## 1. Natural Interest Rates with Z Modelled as a Random Walk ## Source details **Canonical URL:** [1. Natural Interest Rates with Z Modelled as a Random Walk](https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020116-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2020/english/wpiea2020116-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2020/english/wpiea2020116-print-pdf.pdf.json) --- ### Overview and purpose - Focus: estimate the real natural interest rate, r*, over the last two decades for a diverse sample of European countries (France, Germany, Italy, Lithuania, the Netherlands, Poland, Portugal, Romania, Russia, and Spain). - Motivation: assess monetary policy effectiveness in a low-interest-rate environment since the global financial crisis (GFC) and implications for future interest rate paths and public debt dynamics. - Use of sample heterogeneity to examine determinants of r*: currency union membership, volatile capital flows, and advanced vs. emerging economy differences. - Period covered: prior to the COVID-19 crisis (quarterly data mostly from 2000:Q1 to 2019:Q1); conclusions used to discuss factors bearing on future r* and fiscal implications. - Institutional facts preserved from source: - Lithuania joined the EMU on January 1, 2015. - Since February 2002, Lithuania pegged its currency to the euro in the context of the ERM II and operated a currency board framework allowing use of the euro in settlement. ### Key empirical findings - Broad patterns: - A generalized decline in r* over the last 20 years across all methodologies applied. - Economic-model-based estimates (Laubach–Williams variants) show some partial recovery in recent years as growth resumed after the crisis; purely statistical/time-series (factor) models indicate a continuing decline since the end of the crisis. - None of the estimates point to clear prospects for natural rates increasing. - Magnitudes and country specifics: - For Euro Area countries, the average decline in r* was 2 percentage points since 2000, with r* estimated at a value of around zero in 2019:Q1. - Russia shows a decline in r* of around 4 percentage points since the early 2000s. - Romania and Poland show declines of around 1 percentage point since the early 2000s. - In Russia, estimated r* is around 2 percent in early 2019, broadly similar to trend growth and to the Central Bank of Russia’s estimate of 2–3 percent. - For most Euro Area countries in the sample, around half of the overall estimated decline in r* since the GFC can be attributed to the unexplained component, z_t. - In Portugal and Spain, the wedge between r* and g rose to 3–4 percentage points around the time of the Euro Area Debt Crisis. - Monetary conditions and heterogeneity: - By the end of the sample period, monetary conditions were highly accommodative in all Euro Area countries studied; the r − r* gap was around -2 percent in 2019:Q1 (L–W framework with z modeled as a function of economic variables). - Differences in r* across countries produced significant heterogeneity in monetary conditions within the Euro Area under a single monetary policy. - Emerging Europe displayed pro-cyclical policies tendencies (particularly Russia); risk premia played an important role. - Implications: - Persistently low r* suggests unconventional monetary policies (UMPs) may become more conventional. - A lower r* provides some fiscal space, which several countries were already using by end-sample, but declining potential growth and already high debt argue for caution in further debt accumulation. ### Conceptual definition and measurement issues - Definition: r* is the rate that maintains an economy in equilibrium if it starts there and does not interfere with autonomous return to equilibrium; includes the common definition as the real rate prevailing when the output gap is closed and inflation is stable. - r* treated as a short-run real interest rate (e.g., overnight rate or the 3-month government bill rate); in reserve-currency contexts often associated with a risk-free short-term rate. - Distinctions and complications: - r* ≠ average return on capital (which includes credit and duration risk). - Open capital accounts and exchange rate/country risk premia complicate the concept: uncovered interest parity and no-arbitrage conditions imply r* must ensure equilibrium between domestic and foreign real returns. - In a currency union, r* can differ across members because of asymmetric shocks; a common policy can deliver different monetary conditions across members. ### Methodological approach: Laubach–Williams (L–W) specification and estimation - Benchmark model: Laubach and Williams (2003) and later variants (e.g., Holston et al. (2016)); authors follow Bayesian estimation (Pescatori and Turunen (2015)) with Kalman filter. - Core structure (equations preserved conceptually from source): - IS curve (backward-looking): - ȳt = α1 ȳt−1 − α2 (rt − rt*) + εy t - Prevailing real rate rt = nominal policy rate it − one-year ahead inflation expectations πt+1 e (rt treated as exogenous/policy-determined). - Potential output: - yN t = yN t−1 + gt + εN t - gt = gt−1 + εg t (trend growth random walk). - Phillips curve (open-economy backward-looking): - πt = β1 πt−1 + β2 ȳt−1 + β3 πt−1 m + επ t (πm t import price inflation exogenous). - Link between r* and trend growth plus an exogenous component: - rt* = c g t + zt with c > 0; in simplest specification zt follows a random walk. - Role of zt: captures determinants of r* beyond trend growth and can generate a wedge between r* and g. - Estimation choices: - Bayesian priors on variances of shocks (εN t, εy t, εg t) crucial; priors influence how closely r* follows g. - Model variations explore different specifications for zt: pure random walk and formulations with autoregressive terms and observable economic drivers. ### Specifications used to model z_t (exact equations preserved from source) - Euro Area specification (equation (6)): - z_t = δ_1 z_{t−1} + δ_2 z_{t−2} + δ_c ΔREER_t + δ_p RE_t + δ_e Δspreads_t + ε^z_t - ΔREER_t: difference between actual level of the REER and its trend. - RE_t: trading partner growth (external demand). - spreads_t: 10-year country government yield relative to Germany’s 10-year yield (for Germany use CDS). - First two variables reflect current account influence; spreads measure risk and proxy capital account influence. - Emerging Europe specification (equation (7)): - z_t = δ_1 z_{t−1} + δ_2 z_{t−2} + δ_c ΔUSrate_t + δ_p ΔEMBI_t + δ_e Δspunc_t + ε^z_t - ΔUSrate_t: 10-year Treasury Bond yield at constant maturity deflated by expected inflation. - ΔEMBI_t: Emerging Market Bond Index spread. - Δspunc_t: news-based economic policy uncertainty index (Baker, Bloom, Davis (2016)); for Poland and Romania the European policy uncertainty index is used; alternative specification replaces this index with the REER. ### Annex III — Priors and sensitivity (summary) - Priors emphasize variances of key shocks: εN t (potential output), εy t (output gap), εg t (trend growth); priors determine how variance of r* responds to shocks to g and to z_t. - Literature shows wide ranges for parameter ratios (λg = σg / σN and λz = σz / (σy ar √2)); priors chosen within literature ranges. - Sensitivity exercise on autoregressive sum for z (baseline 0.99 vs 0.96) yields: - Changing AR-sum from 0.99 to 0.96 generally produces larger r* for most countries at the crisis trough and at the last data point (2019:Q1). - Selected differences (r* — Difference (0.96 − 0.99), last observation 2019:Q1): FR 0.5, IT 0.7, DE 0.7, NL 0.8, PT -0.1, RO 1.0, RU 0.7, AT 0.6, BE 1.0, FI 0.5 (numbers reproduced exactly from sensitivity table). - Priors specification guidance: priors for standard deviations are inverse gamma; tight priors for the standard deviation of c, output gap persistence (a1 + a2), and persistence of z (d1 + d2); wider priors for λg and λz. ### Annex III — Quantitative summaries and model-comparison context - Consistency with literature: Brand et al. (2018) r* estimates for entire Euro Area concentrated between 0 and -1 percent, encompassing authors’ country estimates (except Lithuania). - Factor-model (Del Negro et al.) results broadly similar in magnitude (around 2 percentage point decline for Euro Area) but differ in dynamics: - Factor models show clearer co-movement across countries and produce r* estimates that are negative at around -1 percent at mid-2019. - L–W framework shows deeper crisis troughs and modest recoveries; factor models dampen crises and rebounds but emphasize common factors. - Factor-model emerging Europe findings: - Russia: r* falls from around 4 percent in the early 2000s to closer to 2 percent by 2018, with jumps in 2008 and 2014 due to risk-premium spikes. - Poland: decline similar in size to Russia but steadier. - Caveat: trend-cycle decompositions are less suited for emerging economies because structural breaks are frequent. ### Annex VI — Drivers of r* and factor interpretation - Declines and cross-country commonalities may reflect a common factor (Jordà and Taylor, 2019) plus country-specific factors: - Country-specific drivers: fiscal shocks (Rachel and Summers, 2019), slow deleveraging post-GFC, financial cycles (Belke and Klose, 2018; Borio et al., 2019), demographics (Brand et al., 2018; Bielecki et al. (2018)). - Role of unexplained component z_t: - Large unexplained component remains after accounting for modeled drivers; persistence motivates autoregressive modeling. - If z_t reflects protracted deleveraging, the wedge between r* and g may diminish over time (agenda for future testing). - Decomposition highlights: - Decline in the U.S. long-term interest rate pushed r* downwards. - Increases in country risk premium (EMBI) pushed r* upwards. - For Russia, decreases in global interest rates and reductions in country risk were offset by increases in perceived economic policy uncertainty, explaining a large part of z_t. - Using REER instead of policy uncertainty suggests a small REER contribution to r*, possibly due to correlation with U.S. rate and EMBI. - Factor models methodology (brief): - Trend real short rate defined as r*; Kalman filter with Bayesian estimation and cointegration restrictions extract common and country-specific trends. - DN17 and DN19 frameworks used to complement L–W approaches by extracting r* directly from financial market data. ### Monetary conditions, UMPs, and market signals - Monetary stance assessment: - The r − r* gap gauges policy stance for currency-issuing countries; for monetary unions it indicates how the common policy is felt in members. - Larger positive (negative) interest rate gap implies more contractionary (expansionary) impulse. - Estimation uncertainty (real-time data lags and end-point issues) complicates assessment; r* estimates should be complemented by other variables and judgment. - Key empirical observations (L–W framework with z as function of economic variables): - Prior to the GFC monetary conditions were loose, tightened in 2007, and following Lehman’s failure rates fell by over 3 percent within one year. - By 2012 the ECB was close to the effective lower bound (ELB); subsequent changes in r − r* were driven largely by r* evolution. - Toward end-sample, the r − r* gap was about -2 percent in 2019:Q1, indicating accommodative conditions despite narrowing/closing output gaps. - Country examples: - France: r − r* gap rose by over 2 percentage points from 2005 to 2008, then fell below zero in 2008:Q3. - Portugal and Spain: r* declined markedly during the Euro Area crisis; conditions were tighter for longer. - Netherlands: r* did not sink as low during stress, so single policy delivered appropriate conditions; end-sample conditions were accommodative while output gap turned positive. - UMPs and shadow rates: - After hitting ELB the ECB used instruments not captured by observed r; shadow rates (Krippner (2015), Wu and Xia (2016)) can assess stimulus from asset purchases and forward guidance. - Replacing observed r with a shadow rate requires r* estimates constructed considering UMPs and potentially different IS transmission. - Conjecture: both shadow r and r* are lower because of UMPs; assessing UMP impact on stance requires further research. - Market-based signals (June 2019): - Forward rates and Nelson–Siegel term-structure techniques indicate markets expected real interest rates to remain well below zero for at least five years ahead across nearly all Euro Area countries. - Market-implied expected values were below the range of the paper’s r* estimates. - Emerging Europe markets: liquidity and credit premia caution; Poland and Romania market data suggested modest increases in real rates but still below paper’s r* estimates; Russia market analysis suggested real rates would remain near mid-2019 levels and above r* over the medium term. ### Implications for debt sustainability and fiscal policy - Standard debt-dynamics relation (equation preserved exactly in source): - Δs_t = (r_t^e − g_t) / (1 + g_t) s_{t−1} − sb_t - Δs_t: change in public debt ratio, s_{t−1}: previous debt stock, sb_t: government primary balance, r_t^e: real effective interest rate on public debt, g_t: real growth. - Key considerations and empirical findings: 1. Interaction with potential growth: - A lower r* may imply lower potential growth; drivers of r* also affect potential growth but not one-for-one. - Estimates indicate r* decreased by 2 percentage points on average comparing post-GFC with pre-GFC, while trend growth fell by around 1 percent. - The decline in the r − g differential was half as large as the decrease in r*, providing additional fiscal space. - Setting Δs_t = 0, a lower r − g implies a lower debt-stabilizing primary balance (DSPB); compared to pre-GFC the DSPB declined by nearly 1 percentage point of GDP on average for the sample (assessed at 2018 debt ratios). 2. Durability of r − g improvements: - Persistence of the r* − g path determines durability of policy space; by end-period r* − g was still below pre-crisis levels for most countries (except Lithuania) but had partially recovered. - Uncertainty about persistence is significant (pandemic collapse in g highlighted). - Some countries had already used extra space by late 2010s: - France, Italy, Spain: used space to stabilize debt with a lower primary balance rather than reduce debt ratios. - Romania: primary balance insufficient to stabilize debt. - Portugal, Germany, Netherlands, Lithuania, Poland, Russia: used extra fiscal space to reduce debt faster. 3. Crisis-related debt increases offsetting fiscal space: - All countries except Germany experienced debt increases during the GFC that raised the DSPB, offsetting part of fiscal space from lower r* − g; in some cases (e.g., Spain) this effect could exceed the fiscal space generated. 4. Short rate vs effective borrowing rate: - r* is a short rate; government borrowing includes term premia that vary over time/maturity; pass-through to effective interest rate is gradual as debt rolls over. - Deep recessions can rapidly worsen debt dynamics via denominator effects (example: Portugal’s effective interest rate minus actual growth). 5. Credit risk premia: - Risk premia critically affect debt sustainability; swift market perception shifts can rapidly raise long-term rates; highly indebted countries are vulnerable to sudden stops. 6. Primary balance and demographic pressures: - Drivers that lower r* and g (e.g., aging) also increase dependency ratios and pressure primary balances. - Lower r* − g reduces DSPB, but maintaining a given primary balance becomes harder over time; fiscal prudence advised even if r* − g is lower. - With lower r* the likelihood of hitting the ELB increases, reducing monetary scope and raising the premium on conserving fiscal space for countercyclical use. ### IV. Policy implications (summarized) - Monetary policy: - Persistently low r* increases the probability of hitting the ELB; UMPs may be used more frequently and become more conventional, particularly in the Euro Area. - Heterogeneity of r* within currency unions implies single policy may be poorly aligned with individual members’ stabilization needs. - Questions raised by frequent UMP use include optimal central bank balance-sheet size, ELB on long-term rates, limits to quantitative easing, viability/risks of helicopter money, adverse side effects from negative rates and asset purchases. - Fiscal policy: - Lower r* offers some fiscal space but declining potential growth and existing high debt warrant caution in additional borrowing. - Fiscal policy may need to play an enhanced stabilization role when monetary policy is constrained; this requires maintaining fiscal space. - Care required before using low r* as justification for tolerance of high debt ratios. ### V. Conclusions (key takeaways) - r* declines across sample over 2000–2019 with substantial uncertainty and large unexplained components for several countries; results require cautious interpretation and policy judgment alongside other indicators. - Broad conclusions: - Natural rates declined in the sample over the last 20 years. - A significant part of the decline is accounted for by a fall in potential growth, larger in advanced European economies than in emerging Europe. - The decline in r* after the GFC has been more pronounced than the fall in potential growth, creating a wedge between r* and g; this wedge became large during the GFC and only moderately decreased in advanced economies. - Part of the wedge is attributable to external factors (trade, capital flows, changing risk perception); country risk premia can push r* upward in emerging markets (e.g., Russia). - Large residuals remain after controlling for observable variables; the wedge may reflect slow-moving factors such as protracted deleveraging, especially in the Euro Area. - If deleveraging was a main driver, the wedge may persist if pandemic-related re-leveraging requires future correction. - Any rise in r* is likely to take time; it is difficult to imagine r* rising above g anytime soon, particularly in advanced economies. - Even without additional shocks, both r* and g will likely remain lower than early 2000s levels given expected European growth trends. - Macro policy implications: - Monetary: lower r* and low inflation increase ELB risk, making UMPs more likely first-resort tools. - Fiscal: lower r* could increase fiscal space, but higher debt levels and the possibility of term-premium spikes necessitate conservatism in using that space. *Source: IMF working paper chapter "1. Natural Interest Rates with Z Modelled as a Random Walk" (excerpt provided).* ### 1. Natural Interest Rates with Z Modelled as a Random Walk...............................................10 ### 1. Natural Interest Rates with Z Modelled as a Random Walk ### Overview and purpose - Focus: apply a few different approaches to estimate the real natural interest rate, r*, over the last two decades for a diverse sample of European countries (France, Germany, Italy, Lithuania, the Netherlands, Poland, Portugal, Romania, Russia, and Spain). - Motivation: assess monetary policy effectiveness in a low-interest-rate environment since the global financial crisis (GFC) and implications for future interest rate paths and public debt dynamics. - Sample heterogeneity is used to examine determinants of r*: currency union membership, volatile capital flows, and differential impacts on advanced vs. emerging economies. - Period covered is prior to the COVID-19 crisis; conclusions allow discussion of factors bearing on future interest rates and fiscal implications. ### Key empirical findings - A generalized decline in r* over the last 20 years, particularly in advanced economies, is found across all methodologies applied. - Economic-model-based estimates that link r* to the real economy show some partial recovery in recent years as growth resumed after the crisis. - Purely statistical/time-series models indicate a continuing decline in the natural rate since the end of the crisis. - None of the estimates point to clear prospects for natural rates increasing. - Differences in r* across countries led to significant heterogeneity in monetary conditions within the Euro Area during the last two decades, even under a single Euro Area monetary policy. - By the end of the sample period, monetary conditions were highly accommodative in all Euro Area countries studied. - Emerging Europe displayed a propensity for pro-cyclical policies (particularly in Russia), influenced by the role of the risk premium. - Persistently low r* across Europe suggests unconventional monetary policies (UMPs) may become more conventional in the future. - A lower r* provides some fiscal space, which several countries were already using by the end of the sample, but declining potential growth and already high debt call for caution in further debt accumulation. ### Conceptual definition and measurement issues - r* defined here as the rate that maintains an economy in equilibrium if it starts there and does not interfere with the autonomous return to equilibrium of an economy initially in disequilibrium; includes the common definition as the real rate prevailing when the output gap is closed and inflation is stable. - r* is treated as a short-run real interest rate (e.g., overnight rate or the 3-month government bill rate). - In reserve-currency contexts, r* is often associated with a risk-free short-term rate; r* is not equivalent to the average return on capital (which includes credit and duration risk). - Open capital accounts complicate the r* concept: real uncovered interest parity and no-arbitrage conditions imply r* must also ensure equilibrium between domestic and foreign real returns; exchange rate risk and country risk premia can push r* upward in emerging markets. - In a currency union, r* can differ across members due to asymmetric shocks; a common monetary policy can produce different monetary conditions across member states. Co-movements of r* within a union may exist but can change over time. - Two specific institutional/date facts preserved from the source: - Lithuania joined the EMU on January 1, 2015. - Since February 2002, Lithuania pegged its currency to the euro in the context of the ERM II and operated a currency board framework allowing use of the euro in settlement. ### Methodological approach: Laubach-Williams (L-W) model specification and estimation - Benchmark: Laubach and Williams (2003) model and later variants (e.g., Holston et al. (2016)) that allow r* to vary over time and link r* to potential growth. - Core idea: simultaneous estimation of r* and potential growth (g) from observable data using a Kalman filter, combining a backward-looking IS curve, a Phillips curve, and stochastic specifications for potential output and trend growth. - IS curve (backward-looking) relates the output gap (ȳt) to its lags and to the difference between prevailing real interest rate (rt) and the natural rate (rt*): - ȳt = α1 ȳt−1 − α2 (rt − rt*) + εy t (Equation (1) in source) - Prevailing real rate rt assumed exogenous in the short run (policy-determined), equal to nominal policy rate it minus one-year ahead inflation expectations πt+1 e. - Output gap definition and potential output dynamics: - Potential output: yN t = yN t−1 + gt + εN t (Equation (2)) - Trend growth modeled as a random walk: gt = gt−1 + εg t (Equation (3)) - Open-economy backward-looking Phillips curve: - πt = β1 πt−1 + β2 ȳt−1 + β3 πt−1 m + επ t (Equation (4)), where πm t (import price inflation) is exogenous. - Relationship between r* and trend growth plus an exogenous component zt: - rt* = c g t + zt with c > 0 (Equation (5)) - In the simplest specification, zt follows a random walk with iid shocks (εz t). - The z term captures determinants of r* beyond trend growth and can create a wedge between r* and g. - Estimation method: Bayesian techniques (following Pescatori and Turunen (2015)) to address pile-up problems in classical inference and to control estimation via priors on variances of error terms (εN t, εy t, εg t). Priors importantly influence how closely estimated r* follows estimated g. - Model variations: different specifications for zt are explored, starting with a random walk and extending to more complex specifications. ### Literature context and quantitative magnitudes cited - Consensus in literature on a global decline in r* over the last two decades (Summers, 2014; Holston et al, 2017; Brand et al, 2018; Del Negro et al, 2019). - Rachel and Smith (2015) document a decline in the global long-term r* of around 450 bps since 1980. - Magud and Tsounta (2012) find a decline in the natural rate of interest in many Latin American countries over the last decade (referenced). ### Implications for policy - Monetary policy: - Persistent low r* implies prolonged accommodative monetary conditions and a potential normalization of unconventional monetary policies (UMPs). - Heterogeneity in country r* within the Euro Area implies that a single monetary policy produces differing stances across member states. - Fiscal policy: - Lower r* provides some fiscal space and reduced public financing costs; some countries were already utilizing this space. - Declining potential growth and high public debt in many countries argue for cautious use of additional fiscal space to avoid further debt accumulation. - Emerging markets: - Exchange rate uncertainty and country risk premia can keep policy rates (and thus r*) elevated; central banks in emerging markets face trade-offs when capital mobility and repricing of domestic risk constrain the effectiveness of lower policy rates. *Source: IMF working paper chapter "1. Natural Interest Rates with Z Modelled as a Random Walk" (excerpt provided).* ### Annex III describe the implications of these priors for the level and volatility of r* estimates. ### Annex III describe the implications of these priors for the level and volatility of r* estimates ### Summary findings on r* levels and trends - In virtually all countries in the sample, both in the Euro Area and outside, natural rates and potential growth rates have fallen relative to the early 2000s, with some modest recovery post-Euro Area Debt Crisis (2012). - r* typically fell more markedly than potential growth in the last two decades, particularly after the GFC. - For Euro Area countries, the average decline in r* was 2 percentage points since 2000, with r* estimated at a value of around zero in 2019:Q1. - For emerging Europe: - Russia shows a decline in r* of around 4 percentage points since the early 2000s. - Romania and Poland show declines of around 1 percentage point since the early 2000s. - The part of the decline in r* explained by the fall in g is generally smaller in Euro Area countries than in emerging economies; Russia stands out for having the largest decline in r* combined with the closest linkage to a change in g. - For most Euro Area countries in the sample, around half of the overall estimated decline in r* since the GFC can be attributed to the behavior of the unexplained component, z_t. - In Portugal and Spain, the importance of this z component is the largest, with the wedge between r* and g rising to 3–4 percentage points around the time of the Euro Area Debt Crisis. - In recent years, r* has picked up somewhat, seemingly spurred by the recovery in potential growth. - In Russia, estimated r* is around 2 percent in early 2019, broadly similar to the estimate for trend growth and similar to the Central Bank of Russia’s (CBR) estimate of 2–3 percent. - In Poland, z_t contributes negatively to r*, with its (absolute) value increasing from about zero in the early 2000s to about 1 percentage point by early 2019, with most of that increase occurring during and after the GFC. ### Role and interpretation of the unexplained component z_t - The unexplained component z_t captures other factors beyond trend growth that influence r*, and its persistence motivates modelling it with autoregressive terms. - "The estimate of the coefficient c in the expression for r* is around unity, which makes it possible to loosely refer to z_t as wedge the between r* and g." - Even after modelling z_t as a function of economic variables, a relatively large unexplained component of r* remains for most Euro Area countries, suggesting important domestic factors (e.g., debt overhangs in private and public sectors) may play a strong role. ### Specifications used to model z_t - Euro Area specification (equation (6), preserved exactly as in source): z_t = δ_1 z_{t−1} + δ_2 z_{t−2} + δ_c ΔREER_t + δ_p RE_t + δ_e Δspreads_t + ε^z_t - ΔREER_t is the difference between the actual level of the REER and its trend. - RE_t is trading partner growth representing external demand. - spreads_t is the difference between the 10-year country government yield relative to Germany’s 10-year government yield (for Germany use Credit Default Swaps, CDS). - First two variables reflect current account influence; spreads measure risk and proxy capital account influence. - Emerging Europe specification (equation (7), preserved exactly as in source): z_t = δ_1 z_{t−1} + δ_2 z_{t−2} + δ_c ΔUSrate_t + δ_p ΔEMBI_t + δ_e Δspunc_t + ε^z_t - ΔUSrate_t refers to 10-year Treasury Bond yield at constant maturity deflated by the expected inflation rate. - ΔEMBI_t is the Emerging Market Bond Index spread (EMBI). - Δspunc_t refers to the news-based index of economic policy uncertainty from Baker, Bloom, and Davis (2016). - For Poland and Romania, where country-specific policy uncertainty is unavailable, the European policy-related economic uncertainty index is used; an alternative specification replaces that index with the REER. ### Effects of modelling choices on level and volatility of r* - Modelling z_t as a function of economic variables (rather than as a pure random walk) increases the volatility of r* estimates for Euro Area countries: - Drops in r* in 2009 and 2012 become steeper. - Subsequent recoveries become more pronounced. - Despite differences in volatility, the estimated overall decrease in r* over the last two decades is broadly similar regardless of how z_t is modelled; large residuals remain in some cases. - The similarity of latest r* estimates whether z_t is modelled or not suggests domestic, possibly long-lasting factors, play an important role. ### Notable country-level illustrations and contributions - Lithuania: In 2009, at the lowest point in Lithuania’s recession, the credit crunch (proxied by a sharp rise in spreads) contributed to a fall in r* of 2 percentage points. - Italy: Italy saw a deep fall in r* associated with worsening spreads during the Euro Area Debt Crisis; heightened uncertainty around debt sustainability drove this movement. - Germany and the Netherlands: The collapse in external demand in 2009 resulted in a 3 percentage point decline in r*, later reversed as external demand rebounded—illustrating r* volatility and sensitivity to external shocks. - Decompositions (figures summarized in source): - Contribution of external demand, spreads, REER, US rate, and country risk to r* are presented for Euro Area and emerging Europe, showing variable importance across countries and periods. ### Consistency with other literature - Brand et al. (2018) gather several r* estimates for the entire Euro Area concentrated between 0 and -1 percent, encompassing the authors' estimates for individual Euro Area countries (except Lithuania). - Fries et al. (2017) and other joint estimates of Spain, Italy, France, and Germany report similar magnitudes in the decline of r* and find r* close to zero as of end-2017. *Source: IMF Working Paper (Annex III section as provided in the content unit).* ### Annex VI). This may reflect a common factor influencing r* (Jordà and Taylor, 2019), ### wpiea2020116-print-pdf - Annex VI). This may reflect a common factor influencing r* (Jordà and Taylor, 2019), ### Drivers of r* and interpretation - Observed declines and cross-country commonalities in r* may reflect a common factor influencing r* (Jordà and Taylor, 2019), coupled with country-specific factors. - Country-specific factors mentioned: - Fiscal shocks (Rachel and Summers, 2019). - The slow deleveraging process following the GFC. - Financial cycles (Belke and Klose, 2018; Borio et al, 2019). - Demographics (Brand et al., 2018; Bielecki et al. (2018)). - If the unexplained part of 푧푧 푡푡 (and r*) reflects protracted deleveraging, the wedge between r* and g may diminish further over time (noted as an agenda item for future testing). - For emerging Europe, r* estimates are more volatile when modeling 푧푧 푡푡 as a function of economic variables; volatility increases after global shocks (e.g., “taper tantrum”) or country shocks (e.g., western sanctions and lower oil prices for Russia in 2014–15). - Decomposition results: - Decline in the U.S. long-term interest rate pushed r* downwards. - Increases in country risk premium (EMBI) pushed r* upwards. - For Russia, decreases in global interest rates and reductions in country risk were more than offset by increases in perceived economic policy uncertainty, which explains a large part of 푧푧 푡푡 (see Figure 2 and Annex VI). - Considering REER instead of policy uncertainty suggests a small contribution of the former to r*, possibly reflecting correlation with U.S. rate and EMBI. ### Factor models: methodology and key quantitative findings - Rationale: - Complement L-W (real-variable) approaches by extracting r* directly from financial market data. - Models assume real interest rates fluctuate around r* and differences decay as shocks dissipate. - Del Negro et al. (2017, 2018) approach (Kalman filter with Bayesian estimation): - Trend real short rate is defined as r*. - Real variables are derived from inflation data, nominal short rates, and nominal long rates. - Cointegration assumptions (as presented): - 휋휋 푡푡 = 휋휋 푡푡 ∗ + 푠푠 푡푡 (Equation (8)) - 푖푖 푡푡 3푚푚 = 휋휋 푡푡 ∗ + 푟푟 푡푡 ∗ + 푝푝 푡푡 (Equation (9)) - 푖푖 푡푡 10 푦푦푦푦 = 휋휋 푡푡 ∗ + 푟푟 푡푡 ∗ + 푡푡푠푠 푡푡 ∗ + 푣푣 푡푡 (Equation (10)) - Trend components follow a random walk and white-noise shocks. - Euro Area results from Factor models: - Show a clear decline in r* for all Euro Area countries of around 2 percentage points, very similar to L-W framework results (Figure 4). - Unlike L-W estimates, Factor models do not show a deep fall in natural rates during crises nor the modest rebound; instead r* estimates are negative at around -1 percent at mid-2019. - Co-movement of r* between countries is much closer in Factor models due to explicit common factor and joint estimation. - Emerging Europe (Del Negro et al. 2017 application): - r* estimates are significantly higher than Euro Area countries (consistent with L-W framework). - Russia: r* falls from around 4 percent in the early 2000s to closer to 2 percent by 2018, with jumps in 2008 and 2014 (risk premium spikes). - Poland: decline in r* similar in size to Russia but much steadier. - Caveat: trend-cycle decompositions are less suited for emerging economies because structural breaks are frequent. ### Co-movement of r* within the Euro Area - Method: - Multivariate Dynamic Conditional Correlation (DCC-) GARCH model with one lag applied to r* estimates and trend growth from L-W model where 푧푧 푡푡 is modeled as a function of external variables. - Caution: r* and trend growth series are median estimates with high uncertainty; coefficients and significance should be interpreted with care. - Findings: - Covariance estimates are almost always positive but vary over time — r* across Euro Area countries co-moves but not uniformly. - Periods of distress (GFC, sovereign debt crisis) see more volatile covariances and greater dispersion in bilateral covariances. - Spain and Portugal show much stronger co-movement during 2011–14 than France and Germany. - Trend growth covariances are lower and sometimes slightly negative, but higher and more dispersed during the sovereign debt crisis. - Highest trend growth covariances generally involve Spain with Portugal, the Netherlands, and Italy; Germany exhibits very low co-movement with other countries. ### Market-based signals: forward rates and term structure implications for future r* - Two techniques used to assess market expectations of future r*: - Forward interest rates: use the three-month treasury bill, five-years ahead, as proxy for the nominal neutral rate; inflation expectations convert nominal into real rates. - Five years chosen as relatively long enough for nominal rigidities not to bind. - Term structure: Nelson-Siegel variant to fit yield curve, separate expected short-rate sequence from term premium, derive implied path of future nominal short rates (three-month treasury bill), five-years ahead; inflation expectations convert to real rates. - Market expectations as of June 2019: - For nearly all Euro Area countries, markets expected real interest rates to remain well below zero for at least the following five years. - Market-implied expected values were below the range of r* estimates presented in this paper. - Implication: markets seemed to expect r* and r to be unlikely to increase toward pre-GFC levels; only modest increases (if any) were expected. - Emerging Europe: - Market data should be viewed with caution due to higher liquidity and credit premia, possibly explaining differences between estimated r* and market-implied paths. - Poland and Romania: market data suggested modest increases in real rates in following years, but remaining well below the paper’s r* estimates. - Russia: market analysis suggested real rates would remain near mid-2019 levels and above r* over the medium term. *Source: wpiea2020116-print-pdf - Annex VI). This may reflect a common factor influencing r* (Jordà and Taylor, 2019),* ### 2019. T he estimates of r* are for the L-W model, the L-W ### IV. POLICY IMPLICATIONS ### Monetary Conditions - The estimate of r* compared to observed values of r provides information on the stance of monetary policy. - In countries that issue their own currencies, the r – r* gap provides a direct assessment of the policy stance; in monetary unions, these gaps indicate how the common monetary policy is “felt” in individual members. - The larger the positive (negative) interest rate gap, the more contractionary (expansionary) is the monetary impulse. - Complications in estimating r* translate into uncertainty in assessing the monetary stance, especially in real time because of data lags and end-point issues (Grigoli et al, 2015). - r* estimates should be complemented by analysis of other variables and judgment. Key empirical observations (sample period, L-W framework with z modeled as a function of economic variables): - Real interest rates are calculated as the difference between the Euro Area one-week inter-bank rate and five-year ahead inflation expectations. - Prior to the GFC, monetary conditions were loose, but began to tighten in 2007. - Following Lehman’s failure, rates fell by over 3 percent within a one-year period, and monetary conditions eased substantially in all countries. - By 2012 the ECB was close to the effective lower bound (ELB), limiting room for further policy cuts; subsequent changes in the r – r* gap were driven largely by the evolution of r*. - Toward the end of the period under study, the analysis points to accommodative monetary conditions in all Euro Area countries, with the r – r* gap at around -2 percent in 2019:Q1. - Country heterogeneity: - France: r – r* gap peaked by mid-2008 (increasing by over 2 percentage points from 2005 to 2008), and fell below zero at 2008:Q3. - Portugal and Spain: r* continued to decline markedly during the Euro Area crisis; monetary conditions were tight in mid-2008 and remained tighter for longer. - Netherlands: r* did not sink so low during stress, so the single Euro Area policy delivered appropriate monetary conditions, though by end-sample conditions remained accommodative while the output gap was turning positive. - Between 2017 and 2019, output gaps narrowed (and likely closed) for many Euro Area countries, but the r – r* gap remained negative for all, partly because inflation remained below 2 percent. - Emerging Europe: - Russia: monetary policy seems broadly pro-cyclical, more so prior to the GFC; the Central Bank of Russia’s 2019 description of policy as “moderately tight” is consistent with results. - Poland and Romania: broadly counter-cyclical during the GFC and taper tantrum, but more pro-cyclical in recent years. Unconventional monetary policies (UMPs) and shadow rates: - The analysis implicitly assumes monetary conditions are described by the r – r* gap, but after hitting the ELB the ECB used new instruments not properly captured by r in that gap. - ‘Shadow’ interest rates (Krippner (2015), Wu and Xia (2016)) can assess stimulus from asset purchases and forward guidance, but replacing observed r with a shadow rate is not straightforward. - Assessing stance using shadow rates would require r* estimates constructed explicitly considering UMPs and a different transmission from the interest rate gap to the output gap in the IS Curve. - Conjecture: both the level of (shadow) r and r* are lower because of UMPs; assessing the impact of UMPs on the monetary stance requires further analysis and is an avenue for future research. ### What do our r* Estimates Imply for Monetary Policy in the Future? - Given difficulties hitting the inflation target and if r* remains not far above estimated values, monetary policy may need to resort to UMPs more often; UMPs may be no longer ‘unconventional’.20 - Frequent use of UMPs raises questions: - Is there an optimal size of central bank assets beyond which further increases are sub-optimal? - Is there an ELB on long term rates? - What policies may lower the ELB on policy rates? - Are there limits to quantitative easing? - Is ‘helicopter money’ a viable policy tool (Turner, 2015)? - What adverse side effects flow from negative interest rates and asset purchases, and how to mitigate them? 20: The Pandemic Emergency Purchase Program launched by the ECB in March 2020 already illustrates frequent use of UMPs in response to extraordinary shocks. ### Can We Say Anything About the Future Path of r*? - The future path of r* is highly uncertain. - After the onset of the pandemic, forming a view on potential growth is extremely difficult; over the medium term long-term drivers such as demographics are likely to reassert influence. - Country risk (sovereign spreads) effects could cause r* to diverge between Euro Area members and other European countries. - Increased uncertainty from COVID-19 is global; the analysis used domestic uncertainty measures, so near-term impacts on r* are hard to assess. - A large unexplained component of r* in estimates drove its decline beyond that of potential growth in many countries (ε_t^z in expressions (6) and (7), after controlling for REER, external demand and country risk). - This unexplained component may be driven by very low frequency events, notably protracted deleveraging in recent years. - Given ongoing re-leveraging during the pandemic and its likely legacy, r* is likely to remain below g, as deleveraging must begin again—as long as risk components remain contained and do not dominate movements in r*. - Other structural factors affecting r* include demographic trends beyond their effect on potential growth and lagging implementation of structural reforms to raise productivity. - Further research is needed to explore these conjectures.21 21: Kiley (2015), Cukierman (2016), Taylor and Wieland (2016), Krustev (2018), and Belke and Klose (2019) argue omission of factors like credit or the financial cycle may result in misspecification affecting inference about the neutral rate of interest. ### Implications for Debt Sustainability and Fiscal Policy - The link between r* and debt dynamics is important but nuanced. - Standard debt dynamics equation (11): Δs_t = (r_t^e − g_t) / (1 + g_t) s_{t−1} − sb_t - Changes in public debt (Δs_t) depend on the debt stock (s_{t−1}), the government’s primary balance (sb_t), the real effective interest rate on public debt (r_t^e), and real growth (g_t). - In principle, a lower r* should in due course translate, other things equal, into a lower r_t^e, but additional considerations apply. Key considerations and empirical findings: 1. Interaction with potential growth: - A lower r* may also imply lower potential growth. - Drivers of r* also affect potential growth (demographics, productivity), but not one-for-one. - Estimates suggest level of r* decreased by 2 percentage points (on average) when comparing the post-GFC with the pre-GFC period, while trend growth fell by around 1 percent. - Therefore, the decline in the r − g differential was half as large as the decrease in r*. - The improvement in the r – g differential did provide additional fiscal space. - Setting equation (11) to zero, a lower r − g gap implies a lower debt-stabilizing primary balance (DSPB). - Compared to the pre-GFC period, the DSPB declined by nearly 1 percentage points of GDP on average for the sample (assessed at 2018 debt ratios). 2. Durability of r − g improvements: - The stability of the r* − g path determines how durable additional policy space is. - By end of period studied r* − g was still below pre-crisis levels for most countries (except Lithuania) but had partially recovered. - Uncertainty about persistence is significant (e.g., pandemic collapse in g). - Some extra space generated by low r* − g had already been used by the late 2010s in some countries. - Country examples: - France, Italy, Spain: used space to stabilize debt with a lower primary balance rather than reduce debt ratios. - Romania: primary balance was not enough to stabilize debt. - Portugal, Germany, Netherlands, Lithuania, Poland, Russia: used extra fiscal space to reduce debt faster. 3. Crisis-related debt increases offsetting fiscal space: - All countries except Germany experienced an increase in debt during the GFC that implied an increase in the DSPB, offsetting part of the fiscal space from lower r* − g. - For some countries (e.g., Spain) this effect can be significant and may exceed the fiscal space generated by lower r* − g. 4. Short rate vs effective borrowing rate: - r* represents a short rate, but government borrowing includes a term premium that varies over time and maturity. - Pass-through from a change in current borrowing costs to the effective interest rate is gradual as existing debt rolls over. - A deep recession can cause debt dynamics to deteriorate rapidly via denominator effects. - Example: Portugal’s effective interest rate minus actual growth rate (equation 13) shows how rapid shifts can change near-term dynamics. 5. Credit risk premia: - Risk premia critically affect debt sustainability; they are determined by domestic factors and external market conditions. - Swift changes in market perceptions can cause rapid increases in long-term rates; highly indebted countries are particularly vulnerable to sudden stops. 6. Primary balance and demographic pressures: - Forces driving r* and g lower (e.g., aging) also affect the primary balance by increasing dependency ratios. - Lower r* − g may reduce the DSPB, but maintaining a given primary balance becomes increasingly hard over time, calling for fiscal prudence even if r* − g is lower. - With a relatively low r*, hitting the ELB is more likely when stimulus is needed; given questions about UMP effectiveness, fiscal policy may need to play an important stabilization role. - To play that role, building and maintaining appropriate fiscal space is important—policy makers should consider how much room is needed to use the primary balance discretionarily for demand management. ### V. CONCLUSIONS - r* was estimated for European countries between 2000 and 2019 and main drivers were examined. - Significant uncertainty around r* estimates and large unexplained components for some countries imply results should be interpreted with caution; policy judgments should be considered jointly with other economic information. - Broad patterns: - Natural rates declined in the sample over the last 20 years. - A significant part of that decline is accounted for by a fall in potential growth, larger in advanced European economies than in emerging Europe. - The fall in natural rates after the GFC has been more pronounced than the fall in potential growth, creating a wedge between r* and g. - The wedge became large during the GFC and has only moderately decreased in advanced economies; for emerging Europe the wedge increased less. - Part of the wedge is attributable to external factors (trade, capital flows, changing risk perception); these can affect emerging markets and reserve currency countries differently (country risk premium pushes r* upwards in Russia; risk increases in reserve currency countries may temporarily decrease r*). - Large residuals remain after controlling for variables; the wedge may reflect slow-moving factors like protracted deleveraging in public and private sectors, especially in the Euro Area. - If deleveraging was a main driver, the wedge may persist if pandemic-related re-leveraging requires future correction. - Any rise in r* is likely to take time; it is difficult to imagine r* rising above g anytime soon, particularly in advanced economies. - Even without additional shocks, both r* and g will likely remain lower than early 2000s levels given expected European growth trends. Macro policy implications of persistently low natural rates: - Monetary policy: - Persistently low r* with low inflation permanently increases the likelihood of hitting the ELB, making UMPs more likely to be first-resort even in moderate downturns—more significant in the Euro Area than in emerging Europe. - Fiscal policy: - In currency areas, interest rates will not necessarily align with stabilization needs of particular countries; with very low interest rates and limited conventional monetary policy, fiscal policy stakes rise—provided there is fiscal space. - Countries with their own currency have better prospects for monetary policy-based stabilization, but monetary policy may still be constrained by capital account shocks and currency mismatches, especially in emerging economies. - Lower r* could increase fiscal space, but some countries had already increased debt ratios before the pandemic, using up space; higher debt levels carry higher risks and spikes in term and risk premia can dominate favorable r* movements. - With lower r* the likelihood of hitting the ELB increases, reducing monetary scope and placing a premium on conserving fiscal space for countercyclical use. - Care should be exercised in judging whether low r* justifies high tolerance for high debt ratios. *Source: Authors’ calculations and analysis from the content unit.* ### References ### wpiea2020116-print-pdf - References ### Literature themes and citations - Key strands cited: - Theoretical and empirical work on the natural/neutral rate of interest (r*), including measurement, drivers, and policy relevance (e.g., Laubach and Williams 2003, Holston, Laubach, and Williams 2017, Barsky et al. 2014, Borio et al. 2019, Brand et al. 2018/2019/2020). - Secular/structural drivers of global real interest rates and trend growth (e.g., Rachel and Smith 2017; Summers 2014; Krustev 2018). - Effects of inequality, demographics, and financial cycles on aggregate demand and r* (e.g., Auclert and Rognlie 2018; Cynamon and Fazzari 2015; Bielecki et al. 2018). - Empirical term-structure and term-premium modeling relevant for low-rate environments and the zero lower bound (e.g., Christensen, Diebold, and Rudebusch 2011; Krippner 2015; Wu and Xia 2016). - Methodological references include Kalman filter and time-varying parameter approaches (Kalman 1960; Stock and Watson 1998; Stock 1991) and DSGE/IS–PHILLIPS frameworks (Gali 2008; Woodford 2003). ### ANNEX I — Defining the Natural Rate - Conceptual framing: - r* linked to supply-side fundamentals and the marginal product of capital in New Keynesian/Euler-equation frameworks; structural determinants include household discount rate (휌휌), labor and capital shares ((1−훼훼) and 훼훼), marginal disutility of work (휑휑), technological progress level (푠푠 푡푡), and utility curvature (휎휎). - Supply-side expression (Gali 2008): - 푟푟 푡푡 ∗ =휌휌+휎휎 1+휑휑 휎휎 ( 1−훼훼 ) +휑휑+ 훼훼 푅푅 푡푡 (∆ 푠푠 푡푡+1 ) (AI.1) - Equilibrium-related notion: r* as the real rate that would keep inflation at target and output at potential; equivalent to the constant term in a Taylor rule in some definitions. - Woodford (2003) perspective: r* as the flexible-price benchmark rate for economies with short-term rigidities. - Role in short-run dynamics: - IS-curve illustration with interest-rate gap: - 푦푦� 푡푡 =훼훼 1 푦푦� 푡푡−1 −훽훽 1 (푖푖 푡푡−1 −푅푅 푡푡 (휋휋 푡푡 )−푟푟 푡푡−1 ∗ ) (AI.2) - Interpretation: r* summarizes real shocks relevant for policy; can move at business-cycle frequencies and be volatile/procyclical (Barsky et al. 2014), but large estimation uncertainty and policy lags complicate attempts to track a volatile r*. ### ANNEX II — Technical details on the L–W model (specification and estimation) - Model overview: - Small-scale closed-economy IS–Phillips framework that simultaneously estimates r*, trend output, and potential growth via the Kalman filter. - Version used follows Pescatori and Turunen (2015) and is related to Laubach–Williams (L–W) and Holston et al. (2016) approaches; criticisms noted (Weber et al. 2008) about identifying individual driving forces and interpreting interlinkages. - Sample period for estimates: quarterly data mostly from 2000:Q1 to 2019:Q1. - IS curve (AII.1): - 푦푦� 푡푡 =훼훼 1 푦푦� 푡푡−1 +훼훼 2 푦푦� 푡푡−2 − 훼훼 푟푟 2 ∑ �푟푟 푡푡−푗푗 −푟푟 푡푡−푗푗 ∗ � 2 푗푗=1 +휀휀 푡푡 퐼퐼퐼퐼 - 푟푟 푡푡 ∗ is endogenous; observed real rate 푟푟 푡푡 =푖푖 푡푡 −휋휋 푡푡+1 푒푒 is exogenous/policy-determined; 휀휀 푡푡 퐼퐼퐼퐼 is iid with standard deviation 휎휎 퐼퐼퐼퐼. - Output and trend dynamics: - Output gap definition (AII.2): 푦푦� 푡푡 =푦푦 푡푡 −푦푦 푡푡 푁푁 - Potential output evolution (AII.3): 푦푦 푡푡 푁푁 =푦푦 푡푡−1 푁푁 +푔푔 푡푡 +휀휀 푡푡 푁푁 - Trend growth random walk (AII.4): 푔푔 푡푡 =푔푔 푡푡−1 +휀휀 푡푡 푔푔 - Phillips curve (AII.5): - Open-economy backward-looking Phillips Curve relating core inflation to lagged inflation terms, the output gap, and the gap between domestic-currency import price and core inflation; import price inflation is taken as exogenous. - Full expression preserved in source. - r* determinants and extensions: - Baseline link (AII.6): 푟푟 푡푡 ∗ =푐푐푔푔 푡푡 +푧푧 푡푡 - c is constant (c>0); zt captures factors other than trend growth. - For emerging economies, zt specification includes autoregressive terms and exogenous drivers (AII.7): 푧푧 푡푡 =훿훿 1 푧푧 푡푡−1 +훿훿 2 푧푧 푡푡−2 +훿훿 푐푐 Δ푐푐 푡푡 +훿훿 푝푝 Δ푠푠 푡푡 +훿훿 푒푒 Δ푠푠 푡푡 +휀휀 푡푡 푧푧 - Alternative emerging-Europe specification replaces the economic policy uncertainty index with the Real Effective Exchange Rate (REER). - Use of external output-gap signal: - WEO output gap as noisy signal (AII.8): 푦푦� 푡푡 푊푊푊푊푊푊 =푦푦� 푡푡−1 +휇휇 푡푡 +휀휀 푡푡 휇휇 - Noise follows AR(1) (AII.9): 휇휇 푡푡 =휌휌 푚푚 휇휇 푡푡−1 +휀휀 푡푡 휇휇 - Purpose: anchoring the filter, especially in relatively short samples. - Data and variable definitions (preserved precisely): - Estimation period: quarterly data mostly from 2000:Q1 to 2019:Q1. - Real interest rate (percent): observed real rate = quarterly average central bank nominal policy rate − quarterly average one-year-ahead headline inflation expectations from Consensus Economics. Russia: policy rate series adjusted for definition changes by the CBR. Romania: interbank rate. - Core and import price inflation: annualized quarter-on-quarter changes in percent from seasonally-adjusted Haver series; import price inflation proxied by GDP deflator on imports in domestic currency. - U.S. 10-year real sovereign yield: nominal yield on 10-year treasury bonds deflated by Long-Term inflation expectations as reported by Haver. - REER: IMF WEO database. - Spread (Euro Area): difference between 10-year country government yield and Germany’s 10-year government yield. - Policy uncertainty index (emerging Europe): news-based index from Baker, Bloom, and Davis (2016); not available for Romania, available for all other countries. - Country risk (emerging Europe): measured as the difference between the Emerging Market Bond Index (EMBI) and the international risk-free international interest rate proxied by the U.S. 10-year real sovereign yield. *Source: wpiea2020116-print-pdf - References* ### ANNEX III. MODEL PRIORS: REVIEW OF THE LITERATURE ### ANNEX III. MODEL PRIORS: REVIEW OF THE LITERATURE ### Literature developments and model extensions - Since Laubach and Williams (L-W, 2003), semi-structural models have continued to be used to estimate the natural rate of interest. - Notable model extensions include: - Incorporation of a Taylor rule, a stationary Phillips curve, and a second dimension of economic activity like unemployment (Brand and Mazelis, 2019). - Addition of an equation for unemployment gap fluctuations and credit conditions in the Phillips curve (Kiley, 2015). - Incorporation of the financial cycle for private sector-leverage (Krustev, 2018; Belke and Klose, 2019). ### Estimation methodology and key prior choices - Predominant estimation methodologies: sequential estimation, median unbiased estimator, and Bayesian estimation. - The authors follow Pescatori and Turunen (2015) and estimate model parameters using Bayesian techniques. - Prior assumptions on the variances of the error terms are emphasized as very important: 휀휀 푡푡 푁푁 (potential output), 휀휀 푡푡 푦푦 (output gap), and 휀휀 푡푡 푔푔 (potential output growth rate). - These priors influence how the variance of r* responds to shocks to potential growth and to the unexplained component, 푧푧 푡푡, and thus determine how closely r* follows g. ### Parameter ratios and range of values observed in the literature - Tables present ranges of estimates (including the authors’) for: - 휆휆 푔푔 = 휎휎 푔푔 / 휎휎 푁푁 - 휆휆 푧푧 = 휎휎 푧푧 / (휎휎 푦푦 푎푎 푟푟 √2) - The literature shows a wide range of values as reflected by the ratio 휆휆 푔푔 / 휆휆 푧푧; priors were selected to be within the range observed in selected papers. - Specific reported examples from the literature (as presented in the table): - Laubach and Williams (2003), US: baseline 휆g = 0.039, 휆z = 0.071, 휆g/휆z = 0.5; alternative low and high values reported (e.g., low λg = 0.000, λz = 0.026, λg/λz = 0.0; high λg = 0.103, λz = 0.060, λg/λz = 1.7). - Laubach and Williams (2016), US: multiple entries including 휆g = 0.042, 휆z = 0.042, 휆g/휆z = 1.0; and variants with 휆g = 0.042, 휆z = 0.058, 휆g/휆z = 0.7, plus confidence-interval variations. - Pescatori and Turunen (2015), Bayesian, US: 휆g = 0.26, 휆z = 0.013, 휆g/휆z = 20 (with z-determinants); 휆g = 0.29, 휆z = 0.013, 휆g/휆z = 22 (without z-determinants). - Brand and Mazelis (2019), Bayesian, US & euro area: 휆g = 0.125, 휆z = 0.119, 휆g/휆z = 1.1. - Krustev (2018), LW, US: 휆g = 0.05, 휆z = 0.02, 휆g/휆z = 2.5. - Arena et al. (2019), Bayesian: priors range 휆g = 0.10–1.48, 휆z = 0.03–0.10, implied 휆g/휆z = 3.3–14.8; posterior range reported 휆g = 0.07–1.57, 휆z = 0.01–0.09, implied 휆g/휆z = 7.0–17.4. - Other entries in the table report diverse country-specific values and calibrated ranges (see the table for multiple country and model-specific values). ### Sensitivity analysis on the autoregressive components of z - Baseline sum of the priors for the autoregressive components of z: 0.99. - Sensitivity exercise: change the sum to 0.96 (similar to Laubach and Williams (2003)). - Results summary from Table AIII.2 (Difference reported as (0.96 - 0.99)): - r* — Difference (0.96 - 0.99) - Average pre-crisis: FR 0.2, IT 0.0, DE 0.0, NL 0.4, PT 1.0, RO 1.0, RU 0.4, AT 0.5, BE 0.3, FI -1.0 - Crisis trough: FR 0.2, IT 0.5, DE 0.1, NL 0.5, PT -2.4, RO 0.9, RU -0.9, AT 0.5, BE 0.8, FI 0.4 - Last observation (2019Q1): FR 0.5, IT 0.7, DE 0.7, NL 0.8, PT -0.1, RO 1.0, RU 0.7, AT 0.6, BE 1.0, FI 0.5 - g — Difference (0.96 - 0.99) - Average pre-crisis: most entries 0.0; BE -0.1; FI -1.2 - Crisis trough: most entries 0.0; PT 0.7; BE 0.1; RU -0.1; AT -0.1; FI 0.6 - Last observation (2019Q1): entries largely 0.0; PT -0.1; RO 0.0; others 0.0; FI 0.5 - r* - g — Difference (0.96 - 0.99) - Average pre-crisis: FR 0.2, IT 0.0, DE 0.0, NL 0.4, PT 1.1, RO 1.0, RU 0.4, AT 0.4, BE 0.4, FI 0.2 - Crisis trough: FR 0.2, IT 0.6, DE 0.1, NL 0.6, PT -3.1, RO 0.9, RU -0.9, AT 0.5, BE 1.1, FI -0.1 - Last observation (2019Q1): FR 0.5, IT 0.8, DE 0.7, NL 0.8, PT 0.0, RO 1.0, RU 0.7, AT 0.5, BE 1.0, FI 0.0 - Interpretation: Changing the AR-sum from 0.99 to 0.96 generally yields larger r* for most countries at the crisis trough and at the last data point (2019:Q1) in the sample (see Table AIII.2). ### Priors specification guidance and connection to Annex IV - Priors for a range of parameters are described as follows (see Annex IV for detailed prior and posterior distributions): - Priors for standard deviations of shocks and for parameters such as c, autoregressive coefficients, and coefficients in the IS and Phillips curves. - Priors for all standard deviations are inverse gamma and follow conventions in Bayesian DSGE literature (Osorio-Butrón, 2016). - Priors are tight for: - the standard deviation of c, - output gap persistence (a1 + a2), - persistence of the exogenous process z (d1 + d2). - Priors are wider for: - the ratio of the standard deviations of trend growth and potential output (λg), - the ratio of the standard deviations of the error of the z-process and the IS curve (λz). - Table of parameter definitions and distributions (as presented): - c: Intertemporal elasticity of substitution — gamma - d1: Autoregressive coefficient on z — gamma - rho d = d1 + d2: (Autoregressive coefficients on z) — beta - a1: Autoregressive coefficient on output gap — gamma - rhoA = a1 + a2: the sum of a1 and a2 — beta - a_r: Coefficient on interest rate gap in the IS curve — gamma - by: Coefficient on output gap in the Phillips curve — beta - b1: Autoregressive coefficient on inflation in Phillips curve — beta - b2: AR coefficient on further lags in inflation in PC — beta - dc, de, dp: Coefficients in z equation for spread (bond yield, CDS), trading partner growth, and REER gap — normal - lambdag: Variation in trend growth — inv. Gamma - lambdaz: Variation in natural interest rate trend (z) — inv. Gamma - eps_n, eps_IS, eps_PC, eps_nu, eps_me: Shocks to potential output, IS curve, Phillips curve, output gap noise, output gap signal — inv. Gamma *Source: ANNEX III. MODEL PRIORS: REVIEW OF THE LITERATURE (from the provided PDF content)* ### ANNEX V. TECHNICAL DETAILS ON FACTOR MODELS --- _Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020116-print-pdf.pdf_