foreclosures and high inventory of unsold homes. However, it has not had a great effect on the overall CPI level because the BLS measures the cost of ownership of one’s primary residence not in terms of current house prices but in terms of how much it would cost to rent a similar domicile (“owners’ equivalent rent”). This change was made in 1983 to compensate for the fact that home ownership serves two purposes: it is a source of shelter (consumption), and it is also an asset like any commodities or stocks (investment). In order that this investment aspect should not be reflected in the CPI (which is, after all, a cost of living measurement), rents, which reflect one’s “consumption” of housing, were substituted (the ECP sidesteps this issue simply by excluding owner-occupied housing from their inflation measure, the Harmonized Index of Consumer Prices). Because of this substitution, the housing bubble and its collapse are not reflected in the Consumer Price Index, which some might argue is a validation of its design. Interestingly, home prices appear to be once again converging with the owners’ equivalent rent component of the CPI, perhaps returning to their pre-bubble synchronicity.
Exhibit 10: Home Prices and Owners’ Equivalent Rent Fig. 7: Home Prices and Owners’ Equivalent Rent
Expert Surveys.Historically, surveys of economists have proved to be among the most reliable predictors of inflation (Croushore ; Ang et al. ). Indeed, Ang et al. report that not only do the Livingston Survey[xxvi] and the Survey of Professional Forecasters[xxvii] (SPF) predict inflation more accurately than any of the other methods they evaluated (including macro variables, time series models, and asset prices), but the Michigan Survey of Consumers, which polls non-experts, is only slightly less accurate than the professionals. This is not wholly surprising when one considers that experts (a) implicitly include the results of other models, (b) are unique in that they can factor in potential policy actions, and (c) are able to quickly integrate new data without the lag or averaging implicit in some other models. Similarly, consumer expectations of inflation are, in the Keynesian view, a major driver of inflation as prices are adjusted and wages are negotiated in light of expected expenses. Unfortunately, for all their accuracy, surveys can still miss turning points in inflationary behavior, as in the 1970s inflation. Similarly, they failed to predict either the 1990 inflationary blip or the 2008 deflationary episode. Currently, both the Livingston and SPF panels predict inflation over the next year at around 2%.
Even though they are the best available predictor of inflation, expert surveys have some major drawbacks. Mehra  notes “that the turning points in expected inflation appear to lag behind the turning points in actual inflation, suggesting the presence of a backward-looking component in inflation expectations. Furthermore, both Livingston and Michigan respondents appear to underestimate inflation in the early period, when inflation is trending upward, and overestimate inflation in the later period, when it is trending downward.” Additionally, Mehra found that while the SPF and Michigan panels can be said to have predictive content about inflation in the sense of Granger causality, the same cannot be said about the Livingston survey. Interestingly, a cursory examination indicates that while surveys may predict inflation better than autoregressions, current inflation predicts the median Livingston survey results one year ahead about as well as the Livingston median predicts the following year’s inflation (for the twenty-five years of Livingston data beginning June 1986, the two have RMSEs 0.01346 vs. 0.013057, respectively).
Fig. 8: One Year Inflation Predictions and Realized Inflation
Fig. 9: Rolling 20-Sample RMSE
TIPS Pricing.The spread between TIPS and nominal bond yields is often used as an inflation estimator. Since TIPS are of only recent vintage, however, historical testing of the accuracy of this estimator is impossible. In theory, while the TIPS-nominal yield spread should provide an accurate gauge of the market’s expectations of inflation, this estimate tends to be somewhat low, perhaps due to a risk premium the TIPS investor forgoes (he is no longer exposed to inflation risk) and a smaller liquidity premium (the TIPS market is less liquid than that of nominal bonds). Of course, the risk and liquidity premiums are not constant. As inflation appears more volatile, the risk premium should increase, and as the TIPS market continues to deepen, the liquidity premium should decrease, thus constant correction is needed for these factors (Carlstrom and Fuerst ; Haubrich et al. ). The Cleveland Federal Reserve Bank uses a model based largely on inflation swap prices to estimate future inflation. This model yields an average 1.26% annual inflation over the next decade. Full details of their methodology and comparison to TIPS-based models and surveys in available in Haubrich et al.Bibliography
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[i] Laffer : “But as bad as the fiscal picture is, panic-driven monetary policies portend to have even more dire consequences. We can expect rapidly rising prices and much, much higher interest rates over the next four or five years, and a concomitant deleterious impact on output and employment not unlike the late 1970s.”
[ii] Cochrane 
[iii] Aizenman and Marion : ”[W]hen economic growth is stalled, the U.S. debt overhang may trigger an increase in inflation of about 5 percent for several years. This additional inflation would significantly reduce the debt ratio, even with some shortening of debt maturities.”
4 There are, of course, other risk factors besides net debt. Krugman , for example, argues that the U.S. current accounts deficit is unsustainable and must eventually result in a devaluation, the magnitude of which depends on whether or not investors have already factored that into their analyses, concluding that “it seems likely that there will be a Wile E. Cayote moment when investors realize that the dollar’s value doesn’t make sense, and that value plunges.”
5 In keeping with Congressional Budget Office (CBO , p. 20; CBO , pp. 14-15) and International Monetary Fund (IMF , pp. 55-59) practice as well as that recommended by various economists (Eisner , p. 17), the debt numbers given in the body of the paper are net figures. Because there is some disagreement about this (c.f. International Monetary Fund , pp. 21-22), gross numbers will be provided in footnotes.
[vi] Specifically, from $6.320 trillion ($10.628 gross) on January 2, 2009 to $11.395 trillion ($16.218 trillion gross) on November 7, 2012 (http://www.treasurydirect.gov/NP/BPDLogin?application=np)
[vii] United States 2011 GDP was $15.094 trillion dollars and is estimated at $15.775 trn for 2012 (http://www.bea.gov/national/xls/gdplev.xls) for a net debt to GDP ratio of 72.3% (gross 102.8%). The gross figure has been topped only three times in US history, in 1945-7 (117.5%, 121.7%, and 110.3%, respectively) (Office of Management and Budget , pp. 139-40). Ignoring the years 1943-1956, every year starting with 2009 has set a record high net debt to GDP ratio, and for gross GDP we only need ignore 1944-1950.
[viii] 56. 95% (68.47% gross) in 2011, estimated to increase to 67.02% (79.04% gross) in 2012 (IMF ). It is perhaps worth noting that if European debt (e.g. to ESFS) is included, these ratio are significantly higher.
[ix] Estimated in 2011 at 117.25% (ibid.)
[x] 95.90% (104.95% gross) in 2011, estimated to increase to 102.93% (113.13% gross) in 2012 (ibid.)
[xi] 99.56% (120.11% gross) in 2011, estimated to increase to 102.26% (123.36% gross) in 2012 (ibid.)
[xii] Estimated in 2011 at 160.81% (160.81% gross) (ibid.)
[xiii] It is perhaps worth noting that the majority of middle-income countries defaulting or restructuring their debt between 1970 and 2008 did so with external debts of no more than 60% of GNP (Reinhart and Rogoff , p. 23).
[xiv] An account of many historical episodes of high debt deleveraging may be found in Reinhart and Rogoff .
[xv] LME PM fix for gold on November 7, 2012 was $1715.25/oz.t.
[xvi] His most significant was the third, in 1260, firmly pegged to silver. These were, however slowly devalued (but never became totally worthless) as more and more currency was issued over the next fifteen years (Steinhardt , pp. 63-66).
[xvii] While The Yuan dynasty’s paper currency was at first well supported by significant reserves (mostly grain), in 1350, overextended largely on military spending, Toghon Timur issued two million ingots worth of poorly inadequately backed paper currency, eventually increased the money supply to the point that it was worthless by 1356 (Brook , p. 120; Dardess , p. 575).
[xviii] During the first eight years of Diocletian’s reign (293-301 C.E.), inflation average annual inflation was 22.9%, peaking at no less than 35% in 301 when he tried to stop inflation by issuing the Edict on Maximum Prices (Wassink ). Moreover there exists a letter dated c. 300 C.E. (P. Ryl. 4 607) in which a Roman official instructs a subordinate to purchase goods at whatever cost before the currency is devalued by half (Roberts and Turner , pp. 92-94).
[xix] Under Emperor Aurelian in 270 C.E. antoninianus coins were minted with a mere 2.5% silver content (0.38g silver), down from their initial purity of 52% (5.1g silver) in 215. This resulted in a rebellion by employees at the mint itself, eventually forcing Aurelian to introduce a new gold coin in 274 in an attempt to restore public confidence (Wassink ).
[xx] Regarding the Edict on Maximum Prices, Lactantius reports “He [Diocletian] also, when by various extortions he had made all things exceedingly dear, attempted by an ordinance to limit their prices. Then much blood was shed for the veriest trifles; men were afraid to expose aught to sale, and the scarcity became more excessive and grievous than ever, until, in the end, the ordinance, after having proved destructive to multitudes, was from mere necessity abrogated.” (Lactantius, p. 169)
[xxii] Source Federal Reserve Economic Data
[xxiii] The one link they do find is for the United States when debt levels cross 90% of GDP. Irons and Bivens , however, point out that the data in this category all with the exception of 2009 (a low-inflation year) all correspond to 1943-1949—WWII and its aftermath.
[xxiv] Such as Krugman 
[xxv] Frazzinia and Lamont  draw this conclusion from mutual fund flows finding “that individual investors have a striking ability to do the wrong thing. They send their money to mutual funds which own stocks that do poorly over the subsequent few years. Individual investors are dumb money, and one can use their mutual fund reallocation decisions to predict future stock returns. The dumb money effect is robust to a variety of different control variables, is not entirely due to one particular time period, and is implementable using real-time information. By doing the opposite of individuals, one can construct a portfolio with high returns.”
[xxvi] Available at http://www.philadelphiafed.org/research-and-data/real-time-center/livingston-survey/
[xxvii] Available at http://www.phil.frb.org/research-and-data/real-time-center/survey-of-professional-forecasters/