E4 | Macro Paper Warehouse

A Restatement of the Quantity Theory of Money

This 1966 American Economic Review paper by Maurice Allais asks whether the quantity theory of money can be given a single operational formulation that holds uniformly across normal times and hyperinflations, across countries, and across historical periods, and proposes the “hereditary, relativistic, and logistic” (H.R.L.) formulation of money demand as that reformulation. Allais derives the H.R.L. law from eight a priori postulates about the psychological basis of monetary behavior: the “relativistic” postulate posits a psychological time scale on which the coefficient of forgetfulness is constant; the “hereditary” postulate makes the psychological rate of expansion of total outlay, z, an exponentially-weighted average of all past rates of growth of total outlay (so current money demand depends on the entire history of outlay growth, more recent history weighted more heavily); an invariance postulate holds that the function relating relative desired money balances to psychological time is the same across all times and countries; a constant-velocity-in-psychological-time postulate; and a “logistic” postulate that the relative change in desired balances is proportional to the relative gap between desired balances and their maximum, yielding a logistic function of the dimensionless variable Z = z/X_0. Three further postulates (asymptotic behavior at the end of hyperinflation, conjunctural symmetry between expansion and recession, and temporal symmetry between past and future) pin down the model’s three universal constants at alpha=1, b=1, and X_0=0.004 per month (derived from a roughly 5% per annum equilibrium real interest rate for the United States, 1880-1956), giving the fully specified common law psi(Z) = 2/(1+e^Z) with dZ/dt = x - 0.002(1+e^Z)Z, where x is the instantaneous rate of growth of nominal total outlay (or national income). Allais then fits this single law, with only two free series-specific integration constants (an initial scale of desired balances and an initial value of Z) and no country- or period-specific universal constants, by nonlinear least squares to fifteen time series from nine countries and monetary regimes: annual/quarterly data for France (1898-1913, 1919-1938, 1947-1962), Great Britain (1925-1940, 1952-1962), and the United States (1895-1915, 1918-1941, 1946-1958), plus seven hyperinflation episodes (Germany, Austria, Greece, Hungary I and II, Poland, and the U.S.S.R. in the 1920s-1940s) using Cagan’s hyperinflation data. The calculated M* depends only on observed national income or the price level, not on observed money M, so the fit is not circular. The fit is extremely close: of the fifteen correlation coefficients between observed and calculated log money, eleven exceed 0.99, eight are at least 0.995, and two exceed 0.999, with a mean unexplained variance of 1.9% across all series, and pooling all 389 paired observations gives a correlation of 0.9984 (0.9930 in logs); Allais remarks that these results “seem too good to be true.” The same three universal constants fit series ranging from near-stable income growth in the interwar United States to the German hyperinflation (price index rising from 15 to about 1.09 billion) and the second Hungarian hyperinflation (price level rising by a factor of roughly 4x10^29); the only “significant exception” Allais reports anywhere in the paper belongs to his earlier (1954) study recapped in Section I — the France 1820-1870 series, built on money and income figures he calls “highly questionable” — and is not one of the fifteen series in this paper’s own Table 2 (whose own French series run 1898-1913, 1919-1938, and 1947-1962), among which no comparable exception is flagged. Allais interprets the results as showing that the quantity theory is “fundamentally correct” once redefined on this hereditary and relativistic basis: a proportional relationship between the price level and M/Q holds instantaneously, but its coefficient of proportionality is not a constant, instead varying with the history of past outlay growth summarized by Z, so that both the traditional quantity-theory view and the anti-quantity-theory view are partially right. He is careful to note that the H.R.L. law is a theory of money demand only, that a full account of monetary dynamics also requires a theory of how the gap between actual money M and desired money M_D (a gap Allais argues is not fully captured by observed M* alone) feeds back into total outlay, and that X_0=0.004 is calibrated to a roughly 5% annual real rate specific to the US sample and may differ in other places or periods; allowing the constants to vary by series would improve the fit further, but the universal constants are advanced on a priori theoretical grounds rather than as the best attainable fit.

A Theory of Macroprudential Policies in the Presence of Nominal Rigidities

This is a theory paper, with no calibration or empirical estimates: its output is a set of analytical formulas rather than numbers. It asks what justifies macroprudential intervention in financial markets, and answers that nominal rigidities alone – without the incomplete markets or price-dependent borrowing constraints that earlier work relied on – are enough. In the baseline model financial markets are complete and frictionless; the only imperfections are sticky goods and labor prices and, in the cases the authors care most about, a constraint that stops monetary policy from undoing them, such as the zero lower bound or a fixed exchange rate. The mechanism is what the authors call an aggregate demand externality: once a state of the world is realised, who holds the wealth matters for how much the economy spends, because agents differ in their marginal propensities to spend, but no atomistic agent takes that macroeconomic consequence into account when choosing a portfolio ex ante. Two sets of results follow. First, using a perturbation argument in the spirit of Geanakoplos and Polemarchakis (1985), any equilibrium that is not first best can be improved by intervening in financial markets “except in non-generic knife-edged cases” – the constrained-inefficiency claim is a genericity claim, not a claim that intervention always helps. Second, optimal monetary and macroprudential policy are characterised jointly by explicit formulas in three sufficient statistics: elasticities of substitution, marginal propensities to spend, and good-specific wedges. The optimal financial tax on an agent’s claim in a given state is the marginal-propensity-weighted sum of that state’s wedges, so wealth should be tilted toward states where the goods an agent buys heavily are depressed. Monetary policy, in parallel, targets weighted averages of wedges, adapting the standard New Keynesian targeting rules. The framework is then extended to include pecuniary externalities as well, and – a result the authors call remarkable – the macroprudential formula is literally unchanged: market incompleteness and price-dependent constraints alter the wedges but not the mapping from wedges to taxes. Four applications illustrate the theory: household deleveraging into a liquidity trap, where the optimal policy mix restricts pre-crisis borrowing (in practice a loan-to-value or debt-to-income limit) while monetary policy still delivers perfect stabilisation during the boom; capital controls under a fixed exchange rate, read as a second-best way of regaining interest-rate autonomy; and two cases with a flexible exchange rate where capital controls are still warranted, one with terms-of-trade-dependent collateral constraints and one with non-contingent local- and foreign-currency debt.

Bank loan portfolios and the monetary transmission mechanism

This 2007 Journal of Monetary Economics paper by Wouter den Haan, Steven Sumner, and Guy Yamashiro asks whether the three main categories of U.S. bank loans – commercial and industrial (C&I), real estate, and consumer – respond uniformly to monetary policy tightening, and uses the answer to adjudicate between a bank-lending-channel view (in which loan supply should contract across the board) and an alternative portfolio-substitution story. Using quarterly Call Report data on bank balance sheets from 1977:Q1 to 2004:Q2, the authors estimate a block-recursive (Cholesky) structural VAR in the style of Christiano, Eichenbaum, and Evans (1999), identifying a monetary policy shock as an innovation to the federal funds rate that is ordered so the Fed does not respond contemporaneously to the other system variables (a second identification, in which the Fed does respond contemporaneously to everything, delivers qualitatively the same results). Following a one-standard-deviation positive innovation to the federal funds rate – which rises by roughly 80 basis points on impact – C&I loans display a substantial and frequently significant increase, while real estate and consumer loans decline significantly, a pattern that runs directly counter to the standard bank-lending-channel prediction that all loan categories should contract when reserves tighten. To isolate whether this is simply a real-activity effect rather than a monetary one, the authors construct a “non-monetary downturn” – a sequence of real-income shocks calibrated to reproduce the same path of real income as the monetary tightening – and find the loan pattern flips: C&I loans fall sharply and immediately while real estate and consumer loans are little affected. The paper also shows this portfolio substitution is not explained by an inventory-financing story (adding inventories to the VAR and matching the inventory path as well as the income path still fails to generate a C&I increase), that bank book equity falls significantly during monetary tightening but not during the matched non-monetary downturn, and that C&I loan rates track the funds rate closely while consumer loan rates are sticky and long-term mortgage/Treasury rates overshoot what the expectations hypothesis predicts. The authors propose four non-exclusive explanations for why tightening pushes banks toward C&I and away from real estate/consumer lending: a stronger balance-sheet channel on the consumer side, stickiness of consumer loan rates, hedging of interest-rate risk via maturity-adjusting portfolio shifts, and Basel-Accord capital requirements that force banks whose book equity has fallen to shed higher risk-weight, long-term assets (real estate) in favor of lower risk-weight, short-term ones (C&I). Results are reported as robust to an alternative identification, a BIC-selected lag length, monthly H8 data over 1960-2003, and Romer-Romer (2004) narrative monetary shocks; the authors are explicit that this is an empirical exercise and that building a single structural model consistent with all the documented patterns is left as “an important challenge for future research.”

Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory

This 1980 Journal of Econometrics paper by William A. Barnett lays out the theoretical foundation for treating monetary aggregates such as M2 as genuine economic quantities and derives the Divisia index as the theoretically correct way to measure them, arguing that the simple-sum index conventionally used by central banks “is severely defective.” Barnett shows that a monetary aggregate is meaningful as an economic variable only if the representative consumer’s utility function is blockwise weakly separable in the relevant monetary assets – utility can be written as a function of “other goods” and a subutility function over the assets to be aggregated – and that, given this separability plus linear homogeneity of the subutility function, Green’s (1964) theorem permits two-stage (or n-stage) budgeting in which total monetary expenditure is allocated first across blocks, such as transaction balances versus a passbook-savings aggregate, and then within each block across its component assets. Extending his own 1978 user-cost formula to incorporate taxation, Barnett prices each asset’s foregone return relative to a benchmark bond yield and estimates nested CES demand systems by full-information maximum likelihood on quarterly U.S. data, 1970Q1-1978Q1: across three types of passbook-savings institutions (commercial bank, savings and loan, mutual savings bank) the estimated elasticity of substitution is high, sigma = 2.66 (beta-hat = 0.62), so high that a near-linear approximation “may be a reasonable approximation” at that level, though unequal estimated weights (alpha-hat = 0.55, 0.26, 0.20) still statistically reject simple summation; but between transaction balances and the passbook aggregate substitutability is much lower, sigma = 0.28 (beta-hat = -2.53), which Barnett calls “too low to justify a linear approximation,” so simple-sum M2 is inappropriate at that level of aggregation. Barnett then shows that the Diewert-superlative Tornquist-Theil Divisia index and the Fisher Ideal index – both exact or near-exact for a broad class of well-behaved aggregator functions – agree to three decimal places when computed for M3 over 1968Q1-1978Q1, while simple-sum M3 velocity over the same period declines secularly (from 1.0 in 1968Q1 to about 0.906 in 1978Q1) even as Divisia M3 velocity stays comparatively stable (roughly 1.00-1.07); Barnett interprets this as evidence that simple-sum aggregation misreads 1970s substitution toward higher-yielding, less-regulated monetary assets as a decline in the “quantity of money,” when in fact the Divisia-measured aggregate is roughly unchanged.

Empirical Evidence on the Recent Behavior and Usefulness of Simple-Sum and Weighted Measures of the Money Stock

This 1994 Federal Reserve Bank of St. Louis Review paper by K. Alec Chrystal and Ronald MacDonald asks whether replacing simple-sum monetary aggregates with expenditure-weighted Divisia (or Rotemberg Currency Equivalent) aggregates actually improves money’s empirical usefulness for predicting nominal income and for detecting causal links with real activity, and it tests this question reduced-form, with no structural identification, across seven countries: the United States, United Kingdom, Australia, Germany, Switzerland, Canada, and Japan. The comparison runs on two tracks: modified St. Louis equations (regressing quarterly log-differenced GNP/GDP on current and four lags of log-differenced government spending and money, plus the Treasury bill rate for the US), scored with three non-nested test statistics (the Akaike Information Criterion, the Davidson-MacKinnon J-test, and the Fisher-McAleer JA-test) and exclusion F-tests; and a time-series causality track using Augmented Dickey-Fuller unit-root tests, Johansen cointegration analysis, and heteroskedasticity-robust Granger-type VECM exclusion tests, with country-specific quarterly samples spanning roughly the late 1960s/1970s through 1987-1992. The results are country-specific rather than uniform: for the US, Divisia dominates simple-sum for M2 and broader aggregates (Divisia M2’s F-test for exclusion is F(5,107)=4.73, p=0.001, versus simple-sum M2’s F(5,107)=4.43, p=0.001) but simple-sum still beats Divisia for the narrow M1/M1A aggregates; the UK and Australia show clearer, broader Divisia superiority (Australia is called “probably the clearest case” of Divisia dominance, especially for broad money); Germany and Switzerland show weak informational content for money generally; Canada shows strong Divisia dominance for M2, M3, and L; and Japan is an explicit outlier where simple-sum is favored by the information criterion yet no aggregate, weighted or unweighted, is significant in the F-tests. A US pre-1980 sub-sample (1960:1-1979:3) shows the Divisia advantage present but markedly weaker, consistent with the authors’ interpretation that Divisia’s edge stems from measurement error in simple-sum aggregates that is largest during the post-1980 period of rapid financial innovation. The authors are explicit that their St. Louis-equation results speak only to relative, not absolute, performance of competing money measures, and they conclude that the evidence for Divisia, while real in several countries, is not yet robust enough to recommend it as a direct policy-targeting variable.

Expectations and the Neutrality of Money

This 1972 Journal of Economic Theory paper by Robert Lucas constructs an overlapping-generations general equilibrium model — young and old traders exchanging in two physically separated, non-communicating markets — to show how a Phillips-curve-like relationship between money and real output can emerge as an equilibrium property of a fully rational, market-clearing economy, without contradicting the classical long-run neutrality of money. The key mechanism is imperfect information: traders in each market observe only the local price, which reflects the ratio of a monetary shock (a random change in the money supply, x) to a real shock (a random reallocation of traders across markets, θ), so they cannot fully distinguish a price increase caused by “more money” from one caused by “more real demand for my goods specifically” — and this confusion causes traders to raise output in response to nominal (monetary) shocks. Lucas proves that when only monetary disturbances are present (no real shocks), money is perfectly neutral in the classical sense (Theorem 2); when only real disturbances are present, real magnitudes vary but money’s neutrality doesn’t apply since there’s no money-supply variation at all (Theorem 3); and in the general case with both shocks present, an unanticipated monetary shock has genuine real effects because it cannot be fully separated from the real shock via the observed price (Theorem 4), while a fully anticipated, proportional (scale) change in monetary policy has no real effects at all (Corollary). He also shows that a constant “k-percent” money growth rule (per Milton Friedman) yields a Pareto-optimal competitive equilibrium allocation (Theorem 5), and that fitting an econometric Phillips-curve regression to data simulated from this model produces a strong positive, but entirely spurious and non-exploitable, inflation-output correlation — “much more convincing” than the corresponding real-world evidence — even though no genuine policy trade-off exists in the model.

International Currencies and Capital Allocation

Using a new security-level dataset covering $32 trillion in global investment positions, this paper establishes that the currency a bond is denominated in – not the nationality of its issuer – is the dominant predictor of who holds it, and that this home-currency bias leaves most firms borrowing only at home while a small number of large foreign-currency issuers capture nearly all foreign bond capital. The data are Morningstar’s complete position-level holdings of open-end mutual funds and exchange-traded funds domiciled in over 50 countries, filtered to the 23 countries (14 of them inside the euro area, leaving 10 effective country units) where Morningstar’s coverage of fixed-income assets under management is at least a quarter of what the Investment Company Institute reports. Four facts follow. First, home-currency bias is strong and is identified within firm: comparing an investor country’s share of two bonds issued by the same parent but denominated differently, and controlling for maturity and coupon, Canadian funds hold a share of a Canadian-dollar bond about 90 percentage points larger than of a non-Canadian-dollar bond from the same issuer, with similarly large and precisely estimated coefficients for every other country (Table 2, p. 12). Running home-country and home-currency indicators side by side, the currency coefficient and R-squared are roughly twice those on country alone, and adding currency collapses the country coefficient while barely moving the currency one – so, at least for corporate bonds, the classic home-country bias documented since French and Poterba (1991) is largely confounded by home-currency bias (Table 4, pp. 14-15). Second, home-currency bias travels with a stark allocation of capital across firms: in each country a small number of large firms issue in foreign currency and borrow from foreigners, while most firms issue only in local currency and are held almost entirely by domestic investors. Probit estimates using Compustat, Worldscope and SDC data show that bigger firms are significantly more likely to issue in foreign currency on all four size proxies used (Table 5, p. 17). That this is not simply about which firms foreigners find unappealing is shown by the fact that the same local-currency-only firms do receive foreign equity investment (Figure 9b, p. 20). Third, the United States is the exception: a significant mass of medium-sized US firms issues only in dollars yet receives substantial foreign financing, which the authors read as the global taste for dollar debt effectively opening the capital account for local-currency US borrowers – a pattern found for no other country in the data (Section 4, pp. 16, 19-20). Fourth, in the time series the dollar’s role is recent rather than permanent: the dollar denominated 41 percent of global cross-border corporate debt holdings in the data in 2005 and the euro 38 percent, shares that were largely stable until 2008, after which the euro’s fell to 22 percent and the dollar’s rose to 63 percent (Introduction, p. 2; Section 5, pp. 21-22). The paper is explicit about its scope: the dataset contains quantities but not prices, so it cannot assess borrowing costs or quantify the value of the dollar’s privilege; it covers bond finance only and excludes bank lending; the analysis is of corporate rather than sovereign bonds; and the authors deliberately establish the four facts without identifying the mechanisms behind them, offering hedging costs, market segmentation by currency and fixed issuance costs as candidate explanations for future work to formalize.

Some Major Problems in Monetary Theory

This 1961 American Economic Association Papers and Proceedings essay by Karl Brunner argues that evaluating monetary policy’s effectiveness requires separately and rigorously assessing two distinct theoretical links: how policy actions (open-market operations, reserve requirements, the discount rate) affect monetary aggregates (“money supply theory”), and how monetary aggregates in turn affect income and prices (“money demand theory” combined with aggregate demand theory) — and that casual empirical patterns commonly invoked in policy debates fail to discriminate between rival hypotheses about either link. Brunner outlines a money-supply theory in which the money stock, bank credit, and interest rates are jointly determined in the bank credit market, and reports that partial-correlation estimates across differently-situated sample periods put the “monetary multiplier” (money stock’s response to the monetary base) in the range of 1.5 to 3.5, with the base identified as the single most important determinant of the money stock — explicitly rejecting the UK’s Radcliffe Report’s claim that the money supply was “evidently uncontrolled.” On the demand side, Brunner confirms the basic Keynesian interest-and-income specification but argues Milton Friedman’s permanent-income-based demand function better explains the secular and cyclical behavior of velocity, and reports his own modified versions (adding an interest-rate term) estimated on 1919-1959 annual data, finding significantly negative interest elasticities (around -0.22 to -0.30) dominated by a substantially larger permanent-income elasticity. The essay’s central substantive claim is a “portfolio adjustment” balance-sheet transmission mechanism — monetary policy works because money-stock changes alter the public’s whole balance sheet, triggering asset substitution across the full range of assets and liabilities (not just money versus bonds), which spills over into demand for newly produced goods and assets — and Brunner marshals four types of observational evidence (money-financed deficits and inflation, delayed post-control price adjustment, cross-sectional asset-holding patterns, and aggregate-demand equation fit) as consistent with this view.

Sovereign Bonds Since Waterloo

The paper asks a question the sovereign debt literature has mostly approached from the borrower’s side: given how often governments default, why do investors keep buying their bonds? It answers by measuring what creditors actually earned, assembling two new datasets and matching them bond by bond. The first is monthly price quotations for 1,552 foreign-currency sovereign bonds issued and traded in London and New York between 1815 and 2016 – 266,134 observations covering up to 91 countries in an unbalanced panel. The second is an archive of external default and restructuring events built largely from the annual reports of nineteenth- and early-twentieth-century bondholder organisations, yielding haircut estimates for 313 restructuring events in 91 countries and, crucially, the timing and size of missed or partial coupon payments at monthly frequency. The central finding is that the average real ex-post yearly return on a global portfolio of external sovereign bonds was 6.85% – about 4 percentage points above the “risk-free” benchmark of long-term UK and US government bonds, with the excess return running 2% to 4% depending on the era. Two things make that survive the defaults. First, defaults do not wipe creditors out: the average haircut is 44% (39% when weighted by amount restructured), with a standard deviation of about 30% and no visible time trend across 200 years, and outright repudiation is confined to revolutions and imperial break-ups. Second, roughly 70% of the 8.0% average nominal return – 5.6 percentage points – comes from coupons rather than capital gains, so returns keep accruing even while prices are depressed. The risk is real and priced: bonds of the 51 “serial defaulters” earn the highest returns (7.1% real, 4.6% excess) and also the highest volatility; after a default the cumulative return index falls about 15%, and an investor entering two years before default breaks even about four years after it, though the lower quartile of episodes never recovers within six years. Compared with other asset classes over the same two centuries, only US equities and a 16-country advanced-economy equity portfolio returned more, while the external sovereign bond portfolio’s Sharpe ratio is on a par with US equities and above US corporate bonds, UK equities, and domestic sovereign bonds. The authors are explicit about the scope limits: the sample is unbalanced with a near-total gap in the 1970s and 1980s syndicated-bank-loan era, so the 1980s debt crisis is largely absent; and they caution that the unusually good modern performance should not be read as a “new normal.”

Term structure evidence on interest rate smoothing and monetary policy inertia

Estimated Taylor-type policy rules typically find the Fed adjusts the funds rate only 20-30 percent of the way to its desired level each quarter, widely read as deliberate “interest rate smoothing.” Reviewing estimates of both a backward-looking Taylor rule and the forward-looking Clarida-Galí-Gertler variant on 1987-1999 U.S. data, the paper confirms the standard result: partial-adjustment coefficients around 0.7-0.9, fitting the data far better than a version with no lagged rate at all. The paper then tests the interest-rate-smoothing interpretation against an implication it must carry: if the funds rate genuinely adjusts only partially each quarter, a large share of its future path should be predictable from information already available, and rational financial markets should price that predictability into the term structure. Using eurodollar futures rates to construct real-time forecasts, the paper finds an R² of 0.57 for the funds-rate change one quarter ahead, but only 0.11 two quarters ahead and 0.03 three quarters ahead – essentially no forecastable variation beyond about three months, sharply at odds with what a highly inertial policy rule implies. The paper then shows that a policy rule with immediate, full adjustment (no smoothing at all) but a persistent, serially correlated shock term fits the historical funds-rate data just as well as the standard partial-adjustment rule on conventional goodness-of-fit measures, and formal tests cannot reliably distinguish the two specifications within available samples. Because only the serially-correlated-shock version is consistent with the term structure’s near-total unpredictability of the policy rate beyond a quarter, the paper concludes that the large lag coefficients found throughout the policy-rule literature are largely a statistical illusion generated by omitted persistent shocks to policy, not evidence that central banks deliberately smooth interest-rate changes over multiple quarters.

Term Structure Modeling with Supply Factors and the Federal Reserve's Large-Scale Asset Purchase Programs

This 2013 International Journal of Central Banking paper by Canlin Li and Min Wei asks whether changes in the supply of Treasury securities and agency mortgage-backed securities (MBS) affect nominal Treasury yields, and uses the answer to evaluate the Federal Reserve’s large-scale asset purchase (LSAP) programs. The authors build a no-arbitrage affine Gaussian term-structure model, motivated by the Vayanos-Vila (2009) preferred-habitat framework, whose state vector consists of two observable yield factors (the level, proxied by the 5-year yield, and the slope, the 5-year-minus-1-month spread, which together capture over 99% of yield variation) plus three observable supply factors: the Treasury ten-year-equivalents-to-GDP ratio, the agency-MBS par-to-GDP ratio, and MBS average duration. The model is deliberately restricted so the short rate loads only on the yield factors and supply factors carry zero own risk premium, meaning supply shocks affect yields only through the term premium and not through interest-rate expectations (the signaling channel is shut down by construction); the model is estimated by a two-step Ang-Piazzesi (2003) procedure on monthly pre-crisis data from March 1994 to July 2007. In-sample, supply factors are significantly and positively related to the term premium (reduced-form R-squared up to 0.89), a one-percentage-point decline in the Treasury ten-year-equivalents-to-GDP or MBS par-to-GDP ratio lowers the 10-year Treasury yield by roughly 10 basis points, a one-year shortening of average MBS duration lowers it by roughly 7 basis points, and supply factors account for about 9% (5-year) and 20% (10-year) of conditional term-premium variance at a 60-month horizon. Applying the estimated model out-of-sample to evaluate the Fed’s 2008-2012 asset purchases, and using the authors’ preferred approach that treats each program as a gradually implemented supply shock that investors expect to be partly reversed by future asset sales, the paper finds LSAP1 lowered 2-/5-/10-year Treasury yields by about 16/52/60 basis points, LSAP2 by about 2/13/19 basis points, and the Maturity Extension Program (MEP) by about 2/13/19 basis points, for a combined 10-year effect of roughly 100 basis points — the paper’s headline number. The authors are explicit that the model captures only the term-premium channel of LSAPs by construction, that estimates are sensitive to assumptions about the pace and timing of expected future asset sales, and that the model is fit on a pre-crisis sample and then applied out-of-sample to the very different 2008-2012 period.

Understanding policy in the great recession: Some unpleasant fiscal arithmetic

This paper uses the government-debt valuation equation – the requirement that the real value of outstanding money plus nominal government debt equal the present value of expected future primary surpluses – together with a money-demand equation, to interpret U.S. fiscal and monetary policy during and after the 2008-2009 financial crisis and to think through the possible paths to inflation or deflation that follow it. Cochrane argues that the depth of the 2008-2009 recession is best understood not as a shortage of money relative to money demand, but as a “flight to quality”: a surge in demand for all government debt, at the expense of private debt and of goods and services, corresponding in the fiscal equation to a fall in the discount rate applied to government liabilities. He argues that conventional “fiscal stimulus” reasoning is upended once government debt is recognized as nominal rather than real: a deficit is stimulative if and only if people do not expect future taxes or spending cuts to pay it off, and if so, future deficits are just as stimulative as current ones, so the standard “stimulus spending arrives too late” objection does not apply in this framework – though credibly communicating that debt will not be paid off is itself difficult, since most fiscal institutions are built to signal the opposite. On monetary policy, Cochrane contends that once nominal interest rates hit zero, “quantitative easing” that merely swaps money for short-term government debt does nothing, because the two are close to perfect substitutes at the margin; purchases of long-term debt can shift the timing but not the total magnitude of eventual inflation; and purchases of private debt can help only by relieving a genuine liquidity premium, an effect that is necessarily exhausted once that premium is satisfied. Extending the valuation equation to long-maturity debt, Cochrane argues that a plausible future “fiscal inflation” – one triggered by a reassessment of the government’s capacity or willingness to run future surpluses – would not appear as a sudden price-level jump but as a gradual process beginning with rising long-term interest rates, and that because credit guarantees, nominal government commitments, and growth effects on the present value of tax revenue can move the effective “fiscal limit” much closer than raw debt-to-GDP ratios suggest, such an event could arrive well before large current deficits, elevated debt/GDP, or overt debt monetization materialize. Finally, because in his account the fiscal valuation equation is itself what anchors inflation expectations, Cochrane argues a fiscal inflation is likely to act as a shift of the Phillips curve rather than a movement along it, so that – as illustrated in a calibrated New-Keynesian simulation in which output falls throughout an anticipated fiscal-inflation episode – such an event is more likely to resemble the stagflation of the 1970s than an inflationary boom, with correspondingly little that the Federal Reserve, legally barred from taking fiscal actions on its own, can do to prevent either outcome.