## wpiea2023033-print-pdf - 2021. Furthermore, there is considerable heterogeneity in housing price growth across cities in

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---

### Housing price trends and heterogeneity
- Real house price index:
  - Continued to increase at an annual rate of 3.1 percent in Vilnius.
  - House prices in the rest of Lithuania have started declining in real terms.
  - Sharpest fall of 4 percent in Šiauliai.
- House price-to-rent ratio:
  - The correction in house prices is even more pronounced and widespread when focusing on the house price-to-rent ratio (Figure 2).
- Historical context and risks:
  - Monetary policy shocks and slower income growth could push real housing prices lower in a panel of emerging European markets, including Lithuania.
  - Large house price corrections can have adverse effects on economic performance and financial stability, as experienced during the GFC and other episodes in history.

### Macroprudential framework and instruments in Lithuania
- Instruments currently in place:
  - loan-to-value (LTV)
  - debt service-to-income (DSTI) ratios
  - maximum loan maturity
  - interest rate stress and sensitivity tests
  - countercyclical capital buffer, (CCyB)
  - other systemically important institutions (O-SII) buffer
  - conservation buffer (CCB)
- Objectives of these measures:
  - Reduce vulnerability in the banking system.
  - Increase resilience of borrowers to asset price or income shocks.
  - Minimize downside risks to financial stability.

### Supervisory actions and recommendations
- Pre-correction actions for authorities:
  - Conduct stress tests for banks and other non-bank financial institutions that have high exposures to real estate.
  - Possibly require higher provisioning for mortgage loans for institutions found to be vulnerable based on the stress tests.

### Data overview (Section III)
- Data source and coverage:
  - Ober-Haus apartment price index for 5 cities: Kaunas, Klaipėda, Panevėžys, Šiauliai and Vilnius, plus national average.
  - Frequency: monthly observations from January 1994 to September 2022.
  - City-specific CPI and its housing component drawn from Statistics Lithuania to calculate house price-to-rent ratio at city level.
- Key historical changes in Lithuanian housing prices (1994–September 2022):
  - Between 1994 and onset of the GFC in 2008:
    - Housing prices increased by 702 percent in nominal terms.
    - Housing prices increased by 170 percent in real terms (adjusted for inflation).
    - Real house price increases by city over same period: Vilnius 177 percent; Šiauliai 159 percent; Kaunas 147 percent.
  - GFC impact:
    - Housing prices declined by 41 percent in nominal terms.
    - Housing prices declined by 52 percent in real terms.
    - Real house prices fell more in smaller cities: average decline 56.5 percent in Klaipėda, Panevėžys, Šiauliai versus average decline 49.5 percent in Vilnius and Kaunas.
  - Post-GFC to September 2022:
    - After the GFC, house prices increased by an average of 95 percent in nominal terms and 36 percent in real terms (adjusted for inflation).
  - COVID-19 period (end-2019 to September 2022):
    - House prices increased by 50 percent in nominal terms and 15 percent in real terms (adjusted for inflation).
  - Note: Ober-Haus index methodology and latest data referenced (Ober-Haus price index covers five large cities).

### Econometric strategy (Section IV)
- Conceptual framework:
  - Bubble defined per Himmelberg, Mayer, and Sinai (2005): buyers pay inflated prices expecting unrealistically high future appreciation; price growth decouples from fundamentals (rents and discount rates).
  - Present-value model linking real house prices (Pt) to rent income (Rt) and constant discount rate (D): Pt = Et[ Rt+1 + Pt+1 /(1+D) ] with iterated expectations yielding infinite-horizon valuation; no-bubbles condition gives Pf_t = sum_{j=1}^∞ Et[ Rt+j /(1+D)^j ].
  - Define St ≡ Pt − (1/D) Rt following Campbell and Shiller (1987) and Wang (2000). If Rt is I(1) and no bubble, Pt is I(1) and St is stationary (cointegration).
- Testing approach:
  - Right-tailed ADF unit-root framework where key parameter β1: null β1 = 0 (unit root) vs alternative β1 > 0 (explosive). ADF t-statistic used.
  - Sup ADF (SADF) test (Phillips, Wu, and Yu, 2011): forward-expanding window; SADF(r0) = sup_{r2 ∈ [r0,1]} ADF_{r1 r2} with r1 fixed at 0.
  - Backward sup ADF (BSADF) and generalized SADF (GSADF) (Phillips, Shi, and Yu, 2015): double-recursive algorithm detecting multiple bubble episodes and dating origination/termination; BSADF_{r2}(r0) = sup_{r1 ∈ [0, r2 − r0]} ADF_{r1 r2}; GSADF(r0) = sup_{r2 ∈ [r0,1]} BSADF_{r2}(r0).
  - Dating rules:
    - Start date r̂e: first r2 with BSADF_{r2}(r0) > scv_{r2,α_T}.
    - Termination r̂f: first r2 after [r̂e + δ log(T)] with BSADF_{r2}(r0) < scv_{r2,α_T}, where δ log(T) is minimal bubble duration.
  - Statistical implementation details:
    - Wild bootstrap per Phillips and Shi (2020) to address unconditional heterogeneity and multiplicity in recursive testing.
    - Time dimension: T = 345 months (January 1994 to September 2022).
    - Maximum number of lags determined by Schwert (1989): maxlag = int(4 (T/100)^0.25).
    - Critical values for right-tail ADF, SADF and GSADF obtained via Monte Carlo simulations.

### Econometric results (Section IV)
- Data suitability:
  - Monthly city-level housing prices for 5 cities plus national average; T = 345 months makes dataset suitable to detect house-price bubbles with recursive tests.
- Main test results (summary of Tables 1 and 2):
  - Real house prices (Table 1):
    - Kaunas: ADF -1.44; SADF 2.90; GSADF 3.69.
    - Klaipėda: ADF -2.32; SADF 3.36; GSADF 3.67.
    - Panevėžys: ADF -1.92; SADF 2.62; GSADF 3.52.
    - Šiauliai: ADF -1.76; SADF 3.19; GSADF 3.83.
    - Vilnius: ADF -2.04; SADF 1.84; GSADF 3.96.
    - National: ADF -2.00; SADF 2.36; GSADF 3.62.
    - ADF critical values reported: 90 = -0.42; 95 = -0.11; 99 = 0.68. SADF critical values reported: 90 = 1.14; 95 = 1.41; 99 = 2.04. GSADF critical values reported: 90 = 1.92; 95 = 2.13; 99 = 2.60.
  - House price-to-rent ratios (Table 2):
    - Kaunas: ADF -1.90; SADF 2.93; GSADF 2.93.
    - Klaipėda: ADF -1.73; SADF 2.59; GSADF 2.59.
    - Panevėžys: ADF -2.13; SADF 2.76; GSADF 3.75.
    - Šiauliai: ADF -2.07; SADF 4.04; GSADF 4.04.
    - Vilnius: ADF -2.24; SADF 3.95; GSADF 3.95.
    - National: ADF -2.15; SADF 3.36; GSADF 3.36.
    - ADF critical values reported for ratios: 90 = -0.45; 95 = -0.14; 99 = 0.60. SADF critical values: 90 = 1.12; 95 = 1.40; 99 = 1.95. GSADF critical values: 90 = 1.88; 95 = 2.11; 99 = 2.56.
- Statistical inference and interpretation:
  - GSADF test preferred as more robust for multiple bubbles.
  - Test statistics (GSADF) for real house prices are significantly greater than the 1 percent critical value, leading to rejection of the null hypothesis of no-bubble.
  - Evidence of explosive behavior in real housing prices across all five cities and at the national level during January 1994 to September 2022.
  - House price-to-rent ratio tests produce similar results but show greater variation across cities, partly due to more limited time dimension (ratio data constrained to 2003–2022).
- Chronology and pattern of exuberance:
  - Two distinct periods of strong exuberance in real house prices at city and national level:
    1. From 2002 until the GFC.
    2. From 2019 until mid-2022.
  - During these periods, estimated GSADF statistics exceed the corresponding 95 percent critical values.
  - Size of bubbles varies across cities but a similar nationwide boom-bust pattern with considerable oscillations is observed.
  - For house price-to-rent ratio (available 2003–2022), explosive behavior observed prior to the GFC across Lithuania, but no significant bubble in recent years except in Panevėžys where extent of explosive behavior gets close to pre-GFC level.
- Visualization:
  - Figures plotted: Figure 3 (Explosive Behavior of Real House Prices: GSADF Test) and Figure 4 (Explosive Behavior of House Price-to-Rent Ratios: GSADF Test) show GSADF series against right-tail CV (95%) and right-tail CV (90%) for each city and national series.

### Financial Conditions and housing prices in Lithuania
- Recent house price dynamics:
  - House prices rose by 3.6 percent in the previous eight months and 9.3 percent in 2021.
  - The price adjustment in the real estate market could deepen as a result of lower income growth and higher interest rates.
- Financial Conditions Index (FCI) and housing price relationship:
  - Macro-financial conditions are an important determinant of house price movements.
  - The continuing recalibration of monetary policy in the eurozone and elsewhere is resulting in a significant tightening of financial conditions in Lithuania.
  - There is a significant relationship between the financial conditions index (FCI) and real house price growth (as shown in Figure 5).
  - The FCI calculated by Sengaviano and others (forthcoming) has been on an upward trajectory since the last quarter of 2020 and gained further momentum in 2022 with repricing of risk and shrinking credit availability.

### Conclusion (Section V) and key quantitative points
- Overall assessment:
  - Recursive right-tailed tests reject the null of no-bubble and find evidence for long and multiple periods of explosive behavior in the Lithuanian real estate market across major cities and nationally for January 1994 to September 2022.
  - Recent acceleration in house price growth occurred during the COVID-19 pandemic after a prolonged post-GFC stability, supported by ultra-low interest rates and double-digit income growth.
  - While bubble sizes vary across cities—especially when using the house price-to-rent ratio—the country exhibits a coherent boom-bust pattern.
- Additional quantitative summary points reiterated:
  - Property prices in Lithuania increased as much as 140 percent since 2010, following a correction of 43 percent during the GFC.
  - Real house price growth slowed to a year-on-year rate of 0.4 percent as of September 2022 (as noted in concluding remarks).

### Policy recommendations and supervisory actions (summary)
- Maintain and deploy borrower-based macroprudential measures and macroprudential capital requirements as needed.
- Conduct targeted stress tests for banks and non-bank financial institutions with high real estate exposures ahead of potential corrections.
- Consider higher provisioning for mortgage loans for institutions found vulnerable in stress tests.
- Monitor FCI developments given its significant relationship with real house price growth and the tightening of financial conditions since the last quarter of 2020 and further in 2022.

- Key statistics and timelines:
  - 3.6 percent — house price increase in the previous eight months.
  - 9.3 percent — house price increase in 2021.
  - last quarter of 2020 — FCI begins upward trajectory.
  - 2022 — FCI gains further momentum with repricing of risk and shrinking credit availability.
  - T = 345 months — January 1994 to September 2022.

*Source: wpiea2023033-print-pdf (IMF working paper content excerpt).*

### 2021. Furthermore, there is considerable heterogeneity in housing price growth across cities in

### wpiea2023033-print-pdf - 2021. Furthermore, there is considerable heterogeneity in housing price growth across cities in

### Housing price trends and heterogeneity
- Real house price index:
  - Continued to increase at an annual rate of 3.1 percent in Vilnius.
  - House prices in the rest of Lithuania have started declining in real terms.
  - Sharpest fall of 4 percent in Šiauliai.
- House price-to-rent ratio:
  - The correction in house prices is even more pronounced and widespread when focusing on the house price-to-rent ratio (Figure 2).
- Historical context and risks:
  - Monetary policy shocks and slower income growth could push real housing prices lower in a panel of emerging European markets, including Lithuania.
  - Large house price corrections can have adverse effects on economic performance and financial stability, as experienced during the GFC and other episodes in history.

### Macroprudential framework and instruments in Lithuania
- Instruments currently in place:
  - loan-to-value (LTV)
  - debt service-to-income (DSTI) ratios
  - maximum loan maturity
  - interest rate stress and sensitivity tests
  - countercyclical capital buffer, (CCyB)
  - other systemically important institutions (O-SII) buffer
  - conservation buffer (CCB)
- Objectives of these measures:
  - Reduce vulnerability in the banking system.
  - Increase resilience of borrowers to asset price or income shocks.
  - Minimize downside risks to financial stability.

### Supervisory actions and recommendations
- Pre-correction actions for authorities:
  - Conduct stress tests for banks and other non-bank financial institutions that have high exposures to real estate.
  - Possibly require higher provisioning for mortgage loans for institutions found to be vulnerable based on the stress tests.

### Document structure note
- The remainder of this paper is structured as follows:
  - Section II provides an overview of literature.

*Source: wpiea2023033-print-pdf - 2021. Furthermore, there is considerable heterogeneity in housing price growth across cities in*

### Section III describes the data used in the empirical analysis. Section IV explains the econometric

### Section III–V: Literature, Data, Econometric Strategy, and Results

### Literature review: theoretical and empirical context
- Theoretical origins of explosive asset-price behavior cited: Flood and Garber (1980), Tirole (1982), Blanchard and Watson (1982).
- Empirical findings summarized:
  - Arshanapalli and Nelson (2008): housing prices and fundamentals in the U.S. share a common stochastic trend and exhibit explosive behavior prior to the GFC.
  - Burnside, Eichenbaum, and Rebelo (2011): boom-and-bust cycles in housing driven by fundamentals and speculative expectations.
  - Holly, Pesaran, and Yamagata (2010): cointegration between house prices and real incomes across a panel of 49 U.S. states; limited role for real interest rates; divergences often temporary but persistent in some states.
  - Geng (2018): macro-financial factors account for significant variation in housing prices across 20 advanced economies; overvaluation can be persistent.
  - Time-series bubble detection literature: Diba and Grossman (1988); Evans (1991) highlights limits of stationarity tests with periodically collapsing bubbles; Phillips, Wu, and Yu (2011) and Phillips, Shi, and Yu (2015) develop recursive and rolling ADF tests to detect and date-stamp explosive episodes.
  - Cross-country macro-financial determinants emphasized: income, real interest rates, credit availability, demographics, supply factors; extensive empirical variation across samples and methods (Terones and Otrok; Tsatsaronis and Zhu, 2004; Girouard and others, 2006; Égert and Mihaljek, 2007; Adams and Füss, 2010; Agnello and Schuknecht, 2011; Cerutti, Dagher, and Dell’Ariccia, 2015).
  - Emerging market evidence: Égert and Mihaljek (2007) for CEE; Ucal and Gökkent (2009) and Jianhua and Huidan (2013) for Turkey and China; Stepanyan, Poghosyan, and Bibolov (2010) for former Soviet Union; Cevik and Naik (2022) using panel quantile regression for Europe.

### Data overview (Section III)
- Data source and coverage:
  - Ober-Haus apartment price index for 5 cities: Kaunas, Klaipėda, Panevėžys, Šiauliai and Vilnius, plus national average.
  - Frequency: monthly observations from January 1994 to September 2022.
  - City-specific CPI and its housing component drawn from Statistics Lithuania to calculate house price-to-rent ratio at city level.
- Key historical changes in Lithuanian housing prices (1994–September 2022):
  - Between 1994 and onset of the GFC in 2008:
    - Housing prices increased by 702 percent in nominal terms.
    - Housing prices increased by 170 percent in real terms (adjusted for inflation).
    - Real house price increases by city over same period: Vilnius 177 percent; Šiauliai 159 percent; Kaunas 147 percent.
  - GFC impact:
    - Housing prices declined by 41 percent in nominal terms.
    - Housing prices declined by 52 percent in real terms.
    - Real house prices fell more in smaller cities: average decline 56.5 percent in Klaipėda, Panevėžys, Šiauliai versus average decline 49.5 percent in Vilnius and Kaunas.
  - Post-GFC to September 2022:
    - After the GFC, house prices increased by an average of 95 percent in nominal terms and 36 percent in real terms (adjusted for inflation).
  - COVID-19 period (end-2019 to September 2022):
    - House prices increased by 50 percent in nominal terms and 15 percent in real terms (adjusted for inflation).
  - Note: Ober-Haus index methodology and latest data referenced (Ober-Haus price index covers five large cities).

### Econometric strategy (Section IV)
- Conceptual framework:
  - Bubble defined per Himmelberg, Mayer, and Sinai (2005): buyers pay inflated prices expecting unrealistically high future appreciation; price growth decouples from fundamentals (rents and discount rates).
  - Present-value model linking real house prices (Pt) to rent income (Rt) and constant discount rate (D): Pt = Et[ Rt+1 + Pt+1 /(1+D) ] with iterated expectations yielding infinite-horizon valuation; no-bubbles condition gives Pf_t = sum_{j=1}^∞ Et[ Rt+j /(1+D)^j ].
  - Define St ≡ Pt − (1/D) Rt following Campbell and Shiller (1987) and Wang (2000). If Rt is I(1) and no bubble, Pt is I(1) and St is stationary (cointegration).
- Testing approach:
  - Right-tailed ADF unit-root framework where key parameter β1: null β1 = 0 (unit root) vs alternative β1 > 0 (explosive). ADF t-statistic used.
  - Sup ADF (SADF) test (Phillips, Wu, and Yu, 2011): forward-expanding window; SADF(r0) = sup_{r2 ∈ [r0,1]} ADF_{r1 r2} with r1 fixed at 0.
  - Backward sup ADF (BSADF) and generalized SADF (GSADF) (Phillips, Shi, and Yu, 2015): double-recursive algorithm detecting multiple bubble episodes and dating origination/termination; BSADF_{r2}(r0) = sup_{r1 ∈ [0, r2 − r0]} ADF_{r1 r2}; GSADF(r0) = sup_{r2 ∈ [r0,1]} BSADF_{r2}(r0).
  - Dating rules:
    - Start date r̂e: first r2 with BSADF_{r2}(r0) > scv_{r2,α_T}.
    - Termination r̂f: first r2 after [r̂e + δ log(T)] with BSADF_{r2}(r0) < scv_{r2,α_T}, where δ log(T) is minimal bubble duration.
  - Statistical implementation details:
    - Wild bootstrap per Phillips and Shi (2020) to address unconditional heterogeneity and multiplicity in recursive testing.
    - Time dimension: T = 345 months (January 1994 to September 2022).
    - Maximum number of lags determined by Schwert (1989): maxlag = int(4 (T/100)^0.25).
    - Critical values for right-tail ADF, SADF and GSADF obtained via Monte Carlo simulations.

### Econometric results (Section IV)
- Data suitability:
  - Monthly city-level housing prices for 5 cities plus national average; T = 345 months makes dataset suitable to detect house-price bubbles with recursive tests.
- Main test results (summary of Tables 1 and 2):
  - Real house prices (Table 1): ADF, SADF, and GSADF statistics reported for Kaunas, Klaipėda, Panevėžys, Šiauliai, Vilnius, and National.
    - Kaunas: ADF -1.44; SADF 2.90; GSADF 3.69. Confidence interval critical values: 90 = -0.42; 95 = -0.11; 99 = 0.68 for ADF; SADF critical values: 90 = 1.14; 95 = 1.41; 99 = 2.04; GSADF critical values: 90 = 1.92; 95 = 2.13; 99 = 2.60.
    - Klaipėda: ADF -2.32; SADF 3.36; GSADF 3.67. (Same listed critical values as Kaunas).
    - Panevėžys: ADF -1.92; SADF 2.62; GSADF 3.52. (Same critical values).
    - Šiauliai: ADF -1.76; SADF 3.19; GSADF 3.83. (Same critical values).
    - Vilnius: ADF -2.04; SADF 1.84; GSADF 3.96. (Same critical values).
    - National: ADF -2.00; SADF 2.36; GSADF 3.62. (Same critical values).
  - House price-to-rent ratios (Table 2):
    - Kaunas: ADF -1.90; SADF 2.93; GSADF 2.93. ADF critical values: 90 = -0.45; 95 = -0.14; 99 = 0.60. SADF critical values: 90 = 1.12; 95 = 1.40; 99 = 1.95. GSADF critical values: 90 = 1.88; 95 = 2.11; 99 = 2.56.
    - Klaipėda: ADF -1.73; SADF 2.59; GSADF 2.59. (Same critical values as Kaunas for ratio).
    - Panevėžys: ADF -2.13; SADF 2.76; GSADF 3.75. (Same critical values).
    - Šiauliai: ADF -2.07; SADF 4.04; GSADF 4.04. (Same critical values).
    - Vilnius: ADF -2.24; SADF 3.95; GSADF 3.95. (Same critical values).
    - National: ADF -2.15; SADF 3.36; GSADF 3.36. (Same critical values).
- Statistical inference and interpretation:
  - GSADF test preferred as more robust for multiple bubbles.
  - Test statistics (GSADF) for real house prices are significantly greater than the 1 percent critical value, leading to rejection of the null hypothesis of no-bubble.
  - Evidence of explosive behavior in real housing prices across all five cities and at the national level during January 1994 to September 2022.
  - House price-to-rent ratio tests produce similar results but show greater variation across cities, partly due to more limited time dimension (ratio data constrained to 2003–2022).
- Chronology and pattern of exuberance:
  - Two distinct periods of strong exuberance in real house prices at city and national level:
    1. From 2002 until the GFC.
    2. From 2019 until mid-2022.
  - During these periods, estimated GSADF statistics exceed the corresponding 95 percent critical values.
  - Size of bubbles varies across cities but a similar nationwide boom-bust pattern with considerable oscillations is observed.
  - For house price-to-rent ratio (available 2003–2022), explosive behavior observed prior to the GFC across Lithuania, but no significant bubble in recent years except in Panevėžys where extent of explosive behavior gets close to pre-GFC level.
- Visualization:
  - Figures plotted: Figure 3 (Explosive Behavior of Real House Prices: GSADF Test) and Figure 4 (Explosive Behavior of House Price-to-Rent Ratios: GSADF Test) showing GSADF series against right-tail CV (95%) and right-tail CV (90%) for each city and national series.

### Conclusion (Section V): synthesis of findings
- Overall assessment:
  - Recursive right-tailed tests reject the null of no-bubble and find evidence for long and multiple periods of explosive behavior in the Lithuanian real estate market across major cities and nationally for January 1994 to September 2022.
  - Recent acceleration in house price growth occurred during the COVID-19 pandemic after a prolonged post-GFC stability, supported by ultra-low interest rates and double-digit income growth.
  - While bubble sizes vary across cities—especially when using the house price-to-rent ratio—the country exhibits a coherent boom-bust pattern.
- Additional quantitative summary points reiterated:
  - Property prices in Lithuania increased as much as 140 percent since 2010, following a correction of 43 percent during the GFC.
  - Real house price growth slowed to a year-on-year rate of 0.4 percent as of September 2022 (as noted in concluding remarks).

*Source: Authors’ calculations and analysis in the referenced IMF working paper sections on data, methodology, results, and conclusion.*

### 3.6 percent in the previous eight months and 9.3 percent in 2021. The price adjustment in the

### Financial Conditions and Housing Prices in Lithuania

### Recent house price dynamics
- House prices rose by 3.6 percent in the previous eight months and 9.3 percent in 2021.
- The price adjustment in the real estate market could deepen as a result of lower income growth and higher interest rates.

### Financial Conditions Index (FCI) and housing price relationship
- Macro-financial conditions are an important determinant of house price movements.
- The continuing recalibration of monetary policy in the eurozone and elsewhere is resulting in a significant tightening of financial conditions in Lithuania.
- There is a significant relationship between the financial conditions index (FCI) and real house price growth (as shown in Figure 5).
- The FCI calculated by Sengaviano and others (forthcoming) has been on an upward trajectory since the last quarter of 2020 and gained further momentum in 2022 with repricing of risk and shrinking credit availability.

### Policy recommendations and supervisory actions
- The Bank of Lithuania has adopted macroprudential tools after the GFC, including borrower-based measures and macroprudential capital requirements, to prevent housing price bubbles and maintain financial stability.
- Purpose of macroprudential measures:
  - Reduce vulnerability in the banking system.
  - Increase resilience of borrowers to asset price or income shocks.
  - Minimize downside risks to financial stability.
- Suggested near-term policy actions:
  - Before the onset of a housing market correction, the authorities should conduct stress tests for banks and other non-bank financial institutions that have high exposures to real estate.
  - Possibly require higher provisioning for mortgage loans for those institutions that are found to be vulnerable based on the stress tests.

### Key statistics and timelines
- 3.6 percent — house price increase in the previous eight months.
- 9.3 percent — house price increase in 2021.
- last quarter of 2020 — FCI begins upward trajectory.
- 2022 — FCI gains further momentum with repricing of risk and shrinking credit availability.

*Source: IMF; Ober-Haus; and authors’ calculations (content excerpt).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023033-print-pdf.pdf_