European Economic Review | Macro Paper Warehouse

A new index of financial conditions

This 2014 European Economic Review paper by Gary Koop and Dimitris Korobilis develops a time-varying-parameter factor-augmented VAR (TVP-FAVAR) with dynamic model averaging (DMA) to construct a financial conditions index (FCI) that lets both the weights on financial variables and the set of financial variables included evolve over time, while estimating the FCI’s relationship with the macroeconomy jointly rather than in a separate step. The model has two blocks: a financial block in which 18 financial variables (asset prices, volatilities, credit, and liquidity measures, with the S&P500 always included and the other 17 subject to variable selection) load on a latent factor (the FCI) and on contemporaneous macro variables (GDP deflator inflation, unemployment, and real GDP growth) with time-varying loadings, and a macro-FCI VAR block in which the macro variables and the FCI jointly evolve with time-varying VAR coefficients; both sets of parameters follow random walks, and the macro variables enter the financial block only to purge the FCI of current macroeconomic effects. Estimation uses a simulation-free two-step dual Kalman filter (no MCMC), with error covariances updated via exponentially weighted moving averages (decay factors 0.96 for observation equations, forgetting factors 0.99 for state equations), and Dynamic Model Averaging/Selection (DMA/DMS) is applied across the 2^17 = 131,072 possible subsets of the 17 optional financial variables using a Raftery et al. (2010) forgetting-factor approach with alpha = 0.99 (alpha = 1 nesting static Bayesian model averaging). Using quarterly U.S. data from 1970Q1-2013Q3, the resulting FCI begins declining before the onset of the 2007-2009 recession and bottoms out in early 2009, tracks the Chicago Fed National Financial Conditions Index most closely among existing indices while dropping earlier and further in 2008, and is built from a DMA-selected subset that averages between about 5 and 8 of the 17 optional variables at any point in time, with substantial switching in which variables are included as conditions change. In out-of-sample forecasting evaluated over 1990Q1-2013Q3 (Table 2) and against existing FCIs over 2000Q1-2013Q3 (Table 3), the TVP-FAVAR-DMA specification with (kappa=0.96, alpha=0.99) delivers lower mean squared forecast error and higher average predictive likelihood than a VAR benchmark at every horizon h=0-4 for inflation, unemployment, and output (e.g., relative MSFE of 0.63 and 0.55 for unemployment at h=0 and h=2), and “TVP-FAVAR-DMA and TVP-FAVAR-DMS almost always forecast better than the TVP-VAR-FCI4” (the TVP-VAR augmented with the Chicago Fed’s index, the best-performing existing-FCI comparator); the authors attribute the largest gains to allowing for stochastic volatility in the model’s parameters, with time-varying VAR coefficients, the FAVAR factor structure, and DMA/DMS each contributing further, smaller improvements.

Fiscal Imbalances and the Dynamics of Currency Crises

This paper builds a model in which a currency crisis is triggered by a “fiscal imbalance” – a current or anticipated future decline in the present value of the government’s real primary surpluses – and studies how the size and maturity structure of the government’s outstanding nominal liabilities, rather than the size of the fiscal gap alone, determine whether and for how long a fixed exchange rate can be defended before it collapses. In a baseline economy where the government holds only short-term nominal debt, the authors derive a “razor-edge” result: if the government tries to delay a devaluation to raise seigniorage revenue after the collapse, the present value of that seigniorage exactly offsets the fiscal cost of defending the peg beforehand (the revenue lost to the pre-collapse contraction in money demand), leaving the net present value of seigniorage equal to zero – so financing a fiscal imbalance through money creation and delaying the exchange-rate adjustment turn out to be mutually inconsistent goals, and with only short-term debt outstanding the peg must break immediately, with the size of the initial devaluation pinned down by the fiscal imbalance and the stock of outstanding money and bonds. Once the model is extended to include long-term, non-indexed government bonds (perpetuities), a different channel opens: news of a future fiscal imbalance causes an immediate, unanticipated fall in the price of those bonds, transferring wealth from private bondholders to the government exactly as an unexpected devaluation would, which can let the government postpone the collapse of the peg for a time even when the net present value of seigniorage is zero, provided the outstanding stock of long-term liabilities is large enough. Government solvency alone leaves the exact date of a delayed collapse indeterminate within a finite window; adding a monetary policy rule under which the central bank defends the peg only as long as the domestic interest rate stays below some threshold pins the timing down uniquely, via a backward-induction argument analogous to Krugman’s (1979) classic model but expressed in terms of an interest-rate rather than a reserve-based defense criterion. The paper also shows that when investors can trigger a self-fulfilling run on the government’s short-term debt – a coordination failure distinct from the fiscal mechanism – the exact timing of collapse becomes genuinely indeterminate and unpredictable even though the underlying fiscal imbalance still bounds how long the peg can possibly survive. Framed explicitly as an extension of the fiscal theory of the price level to a currency-crisis setting, and as a bridge to first-generation, Krugman-style crisis models, the paper’s authors are careful to note that a precisely zero net seigniorage result is a feature of their specific model, but argue the underlying lesson – that the fiscal costs of peg defense constrain what seigniorage policy can actually achieve – is more general.

Rule-of-thumb behaviour and monetary policy

Standard optimisation-based sticky-price models have no lagged variables in their structural equations, which makes them hard to square with the high serial correlation actually observed in output and inflation; this paper asks what happens to optimal monetary policy once a fraction of agents is allowed to skip the optimisation and follow a simple backward-looking rule instead. The model is otherwise identical to Woodford’s – a closed economy with no capital accumulation, a continuum of monopolistically competitive household-producers, and Calvo price setting – and the two departures are deliberately symmetric. Each period a household draws an independent optimisation cost; a fraction of households with costs above a threshold sets consumption equal to last period’s aggregate per-capita consumption rather than solving its Euler equation, and among firms offered a Calvo price-reset opportunity a fraction follows Gali and Gertler’s rule of setting its price to last period’s average newly chosen price scaled up by last period’s inflation. Both departures put a lagged endogenous variable into the structural equation – lagged output into the IS curve, lagged inflation into the Phillips curve – and both, the paper shows, also change the welfare criterion that policy should be maximising, a point not previously noted in the literature: rule-of-thumb price setting adds a penalty on the squared change in inflation, and rule-of-thumb consumption adds a penalty on the squared change in output. Rule-of-thumb behaviour works in two opposing directions. It raises endogenous persistence, which on its own would make inflation and the output gap more variable; but it also weakens transmission, reducing the sensitivity of inflation to the output gap and of output to expected real interest rates. In the paper’s calibration – Woodford’s parameter values, based on Rotemberg and Woodford’s estimates on U.S. data for 1980-95, with Calvo parameter 0.66 per quarter, discount factor 0.99, and a natural-rate-of-interest shock with standard deviation 0.93 percent per quarter – the weakening of transmission dominates, so inflation variability falls as rule-of-thumb price setting becomes more prevalent and output gap variability falls sharply as rule-of-thumb consumption becomes more prevalent. The central policy result is that highly inertial, indeed “superinertial,” interest rate policy – a sum of coefficients on lagged interest rates exceeding one – remains optimal at every fraction of rule-of-thumb behaviour examined (the paper reports results for optimising fractions of 1, 0.6 and 0.2), and survives every robustness check it runs: a lower weight on interest rate variability, logarithmic preferences, serially correlated shocks, and the introduction of inefficient supply shocks that create a genuine inflation/output-gap trade-off. Two rules stand out as robust: the four-argument rule that implements the optimal plan when all agents optimise (current inflation, the change in the output gap, and two lags of the interest rate), and a first-difference version of Taylor’s 1993 rule. By contrast, rules feeding back only from inflation and the lagged interest rate, and price-level rules, have optimal coefficients that shift dramatically with the rule-of-thumb fraction – an unattractive property given how hard that fraction is to measure. Throughout, the policymaker is assumed able to commit; the authors are explicit that further work is needed to show these particular rules of thumb are good approximations to actual decision making.

Stepping on a rake: The role of fiscal policy in the inflation of the 1970s

Sims argues that the standard account of the 1970s US inflation – which treats it as attributable solely to monetary policy errors, and monetary policy as the only instrument that could have prevented it – omits an important part of the story: US fiscal policy underwent dramatic shifts over the decade, and economic theory shows that when the public is uncertain about the future course of fiscal policy, raising interest rates to fight inflation can lose its potency or even produce perverse effects. The theoretical mechanism, standard in “fiscal theory of the price level” (FTPL) models, is that when forward-looking agents believe newly issued nominal government debt is only partially backed by expected future taxes, debt issuance is inflationary, and interest-rate increases can raise rather than lower inflation, because higher debt-service payments flow directly into higher nominal government spending without any offsetting restraint on private spending. Sims documents that the primary surplus relative to the market value of privately held federal debt – his preferred single measure of fiscal stance – shows the US running surpluses most of the postwar period, with the first sustained large primary deficits appearing only in 1975 during the Ford tax cut and rebate (briefly reaching an annualized 20 percent of debt, “a level not approached before or since” since 1950), a pattern he argues would have left contemporaries genuinely uncertain about the future path of fiscal policy. Building a progression of models – a globally solvable flexible-price endowment economy, a bare-bones flexible-price FTPL model with only short-term debt, and a New Keynesian-style sticky-price model with long-term debt, habit formation, and a countercyclical primary surplus – Sims shows first that even a Taylor rule satisfying the “Taylor principle” (responding more than one-for-one to inflation) can be consistent with a unique but explosive inflation equilibrium once fiscal policy is “active” (the primary surplus set exogenously, without regard to debt), and second that in the more realistic sticky-price model, an “active fiscal, passive money” policy configuration leaves monetary policy able to produce a genuine recession in the short run, but not to control the long-run price level: after an interest-rate increase, inflation initially falls but then “rises back above its steady state level by as much as it initially fell,” a delayed-reversal pattern the paper names “stepping on a rake.” A companion result shows that an expansionary fiscal shock produces a consumption boom and a jump in inflation that monetary policy can temporarily choke off by raising rates, but the associated increase in government debt is ultimately financed through a permanent, unanticipated rise in the price level rather than future primary surpluses. Turning to the data, a seven-variable Bayesian VAR estimated on 1960-2010 U.S. data finds that price-level variance is dominated by output and price innovations, but that the difference between these two shocks produces a response pattern – rising prices alongside declining projected future primary deficits – that qualitatively resembles the paper’s theoretical fiscal-shock pattern, albeit with a negative output response inconsistent with a pure fiscal disturbance and more consistent with the fiscal surprises that may have accompanied the 1970s oil shocks; this fiscal-like channel accounts for a “non-trivial, but far from dominant” share of historical inflation variation. Sims concludes that econometric models used for monetary policy analysis have no excuse to continue omitting serious treatment of fiscal behavior, a point he argues is especially urgent in 2010 given the scale to which central-bank balance sheets have expanded since the financial crisis.

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.