## wpiea2025066-print-pdf ## Source details **Canonical URL:** [wpiea2025066-print-pdf](https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025066-print-pdf.pdf) ## Other formats - [Markdown version](/-/media/files/publications/wp/2025/english/wpiea2025066-print-pdf.pdf.md) - [Structured JSON version](/-/media/files/publications/wp/2025/english/wpiea2025066-print-pdf.pdf.json) --- ### Introduction: context, objective, and high-level insights - Context and motivation: - Central banks deployed unconventional monetary policy (UMP) tools — including large scale asset purchases (LSAP), negative policy rates, and forward guidance — after the Global Financial Crisis and the Euro area debt crisis. - Sveriges Riksbank cut its policy rate into negative territory and began LSAPs in early 2015. - By April 2024 the Riksbank’s balance sheet had absorbed substantial losses from its LSAP program, prompting a petition for a capital injection of SEK 43.7 billion (approximately 0.7 percent of 2023 nominal GDP). - In June (year implied in source), the Riksdag approved a capital injection of SEK 25 billion (0.4 percent of 2023 nominal GDP); this capital injection will raise the Riksbank’s equity to SEK 23 billion. - In December 2024, the Riksdag changed the Riksbank’s authority to propose equity restoration from an obligation to an option and amended the Sveriges Riksbank Act to allow requiring credit institutions to hold interest-free deposits when equity falls below the target level. - Data from Federal Reserve, Eurosystem, and Bank of England indicate maximum annual losses range between 0.3% and 1.5% of GDP. The ECB reported a net loss of €1,266 million in its 2023 audited financial statements and fully released its €6,620 million provision for financial risks, resulting in no profit distribution to euro area national central banks for 2023. - Research objective and approach: - Aim: enhance understanding of macroeconomic and fiscal implications of UMPs in a small open economy framework, focusing on the exchange rate channel. - Builds on closed-economy results in Adrian et al. (2024) and recalibrates in an open economy setting; considers QE phase followed by gradual QT depending on maturity structure. - Takes a conservative view on LSAP transmission by calibrating toward the lower end of empirical estimates (meta study Fabo et al. (2021)). - Key model insights: - Open-economy exchange rate channel: LSAPs lower domestic long-term rates relative to foreign rates, weakening the exchange rate, enhancing net exports, and supporting inflation. - Equivalence result: purchases of domestic long-term government bonds financed by issuing short-term central bank reserves have nearly the same impact as purchases of foreign long-term bonds (financed by reserves) under a "long" Uncovered Interest Parity (long-UIP) maintained in the model. - NIRPs: model imposes a negative Effective Lower Bound (ELB) and assumes transmission of unanticipated short-term policy rate changes is similar when policy rates are positive or (moderately) negative; Appendix 1 provides empirical evidence supporting aggregate pass-through during 2015-2019. ### Quantitative model: structure and calibration - Model departures and features: - Bond market segmentation (short- vs long-term imperfect substitutes) allows LSAPs to affect term premiums and real activity. - Cognitive discounting (Gabaix (2020)) to address forward guidance puzzle. - Kinked demand / Kimball aggregator and nonlinear Phillips curves (Harding et al. (2022, 2023)). - Habit formation and gradual nominal wage adjustment (Erceg et al. (2000); Kolasa and Wesołowski (2020)). - Abstracts from financial accelerator mechanisms; calibrated to match empirical transmission of short rates, LSAPs, and fiscal shocks. - Key calibration targets and steady-state values: - Time period: one quarter. - Government expenditure-output ratio: g/y = 0.28. - Net Foreign Assets to GDP: 0. - Long term bonds to total bonds: 0.8. - Central bank portfolio: 0. - Home long-term bonds held by residents: 0.65. - Small economy relative size parameter: ω = 0.015 (Sweden’s nominal GDP fraction of BIG3 over 1995–2019). - Steady state gross quarterly inflation rate: π = 1.005 (implied by Riksbank target of 2 percent annual). - Discount rates: - restricted households: β_r = 0.99813, - unrestricted households: β_u = 0.99875. - Implied steady-state interest rates: short-term 2.5 percent and long-term 2.75 percent. - Home bias parameters: private consumption η_c = 0.7, public consumption η_g = 0.95. - Elasticities and labor parameters: elasticity domestic vs imports = 1.3, σ = 2, φ = 4, labor-income tax τ_y = 0.24, consumption tax τ_c = 0.17. - Household and firm table parameters (selected exact values from Table 2): - ω = 0.015; ω_r = 0.1; σ = 1 (table value); φ = 2 (table value); β_u = 0.99875; β_r = 0.99813; m_u = 0.95; m_r = 1; φ_w = 1.5; θ_w = 0.75; ξ = 0.025. - Firms: v = 1.3; η_c = 0.7; η_g = 0.95; μ = 1.15; ψ_H = -12; ψ_F = -6.5; θ_H, θ_F = 0.667. - Bond market specifics: - Steady-state ratio of sovereign bonds to annual GDP: 1.4 (4 × 0.35). - Initial central bank holdings of domestic and foreign government bonds: 0. - Share of long-term bonds in sovereign issuance: 0.8. - Average duration domestic long-term bonds: 6 years. - Average duration foreign long-term bonds: 7.5 years. - Steady-state share resident holdings in home long-term bonds: 0.65. - Policy parameters (selected exact values from Table 3): - Fiscal: τ_c = 0.2; τ_n = 0.3; g/y = 0.28; (b_f + P_L b_L^f)/y = 1.4; ψ_τ = 0.98; ψ_b = 0.01; ρ_g,1 = 0.70; ρ_g,2 = 0.01; D = 24; D* = 30. - Monetary: γ_r = 0.9; γ_π = 1.5; γ_y = 0.5; ρ = 0. - Transaction-cost parameter governing LSAP effects: ξ = 0.025 (calibrated to match LSAP effects on bond term premia; produces a max peak in output after a 1 percent of GDP increase in asset purchases materially lower than mean peak effects in Fabo et al. (2021)). - Solution method and nonlinearities: - Model solved nonlinearly using the extended path method (Fair and Taylor (1983)) implemented in Dynare. - Nonlinear Kimball aggregator and effective lower bound preserved; nonlinear Phillips curves imply lower sensitivity of inflation to shocks when slack exists and inflation is below target. ### Model impulse responses and calibrated quantitative findings - Policy shocks and quantitative responses (exact reported magnitudes): - A 0.25 percentage point reduction in the policy rate: - increases output and inflation by approximately 0.1 percent. - LSAPs (1 percent of baseline GDP): - slightly smaller effect on output than a 25 basis point rate cut, - long-term rates decrease by about 0.1 percentage points, - result in a 0.65 percent depreciation of the exchange rate (when asset purchases equal 1 percent of GDP and then run off according to bond maturities). - Fiscal multipliers: - With AR(2) government spending: fiscal multiplier ≈ 0.72 over first 1 year and 0.67 over first 2 years. - With AR(1) government spending (Section 4.3): multipliers 0.85 (first year) and 0.77 (two years). - Headline multiplier ~0.8. - Budget (revenue) elasticity: approximately 0.5 (tax revenues rise by about half of the increase in output). - Effect of government spending on core CPI (open economy): core CPI inflation falls when government spending on domestic goods increases due to exchange rate appreciation. ### Market-clearing and fiscal accounting conventions - Consolidated government debt measurement: - GD_t^con = B_t^f + 1/(1−κ) B_{L,t}^f / (4 P_t Y) — long-term government debt valued using the face value principle; central bank secondary-market purchases that alter prices do not immediately change GD_t^con. - Fiscal rule for labor tax: - τ_t^n − τ_n = ψ_τ (τ_{t−1}^n − τ_n) + (1−ψ_τ) ψ_b (GD_t^con − GD^con) with ψ_τ close to unity and ψ_b small to ensure gradual tax adjustment and debt sustainability. ### Central bank asset operations and profits accounting - Central bank purchases: - Domestic purchases QEP_t ≡ P_{L,t} B_{L,t}^c evolve per QEP_t = [1 + (1−ρ) (κ P_{L,t}/P_{L,t−1} − 1)] QEP_{t−1} + ε^QQ_t with 0 < ρ < 1. - Sterilized FX interventions modeled analogously with FXR_t ≡ S_t P_{L,t}^* F_{L,t}^c. - Central bank portfolio profits (one-period holding profits): - Φ_t^c ≡ R_{t−1} B_{t−1}^c + (1+κ P_{L,t}) B_{L,t−1}^c + (1+κ^*) P_{L,t}^* S_t F_{L,t−1}^c. - Accumulated central bank profits over h periods: - CBPRCF_{t+h}^{Acc} ≡ Φ_t^c + Φ_{t+1}^c + ⋯ + Φ_{t+h}^c. ### Market segmentation and long-UIP - Long-UIP links expected one-period holding returns on long domestic and foreign bonds to expected exchange rate changes; this condition underpins the model’s exchange rate response to LSAPs and the near-equivalence of domestic LSAPs and foreign bond purchases financed by reserves. ### Empirical reinforcement - SVAR evidence (Appendix 4): LSAP announcement shocks lead to persistent real exchange rate depreciation and increases in Riksbank government bond holdings; SVAR suggests somewhat more sustained central bank balance-sheet impacts than embedded in the DSGE. ### Appendix 1 empirical finding (pass-through) - Retail household deposit rates face a deposit lower bound (DLB); once reached, further policy rate cuts have significantly reduced pass-through to mortgage lending rates (Eggertsson et al. (2024)). - For the aggregate level of lending rates across the economy during 2015-2019, the pass-through effect remained unaffected by additional policy rate cuts. ### Model limitations (as stated) - Analysis stops before the COVID pandemic. - Excludes spillovers from UMPs by other major central banks. - Conservative calibration of LSAP transmission; nonlinearities reduce Phillips curve sensitivity at low inflation. ### Sources of nonlinearity and conservative inflation responses - Nonlinear ("banana-shaped") Phillips curves imply the model produces smaller inflation responses to UMPs when inflation is low and slack is present; linearized variants produce about twice as large effects on inflation and output. ### Numerical solution note - Behavioral agents introduce minor additive terms related to asset holdings that are quantitatively small and approximated in linearized first-order conditions; full nonlinear solution preserves key convexities and ELB constraints. ### Transmission: LSAPs, short rates, FX interventions, and fiscal policy (mechanisms) - LSAP mechanism: - Central bank purchases reduce the supply of long-term bonds to private sector, compress term premium, lower long-term yields. - Restricted households (who hold long-term bonds only) increase consumption when long-bond returns fall; unrestricted households’ intertemporal choices tied to short-term real rates. - Exchange rate channel: via long-UIP, domestic long-term yield compression relative to foreign yields leads to real exchange rate depreciation, boosting net exports and inflation. - Equivalence of LSAP and FX interventions: - Central bank purchases of foreign long-term bonds financed by issuing reserves can produce similar real exchange rate depreciation and similar macro responses as domestic LSAPs when real exchange rate paths are aligned and FX-market frictions are absent. - Open vs closed economy: - In the open economy, LSAP effects on output and inflation are driven almost entirely by exchange rate adjustment and net exports. - Fiscal expansion in open economy may lower CPI inflation by strengthening the currency; in closed economy it raises CPI inflation. ### Robustness and caveats - If long-UIP contained an endogenous risk premium that decreased in response to LSAP, exchange rate transmission could be weaker. - FX market depth and frictions matter: presence of FX-market-specific frictions could break LSAP–FX intervention equivalence. - Cross-border holdings introduce modest wealth-transfer channels that are quantitatively small in simulations. ### Riksbank 2015–2019 case study: scenario design and historical facts - Key historical policy actions and timing: - February 2015: repo rate lowered to -0.10%. - Repo rate lowered to -0.35% in July 2015 and -0.50% by early 2016. - Initial bond purchase commitment: SEK 10 billion. - By end-2015: total bond purchase announcements increased to SEK 190-200 billion (more than 30% of Sweden’s outstanding stock of nominal government bonds and about 5% of annual GDP). - April 2016: Riksbank broadened purchases to include nominal and inflation-linked bonds, purchasing an additional SEK 45 billion in latter half of 2016. - By end-2017: cumulative bond purchases reached SEK 290 billion (SEK 252.5 billion nominal, SEK 37.5 billion inflation-linked) representing approximately 39% of the outstanding stock of nominal bonds and about 20% of inflation-linked bonds. - Cumulative announced LSAP plans slightly exceeded 10 percent of 2014 GDP by the end of 2019. - Reinvestments: December 2016 SEK 30 billion (Jan–Jun 2017); December 2017 reinvest SEK 65 billion (Jan 2018–Jun 2019). - Simulation setup: - Initialized 2014Q4; asset purchase plans replicated via sequences of expected asset purchase shocks ε^Q aligned with announced timing and scale. - Domestic and foreign discount factor shocks ε_t^d and ε_t^{d*} and ELB λ_t chosen to match Riksbank announced interest rate path and LSAPs; ELB allowed to vary and be slightly negative. ### Counterfactual scenarios used (exact definitions) - A. LSAP = 0 and ELB < 0 - No asset purchases, but policy rate allowed to drop below zero; isolates negative ELB effects without LSAP support. - B. LSAP > 0 and ELB = 0 - Active asset purchases but a binding ELB at zero interest rate; illustrates world with only LSAPs. - C. No UMP (LSAP = 0 and ELB = 0) - Neither asset purchases nor a negative policy rate; illustrates no unconventional monetary policy tools. ### Macroeconomic and fiscal effects for Sweden 2015–2019 (key quantitative findings) - Aggregate/cumulative impacts reported (exact magnitudes preserved): - Cumulated contribution to GDP (2015–2019): exceeds 1 percent. - Impact on year-on-year inflation: close to 0.5 percentage points in early 2016. - Associated impact on the price level: exceeds 1.25 percent. - Five-year yield reduction: approximately 1 percentage point. - Term premium reduction: around 50 basis points. - LSAPs size: close to 10 percent of GDP. - Sustained krona depreciation: more than 5 percent (real exchange rate depreciation about 5 percent persistent in other model mentions). - Cumulative contribution to tax revenue by end-2019: approximately 2.5% of trend GDP. - Maastricht debt-to-GDP: fell from 45 to about 37 percentage points during 2015–2019. - UMPs’ contribution to the debt decline by end-2019: nearly 5 percentage points. - Okun’s law estimation for unemployment response: R^2 = 0.58; lag parameters -0.102, -0.106, -0.021, -0.078, -0.055. - Interpretation: - Quarter-by-quarter impacts of UMPs were almost indiscernible; accumulated effects over time were meaningful. - UMPs (LSAPs and NIRP) together stimulated output by about 1 percent 2016-2018 and increased inflation by 0.4 percentage points in 2016 (Swedish case study summary). - UMPs led to a persistent real exchange rate depreciation of about 5 percent. - Consolidated public sector fiscal position improved by about 5 percent of GDP by end-2019; without UMPs government debt would have been about 5 percent of GDP higher by end-2019. - Fiscal gains by end-2019 outsize Riksbank’s subsequent balance sheet losses in 2022 several times, though LSAPs pose ex ante risks to central bank balance sheets and potential consolidated fiscal risks. ### Counterfactual fiscal substitution (conventional fiscal stimulus replacing Riksbank UMPs) - Scenario design and results: - Counterfactual increases government consumption (G > 0) to replicate the same output path achieved under Riksbank UMPs; government consumption follows an AR(1) to boost multiplier. - Required fiscal adjustment: government consumption increased by a little more than 1 percent over time to replicate peak output of 1.2 percent under UMPs. - Implied fiscal multiplier: around unity in this exercise. - Inflation outcome: for the same output path, fiscal stimulus produces notably lower CPIF inflation relative to UMPs because fiscal stimulus appreciates the currency, lowering import prices. - Fiscal cost and debt dynamics: - Fiscal-only scenario raises consolidated public debt by nearly 5 percentage points by end-2019 (compared with actual). - Conditioning on conventional fiscal policy to achieve same output implies consolidated debt about 10 percent of GDP higher relative to actual by end-2019 in the fiscal scenario (text notes roughly 10 percent of GDP difference). - Direct fiscal spending cost accumulates to nearly 5 percent of baseline GDP over time. - Revenue and financing channels: - Tax revenue increases under fiscal stimulus are smaller than under UMPs because fiscal stimulus is less effective at raising private consumption and inflation. - Fiscal stimulus raises short-term policy rates and term-premiums, increasing debt financing costs; UMPs reduce debt service costs via lower yields. - Interpretation and caveats: - Under the model’s fiscal spending specification, replicating UMP output effects with conventional fiscal stimulus would have been much more costly and produced less favourable inflation outcomes during 2015–2019. - Alternative fiscal instruments (infrastructure, R&D, transfers) could alter welfare and fiscal costs, but empirical estimates for Sweden suggest transfers alone are unlikely to be more favourable. ### Conclusions and policy recommendations (explicit items) - Exchange rate channel importance: - LSAPs in a small open economy stimulate activity and inflation primarily via exchange rate depreciation. - When short-term interest rate is at the ELB, QE can provide meaningful macroeconomic effects even if agents do not directly alter consumption from term-premium changes. - Equivalence of domestic vs foreign long-term bond purchases: - Model implies near-equivalence of domestic LSAPs and foreign long-term bond purchases financed by reserves, conditional on long-UIP and absence of FX-market-specific frictions. - Use and caution for LSAPs and NIRP: - Both NIRP and LSAPs can raise inflation and output; empirical evidence supports similar transmission when policy rates are mildly negative. - LSAPs expose central bank balance sheets to risk and may reduce bond market liquidity; deploy cautiously and primarily when rates are expected to be pinned at ELB for prolonged periods and inflation expectations risk de-anchoring. - Fiscal vs monetary stimulus: - Fiscal stimulus can raise output but may be less effective than LSAPs at raising inflation in an open economy because it tends to appreciate the currency. - Replacing Riksbank UMPs with conventional fiscal stimulus to achieve same output path would be significantly more expensive fiscally and produce less favourable inflation outcomes in the Swedish episode. - Suggested avenues for further research (selected): - How deeply negative rates can be tolerated. - Robustness to alternative policy rules for short-term rate and LSAPs. - Extensions to include physical capital, COVID dynamics, FX-market frictions (Gabaix and Maggiori (2015)), and targeted transfers. *Source: wpiea2025066-print-pdf* ### 1. Introduction ### 1. Introduction ### Context and motivation - Following the Global Financial Crisis and the Euro area debt crisis, central banks deployed unconventional monetary policy (UMP) tools – including large scale asset purchases (LSAP), negative policy rates, and forward guidance – to stimulate economic activity, bring inflation closer to target, and reduce the risk of deflationary spirals. - The Swedish Central Bank (Sveriges Riksbank) cut their policy rate into negative territory and began large scale asset purchases in early 2015. - Asset purchases have been controversial because they are seen as blurring the line between monetary and fiscal policy and led to substantial central bank balance sheet losses during the Post-COVID inflation surge (illustrated by Sveriges Riksbank and U.S. Federal Reserve developments in Figure 1). - By April 2024, the Riksbank’s balance sheet had absorbed substantial losses from its LSAP program, prompting a petition to the Swedish parliament for a capital injection of SEK 43.7 billion (approximately 0.7 percent of 2023 nominal GDP) to restore a positive level of capital of the central bank. - In June (year implied in source), the Riksdag approved a capital injection of SEK 25 billion (0.4 percent of 2023 nominal GDP); this capital injection will raise the Riksbank’s equity to SEK 23 billion. - In December 2024, the Riksdag changed the Riksbank’s authority to propose equity restoration from an obligation to an option and amended the Sveriges Riksbank Act to allow requiring credit institutions to hold interest-free deposits when equity falls below the target level. - Data from Federal Reserve, Eurosystem, and Bank of England indicate maximum annual losses range between 0.3% and 1.5% of GDP. The ECB reported a net loss of €1,266 million in its 2023 audited financial statements and fully released its €6,620 million provision for financial risks, resulting in no profit distribution to euro area national central banks for 2023. ### Research objective and approach - Aim: enhance understanding of macroeconomic and fiscal implications of unconventional monetary policies in a small open economy framework, with particular focus on the exchange rate channel. - Builds on closed economy results in Adrian et al. (2024) and recalibrates in an open economy setting to capture exchange rate propagation mechanisms. - Considers LSAPs with a QE phase followed by a more gradual quantitative tightening (QT) phase; normalization time depends on maturity structure of purchased assets. - Takes a conservative view on LSAP transmission by calibrating model towards the lower end of empirical estimates (see meta study by Fabo et al. (2021)). ### Key mechanisms and model insights - Closed-economy vs open-economy transmission: - Closed economy: LSAPs compress long-term yields but may leave private spending unaffected if agents can arbitrage long and short yields via access to short-term bonds. - Open economy: LSAPs lower domestic long-term rates relative to foreign rates, weakening the exchange rate, enhancing export competitiveness, and supporting inflation — the exchange rate channel thus provides modest but meaningful macroeconomic impact. - Equivalence of domestic vs foreign long-term bond purchases: - Model documents that purchases of domestic long-term government bonds financed by issuing short-term central bank reserves have nearly the same impact as purchases of foreign long-term bonds (also financed by reserves). - This follows from a "long” Uncovered Interest Parity holding in the model, consistent with empirical evidence for advanced economies. - Implication: if domestic long-term bond supply is thin, the central bank can stimulate via foreign long-term bond purchases; LSAPs and “foreign exchange interventions” can be similar under some circumstances. - Negative interest rate policies (NIRPs): - NIRPs were used alongside LSAPs by several central banks. Empirical literature is mixed on pass-through to lending rates. - The paper imposes a negative Effective Lower Bound (ELB) and assumes transmission of unanticipated short-term policy rate changes is similar when policy rates are positive or (moderately) negative; Appendix 1 provides empirical evidence supporting this assumption. ### Model specification and calibration - Uses an open economy formulation of the Adrian et al. (2024) model with additions: - Discounting following Gabaix (2020) and Kolasa et al. (2025) - Kinked demand and nonlinear Phillips curves as in Harding et al. (2022, 2023) - Habit formation in consumer preferences and sticky wages following Erceg et al. (2000) into Kolasa and Wesołowski (2020) model - Calibration targets: - Conservative impact of LSAPs (weaker than academic estimates in Fabo et al. (2021)) - Short-term policy rate cuts and conventional fiscal expansions aligned with international literature and recent findings on fiscal transmission in open economies - Budget elasticities for Sweden to translate policy-driven changes into tax revenue and debt impacts - Structural modeling advantages: - Enables counterfactuals where the Riksbank could not cut short-term policy rates below zero and did not use LSAPs - Allows calculation of broad macroeconomic and fiscal variables under stock-flow consistency - Analysis excludes spillovers from UMPs by other major central banks ### Empirical case study: Riksbank 2015–2019 - Scope: assesses fiscal and economic implications of Riksbank unconventional monetary policies between 2015 and 2019 (stops before COVID pandemic). - Calibration from Riksbank monetary policy reports; assumes measures were discretionary central bank actions. - Main findings from Swedish case study: - Unconventional measures had almost indiscernible quarter-by-quarter impact on output growth and core inflation as tools were gradually expanded in an unanticipated fashion. - Near-term effects were very small despite raising bond prices and lowering term premiums. - Significant accumulated effects over time: - UMP stimulated output by about 1 percent 2016-2018. - UMP increased inflation by 0.4 percentage points in 2016. - UMP led to a persistent depreciation of the real exchange rate of about 5 percent. - Local projection evidence (Appendix 3) supports that a weaker exchange rate leads to a sustained increase in Swedish net exports. - Assessment is conservative: limited LSAP impact assumed, nonlinear model implies a flatter Phillips curve when inflation is low, and LSAPs are not allowed to serve as signaling for additional forward guidance. - Fiscal impacts: - Taken together, Riksbank unconventional measures led to an improvement in the consolidated public sector’s fiscal position by about 5 percent of GDP by end-2019. - Counterfactual: without Riksbank UMPs 2015-2019, government debt would have been about 5 percent of GDP higher by end-2019. - These fiscal gains by end-2019 outsize the Riksbank’s subsequent balance sheet losses in 2022 several times. - Nonetheless, LSAPs present ex ante risks to central bank balance sheets and potential consolidated fiscal risks; LSAPs and negative rates may foster financial vulnerabilities (Acharya et al. (2024)). ### Counterfactual fiscal substitution scenario - Scenario: conventional fiscal stimulus (higher government consumption spending) replaces Riksbank unconventional measures and is normalized to achieve the same output path as UMPs. - Findings: - Achieving same output path via fiscal stimulus results in significantly higher fiscal costs: increased public spending or tax cuts widen the budget deficit and worsen public debt. - Fiscal stimulus in isolation has a less favorable impact on inflation because the currency appreciates, reducing the inflationary effects that UMP achieves through exchange rate depreciation. - Implication: fiscal policy can stimulate output (especially if applied without delay) but may be less effective than UMP in achieving higher inflation and is likely to carry a notably more expensive fiscal bill. ### Scope, limitations, and structure of the paper - Limits: - Stops before COVID pandemic because the episode may not be well captured by the model. - Does not include spillovers from UMPs by other major central banks. - Conservative calibration of LSAP transmission; nonlinearities reduce Phillips curve sensitivity at low inflation. - Paper structure: - Section 2: model description, calibration, and solution. - Section 3: discussion of transmission of NIRPs, LSAPs, and government spending via exchange rate and openness. - Section 4: case study results for Riksbank 2015-2019 and comparison with fiscal policy alternative. - Section 5: concluding remarks. - Appendices 1 and 2: additional results; Appendix 3: local projection evidence on exchange rate and net exports. *Source: wpiea2025066-print-pdf - 1. Introduction* ### 2. The Quantitative Model ### 2. The Quantitative Model ### Overview - Model builds on Kolasa and Wesołowski (2020), Erceg et al. (2024), and Adrian et al. (2024). - Key departures from a standard DSGE: - Bond market segmentation: short- and long-term bonds are imperfect substitutes, allowing central bank asset purchases to influence term premiums and have real effects (following Andres et al. (2004), Chen et al. (2012), and Kiley (2014)). Long-term bonds can be traded internationally (as in Kolasa and Wesolowski (2020)), so term premiums affect the exchange rate even with domestic arbitrage. - Cognitive discounting (Gabaix (2020)) to address the forward guidance puzzle; introduces need for additional policy tools (asset purchases or fiscal expansion) when the policy rate is constrained by the effective lower bound. - Strategic complementarities in price setting to address the missing deflation puzzle and to explain sharp inflation rise during rapid recoveries (see Harding, Lindé, and Trabandt, 2022; 2023). - Two additional modifications (following Adrian et al. (2024)) to ensure realistic transmission of monetary and fiscal shocks: - Habit formation in consumption preferences to generate gradual, hump-shaped output responses to short-term interest rate cuts and to mitigate crowding out after government consumption increases. - Gradual nominal wage adjustment to temper inflation responses and produce realistic wage and profit dynamics (consistent with Christiano, Eichenbaum, and Evans (2005) and Bilbiie and Trabandt (2024)). - Abstracts from financial accelerator mechanisms (Bernanke, Gertler and Gilchrist (1999); Gertler and Karadi (2011)) since focus is on LSAPs and negative rates outside episodes of acute financial stress; model is calibrated to match empirical transmission of the three policy tools considered. ### Households (Section 2.1) - Two household types: “restricted” and “unrestricted”, indexed by j∈{r,u}; proportion of restricted households is ω_r ∈ (0, 1). - Lifetime utility (eq. (1)) features: - Subjective discount factor β_j ∈ (0, 1). - Inverse Frisch elasticity φ (denoted 휑휑>0). - Relative risk aversion σ (denoted 휎휎>0). - Habit formation: consumption c depends on habits tied to aggregate consumption of same type (c̅_j). - Discount factor shock ε^d_t modeled as stationary AR(1) with unit mean. - Deviations from rational expectations introduced via Gabaix (2020) myopia specification. - Two nominal asset types in home (H) and foreign (F) economies: short-term bonds and long-term bonds. Notation: - Holdings by type j: B_{k,t}^j and B_{k,L,t}^j for k ∈ {H,F}. - Long-term bonds modeled as Woodford (2001) perpetuities paying exponentially decaying coupons 1, κ, κ^2, ... with κ ∈ (0, 1]. Relation: P_{L−s,t} = κ^s P_{L,t}. Long-term yield R_{L,t} = κ + 1/P_{L,t}. - Unrestricted households can trade both short- and long-term domestic bonds and foreign long-term bonds but incur transaction costs ζ_{H,t} and ζ_{F,t} to hold long-term bonds; transaction costs are rebated lump-sum via Υ_{t}^u. Transaction-cost scaling equation (eq. (3)): - (1+ζ_{k,t})/(1+ζ_k) = (P_{L,t} b_{k,L,t}^u)/(P_L b_{k,L}^u)^ξ. - Budget constraints: - Unrestricted households: flow constraint shown in eq. (2) with taxes τ_t^c (value added) and τ_t^n (labor income), lump sum taxes T_t^u, short-term rate R_t−1, nominal exchange rate S_t, pre-tax labor income W_t n̅_t^u, dividends D_t^u, and rebate Υ_t^u. - Restricted households: trade exclusively in domestic long-term bonds with negligible transaction costs; budget constraint shown in eq. (4). - Restricted households in the large foreign economy trade both domestic and foreign long-term bonds (note in footnote 9). ### Wage Setting (Section 2.2) - Labor is differentiated at household level and pooled by perfectly competitive labor unions via CES aggregation with parameter φ_w > 0; aggregate labor n_t given by equation (5). - Staggered Calvo-style wage setting: - Each period fraction 1−θ_w of households reset nominal wages; others adjust mechanically toward steady-state inflation π. - When unions reset wages, they maximize an intertemporal objective (eq. (6)), taking into account population-weighted average marginal utility of consumption Λ_t and a wage cost-push shock ε_t^w following a stationary AR(1). - Model assumes perfect insurance across individual income risk arising from staggered wage setting (footnote 10). ### Firms (Section 2.3) - Three-stage production to introduce price stickiness and imperfect substitution between domestic and imported goods: - Final goods aggregator (eq. (7)): private and public consumption goods produced from domestic y_H,t and imported y_F,t inputs with home-bias parameters η_c, η_g ∈ (0, 1) and elasticity of substitution ν > 0. - Middle stage uses Kimball aggregator G(x) parameterized as in Dotsey and King (2005) with ψ ≤ 0 (eq. (9)), implying steady-state markup μ = φ/[(1−φ)(1+ψ)+φ]. Dixit–Stiglitz is special case when ψ = 0. - Asymmetric price responses: firms raise prices more than they reduce them for symmetric changes in marginal costs (quasi-kinked demand). - Intermediate inputs produced by monopolistically competitive firms with linear production in local labor (eq. (10)): y_H,t(d) + y_H,t^*(d) = e^{ε^z_t} z n_t(d) − f, where ε^z_t is productivity shock (AR(1)), n_t(d) hours at firm, and f > 0 fixed cost. - Price reoptimization: - Firms reoptimize domestic prices with probability 1−θ_H each period and export price with probability 1−θ_H^*; non-resetting firms index prices to steady-state inflation. - Marginal-cost shock ε^m_t is exogenous stationary AR(1) (interpretable as stochastic proportional taxes on firms, rebated lump-sum). - Reoptimization problems for home-market and foreign-market prices given in eqs. (11) and (12); inflation measures π_t and π_t^* defined. ### Fiscal Authority (Section 2.4) - Nominal flow budget constraint (eq. (13)): - B_t^f + P_{L,t} B_{L,t}^f + T_t + Φ_t^c = R_{t−1} B_{t−1}^f + (1+κ P_{L,t}) B_{L,t−1}^f + P_{G,t} g_t. - Government funds expenditures P_{G,t} g_t (P_{G,t} defined via eq. (7)) using taxes T_t and central bank portfolio profits Φ_t^c, issuing short-term (B_t^f) and long-term (B_{L,t}^f) nominal bonds. - Consolidated government debt measurement: - Long-term government debt valued using face value principle by discounting outstanding stock of long-term bonds by 1/(1−κ). - Consolidated government debt as share of annualized trend GDP (eq. (14)): - GD_t^con = B_t^f + 1/(1−κ) B_{L,t}^f / (4 P_t Y). - This preferred measure is not mark-to-market: central bank purchases on secondary market that alter prices of outstanding long-term debt do not immediately affect GD_t^con (footnote 11). - Government consumption process: - g_t = ḡ e^{ε^g_t} with ε^g_t following AR(2) as in eq. (15): - Δε^g_t = ρ_{g,1} Δε^g_{t−1} − (ρ_{g,2})(ε^g_{t−1} − 1) + u_{g,t}, u_{g,t} ~ N(0, σ_g). - AR(2) chosen to (i) evaluate inflation responses to output boosts similar to unconventional monetary policy; and (ii) capture implementation delays of fiscal stimulus. - Tax and revenue structure: - Total nominal tax revenues (eq. (16)): T_t = τ_t^c P_t c_t + τ_t^n W_t n_t + T_t (lump sum). - Consumption sales tax constant: τ_t^c = τ_c. - Labor income tax τ_t^n varies gradually around steady-state τ_n to stabilize consolidated government debt GD_t^con per tax rule (eq. (17)): - τ_t^n − τ_n = ψ_τ (τ_{t−1}^n − τ_n) + (1−ψ_τ) ψ_b (GD_t^con − GD^con). - Setting ψ_τ close to unity and ψ_b small (see Section 2.8) ensures long-term debt sustainability with gradual tax adjustment. - Fiscal deficit defined (eq. (18)): - D_t^f = (R_{t−1} − 1) B_{t−1}^f + B_{L,t−1}^f + P_t g_t − T_t − Φ_t^c. - Real-term debt and deficit dynamics (eq. (19)): - d_t^f = b_t^f − b_{t−1}^f/π_t + P_{L,t} (b_{L,t}^f − κ b_{L,t−1}^f/π_t). - Preferred real measure of long-term debt (pre-adjustment by steady-state output) given by b_{L,t}^f + b_{L,t}^f/(1+κ). - Equation (19) highlights positive influence of fiscal deficits on this debt measure and negative impacts from increases in inflation and long-term bond prices (debt deflation channel and higher bond prices allowing issuance of fewer bonds at given face value). ### Monetary Authority (Section 2.5) - Monetary policy uses a Taylor-type feedback rule for gross nominal policy rate R_t constrained by an effective lower bound (ELB) that is time-varying and slightly negative to allow for negative interest rate policy. - Policy formulation (eq. (20)): - R_t = max{λ_t,R̄_t, R̃_t?} (model text: R_t = mmx{λ_t, R̃_t}, with R̃_t evolving per the specified feedback) - Unrestricted (shadow) rate R̃_t follows: - R̃_t / R̃_{t−1} = (R̃_{t−1} / R̃_{t−1})^{γ_r} [(π_t/π̄)^{γ_π} (y_t/y_{t−1})^{γ_y}]^{1−γ_r} e^{ε^r_t}. - Parameters: - γ_r ∈ (0, 1] controls interest rate smoothing. - γ_π and γ_y determine responsiveness to core CPI inflation π_t and output growth y_t/y_{t−1}. - Neutral gross policy rate R̃_t is the steady-state nominal gross policy rate adjusted for expected change in discount factor shock ε^d_t (eq. (21)): - R̃_t = R̄ E_t [ε^d_t / ε^d_{t+1}] (text indicates R̃_t = R^E_t ε^d_t / ε^d_{t+1}). - Discount factor shock dynamics (eq. (22)): - ε^d_t − 1 = ρ_d (ε^d_{t−1} − 1) + u_{d,t}, u_{d,t} ~ N(0, σ_d). - This allows a gradual and persistent decline in R̃_t below the ELB; policy rule (20) also accommodates i.i.d. short-term policy rate shock ε^r_t. - Central bank asset purchase operations: - Central bank may hold domestic long-term bonds B_{L,t}^c funded by issuing one-period reserves paying R_t. Domestic asset purchases defined QEP_t ≡ P_{L,t} B_{L,t}^c. - Purchase rule (eq. (23)): - QEP_t = [1 + (1−ρ) (κ P_{L,t}/P_{L,t−1} − 1)] QEP_{t−1} + ε^QQ_t, with 0 < ρ < 1 governing reinvestment strategy. - Coefficients in eq. (23) set so that an asset purchase announcement ε^QQ_t raises QEP_t in line with empirical evidence (see Section 2.8). - Announced purchase programs modeled as sequences of expected innovations in ε^QQ_t (Laséen and Svensson (2011) approach). - Sterilized FX interventions: - Modeled as purchases of foreign long-term bonds F_{L,t}^c financed with newly created reserves (following Kolasa and Wesolowski (2023)). - Stock of FX reserves (in domestic currency) FXR_t ≡ S_t P_{L,t}^* F_{L,t}^c evolves per eq. (24), analogous to domestic purchases, with same reinvestment parameter ρ. - Central bank portfolio, profits, and transfer mechanics: - Central bank’s portfolio value: P_{L,t} B_{L,t}^c + S_t P_{L,t}^* F_{L,t}^c = −B_t^c; profits/losses fully backed by government. - One-period holding profits from previous central bank purchases (eq. (25)): - Φ_t^c ≡ R_{t−1} B_{t−1}^c + (1+κ P_{L,t}) B_{L,t−1}^c + (1+κ^*) P_{L,t}^* S_t F_{L,t−1}^c. - Positive stock of long-term assets implies B_{t−1}^c negative; combined positions yield net profit for central bank transferred to or financed by the treasury. - Accumulated profits over h periods defined in eq. (26): - CBP R CF_{t+h}^{Acc} ≡ Φ_t^c + Φ_{t+1}^c + ⋯ + Φ_{t+h}^c. *Italic line: Source: wpiea2025066-print-pdf - 2. The Quantitative Model* ### 2.6 Market Clearing Conditions ### 2.6 Market Clearing Conditions ### Goods Market Equilibrium - Equilibrium in the goods market requires: - 푦푦푡 ≡ 푦푦퐻,푡 ∆퐻퐻,푡 + 1−휔휔휔 휔휔 푦푦퐻퐻,푡 ∗ ∆퐻퐻,푡 ∗ = 푒푒휀휀푡 푧푧푛푛푡 − 푓푓, (Equation (27) as given) - Aggregate labor input: 푛푛푡 = 휔휔푟푟 푛푛푡푟푟 + (1−휔휔푟푟) 푛푛푡푢푢. - ∆퐻퐻,푡 and ∆퐻퐻,푡 ∗ are price-dispersion terms resulting from staggered price-setting in the intermediate goods sector, defined exactly as in Equations (28) and (29) (integral expressions preserved in the source). ### Bond Market and Government Debt Clearing - Market-clearing conditions for bonds issued by the domestic government, including central bank reserves: - (1−휔휔푟푟) 퐵퐵퐻,푡푡푢푢 = 퐵퐵푡푡푓푓 − 퐵퐵푡푡푐푐. (Equation (30)) - 휔휔푟푟 퐵퐵퐻,퐿,푡푡푟푟 + (1−휔휔푟푟) 퐵퐵퐻,퐿,푡푡푢푢 + 1−휔휔휔 휔휔휔 휔휔푟푟 ∗ 퐵퐵퐻,퐿,푡푡푟푟,∗ + 1−휔휔휔 휔휔 (1−휔휔푟푟 ∗ ) 퐵퐵퐻,퐿,푡푡푢푢,∗ = 퐵퐵퐿,푡푡푓푓 − 퐵퐵퐿,푡푡푐푐. (Equation (31)) - Interpretation: long-term government bonds 퐵퐵퐿,푡푡푓푓 are held by: - domestic central bank (퐵퐵퐿,푡푡푐푐), - restricted households at home (퐵퐵퐻,퐿,푡푡푟푟) and unrestricted households at home (퐵퐵퐻,퐿,푡푡푢푢), - foreign economy holdings (퐵퐵퐻,퐿,푡푡푟푟,∗ and 퐵퐵퐻,퐿,푡푡푢푢,∗). ### Price Dispersion - ∆퐻퐻,푡 and ∆퐻퐻,푡 ∗ quantify price dispersion from Calvo/Kimball staggered pricing (full integral expressions are provided in the source and preserved in the model’s equilibrium conditions). --- ### 2.8 Model Calibration and Solution ### Calibration Objectives and Strategy - Calibrated to match: - transmission of short-term monetary policy shocks, - empirical evidence on government spending shocks in open economies (Sweden in particular), - effects of LSAP according to academic studies. - Time period: one quarter. - Calibration sequence: - standard steady-state parameters (fiscal flows), - bond market parameters tailored to Swedish conditions, - sticky prices, sticky wages, habit formation to ensure realistic transmission. - Emphasis: bond market adjustment costs specific to Sweden. ### Key Steady-State Targets and Values (from Table 1 and text) - Core CPI Inflation (annual): 400(휋휋−1) / 2 (as reported in table header). - Government expenditure-output ratio: 푔푔/푦푦 = 0.28. - Net Foreign Assets to GDP: 0. - Long term bonds to total bonds: 0.8. - Central bank portfolio: 0. - Home long-term bonds held by residents: 0.65. - Small economy relative size parameter: 휔휔 = 0.015 (Sweden’s nominal GDP fraction of BIG3 over 1995–2019). - Steady state gross quarterly inflation rate: 휋휋 = 1.005 (implied by Riksbank target of 2 percent annual). - Discount rates: - restricted households: 훽훽푟푟 = 0.99813, - unrestricted households: 훽훽푢푢 = 0.99875. - Implied steady-state interest rates: short-term 2.5 percent and long-term 2.75 percent. - Home bias parameters: - private consumption 휂휂푐푐 = 0.7, - public consumption 휂휂푔푔 = 0.95. - Elasticities and labor parameters: - elasticity of substitution domestic vs imports: 1.3, - elasticity of intertemporal substitution 휎휎 = 2, - inverse Frisch elasticity 휑휑 = 4, - labor-income tax 휏휏푦푦 = 0.24, - consumption tax 휏휏푐푐 = 0.17. ### Bond Market Calibration Details - Steady-state ratio of sovereign bonds to annual GDP: 1.4 (4 × 0.35). - Assume initial central bank holdings of domestic and foreign government bonds: 0. - Share of long-term bonds in total sovereign issuance: 0.8. - Average duration domestic long-term bonds: 6 years. - Average duration foreign long-term bonds: 7.5 years. - Steady-state share of resident holdings in home long-term bonds issuance: 0.65. - Restricted and unrestricted households assumed to have same home bias in long-term bond portfolios. ### Household and Firm Parameter Calibration (Table 2 exact values) - Households: - 휔휔 = 0.015 (Size of the small economy), - 휔휔푟푟 = 0.1 (Share of restricted households), - 휎휎 = 1 (Inv. elasticity of intertemporal substitution), - 휑휑 = 2 (Inv. Frisch elasticity of labor supply) [note: elsewhere text sets 휑휑 = 4 as inverse Frisch; table lists 2], - 훽훽푢푢 = 0.99875, - 훽훽푟푟 = 0.99813, - 푚푚푢푢 = 0.95 (Cognitive discounting, unrestricted households), - 푚푚푟푟 = 1 (Cognitive discounting, restricted households), - 휙휙푤푤 = 1.5 (Wage markup), - 휃휃푤푤 = 0.75 (Calvo wage probability), - 휉휉 = 0.025 (Transaction cost on long-term bonds). - Firms: - 푣푣 = 1.3 (Elasticity of substitution btw. domestic production and imports), - 휂휂푐푐 = 0.7 (Home bias in private consumption), - 휂휂푔푔 = 0.95 (Home bias in public consumption), - 휇휇 = 1.15 (Gross price markup), - 휓휓퐻퐻 = -12 (Kimball parameter for domestic producers), - 휓휓퐹퐹 = -6.5 (Kimball parameter for imports), - 휃휃퐻퐻,휃휃퐹퐹 = 0.667 (Calvo probability for domestic production and imports). - Note (from table): 휇휇 is defined as 휇휇 = 휙휙 / [ (1−휙휙)(1 + 휓휓) + 휙휙 ]. ### Parameters Governing Market Segmentation and LSAP Effects - Share of restricted households (휔휔푟푟) = 0.1 (following Kolasa and Wesolowski (2020)). - Transaction cost parameter (휉휉) = 0.025 (calibrated to match LSAP effects on bond term premia; chosen to produce a max peak in output after a 1 percent of GDP increase in asset purchases materially lower than mean peak effects in Fabo et al. (2021)). ### Policy Parameter Calibration (Table 3 exact values) - Fiscal: - Steady state consumption value added tax 휏휏푐푐 = 0.2, - Steady state labor income tax 휏휏푛푛 = 0.3, - 푔푔/푦푦 = 0.28, - (푏푏푓푓 + 푃푃퐿퐿푏푏퐿퐿푓푓)/푦푦 = 1.4 (Share of government debt in quarterly GDP), - 휓휓휏휏 = 0.98 (Tax Smoothing Coeff in eq. (17)), - 휓휓푏푏 = 0.01 (Gov.t Debt Response Coeff in eq. (17)), - 휌휌푔푔,1 = 0.70 (First difference coeff in eq. (15)), - 휌휌푔푔,2 = 0.01 (Error correction coeff in eq. (15)), - 퐷퐷 = 24 (Long-term bond duration (domestic)), - 퐷퐷∗ = 30 (Long-term bond duration (foreign)). - Monetary: - 훾훾 = 0.9 (Interest rate smoothing), - 훾훾휋휋 = 1.5 (Interest rate response to inflation), - 훾훾푦푦 = 0.5 (Interest rate response to output growth), - 휚휚 = 0 (Reinvestment strategy). - Note: 퐷퐷 is defined as 퐷퐷 = 휋휋 훽훽푟푟 −1 / (휋휋 훽훽푟푟 −1 − 휅휅) per the source. ### Dynamic Calibration Choices - Cognitive discounting for unrestricted households: 0.95 (minor departure from rational expectations). - Kimball curvature parameters: -12 for domestic firms and -6.5 for export firms, yielding log-linearized slopes of the Phillips curves of 0.02 and 0.01 respectively (as specified via Harding et al. (2022)). - Calvo probabilities set to 0.667, consistent with empirical average price durations. - Monetary policy reaction function coefficients: - coefficient on inflation 훾훾휋휋 = 1.5, - coefficient on output growth 훾훾푦푦 = 0.5, - interest rate smoothing 훾훾푟푟 = 0.9. - Policy rule uses output growth instead of output gap to avoid central bank leaning against fiscal-driven output expansions. ### Model Impulse Responses and Quantitative Findings - A 0.25 percentage point reduction in the policy rate: - increases output and inflation by approximately 0.1 percent. - LSAPs (1 percent of baseline GDP): - slightly smaller effect on output than a 25 basis point rate cut, - cause a more persistent decline in long-term nominal interest rates (long-term rates decrease by about 0.1 percentage points), - result in a 0.65 percent depreciation of the exchange rate (when asset purchases equal 1 percent of GDP and then run off according to bond maturities). - Fiscal multipliers: - With government spending following an AR(2) process: fiscal multiplier ≈ 0.72 over first 1 year and 0.67 over first 2 years. - With government spending following an AR(1) process (adopted in Section 4.3): multipliers 0.85 (first year) and 0.77 (two years). - Model’s headline multiplier ~0.8 (noted to fall within empirical range, though with considerable uncertainty). - Budget (revenue) elasticity: - approximately 0.5 (tax revenues rise by about half of the increase in output). - Effect of government spending on core CPI (open economy result): - core CPI inflation falls when government spending on domestic goods increases, driven primarily by exchange rate appreciation accompanying higher fiscal spending. In trade-autarky (no exchange rate movements), inflation would increase with government consumption. ### Empirical Reinforcement and SVAR Evidence - Appendix 4: SVAR analysis with external instrument: - LSAP announcement shocks lead to persistent real exchange rate depreciation. - SVAR results imply LSAP shocks increase the Riksbank’s government bond holdings. - SVAR suggests a somewhat more sustained impact of LSAPs on central bank balance sheets than embedded in the DSGE (i.e., DSGE assumes somewhat faster systematic QT than SVAR evidence suggests). - Exchange rate channel is a key transmission mechanism for both LSAPs and fiscal policy in the small open economy setting. ### Solution Method and Nonlinearity Treatment - Model solved nonlinearly to preserve Kimball aggregator nonlinearities and the effective lower bound constraint. - Behavioral (cognitively discounted) agents: - linearized first-order conditions derived and used to construct approximations consistent with linear derivations (minor additive term related to asset holdings is quantitatively small and thus approximated). - Numerical solution technique: - extended path method of Fair and Taylor (1983) implemented in Dynare (Adjemian et al., 2024). - Nonlinear solution exploits convexities in the Phillips curves: - lower sensitivity of inflation to shocks when slack exists and inflation is below target, - implies the model’s inflation impacts for alternative policies are conservative relative to a linearized solution (apart from ELB effects). *Source: wpiea2025066-print-pdf — 2.6 Market Clearing Conditions section and adjoining calibration/solution text.* ### 3. Transmission of Asset Purchases, Conventional Interest Rates and Fiscal Policy: The ### 3. Transmission of Asset Purchases, Conventional Interest Rates and Fiscal Policy: The Role of Open Economy Dynamics ### Key mechanisms of LSAP transmission and term structure effects - The analysis studies three policy tools: long-term asset purchases (LSAPs), short-interest rate cuts, and higher government spending. Scenarios considered include a policy rate cut of 25 basis points and an LSAP worth one percent of baseline GDP. - LSAPs work through their effect on the term structure of interest rates and the exchange rate via a linearized arbitrage condition linking the expected one-period holding return on long-term bonds (푅푅퐿,푡+1 1) to the risk-free rate (푅푅푡), with transaction costs creating a term premium. - Central bank purchases of long-term bonds reduce the supply of these bonds to the private sector and thereby lower the expected return on them, compressing the term premium. - Unrestricted households (who can trade short- and long-term assets) have intertemporal choices pinned down by short-term real interest rates; therefore, changes in term premiums do not alter their consumption path unless short-term real rates change. - Restricted households (who trade only long-term assets) are directly affected by bond price changes; LSAP-induced lower expected returns on long bonds raise restricted households’ consumption. - The aggregate demand effect of LSAPs depends on the proportion of restricted agents in the economy. ### Long-UIP, exchange rate channel, and open economy linkages - The model features a "long" Uncovered Interest Parity (long-UIP) condition equating expected one-period holding returns on long-term domestic and foreign bonds up to expected exchange rate changes; 푆푡 denotes the nominal exchange rate. - Because of long-UIP, if LSAPs lower the expected return on domestic long-term bonds while foreign returns remain unchanged (small open economy assumption), the domestic currency must be expected to appreciate next period; LSAPs therefore tend to depreciate the implementing country’s exchange rate on impact and persistently if purchases are not expected to be quickly reversed. - Long-term bond and FX markets are tightly connected in the model: the exchange rate can only move if long-term yields move and vice versa. - The above linkage implies LSAPs may operate similarly to FX interventions, conditional on the absence of FX market–specific frictions. - The exchange rate channel operates irrespective of the share of restricted agents (e.g., even if 휔휔_r = 0), so LSAPs can materially affect activity and inflation through exchange rate adjustments alone. ### Open versus closed economy responses; role of openness - Simulations show that in a closed economy (trade autarky) configuration—setting home-bias parameters 휂휂_c = 휂휂_g = 1 and the elasticity of substitution across consumption goods 휈휈 = ∞—the model replicates closed-economy results from Fabo et al. (2021). - In the baseline open economy model, the effects of LSAPs on output and inflation are driven almost entirely by exchange rate adjustment and net exports; the open-economy aspects are crucial to LSAP effectiveness. - Fiscal policy transmission differs across open and closed setups: - In the open economy model, an increase in government consumption leads to a decline in CPI inflation because the fiscal expansion strengthens the domestic currency, lowering import prices and dampening inflation. - In the closed (trade autarky) model, government consumption increases CPI inflation because external trade and exchange rate effects are absent and domestic demand dominates. ### Isolating the exchange rate channel: restricted households and variants - A model variant sets the share of restricted households to zero (휔휔_r = 0) to remove direct effects of long-term yields on household intertemporal choices; this isolates the long-UIP exchange rate channel as the primary LSAP transmission mechanism. - Figure 4 (described in the source) compares IRFs for a 1 percent of baseline GDP LSAP in the baseline open economy and the 휔휔_r = 0 variant; results closely resemble each other, confirming the exchange rate channel is the primary driver. - Quantitatively, the elasticity between the REER and net exports (NX) in the model is similar to empirical evidence for Sweden reported in Appendix 3 of the source. - Even if the calibrated share of restricted households were larger, the exchange rate channel would remain central; increasing 휔휔_r (e.g., to 0.25 or higher) raises the output impact of a given-sized LSAP and FX intervention commensurately, but does not eliminate the exchange rate’s primacy. ### Comparison of LSAPs and FX interventions - An FX intervention is modeled as central bank purchases of long-term foreign government bonds paid for by issuing short-term central bank reserves; the intervention size is chosen to match the real exchange rate path achieved with LSAP. - Despite differing instruments, LSAPs and FX interventions produce approximately identical responses of long-term rates, output, and inflation when the real exchange rate paths are closely aligned. - Mechanism: FX interventions are sterilized and involve issuance of domestic short-term liabilities that must be absorbed by domestic agents, prompting unrestricted households to sell domestic long-term bonds to foreigners—reducing private sector holdings of domestic long-term bonds similarly to LSAPs and compressing term premia. - This equivalence arises from market segmentation and the long-UIP link; it is conditional on the absence of FX-market-specific frictions (e.g., Gabaix and Maggiori (2015) type frictions). ### Empirical context and robustness considerations - The long-UIP relationship is supported by empirical work when using long (10-year) maturity bonds (Lustig et al. (2019); Chinn and Meredith (2005)), contrasting with the well-documented failure of standard short-rate UIP. - If long-UIP included an endogenous risk premium that decreased in response to LSAP, the exchange rate transmission could be weaker, but only under that specific endogenous premium response. - FX market depth and frictions can materially affect transmission of FX interventions to output and inflation (Adrian et al. (2021)) and could alter the LSAP vs FXI similarity if present. - The model allows cross-border holdings of long-term bonds, introducing modest wealth-transfer channels even when 휔휔_r = 0, but these were found quantitatively small in simulations. ### Case study setup: Riksbank unconventional monetary policies (overview) - Section 4 uses the calibrated model to assess the macroeconomic and fiscal impacts of the Riksbank’s unconventional monetary policies—negative policy rates and LSAPs—implemented between 2015 and 2019. - The baseline scenario incorporates Riksbank LSAPs and short-term policy rates under the assumption these UMPs were discretionary and not predominantly priced into market expectations before announcement; this assumption is considered conservative and yields smaller measured effects. - Counterfactual scenarios are used to parse total and partial impacts of the Riksbank’s UMPs, including a counterfactual where fiscal stimulus (higher government spending) replaces the Riksbank’s UMPs. The fiscal stimulus is sized to produce the same output path as achieved by the UMPs during 2015–2019. *Source: IMF working paper chapter "3. Transmission of Asset Purchases, Conventional Interest Rates and Fiscal Policy: The Role of Open Economy Dynamics."* ### 4.1 Scenario Design ### 4.1 Scenario Design ### Historical context and policy motivation - By autumn 2014, inflation in Sweden had been below the target of 2 per cent for several years and medium-term inflation expectations of market participants had drifted well below the Riksbank’s 2 percent inflation objective. - The Riksbank reduced its policy (repo) rate to zero by October 2014 and signalled commitment to additional expansionary measures if necessary. - Global divergence in monetary policy: U.S. Federal Reserve moved toward a less expansionary stance, while the European Central Bank announced monthly purchases of EUR 60 billion until at least September 2016, posing exchange rate appreciation risks for the Swedish krona and downward pressure on import prices and domestic inflation. ### LSAP implementation and negative policy rates (2015–2017) - February 2015: Riksbank lowered the repo rate to -0.10%, Sweden’s first negative interest rate. - Initial government bond purchase commitment: SEK 10 billion to enhance liquidity and exert downward pressure on longer-term interest rates. - Repo rate trajectory: lowered to -0.35% in July 2015 and -0.50% by early 2016. - By end-2015: total bond purchase announcements increased to SEK 190-200 billion, equivalent to more than 30% of Sweden’s outstanding stock of nominal government bonds and about 5% of annual GDP. - April 2016: Riksbank broadened purchases to include both nominal and inflation-linked government bonds, purchasing an additional SEK 45 billion in bonds over the latter half of 2016. - By end-2017: cumulative bond purchases reached SEK 290 billion, comprising SEK 252.5 billion in nominal bonds and SEK 37.5 billion in inflation-linked bonds. - These purchases represented approximately 39% of the outstanding stock of nominal bonds and about 20% of inflation-linked bonds. - End-2017: as inflation approached 2%, the Riksbank gradually reduced net asset purchases but continued reinvestments to maintain expansionary impact. - Cumulative announced LSAP plans slightly exceeded 10 percent of 2014 GDP by the end of 2019. - Timing and communication: - Most LSAP announcements happened 2015-2016; only three additional LSAP program announcements were made thereafter (2017-2019). - Early rounds were explicitly front-loaded; subsequent purchases phased more gradually. - Riksbank never communicated a flat nominal rate path and consistently communicated that it would start normalizing rates during the 3-year forecast horizon. - Reinvestments and special announcements: - December 2016: SEK 30 billion purchase of nominal Swedish government bonds for January–June 2017, with reinvestments beginning early 2017 and continuing throughout the year. - December 2017: decision to reinvest SEK 65 billion, starting January 2018 and ending June 2019. ### Simulation setup to replicate 2015–2019 policies - Initialization: - Simulation initializes in 2014Q4 to reflect the period just before the negative interest rate period and potential for the zero lower bound (ZLB) to become binding. - Domestic and foreign discount factor shocks ε_t^d and ε_t^{d*} are chosen to match the level of the Riksbank’s policy interest rate in 2014Q4; state associated with projected inflation below target and economic slack. - Replicating LSAP plans: - Starting 2015Q1, asset purchase plans as announced by the Riksbank (Figure 6) are sequentially replicated by introducing expected asset purchase shocks ε_{t}^{Q} , ε_{t+1}^{Q}, …, ε_{t+n}^{Q} aligned with timing, scale, and length of LSAP announcements. - Phasing in NIRP and adverse demand shocks: - From 2015Q1 introduce an adverse demand shock in the current quarter to align the model with the Riksbank's announced duration of an effective lower bound (ELB) on the policy rate (minus 10 basis points at the time). - Domestic and foreign discount factor shocks ε_t^d and ε_t^{d*} and the effective lower bound λ_t are chosen by minimizing distance between model-implied interest rate path for the coming 12 quarters and the Riksbank’s announced interest rate path and known LSAP announcements up to that point. - The ELB variable λ_t in R_t = max{λ_t, R̃_t} is allowed to vary from period to period. - Iterative procedure: - Steps of replicating LSAP plans and phasing in shocks are repeated for all quarters 2015Q1–2019Q2, stepping forward one period at a time and adding Riksbank announcements in the quarters when announced. - This yields series of adverse discount factor shocks ε_t^d and ε_t^{d*} and effective lower bounds λ_t conditional on communicated LSAP announcements up to each quarter. ### Counterfactual scenarios simulated - Experiments are conditioned on the domestic and foreign demand shocks optimized to fit the actual and projected Riksbank policy rate in t = 2015Q1,...,2019Q2. - Three distinct counterfactuals: A. LSAP = 0 and ELB < 0 - No asset purchases, but policy rate allowed to drop below zero. Isolates effects of a negative ELB without LSAP support. - Implemented by enforcing the same string of negative demand shocks and excluding asset purchase announcements. B. LSAP > 0 and ELB = 0 - Active asset purchases but a binding ELB at zero interest rate. Illustrates a world where only LSAPs were deployed. C. No UMP (LSAP = 0 and ELB = 0) - Neither asset purchases nor a negative policy rate. Illustrates a world without unconventional monetary policy tools. - Purpose: - These counterfactuals (graphically shown in Panel A in Figure 7) allow assessment of the total impact of Riksbank UMPs and the relative contributions of asset purchases and negative interest rates on the economy during 2015–2019. ### Assumptions and interpretation - Key maintained assumption: gradual implementation of LSAP and NIRP policies were not anticipated in advance by households and firms. - Supported by market expectations in December 2014: market pricing did not expect negative policy rates nor a substantial LSAP program. - Assumption implies the intensification of these measures came as surprises, leading to a conservative assessment of policy effectiveness in the forward-looking model framework. - Figures referenced: - Figure 6: Riksbank Negative Policy Rates Forecasts and Announced Asset Purchase Plans (percent, SEK Billion, Share and cumulative share of 2014 quarterly GDP). - Figure 7: Counterfactual Scenarios of Riksbank Unconventional Monetary Policies 2015–2019. - Figure 8: Impact of Riksbank UMP on GDP and Inflation in Sweden 2015–2019 (Panel A: quarterly actual and counterfactuals; Panel B: yearly actual and counterfactuals; Panel C: deviations from actual). *Source: wpiea2025066-print-pdf - 4.1 Scenario Design* ### 4.2 Macroeconomic Effects of Riksbank Unconventional Monetary Policies 2015-2019 ### 4.2 Macroeconomic Effects of Riksbank Unconventional Monetary Policies 2015-2019 ### Overview of scenarios and methodology - Evaluated nine asset purchase programs and twelve policy interest rate forecasts, 8 of which indicated a lowering of the effective lower bound from zero to -0.56 percent. - Counterfactual scenarios analyzed: - No negative interest rate policy (NIRP). - No large-scale asset purchases (LSAPs). - Neither NIRP nor LSAPs. - Figures referenced describe: - Panel A: annualized quarter-on-quarter growth rates of real GDP and the CPIF price level, 2014Q4–2020Q1. - Panel B: year-on-year (4-quarter) changes in GDP growth rates and CPIF inflation. - Panel C: cumulated (medium-term) effects on GDP and inflation. - Figure 9: transmission to financial and labor markets using Adrian, Crump, and Moench (ACM) five-year yield and term premium, trade-weighted real exchange rate (KIX), and unemployment rate. - Figure 10: fiscal implications (tax revenue and Maastricht debt as percent of GDP; cumulative contributions). ### Macroeconomic impacts (real economy and prices) - Short-term (Panel A): - Actual data (red solid lines) show that positive gradual impacts of UMPs are swamped by other fluctuations, making UMP effects difficult to filter out in real time. - Risk: forecasters focusing on short-term forecast revisions may erroneously conclude LSAPs and NIRP are ineffective. - Medium-term and cumulative (Panels B and C): - Year-on-year (4-quarter) changes filter high-frequency idiosyncratic movements and demonstrate a notable yet modest transmission of LSAPs and NIRP on GDP growth and inflation. - Cumulated impacts: - Contribution to GDP (cumulating growth rates) exceeds 1 percent. - Impact on year-on-year inflation is close to 0.5 percentage points in early 2016. - Associated impact on the price level exceeds 1.25 percent. - Both LSAPs (magenta dashed lines) and NIRPs (black dashed lines) made meaningful contributions to the total UMP impact (blue solid lines). - Model specification note: - The nonlinear model embeds convex “banana-shaped” Phillips curves, which implies smaller effects on inflation of UMP tools than a standard linearized solution. - Re-running simulations with a linearized variant yields notably larger — about twice as high — effects on inflation and output compared with results reported in Figure 8. ### Transmission to financial and labor markets (Figure 9) - Interest rates and term premium: - UMPs, especially LSAPs, contributed to reducing long-term rates and the term premium. - Quantitative estimates: - Reduction of approximately 1 percentage point in the five-year yield. - Reduction of around 50 basis points in the term premium. - LSAPs close to 10 percent of GDP are consistent with observed yield declines. - Exchange rate and trade competitiveness: - UMPs contributed to a sustained depreciation of the Swedish krona, with more than 5 percent depreciation increasing prices of imported goods and improving exporters’ competitiveness. - Exchange rate pass-through raises import prices and boosts net exports and domestic labor demand. - LSAPs weakened the real exchange rate much more than negative policy rates, but both tools contributed equally to lower unemployment in the counterfactual analysis. - Unemployment and Okun’s law: - Counterfactual unemployment rates derived from estimated Okun’s law: ∆u_t = β(L) ∆y_t + ε_t on Swedish quarterly data from 2001-2023. - Estimation results: - R^2 of 0.58. - Estimated parameters for the lags: -0.102, -0.106, -0.021, -0.078, and -0.055. ### Fiscal implications (Figure 10) - Tax revenue: - Period-by-period contribution to tax revenues appears small in levels. - Cumulated over time, contributions of Riksbank UMPs to tax revenue become sizable. - By end-2019, the cumulative contribution of LSAPs and NIRP combined amounts to approximately 2.5% of trend GDP. - Government debt (Maastricht debt-to-GDP): - Actual Maastricht debt-to-GDP ratio fell from an initial level of 45 to about 37 percentage points during 2015–2019. - Counterfactual analysis indicates UMPs contributed materially — nearly 5 percentage points — to the decline in consolidated public debt by end-2019. - Without Riksbank UMPs, government debt would have remained well above 40 percent of GDP. - Drivers of debt reduction: - Primary drivers are higher tax revenues and lower debt service costs. - Net fiscal assessment of UMPs: - Conservative counterfactual analysis suggests consolidated gains from Riksbank UMPs 2015–2019 paid for subsequent central bank losses several times over. - However, if the recovery had been faster, central bank losses on LSAP portfolios could have been notably larger and could possibly have resulted in negative impacts on the consolidated public fiscal position. - Central bank losses should be weighed against tax revenue gains and lower debt service costs implied by UMPs. - The macroeconomic benefits and fiscal costs of unconventional policy should be compared with costs and benefits of alternative means to stimulate the economy. ### Key quantitative findings and magnitudes - Nine asset purchase programs evaluated. - Twelve policy interest rate forecasts; 8 signaled lowering the effective lower bound from zero to -0.56 percent. - Cumulated contribution to GDP growth: exceeds 1 percent. - Year-on-year inflation impact: close to 0.5 percentage points in early 2016. - Price level impact: exceeds 1.25 percent. - Five-year yield reduction: approximately 1 percentage point. - Term premium reduction: around 50 basis points. - LSAPs size: close to 10 percent of GDP. - Sustained krona depreciation: more than 5 percent. - Cumulative contribution to tax revenue by end-2019: approximately 2.5% of trend GDP. - Maastricht debt-to-GDP: fell from 45 to about 37 percentage points during 2015–2019. - UMPs’ contribution to the debt decline by end-2019: nearly 5 percentage points. - Okun’s law estimation: R^2 of 0.58; lag parameters -0.102, -0.106, -0.021, -0.078, -0.055. - Linearized model alternative produces about twice as high effects on inflation and output compared with the nonlinear specification. ### Interpretations and policy-relevant implications - Short-term event studies can understate UMP effectiveness; cumulative (level) analysis reveals meaningful medium-term effects on output, inflation, and fiscal positions. - LSAPs and NIRP worked through different channels: - LSAPs primarily via net exports (exchange rate depreciation). - NIRP primarily by boosting domestic demand. - Policymakers and analysts should: - Consider level dynamics and cumulative contributions when evaluating unconventional policies. - Account for model nonlinearity (Phillips curve shape) when interpreting inflation effects. - Weigh central bank portfolio losses against macro-fiscal gains (higher tax revenues and lower debt service costs). - Compare UMPs’ macroeconomic and fiscal costs/benefits with alternative stimulus measures, recognizing that LSAPs are not always a “free lunch.” *Source: wpiea2025066-print-pdf - 4.2 Macroeconomic Effects of Riksbank Unconventional Monetary Policies 2015-2019* ### 4.3 Counterfactual where Conventional Fiscal Stimulus Replaces Riksbank UMPs ### 4.3 Counterfactual where Conventional Fiscal Stimulus Replaces Riksbank UMPs ### Scenario design and methodology - Counterfactual: fiscal-only intervention in which large-scale asset purchases (LSAP = 0) and negative interest rates (ELB = 0) are replaced by higher government spending (G > 0). - Initial state and shocks: begins in 2014Q4 and incorporates the same sequence of adverse shocks observed between 2015Q1 and 2019Q2. - Policy instrument in counterfactual: government consumption path (ggt) is determined iteratively from 2015Q1 to 2019Q2 to replicate the output path observed under Riksbank UMPs (actual data). - Government consumption is modeled to follow an AR(1) process to boost the fiscal output multiplier. - Calibration notes: government tax rule parameters are in Table 3 and the tax rule is given by eq. 17; the debt anchor equals 35 percent of annualized GDP. ### Key quantitative findings on output and inflation - Required fiscal adjustment: government consumption in the counterfactual scenario needs to be increased by a little more than 1 percent over time to replicate the gradual percent output expansion with a peak of 1.2 percent under Riksbank UMPs (Panel C in Figure 8). - Implied fiscal multiplier: the model implies a fiscal multiplier around unity. - Output: by construction, the contribution to GDP is identical across the two scenarios when alternative policy mixes are normalized to achieve the same output level. - Inflation (CPIF): fiscal interventions sized to provide the same output boost as Riksbank UMPs produce notably less favourable inflation outcomes — fiscal stimulus results in lower CPIF inflation relative to scenarios without fiscal support. ### Transmission mechanisms explaining divergent inflation responses - Cognitive discounting and Kimball aggregation: conventional fiscal stimulus is much less effective at the ZLB than in a standard New Keynesian model (actual and expected inflation move less). - Exchange rate channel in a small open economy: - Monetary loosening (UMP) depreciates the domestic currency, raising inflation via higher import prices. - Fiscal stimulus in isolation worsens the external balance and strengthens the exchange rate (the KIX "the krona index" real exchange rate declines = real appreciation), as domestic interest rate differentials widen. - Result: exchange rate appreciation from fiscal stimulus offsets domestic inflationary pressure; with calibrated sizable trade shares and exchange rate pass-through in the model, fiscal stimulus leads to an overall CPIF inflation reduction because lower import prices more than offset domestic price boosts. - Financial market response: fiscal stimulus leads to slightly higher term-premiums and long-term yields by driving up issuance of long-term bonds. - Labor market: unemployment rate is about the same across scenarios, as Okun’s law is applied to the actual output path. ### Financial and labor market estimation details - Financial variables reported: Adrian, Crump, and Moench (ACM) model-implied five-year yield and ACM five-year term premium. - Okun's law estimation (Swedish quarterly data 2001-2023): - Relationship: ∆ut = β(L) ∆yt + εt - R2 = 0.58 - Estimated lag parameters: -0.102, -0.106, -0.021, -0.078, -0.055 ### Potential output and output-gap considerations - When monetary policy is used to stimulate output, the output boost increases the output gap because negative interest rates and LSAPs leave potential output unchanged. - Fiscal stimulus (higher government consumption) uses real resources and is associated with an increase in potential output as well. - Implication: for the same increase in actual output, the output gap increases less under fiscal stimulus than under UMPs, implying less upward pressure on wages and domestic inflation under fiscal stimulus. ### Fiscal consequences and debt dynamics - Short-term financing: fiscal deficits are almost exclusively financed through debt issuance in the short term given the tax-rule calibration. - Consolidated government debt effects: - Fiscal scenario raises consolidated public debt by nearly 5 percentage points by the end of 2019 (counterfactual green dashed line in Figure 14 lower right panel). - Conditioning on conventional fiscal policy to achieve the same output and unemployment outcomes as under Riksbank UMP implies the Riksbank UMP improved the consolidated debt position by roughly 10 percent of GDP relative to the fiscal-only counterfactual (upper right panel in Figure 14 indicates about 10 percent higher debt than actual by end-2019 in the fiscal scenario). - Revenue and cost channels: - Increase in tax revenues under fiscal stimulus is smaller than the contribution to revenues from Riksbank UMPs because (i) higher government purchases are less effective at stimulating private consumption and sales tax revenues, and (ii) fiscal stimulus exerts less upward pressure on inflation and real wages, generating lower labor income tax revenues. - Debt financing costs diverge: UMP lowers short-term policy rates and term-premium, raising bond prices and reducing debt service costs (captured as “debt financing costs”); fiscal stimulus raises short-term policy rates and term-premiums, lowers bond prices, and increases debt financing costs — this component contributes slightly more under fiscal stimulus because the policy mix increases debt more. - Cumulative fiscal cost: direct fiscal spending cost of the stimulus accumulates to nearly 5 percent of baseline GDP over time. ### Interpretation and caveats - Welfare and cost assessment: during the 2015–2019 period analyzed, stimulating the economy with conventional fiscal policy would have been much more costly — and welfare deteriorating — than Riksbank UMPs under the model’s fiscal spending specification. - Model limitations and alternative fiscal instruments: - The model's fiscal spending does not increase the long-term growth path; other fiscal instruments (e.g., fiscal infrastructure, R&D) could have different effects. - Following Correia et al. (2013) and Itskhoki et al. (2014), alternative fiscal instruments or mixes may deliver lower fiscal costs and higher inflation, but empirical estimates for Sweden discussed in Section 2.8 suggest increases in targeted transfers used in isolation are unlikely to be more favourable. - Central bank balance-sheet risk caveat: the analysis does not claim larger LSAP would always be less costly than fiscal stimulus in the future — larger LSAP with more negative term-premiums could trigger substantial central bank portfolio losses. *Source: wpiea2025066-print-pdf - 4.3 Counterfactual where Conventional Fiscal Stimulus Replaces Riksbank UMPs* ### 5. Conclusions ### 5. Conclusions ### Exchange rate channel and transmission of unconventional monetary policy - Large-scale asset purchases (LSAPs) in a small open economy stimulate economic activity and inflation primarily by depreciating the exchange rate. - When the short-term interest rate is at the effective lower bound (ELB), quantitative easing can provide meaningful macroeconomic effects even if households and firms are not directly affected by lower term-premiums and long-term yields. - Lower yields on long-term domestic bonds and an associated larger supply of short-term central bank reserves weakens the exchange rate. - A depreciated exchange rate makes imports more expensive and enhances export competitiveness of domestic firms, leading to higher demand for labor services, higher wage pressures, and higher domestic core inflation. - A weaker exchange rate supports both output and inflation in a manner that conventional fiscal policy (for example higher government consumption or transfers to households) often cannot replicate. ### Equivalence of domestic and foreign long-term bond purchases (LSAP vs FX intervention) - In the model, LSAPs are approximately equally effective if the central bank buys domestic or foreign long-term bonds and pays with short-term domestic reserves. - Purchases of foreign long-term bonds paid by issuing short-term central bank reserves can be thought of as an FX intervention aimed at raising inflation rather than merely weakening the exchange rate. - LSAPs and FX interventions can have very similar local effects when they generate a similar-sized real exchange rate depreciation. ### NIRP (negative interest rate policy), LSAPs, and policy effectiveness - Empirical evidence indicates policy rates transmit to market rates and interest rates relevant to firms and households in a similar fashion when policy rates are positive (normal situation) and mildly negative (so that financial stability considerations can be ignored). - Both NIRP and LSAP policies provide economic stimulus and raise inflation in the quantitative model when adopted for monetary policy purposes. - Frequent use of LSAPs exposes the central bank balance sheet and may adversely impact bond market pricing by making them less liquid; central banks should first explore where the ELB is and only thereafter deploy LSAP as needed. - The experience of the Swiss National Bank, Swedish Riksbank and the ECB suggests that the ELB on policy rates is notably lower than thought prior to the European debt crisis. - LSAPs carry risks—particularly for central bank balance sheets—and should be deployed cautiously and, apart from episodes with financial stress, reserved for situations when policy rates are expected to be pinned at the ELB for a prolonged period and there is risk of de-anchoring of inflation expectations from target. ### Swedish case study (Riksbank, 2015–2019) - Between 2015 and 2019, the Riksbank's unconventional monetary measures—a mix of negative policy rates and LSAPs—provided meaningful macroeconomic stimulus and improved the consolidated fiscal position by about 5 percent of GDP. - Negative rates and LSAPs contributed about equally to the positive output and inflation gains in the analysis. - A counterfactual relying on fiscal stimulus alone to achieve comparable economic activity implies significantly higher fiscal costs and less favourable inflation outcomes, because the stronger currency associated with fiscal measures dilutes inflationary pressures. - The quantitative model suggests the fiscal benefits of the Riksbank UMP during this period were substantial, and large enough to pay for the subsequent balance sheet losses by the Riksbank in the post-COVID pandemic period by an order of magnitude. - The assessment is conservative because it uses a nonlinear model with convex “banana-shaped” Phillips curves that are less sensitive to policy when there is economic slack and inflation is below target. - The analysis includes a gradual QT (i.e., a gradual normalization of the long-term asset position), so the favourable impact on output and inflation is not reversed when the assets the Riksbank bought gradually mature. - An unexpected increase in long-term and short-term rates (falling bond prices) can adversely impact the consolidated fiscal cost of UMPs down the road (and in fact this happened following the COVID pandemic), but the overall resulting Riksbank balance sheet losses were notably smaller than the gains documented in the study. ### Policy implications and recommendations - Unconventional monetary policy tools such as NIRPs and LSAPs can be useful to stimulate economic activity and address persistent below-target inflation in small open economies. - LSAPs should be deployed cautiously given balance sheet risks; they are best used when policy rates are expected to be pinned at the ELB for a prolonged period and there is a risk of de-anchoring of inflation expectations. - Central banks should first explore the ELB before resorting to LSAPs because frequent LSAP use may reduce bond market liquidity and expose balance sheet risks. - Adrian et al. (2024) provides an in-depth discussion of how to balance benefits and costs of LSAPs against associated risks to central bank and public sector finances. ### Suggested avenues for further research - Reexamine how deeply negative short-term policy rates can be tolerated by the public and thus meaningfully implemented. - Examine robustness of results with alternative empirically relevant policy rules—both for the short-term interest rate and LSAPs. - Extend analysis to alternative viable policy mixes as in Leeper (1991), including the possibility of fiscal dominance. - Extend the model with physical capital (i.e., investment) and features better suited to capture dynamics during the COVID pandemic. - Explore consequences and merits of alternative monetary and fiscal policy mixes when some households consume hand-to-mouth, and when targeted transfers are a viable instrument to stimulate the economy. - Study merits of fiscal policies based on taxes and transfers in the open economy framework, following insights in Correia et al. 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Evidence from Sweden," Working Paper Series 402, Sveriges Riksbank. - Gustafsson, Peter (2022), “An event study of the effects of asset purchases on financial prices during the pandemic”, Staff memo, Sveriges Riksbank. - Alsterlind, Jan (2021), "The development of risk premiums on covered bonds during the coronavirus pandemic", Economic Commentaries, no 13, Sveriges Riksbank. - Melander, Ola (2021), “Effects on financial markets of the Riksbank's purchases of government bonds 2015–2017”, Sveriges Riksbank Economic Review, no. 1, p. 89–112, Sveriges Riksbank. - Beechey, Meredith (2022), "The Riksbank's bond purchases: who sold bonds to the Riksbank?", Sveriges Riksbank Economic Review, no. 2, pp. 79-104, Sveriges Riksbank. ### Theoretical contributions on policy design and welfare - Benigno, Pierpaolo and Michael Woodford (2003), “Optimal monetary and fiscal policy: A linear-quadratic approach”, NBER Macroeconomics Annual, Vol. 18, p. 271-333. - Leeper, Eric M. (1991) "Equilibria under 'active' and 'passive' monetary and fiscal policies," Journal of Monetary Economics, Vol. 27, no. 1, p. 129-147. - Corsetti, Giancarlo and Paolo Pesenti (2001), “Welfare and macroeconomic interdependence”, The Quarterly Journal of Economics, Vol. 116, no. 2, p. 421–445. - Debortoli, Davide, Jinill Kim, Jesper Lindé, Ricardo Nunes (2019), “Designing a simple loss function for central banks: Does a dual mandate make sense?”, The Economic Journal, Vol., no. 621, p. 2010–2038. - Svensson, Lars, E.O. (2003), "Escaping from a liquidity trap and deflation: The foolproof way and others", Journal of Economic Perspectives, Vol. 17, no. 4, p. 145–166. ### IMF and policy guidance - IMF (2024), “Central bank stress testing—Guidance note”, Policy Paper No. 2024/067. - Adrian, Tobias, Christopher J. Erceg, Marcin Kolasa, Jesper Lindé and Pawel Zabczyk (2021), ”A quantitative microfounded model for the integrated policy framework”, IMF Working Paper No. 2021/292. - Erceg, Christopher J., Marcin Kolasa, Jesper Lindé, Haroon Mumtaz and Pawel Zabczyk (2024), “Central bank exit strategies domestic transmission and international spillovers,” IMF Working Papers 2024/073. - Chen, Jiaqian, Era Dabla-Norris, Carlos Goncalves, Zoltan Jakab and Jesper Lindé (2023), "Can fiscal consolidation help central banks fight inflation?", IMF Working Papers 2023/260, International Monetary Fund. - Dao, Mai, Allan Dizioli, Chris Jackson, Pierre-Olivier Gourinchas and Daniel Leigh (2023), "Unconventional fiscal policy in times of high inflation", IMF Working Papers 2023/178, International Monetary Fund. *References list as provided in the source content unit.* ### Appendix 1. Pass-Through of Policy Rate Cuts to Lending Rates Under ### Appendix 1. Pass-Through of Policy Rate Cuts to Lending Rates Under Negative Interest Rates ### Key findings - Retail household deposit rates face a lower bound (DLB); once this bound is reached, further policy rate cuts have a significantly reduced pass-through effect on mortgage lending rates (Eggertsson et al. (2024)). - When broadening the focus to the general level of interest rates across the entire economy, the pass-through effect on lending rates overall remains unaffected by additional policy rate cuts during the NIRP period. - The NIRP period examined for aggregate lending-rate pass-through is 2015-2019. ### Data and measurement - Empirical analysis draws on Swedish data, including daily bank-level lending rates. - Figure 15 presents Swedish Monetary Financial Institutions (MFI) lending rates and central bank policy rate before, during and after NIRP (2015-2019). The unit on the figure is Percent. - Definition note: "New lending" refers to agreements entered during the month in question, including all financial agreements where the terms and conditions that affect the interest are decided for the first time and other agreements where renegotiations or direct negotiations concerning existing deposits and loans result in new agreements. - Example provided for calculation of average rate: if loan types have interest rates 10 and 12 percent with respective loan stocks 120 and 50, the average rate is (120/170)10 + (50/170)12 =10.6 percent. - Source of series: Statistics Sweden. ### Interpretation and literature context - The empirical and theoretical literature on negative interest rate policies (NIRP) examines impacts through channels including bank profitability, lending, and broader macroeconomic effects. - Recent findings suggest both benefits and challenges in using NIRP as a monetary policy tool. - Eggertsson et al. (2024) find differential pass-through: constrained retail deposit rates imply reduced mortgage pass-through once the deposit lower bound is reached, while aggregate lending-rate pass-through may remain intact. - Cross-references: See also Erikson, and Vestin (2019 and 2021). *Source: Appendix 1, wpiea2025066-print-pdf.* --- _Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025066-print-pdf.pdf_