## _wp08251

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---

### I. Introduction — characterization of Turkish real interest rates
- Over the last decade, (ex-post) real interest rates have been around 20 percent on average, with a high degree of variability.
- Medium-term real interest rates, as implied by yields on inflation-indexed bonds, still hover around 10 to 11 percent.
- Cross-country comparison (average January 2004 to June 2007) shows Turkey (and Brazil) as outliers with real interest rates on the order of 10-12 percent; the next highest country in the sample has a real interest rate that is only 3 ½ percent.
- The period used for averaging featured low global interest rates, making Turkey’s high real rates particularly puzzling.

### II. “Fundamental” considerations (neoclassical growth model and marginal product of capital)
- Euler-equation benchmark (balanced-growth path, CRRA utility):
  - ρ + σ g ≈ r
    - where r is the net real interest rate and ρ = (β^−1 − 1).
- Parameter inputs and implications for Turkey:
  - Medium-term output per capita growth rate g ≈ 3.8 percent (World Economic Outlook forecast).
  - Literature ranges for σ: 1 to 2.
  - Even with σ = 2, matching Turkey's high real interest rates requires only small discount rates ρ; parameter values are not implausible in isolation.
- Cross-country empirical failure:
  - Scatter of ex-post real interest rates vs. steady-state growth rates g shows a negative relationship (contrary to Euler prediction).
  - Conclusion: the Euler mechanism is discounted as a serious cross-country explanation for Turkey’s high real rates.
- Marginal product of capital estimation (Caselli and Feyrer (2007) framework):
  - Naïve: MPKN = α Y / K
  - Land-corrected: MPKL = α_k Y / K
  - Price-corrected: PMPKN = α (P_y / P_k) Y / K and PMPKL = α_k (P_y / P_k) Y / K
- Data and calibration details:
  - Penn World Tables version 6.2 for Y, P_y/P_k, K.
  - Initial capital stock K_0 from K_0 = I_0 / (δ + μ) with δ = 6 percent and μ = average geometric growth rate of investment.
  - Capital share defaults: 0.35 where unavailable; Brazil set to 0.45.
- Selected empirical values (average 2002-2004):
  - Turkey: MPKN = 0.20; PMPKN = 0.15; MPKL = 0.11; PMPKL = 0.09.
  - USA: MPKN = 0.11; PMPKN = 0.13; MPKL = 0.08; PMPKL = 0.09.
  - Brazil: MPKN = 0.22; PMPKN = 0.15; MPKL = 0.11; PMPKL = 0.07.
- Findings:
  - PMPKL distribution appears bimodal (groups in 4-7 percent and 8-10 percent ranges); Turkey lies in the higher group with a rate of return on capital of around 9 percent.
  - Estimated marginal product measures do not correlate well with ex-post real interest rates; Turkey’s real rates remain far above fitted values.
  - Conclusion: marginal product of capital estimates cannot satisfactorily explain cross-country variation in real interest rates nor Turkey's high real rates alone.

### III. Cross-country regressions: determinants of real rates (2003 predictors → 2004–2007 real rates)
- Predictors used (predetermined 2003 values): public-sector gross debt (% of GDP), inflation rate, gross national savings (% of GDP).
- Key regression coefficients (dependent variable = ex-post real interest rates averaged 2004-2007):
  - Gross domestic debt (% of GDP):
    - Coefficient 0.047 with standard error (0.025) in (1) — significance indicated as *.
    - Coefficient 0.045 with standard error (0.022) in (2) — *.
  - Inflation rate:
    - Coefficient 0.388 with standard error (0.146) in (2) — **.
    - Coefficient 0.358 with standard error (0.143) in (4) — **.
  - Gross national savings (% of GDP):
    - Coefficient -0.126 with (0.141) in (3) — not significant.
    - Coefficient -0.095 with (0.136) in (4) — not significant.
  - Constants reported:
    - -1.199 (1.610) in (1); -0.211 (0.920) in (2); 4.046 (3.005) in (3); -0.716 (3.216) in (4).
  - Sample sizes N: 21, 22, 22, 21 for (1)–(4).
  - R-square: 0.15, 0.26, 0.04, 0.42 for (1)–(4).
  - Notes: Standard errors in parentheses. *, ** and *** denote significance at the 10, 5 and 1 percent levels respectively.
- Interpretation:
  - Positive association of real interest rates with government debt and inflation consistent with risk-premium channels.
  - Savings rate’s negative coefficient not statistically significant in this open-economy sample.
  - Cross-country evidence motivates focusing on credibility of disinflation and foreign-exchange risk premium in Turkey.

### IV. Credibility of disinflation: regime-switching model and evidence
- Motivation:
  - Turkish inflation fell from average 45.1 percent in 2002 to 8.8 percent in 2007, yet real interest rates remained high.
  - Credibility channel: agents place positive probability on reversion to high-inflation regime; ex-ante inflation forecasts are biased upward during learning, generating high nominal rates and high ex-post real rates after realized inflation is low.
- Model specification:
  - Regime-switching AR(q) for Δp_t (seasonally-adjusted CPI) with two states i ∈ {l, h} (low, high inflation); state-dependent variances.
  - Time-varying transition probabilities Π_t; probability of transiting from low to high depends on:
    - M_t: real growth rate of credit to the private sector.
    - D_t: real annual change in gross debt of the central government.
  - Symmetry imposed on transition specification to reduce parameters; AR(1) found adequate.
- Data: monthly January 1995 to May 2008; 161 observations. CPI from IMF IFS; credit from Central Bank of Turkey; gross central government debt from Treasury series.
- Estimated coefficients (Table 3 maximum-likelihood estimates):
  - α_l = 0.0039 (z-ratio (11.96))
  - α_h = 0.0048 (z-ratio (4.388))
  - β_{1l} = 0.6047 (z-ratio (9.834))
  - β_{1l} [second labeled β in table] = 0.9048 (z-ratio (79.45))
  - σ_h = 0.0087 (z-ratio (7.144))
  - δ_m = 1.1140 (z-ratio (0.908))
  - δ_d = 1.4811 (z-ratio (1.169))
- Implied regime properties:
  - Estimated unconditional mean inflation:
    - High-inflation regime ≈ 5 percent.
    - Low-inflation regime ≈ 0.9 percent.
  - High-inflation regime is more persistent and has higher expected inflation than low-inflation regime.
  - δ_m and δ_d positive: faster credit growth and larger changes in debt stock increase probability of reverting to high-inflation regime; coefficients are imprecisely estimated.
- Time-varying priors and historical interpretation:
  - φ_pr_t,h (prior probability of switching to high-inflation) falls sharply with 1999 stabilization, reverts during 2001 crisis, shows peaks (e.g., May–June 2006), and displays a downward trend with fluctuations.
- Forecast performance and implications:
  - Forecast errors: up to 2003 close to zero; from 2003 onward agents systematically overestimated inflation (overly pessimistic about durability of low-inflation regime).
  - Average difference between ex-post and ex-ante real interest rates ≈ 3 percent over the period — agents assumed real rates were 3 percent lower than realized, leading to overestimation of real returns to capital and supporting higher nominal/real interest rates.

### V. Open-economy considerations, UIP/CIP tests, and foreign-exchange risk premium
- UIP/CIP conceptual relations:
  - UIP (log-approx.): i_t = i_t^* + E_t(s_{t+1} - s_t).
  - CIP relation used: i_t = i_t^* + fd_t where fd_t = f_t - s_t.
  - Fisher (log-approx.): r_{t+1} = i_t - π_t.
- Tests for forward discount bias (one-year horizon, monthly data: Δs_{t+12} = α + β fd_t + η_t):
  - Table 4 regression coefficients:
    - Column (1): β_i = 0.250 with (0.099) — **; α_i = -0.070 with (0.025) — ***; N = 75; R-square = 0.09.
    - Column (2): β_i = 0.349 with (0.046) — ***; α_i = 0.043 with (0.010) — ***; N = 88; R-square = 0.49.
    - Column (3): β_i = 0.077 with (0.116) — not significant; α_i = 0.124 with (0.029) — ***; N = 75; R-square = 0.51.
- Decomposition using Consensus Economics 1-year ahead forecasts:
  - Risk premium defined: rp_{t+12} ≡ fd_t - Δs^e_{t+12}.
  - Table 5 (percent of implied forward discount bias; Consensus Forecasts, N = 88):
    - Failure of rational expectations b_re (%) = 13.4
    - Existence of risk premium b_rp (%) = 86.6
  - Interpretation: most of forward discount bias is attributable to a risk premium rather than systematic expectational errors.
- Behavior and magnitudes of the risk premium:
  - Risk premium declined substantially since the 2001 financial crisis.
  - 2001–2003: risk premium fluctuated in 20-40 percent range.
  - Since then: moderated to 0-10 percent range with peaks in May–June 2006 and early 2008.
  - For 2004 to 2008, risk premium averaged about 5 percent.
  - Benchmark steady-state real interest rates for US ≈ 4 percent → implies Turkey real rates ≈ 9 percent when adding average risk premium.
- Portfolio-balance evidence linking fiscal deficits to risk premium:
  - Estimated equation: rp_t^e = α + β DEF_t^e + β^* DEF_t^{*e} + ω_4.
  - Table 6 (selected results):
    - OLS domestic budget deficit to GDP coefficient = 1.091 with (0.25) — ***; Constant = 0.048 with (0.018) — ***; N = 84; R-square = 0.15.
    - Robust / alternative columns:
      - Domestic deficit coefficient = 1.165 with (0.24) — *** and 1.171 with (0.37) — ***.
      - Foreign (US) deficit coefficients not significantly different from zero (0.802 ((2.09)) and -0.15 ((2.08))).
      - Constants reported: 0.022 with (0.012) — * and 0.032 with (0.028).
      - Estimated residual AR(1) coefficient ρ_b = 0.637 in FGLS column.
      - N = 79 for FGLS columns; R-square = 0.32 and 0.17.
  - Interpretation: higher domestic budget deficits raise the foreign-exchange risk premium; magnitudes suggest near one-for-one relationship between budget deficit and measured risk premium. Foreign deficits not significant.

### VI. Main conclusions and policy-relevant findings
- Key conclusions:
  - Standard growth-model predictions for real interest rates cannot explain Turkey’s high real rates in a cross-country context.
  - Two main drivers of high real interest rates in Turkey:
    - Credibility concerns about disinflation (time-varying probability of reverting to a high-inflation regime).
    - A substantial foreign-exchange risk premium on lira-denominated assets.
- Quantitative highlights:
  - Estimated unconditional mean inflation: ≈ 5 percent (high regime) and 0.9 percent (low regime).
  - Average difference between ex-post and ex-ante real interest rates ≈ 3 percent.
  - Risk premium averaged about 5 percent for 2004–2008; historically 2001–2003 levels 20-40 percent; post-2003 mostly 0-10 percent.
  - Decomposition of forward discount bias (Consensus Forecasts sample): 86.6 percent due to risk premium, 13.4 percent due to failure of rational expectations.
  - Domestic budget deficit to GDP raises risk premium with coefficient ~1.09–1.17.
- Policy implications and recommendations:
  - Lock in fiscal consolidation gains to reduce risk premiums: credible and prudent fiscal policy is important to lower real interest rates.
  - Improve and sustain policy credibility regarding disinflation to reduce φ_pr_t,h (probability of reverting to high-inflation) and thereby lower excess real interest premia.
  - Monitor credit growth and changes in debt stock because faster credit growth and larger debt changes increase probability of switching to high-inflation regime (δ_m and δ_d > 0).
- Outlook:
  - Favorable trends in credibility about disinflation (declining φ_pr_t,h) and a declining foreign-exchange risk premium bode well for a gradual decline of real interest rates over time, contingent on locking in fiscal and credibility gains so medium-term real rates can converge toward world averages.

*Source: _wp08251 - References; Section IV and concluding remarks (IMF working paper content provided)._*

### References..............................................................................................................

### _wp08251 - References..............................................................................................................

### I. Introduction — characterization of Turkish real interest rates
- Over the last decade, (ex-post) real interest rates have been around 20 percent on average, with a high degree of variability.
- Medium-term real interest rates, as implied by yields on inflation-indexed bonds, still hover around 10 to 11 percent.
- Cross-country comparison (average January 2004 to June 2007) shows Turkey (and Brazil) as outliers with real interest rates on the order of 10-12 percent; the next highest country in the sample has a real interest rate that is only 3 ½ percent.
- The period used for averaging featured low global interest rates, making Turkey’s high real rates particularly puzzling.

### II. "Fundamental" considerations (neoclassical growth model)
- Two benchmark predictions from the standard neoclassical growth model:
  - From the household's Euler equation along a balanced growth path: real interest rates should be positively associated with the steady-state growth rate of output per capita.
  - From the marginal product of capital: countries with lower capital-labor ratios should have higher rates of return on capital and thus higher real interest rates.
- Application to Turkey:
  - Turkey’s high growth potential and relatively low capital-labor ratio can rationalize high real interest rates for not too implausible parameter values.
  - However, the cross-country evidence undermines a purely “fundamental” explanation: countries with similar characteristics as Turkey have much lower real interest rates, reflecting shortcomings of the neoclassical model in explaining international capital flows.
- Data and measurement note:
  - For cross-country comparisons, the 1-year interbank rate from DataStream was used to enhance comparability across countries where bond markets are less developed and traded securities have short maturities.

### III. Credibility of disinflation and inflation-expectation bias
- Lack of credibility regarding the sustainability of recent disinflation can generate a positive bias in inflation expectations and higher nominal interest rates.
- Empirical finding in the paper: such a bias exists and is significant.
  - Consequence: agents have been repeatedly over-estimating the real return to capital, keeping nominal rates at high levels despite improved macroeconomic fundamentals.

### IV. Risk premia and open-economy considerations
- Open-economy context: Turkey’s relatively liberal exchange control regime makes high domestic interest rates more puzzling.
- Uncovered interest rate parity fails in part due to a substantial risk premium.
  - The risk premium is estimated to be substantial, averaging around 5 percent in recent years.
  - Implication: the wedge created by the risk premium between domestic and foreign real interest rates implies higher domestic interest rates are not necessarily yielding excess returns for investors.

### V. Role of fiscal policy and policy implications
- Fiscal variables matter:
  - Increases in the public sector's stock of debt relative to GDP reduce policy credibility and increase the risk premium.
- Policy implication:
  - Credible, and prudent, fiscal policy is an important ingredient of any effort to reduce real interest rates in Turkey.
  - Credibility takes time to develop; there are no quick fixes to the phenomenon of high real rates.

### VI. Related empirical findings in the literature (select references described)
- Berument and Malatyali (2001): inflation uncertainty (modeled using a GARCH process) positively affects nominal interest rates.
- Berument and Günay (2003): conditional volatility of exchange rates is an important determinant of interest rates in Turkey.
- Basçi and Ekinci (2005): document a “bond premium” in Turkey where returns on T-bills have historically exceeded equity returns; explain by inflation and default risk.

### VII. Paper organization (as described)
- Section II: implications of the standard growth model for interest rates in Turkey
  - Section II.A: household's Euler equation
  - Section II.B: marginal product of capital
- Section III: credibility concerns as an explanation during the recent disinflation period
- Subsequent section(s): open-economy considerations, in particular foreign exchange risk premia

*Source: _wp08251 - References..............................................................................................................*

### Section IV. Finally, Section V contains some concluding remarks.

### _wp08251 - Section IV. Finally, Section V contains some concluding remarks.

### Fundamental considerations: model setup and Euler equation
- Benchmark: deterministic neoclassical growth model (King, Plosser and Rebelo (1988)).
- Household Euler equation (as presented):
  - ()
    ()
    1
    1
    '
    '
    +
    +
    =
    t
    t
    t
    CU
    CU
    R
    β
    (1)
  - Along a balanced growth path with CRRA utility U(C) = C^(1−σ)/(1−σ), Euler equation approximates to:
    - ρ + σ g ≈ r      (2)
    - where r is the net real interest rate and ρ is the discount rate ρ = (β^−1 − 1).
- Parameter inputs and implications for Turkey:
  - Medium-term output per capita growth rate g ≈ 3.8 percent (World Economic Outlook forecast).
  - Literature ranges for σ: 1 to 2 (Kydland and Prescott (1982), Cooley and Prescott (1995)); finance literature uses higher σ.
  - Even with σ = 2, matching Turkey's high real interest rates requires only small discount rates ρ.
  - Conclusion: Parameter values required to explain Turkey's high real rates via (2) are not implausible in isolation, but cross-country evidence contradicts the mechanism.

### Empirical cross-country failure of the Euler explanation
- Empirical finding:
  - Scatter plot of ex-post real interest rates vs. steady-state growth rates g shows a negative relationship (contrary to equation (2)).
  - Countries with higher medium-term growth rates have lower real interest rates in the cross-section.
  - Turkey and Brazil are outliers relative to fitted values.
- Conclusion: The Euler equation mechanism is discounted as a serious cross-country explanation for high real rates in Turkey.

### Marginal product of capital: theory, measurement framework, and Turkey
- Theoretical expectation:
  - Diminishing returns to capital imply countries with lower capital-labor ratios should have higher marginal products of capital and hence higher real returns.
- Caveats:
  - Lucas (1990a) vs. empirical international capital flows: predicted massive return differentials not observed; capital can flow opposite direction (Gourinchas and Jeanne (2007)).
  - Mulligan (2002): in presence of risk premia, financial interest rates may correlate poorly with firms' rental rates.
- Estimation framework (Caselli and Feyrer (2007), CF):
  - Naïve measure: MPKN = α Y / K    (3)
    - α = share of capital in GDP.
  - Land/natural-resource corrected: MPKL = α_k Y / K    (4)
    - α_k = reproducible-capital share of income.
  - Price-corrected measures to adjust for higher relative price of capital in poor countries:
    - PMPKN = α (P_y / P_k) Y / K    (5)
    - PMPKL = α_k (P_y / P_k) Y / K    (6)
- Data and construction:
  - Output (Y), relative price of capital (P_y/P_k), and capital stock (K) from Penn World Tables version 6.2.
  - Initial capital stock K_0 constructed from real investment series using K_0 = I_0 / (δ + μ)  (7) with δ = 6 percent and μ = average geometric growth rate of investment.
  - Capital share data sourced from Bernanke and Gürkaynak (2001), Gollin (2002), World Bank (2006); where unavailable, flat capital share of 0.35 assumed (following Bosworth and Collins (2003) practice).
  - For Brazil, capital share used = 0.45 (IMF desk economist suggestion).
- Empirical distribution:
  - PMPKL distribution appears bimodal: one group in 4-7 percent range, another in 8-10 percent range.
  - Turkey lies in the higher group with a rate of return on capital of around 9 percent.
- Select results from Table 1 (average 2002-2004):
  - Turkey: MPKN = 0.20; PMPKN = 0.15; MPKL = 0.11; PMPKL = 0.09.
  - USA: MPKN = 0.11; PMPKN = 0.13; MPKL = 0.08; PMPKL = 0.09.
  - Brazil: MPKN = 0.22; PMPKN = 0.15; MPKL = 0.11; PMPKL = 0.07.
- Cross-country correlation:
  - The estimated marginal product of capital measures do not correlate well with ex-post real interest rates (fitted regression lines not statistically significant).
  - Turkey, despite high PMPKL (~9 percent), has real interest rates far above fitted lines.
- Conclusion: Marginal product of capital estimates cannot satisfactorily explain cross-country variation in real interest rates nor Turkey's high real rates alone.

### What explains the cross-section of real rates: regressions and evidence
- Variables considered (predetermined 2003 values; dependent variable = ex-post real interest rates averaged 2004-2007):
  - Public-sector gross debt (% of GDP).
  - Inflation rate.
  - Gross national savings (% of GDP).
- Rationale:
  - Debt-to-GDP: associated with higher risk premiums in term structure and FX markets (Favero and Giavazzi (2002); Giorgianni (1997)).
  - Inflation: theoretical ambiguity — Mundell (1963) and Tobin (1965) predict negative effects on real rates via capital accumulation; Feldstein (1976) via taxation; Evans (1998) and Buraschi and Jiltsov (2005) find inflation risk premia can make the association positive.
  - Savings rate: in closed economy should lower real rates; in open economies relevance is limited.
- Bivariate scatter plot findings (Figure 4) and regression coefficients (Table 2):
  - Regressions (columns (1)-(4)) report:
    - Gross domestic debt (% of GDP):
      - Coefficient 0.047* with (0.025) in (1).
      - Coefficient 0.045* with (0.022) in (2).
    - Inflation rate:
      - Coefficient 0.388** with (0.146) in (2).
      - Coefficient 0.358** with (0.143) in (4).
    - Gross national savings (% of GDP):
      - Coefficient -0.126 with (0.141) in (3).
      - Coefficient -0.095 with (0.136) in (4).
    - Constants:
      - -1.199 (1.610) in (1).
      - -0.211 (0.920) in (2).
      - 4.046 (3.005) in (3).
      - -0.716 (3.216) in (4).
    - Sample sizes N: 21, 22, 22, 21 for (1)–(4) respectively.
    - R-square: 0.15, 0.26, 0.04, 0.42 for (1)–(4) respectively.
    - Notes: Standard errors in parentheses. *, ** and *** denote significance at the 10, 5 and 1 percent levels respectively.
- Interpretation:
  - Debt ratio and inflation have positive associations with real interest rates; debt result consistent with risk-premium channels.
  - Savings rate coefficient negative but not statistically significant in this open-economy sample.
  - Inflation’s positive and significant coefficient suggests inflation-related risk premia are important.
- Conclusion: Positive dependence of real interest rates on government debt and inflation points toward risk premium considerations. The cross-country analysis motivates a focused case study of Turkey emphasizing:
  - Lack of credibility in achieving disinflation (risk of reverting to a high-inflation state).
  - Existence of a foreign exchange risk premium.

### Credibility concerns as an explanation for high real rates (motivating evidence and context)
- Phenomenon:
  - Real interest rates in Turkey remained high despite improved macro fundamentals and large inflation decline.
  - Turkish inflation: average 45.1 percent in 2002 to 8.8 percent in 2007.
- Comparable episodes:
  - Argentina, Israel, Mexico experienced ex-post real rates of 20-40 percent following stabilization programs (Kaminsky and Leiderman (1998)).
  - Industrialized countries in the 1980s also saw elevated real rates after disinflation (Blanchard and Summers (1984)).
- Credibility mechanism overview:
  - Agents during early disinflation attach positive probability to reversion to high-inflation regime.
  - Inflation expectations are weighted averages over “low” and “high” regimes per agents’ priors.
  - If agents over-forecast inflation ex-ante (since they hedge against reversion), nominal rates reflect these expectations; ex-post real rates appear high even if realized inflation is low.
  - Analogy with “peso problem” in FX markets (Krasker (1980); Lewis (1989)).
- Turkish institutional and historical context:
  - Long history of high inflation and failed stabilizations.
  - Political fragmentation and fragile coalitional governments challenging durable stabilization.
  - Late-1999 exchange rate-based stabilization under IMF initially reduced interest rates and moderated inflation; a later financial and currency crisis led to abandonment of crawling peg, soaring interest rates and resumed high inflation.
  - Even after recovery and improved stability, credibility concerns remain important in Turkey.
- Analytical approach to credibility (framework preview):
  - Methodology of Kaminsky and Leiderman (1998): two-state Markov-switching process with time-varying transition probabilities.
  - Two regimes: “high-inflation regime” and “low-inflation regime.”
  - Agents form priors each period based on macro observations; next-period inflation expectations are weighted averages of the two regime processes using these priors as weights.
  - This mechanism produces biased ex-ante inflation forecasts during the “learning” period and can generate high ex-post real interest rates even as realized inflation falls.
- Empirical visualization:
  - Figure 5 (referenced) shows seasonally-adjusted monthly inflation rate for Turkey from 1995 to June (figure contents described but not reproduced here).

*Italicized source attribution: _wp08251 - Section IV. Finally, Section V contains some concluding remarks.*

### 2008. The horizontal lines mark the average monthly inflation rate over the period 1995 to

### _wp08251 - 2008. The horizontal lines mark the average monthly inflation rate over the period 1995 to

### Model specification and data
- Model: regime-switching extension of Hamilton (1988) with time-varying transition probabilities (Diebold, Lee and Weinbach (1994) style).
- Inflation process: Δp_t (seasonally-adjusted consumer price index) modeled as AR(q) with coefficients indexed by state i ∈ {l, h} (low- and high-inflation regimes). Error term has state-dependent variance.
- Transition probabilities: Π_t with element λ_ij_t denoting probability of transitioning from state i to j; Σ_j λ_ij_t = 1; λ_ij_t time-varying.
- Transition probability drivers: probability of transiting from low to high depends on:
  - M_t: real growth rate of credit to the private sector (proxy for monetary conditions).
  - D_t: real annual change in gross debt of the central government (proxy for budget balance).
- Functional form ensures λ remains in [0,1]; symmetry imposed so variables have opposite effect (same magnitude) on transition probability from high to low to reduce parameter count.
- Estimation:
  - Compute f(Δp_t | I_{t-1}) across states using priors as weights; prior φ_pr_t,i computed using posterior φ_po_t,i and λ elements (equation (8) shown).
  - Maximize sample log likelihood L(Θ) = Σ_{t=1}^T ln f(Δp_t | I_{t-1}) (equation (9)); standard errors via White (1982) combining second-derivative and cross-product estimates.
- Data: monthly January 1995 to May 2008; 161 observations per variable.
  - CPI: IMF International Financial Statistics.
  - Credit to private sector: Central Bank of Turkey's Monetary Survey.
  - Gross outstanding debt of central government: Treasury series.
- Technical choices:
  - Agnostic starting values: 0.5 for all variables.
  - To avoid σ_l ≈ 0 numerical issues, fix σ_h / σ_l to match data (assuming h and l states match periods in Figure 5) and estimate σ_h as free parameter.
  - AR(1) found adequate; q set to 1.

### Estimated coefficients and regime properties (Table 3 results)
- Table 3: Maximum-likelihood estimates of coefficients in regime-switching model
  - α_l = 0.0039 (z-ratio (11.96))
  - α_h = 0.0048 (z-ratio (4.388))
  - β_{1l} = 0.6047 (z-ratio (9.834))
  - β_{1l} [sic in table; second β label repeated] = 0.9048 (z-ratio (79.45))
  - σ_h = 0.0087 (z-ratio (7.144))
  - δ_m = 1.1140 (z-ratio (0.908))
  - δ_d = 1.4811 (z-ratio (1.169))
- Interpretation:
  - β_{1i} measures persistence; α_i/(1-β_{1i}) measures unconditional mean (stationary process).
  - Estimated unconditional mean inflation:
    - High-inflation regime ≈ 5 percent.
    - Low-inflation regime ≈ 0.9 percent.
  - High-inflation regime more persistent and higher expected inflation than low-inflation regime.
  - δ_m and δ_d positive: faster credit growth and larger changes in debt stock increase probability of reverting to high-inflation state; these coefficients are imprecisely estimated.

### Time-varying transition probabilities and credibility
- φ_pr_t,h: time-varying prior probability of switching to high-inflation regime computed and plotted (Figure 6; six-month moving average shown, dashed line = linear trend).
- Historical episodes highlighted:
  - Introduction of stabilization program in 1999: φ_pr_t,h experienced a sharp drop (initial credibility).
  - 2001 financial crisis: φ_pr_t,h reverted to early-sample levels.
  - May–June 2006 turbulence: most recent peak in φ_pr_t,h highlighted.
- Trend: probability of transitioning to high-inflation has decreased over years but with fluctuations.

### Forecast errors and implications for real interest rates
- Forecasts based on time-varying priors and estimated coefficients (Table 3).
- Forecast errors for monthly inflation (Figure 7):
  - Up to 2003: forecast errors close to zero.
  - From 2003 onwards: agents systematically overestimated inflation (agents overly pessimistic about durability of low-inflation regime).
- Ex-post vs ex-ante real interest rates (Figure 8):
  - Ex-post real interest rates consistently higher than ex-ante.
  - On average, difference around 3 percent over this period.
  - Implication: agents assumed real interest rates were 3 percent lower than realized → agents overestimated real return to capital → demand for capital remained elevated supporting high nominal/real interest rates.

### Open-economy considerations: UIP, CIP, and foreign exchange risk premium
- UIP (log-approximation): i_t = i_t^* + E_t(s_{t+1} - s_t) (equation (10) rearranged in text).
- CIP: i_t = i_t^* + fd_t where fd_t = f_t - s_t (equation (11)).
- Fisher equation (log-approximation): r_{t+1} = i_t - π_t (implied by equation (12) in text).
- Real UIP: domestic real rate = foreign real rate + expected real depreciation; if PPP holds long-run, domestic real rates pinned to foreign real rates.
- Puzzle: Turkey's real interest rates substantially higher than cross-section of countries (Figure 1 referenced).
- Sources of wedge between domestic and foreign rates:
  - Time-varying risk premium.
  - Departures from rational expectations.

A. Tests for forward discount bias and decomposition
- Regression used (one-year horizon, monthly data): Δs_{t+12} = α + β fd_t + η_t (equation (13)); null β = 1 under unbiased forward rate.
- Table 4 (Froot and Frankel (1989) regressions) — coefficients:
  - Column (1): β_i = 0.250** (standard error (0.099)); α_i = -0.070*** ((0.025)); N = 75; R-square = 0.09.
  - Column (2): β_i = 0.349*** ((0.046)); α_i = 0.043*** ((0.010)); N = 88; R-square = 0.49.
  - Column (3): β_i = 0.077 ((0.116)); α_i = 0.124*** ((0.029)); N = 75; R-square = 0.51.
  - Notes: Robust standard errors in parentheses. *, ** and *** represent significance at the 10, 5 and 1 percent respectively.
- Decomposition using survey-based expected Δs (Consensus Economics mean 1-year ahead forecasts) and definition:
  - Risk premium: rp_{t+12} ≡ fd_t - Δs^e_{t+12} (equation (14)).
  - β_1 from regression relates to components: β_1 = 1 - b_rp - b_re (equation (15) definitions provided).
- Table 5: Components of failure of unbiasedness hypothesis (percent of implied forward discount bias)
  - Consensus Forecasts, N = 88:
    - Failure of rational expectations b_re (%) = 13.4
    - Existence of risk premium b_rp (%) = 86.6

- Tests (equations (16) and (17)):
  - Column (2) evidence: β_2 significantly less than 1 → significant risk premium component.
  - Column (3) evidence: no systematic expectational errors in exchange rate forecasts → agents efficiently use information at time t for forward discount.

- Behavior of risk premium (Figure 9):
  - Declined substantially since 2001 financial crisis.
  - 2001–2003: risk premium fluctuated in 20-40 percent range.
  - Since then: moderated to 0-10 percent range, with peaks in May–June 2006 and early 2008.
  - For 2004 to 2008, risk premium averaged about 5 percent.
  - Benchmark steady-state real interest rates for US ≈ 4 percent (Cooley and Prescott (1995); Laubach and Williams (2003)) → implies Turkey real rates ≈ 9 percent when adding average risk premium.

B. Portfolio-balance evidence: fiscal deficits and risk premium
- Portfolio-balance model: risk premium arises because domestic and foreign bonds are imperfect substitutes; increased relative supply of domestic bonds requires higher expected excess return.
- Estimated equation (18): rp_t^e = α + β DEF_t^e + β^* DEF_t^{*e} + ω_4 (notation in text).
  - DEF_t^e: expected budget deficit of central government (relative to GDP) for Turkey.
  - DEF^{*e}_t: foreign equivalent (US used).
- Estimation issues: residual serial correlation addressed via robust standard errors and FGLS.
- Table 6: Impact of budget deficits on risk premium
  - OLS:
    - Domestic budget deficit to GDP coefficient = 1.091*** ((0.25))
    - Constant = 0.048*** ((0.018))
    - N = 84; R-square = 0.15
  - Robust OLS / alternative columns:
    - Domestic budget deficit to GDP = 1.165*** ((0.24)) and 1.171*** ((0.37))
    - Foreign (US) budget deficit to GDP coefficients reported (0.802 ((2.09)) and -0.15 ((2.08))) not significantly different from zero.
    - Constant values reported: 0.022* ((0.012)) and 0.032 ((0.028))
    - Estimated residual AR(1) coefficient ρ_b = 0.637 in FGLS column.
    - N = 79 for FGLS columns; R-square = 0.32 and 0.17 respectively.
  - Interpretation: higher domestic budget deficits raise the foreign-exchange risk premium; magnitudes suggest near one-for-one relationship between budget deficit and measured risk premium. Foreign deficits not significant.

### Conclusions and policy-relevant findings
- Main conclusions:
  - Standard growth model predictions for real interest rates dismissed due to failure along cross-country dimension: countries similar to Turkey have much lower interest rates.
  - Two key positive explanations for high real interest rates in Turkey:
    - Credibility concerns about disinflation (time-varying probability of reverting to high-inflation regime).
    - High foreign-exchange risk premium on lira-denominated assets.
- Quantitative highlights:
  - Estimated unconditional mean inflation: ≈ 5 percent (high regime) and 0.9 percent (low regime).
  - Average difference between ex-post and ex-ante real interest rates ≈ 3 percent (agents underestimating realized real rates).
  - Risk premium averaged about 5 percent for 2004–2008; historical 2001–2003 levels 20-40 percent; post-2003 mostly 0-10 percent.
  - Decomposition of forward discount bias: Consensus Forecasts sample attributes 86.6 percent to risk premium and 13.4 percent to failure of rational expectations (Table 5).
  - Domestic budget deficit to GDP raises risk premium with coefficient ~1.09–1.17 (Table 6).
- Policy implications and recommendations implied by results:
  - Lock in fiscal consolidation gains to reduce risk premiums: continued fiscal discipline can lower domestic risk premium and thereby help reduce real interest rates.
  - Improve and sustain policy credibility regarding disinflation to lower φ_pr_t,h (probability of reverting to high-inflation regime) and reduce the excess real interest rate premia driven by credibility concerns.
  - Monitor credit growth and changes in debt stock (M_t and D_t) because faster credit growth and larger debt changes increase probability of switching to high-inflation regime (δ_m and δ_d > 0).
- Outlook: favorable trends in both credibility about disinflation (Figure 6) and foreign exchange risk premium (Figure 9) over recent years bode well for a gradual decline of real interest rates over time, contingent on locking in fiscal and credibility gains so medium-term real rates can converge toward world averages.

*Source: _wp08251 - 2008. The horizontal lines mark the average monthly inflation rate over the period 1995 to (IMF working paper content provided).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08251.pdf_