## _wp07150

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---

### I. INTRODUCTION
- Hong Kong SAR has amongst the most volatile fiscal revenues in the world, and faces significant spending pressures due to population aging.
- Revenue volatility creates risks to government service provision and complicates government planning because revenues frequently and unexpectedly fall short of expenditure needs even if revenues cover spending on average.
- Sudden falls in revenue may require governments to draw down accumulated savings or borrow, which can threaten sustainability given uncertainty about the duration of the revenue fall.
- The government has commenced, and plans further, public discussions on how to reform the healthcare financing systems, and on ways to broaden the revenue base.
- Methodology and policy scenarios studied:
  - Application of value at risk methodology to measure risks from extreme fiscal events and to provide numerical estimates of potential losses over various horizons and probability levels.
  - Sensitivity analysis of how measured risks change under alternate policies, specifically:
    - (i) the introduction of a broad-based goods and services tax; and
    - (ii) smoothing the return the government receives on its financial assets.
- Fiscal savings (fiscal reserves) have been integral given revenue volatility:
  - Fiscal reserves currently over 20 percent of GDP.
  - In the absence of policy change or reforms, reserves aimed at anticipating age-related fiscal pressures could be up to 30 percent of GDP by 2030.
  - Estimates of “prudential” reserves reflecting historical volatility could be around 30–50 percent of GDP.
- Broad conclusions:
  - Fiscal reserves will likely remain an important feature of future fiscal policy to anticipate age-related spending pressures and provide a buffer against fiscal shocks.
  - The optimal amount of self-insurance provided by accumulated fiscal savings is discussed (implicit market value and measurement).

### II. ANTICIPATED RISKS: AGE-RELATED FISCAL PRESSURES
- Demographic and fiscal projections:
  - Old-age dependency is expected to double by 2030.
- Expected fiscal impacts under current policies:
  - Most pressures likely to reflect health care spending because the government provides a relatively limited pension and the Mandatory Provident Fund (MPF) will be an increasing source of retirement income over time.
  - Pension-related transitional spending is unlikely to cumulatively amount to more than 5 percent of GDP by 2030–2035, when it stabilizes and begins declining as the MPF becomes a growing source of retirement income.
  - Without changes in healthcare financing or other fiscal policies, Leigh (2006) finds healthcare costs could result in cumulative deficits of almost 20 percent of GDP by 2030 and 50 percent of GDP by 2050.
- Policy options and limits:
  - If healthcare costs are mostly covered by individuals—possibly by raising the current contribution to the MPF by about 5 percentage points and earmarking it purely to finance the rise in healthcare due to aging—the fiscal impact could be limited.
  - A 2½ percentage point rise in the MPF contribution rate could account for only half of average age-related costs.
  - Private savings or voluntary insurance alone cannot fully mitigate risks because without universal catastrophic coverage the least healthy could remain uninsured, exposing the government to remaining fiscal risks.
- Institutional constraint:
  - Hong Kong SAR’s Basic Law directs the government to “... strive to achieve a fiscal balance, ... and keep the budget commensurate with the growth rate of its gross domestic product.”

### III. UNANTICIPATED RISKS: REVENUE VOLATILITY
- Measured volatility and historical ranges:
  - Since 1981, shares of Hong Kong SAR’s total and tax revenue in GDP have varied between 13½ percent and 20¾ percent (total revenue) and 8½ percent and 12¼ percent (tax revenue).
  - Measured by the coefficient of variation, the volatility of tax and total revenue (as shares of GDP) have each been around 11 percent of their average levels since 1981.
  - Even after controlling for tax policy changes, Hong Kong SAR has considerably more volatile revenue than other Asian countries, although volatility has fallen more recently.
- Drivers of volatility:
  - Revenue volatility principally reflects the importance of volatile non-tax revenue.
  - Non-tax revenue has accounted for over 90 percent of the variance of the SAR’s total revenue since FY1981/82.
  - The most volatile non-tax revenue items are investment income and the land premium, which make sustainable contributions to revenue.
  - Contribution to revenue volatility has varied over time; tax revenue contributed more to volatility during the period up to April, 1998 when fiscal reserves were treated as a time deposit with the Exchange Fund.
- Implications:
  - High reliance on non-tax revenue increases exposure to large swings in government receipts.
  - Policies that lower revenue volatility (for example, smoothing investment returns or introducing a broad-based consumption tax) would reduce fiscal risks and can help shore up the tax base as the aging population limits income tax revenue.

### Box 1: Fiscal Policy in Volatile Environments — Key Elements
- Overview:
  - Volatile economic and fiscal environments complicate fiscal policy; theory highlights an important role for the government’s net asset position when the fiscal environment is volatile.
  - Two theoretical approaches are discussed:
    - Optimal fiscal policy with distortionary taxes, fluctuating spending pressures, and incomplete markets.
    - Government spending chosen to “insure” the private sector when revenue volatility is taken as given.

- Optimal fiscal policy results:
  - With complete markets and state-contingent bonds: minimize distortions by keeping tax rates relatively stable and allowing net assets to fluctuate (Chari, et. al., 1994).
  - With incomplete markets (government issues only risk-free bonds): under some conditions the government’s tax-setting problem can be recast as a permanent income problem (Aiyagari, et. al., 2002).
    - Government will choose taxes less volatile than exogenous spending and allow net assets to fluctuate.
    - If the government can accumulate assets up to its “natural” limit, it will do so and reduce taxes to zero, financing spending from the (fixed) return on assets.
    - If asset income is sufficiently volatile, it may still be optimal to maintain low taxes (conjecture).
    - If assets cannot reach the “natural” limit, distortionary taxes remain positive and net assets fluctuate.

- Government as insurer when revenue is volatile:
  - Incomplete markets calibrated evidence (Mendoza and Oviedo, 2005) shows governments with more volatile revenue cannot borrow as much, spending absorbs volatility, and holding net assets can be optimal.
  - A consumption tax should ease governmental borrowing constraints by stabilizing revenues.

### Value at Risk (VaR) estimates and findings
- Purpose and data:
  - VaR provides a probability-based measure of a series of weak fiscal outcomes and therefore desired reserve holdings.
  - Data availability: FY1981/82–FY2004/05.
- Methods:
  - Monte Carlo and bootstrap (moving block and stationary) simulation techniques applied.
  - Simulation count: 20,000 simulations for VaR estimates.
  - Measure: VaR based on cumulative fiscal balances over a number of years (sum of overall consolidated fiscal balances as a share of the final period GDP).
  - Reported results for accumulation periods T = 2–7 years (5–7 year period highlighted as reasonable).
- Key VaR findings:
  - Bootstrap estimates suggest reserves within the range of 25–50 percent of GDP for consecutive balances over 5–7 years and confidence levels between 92.5 and 97.5 percent.
  - Monte Carlo estimates are larger, varying between 40 and 80 percent of GDP over the same range of parameters.
  - VaR increases with both the confidence level and the number of accumulated balances (T), and at an increasing rate.
  - The Monte Carlo method produces larger VaR because the large majority of cumulative balances are negative; Brownian motion model of risk factors may be too simple.
  - Bootstrap estimates reflect only historical volatility and do not depend on model choice.
  - Both estimates are affected by the limited historical fiscal data available.

### The insurance value of fiscal reserves (market-equivalent valuation)
- Approach:
  - Value insurance equivalently to a put option guaranteeing desired liquidity D given asset value V; European option pricing formula used as approximation.
- Assumptions and inputs:
  - Asset insured: annual revenue (as a share of GDP).
  - Desired insurance (D) considered at 15, 20, and 23 percent of GDP (23 percent approximates current reserve holdings).
  - Revenue-to-GDP values used: minimum 13.5, average 16.5, FY2004/05 outcome 18.4, maximum 20.7 (FY1981/82–FY2004/05 sample).
  - Risk-free interest rate assumption: 3 percent.
- Results:
  - Based on revenue and reserve holdings in FY2004/05, the average annual implicit market price of insurance would be around 0.17.
  - Implication: the cost of insurance equivalent to self-insurance provided by fiscal reserves of 23 percent of GDP would be around 3¾ percent of GDP annually.
  - Given the Exchange Fund’s historical average rate of return of 6.3 percent over 1994–2005, market insurance would likely not have been a cost-effective alternative to self-insurance at the levels held.
- Notes:
  - Implicit insurance prices fall rapidly as desired insurance falls and revenue increases.
  - The European option approximation may understate the cost of obtaining insurance even at “efficient” prices.
  - Borrowing is the likeliest market avenue for a buffer, but borrowing is not equivalent to insurance because its cost is not fixed ex ante and tends to be highest when needed most.

### Self-insurance and optimal share of self-insured coverage
- Concept and determinants:
  - For a given desired insurance level, choose the share of self insurance where marginal benefit equals marginal cost.
    - Marginal cost: lower return from holding more liquid assets.
    - Marginal benefit: reduction in implicit per unit market cost from purchasing less market insurance.
- Findings:
  - Optimal share of self insurance decreases monotonically with the liquidity premium of a less liquid portfolio relative to reserves (Lee, 2004).
  - Given the Exchange Fund’s high historical return, the liquidity premium on these assets is likely low; high levels of self insurance can be optimal.
  - Calculations for desired insurance levels:
    - Around current levels (20 percent of GDP or slightly more than FY2004/05 revenue): less than complete self insurance is optimal for low liquidity premia.
    - 30 percent of GDP (1.6 times FY2004/05 revenue) and 50 percent of GDP (2.7 times FY2004/05 revenue): as revenue volatility increases, the optimal share self insured increases; for larger desired insurance levels, complete self-insurance quickly becomes optimal.
  - Availability and pricing of market insurance are uncertain; equivalence to European option pricing may understate market costs.

### Policy choices that can limit fiscal risks (summary and sensitivity)
- VaR-based desired reserve estimates are backward looking but desired reserves should be forward looking and reflect expected future volatility and policy settings.
- Two examined policy changes for sensitivity of desired reserves:
  - Introduction of a goods and services tax (GST).
  - Move to fixed returns on fiscal reserves.
- Partial conclusion:
  - Moving to a fixed rate of return on reserves could significantly reduce fiscal risks and desired reserves (analysis continued in subsequent sections).

### A. Introduction of a GST — purpose, assumptions, and effects
- Purpose and channels:
  - A GST should limit the need for fiscal reserves by providing a more stable revenue base as the population ages and by limiting revenue volatility.
  - The consumption tax base could grow by 40 percent more than the salaries tax base as the aging population increasingly lives off previous savings, even assuming "moderate and declining real per capita consumption grow" and "moderate real wage growth."
  - Real per capita consumption growth is assumed to decline but average less than 1 percent per annum between 2005 and 2050, while real wages are assumed to grow at 1 percent during this period.
- Estimated volatility reduction from revenue-neutral substitution:
  - Replacing some historical indirect taxes with a revenue-neutral GST could reduce the variance of indirect taxes-to-GDP by 60–83 percent at rates of 3–5 percent.
  - The variance of total revenue-to-GDP could possibly fall by 6–8 percent.
  - Most of the variance reduction occurs at lower GST rates; the impact on overall revenue volatility is more muted than on indirect-tax variance.
- Tax base and yield assumptions:
  - Only household-related (including rent) spending are exempt, and there is a 25 percent leakage rate.
  - Such a tax base would imply that each percentage point in GST rate would yield around ½ percent of GDP revenue in FY2004/05, with a rate of 8–9 percent being able to completely replace historical indirect tax revenue.
- Fiscal risk and reserves:
  - Using the Monte Carlo VaR method, a GST introduced at rates of 3–5 percent, offsetting indirect tax revenue, could reduce fiscal risks by around 2–4 percentage points of GDP depending on the length of consecutive deficits considered.
  - The reduction in VaR is smaller than the direct impact on revenue variance because of interactions of risk factors with the GST base.
  - Although modest, this reduction in fiscal risks is a side-benefit of a policy that also offers longer-run stability and efficiency gains.

### B. Fixed investment returns — trade-offs and impacts
- Trade-offs:
  - Fixing investment returns should reduce revenue volatility but would also involve costs, including the removal of the possibility of very high investment income.
  - The party bearing return risk (probably the Exchange Fund) would implicitly charge for this risk-bearing by offering a lower rate of return.
- Estimated impact on VaR and reserves from fixing returns:
  - Assuming investment income equals income from fiscal reserves earning a fixed annual return equal to the historical average, moving to a fixed (or smoother) investment return could reduce reserves required to withstand a string of five deficits by around 7–10 percentage points of GDP.
  - Over a 7 year horizon, the reduction could be as much as 20 percentage points of GDP.
  - The reduction in required reserves increases significantly with the number of balances accumulated, but decreases with the confidence level.
  - Alternatives to a fixed return (e.g., moving average of historical returns) should reduce the fiscal VaR by some fraction of the fixed-returns estimate.
- Assumption used for fixed-return scenario:
  - Assumes fixed investment return of 6.4 percent.

### V. CONCLUSION
- Key message:
  - Significant reserves could continue to play an essential role in Hong Kong SAR’s fiscal policy as a buffer against fiscal risks.
  - The size of fiscal risks depends on policy choices, future volatility, and the extent of the government’s risk aversion.
  - Timely policy action, such as moving towards less volatile revenue sources, could significantly reduce the need for sizable reserves.

### Appendix: Methodological issues (VaR estimation)
- VaR techniques used and their properties:
  - Monte Carlo simulations:
    - Rely on model-based assumptions about behavior of fiscal variables and underlying risk factors.
    - Risk factors assumed to affect fiscal outcome include direct revenue and expenditure risks, interest rates, Hong Kong’s GDP and private consumption, CPI inflation, and equity and residential property prices in Hong Kong.
    - For this exercise: interest rates assumed to follow a mean-reverting process; other economic and financial risk factors follow geometric Brownian motion processes.
    - Captures correlation structure of risk factors; same as used in previous fiscal VaR applications (Barnhill and Kopits, 2003; Adrogué, 2005).
    - Main weakness: dependence on assumed model structure.
  - Bootstrapping:
    - Estimates VaR by resampling observed historical data.
    - Two bootstrap approaches used: the moving block bootstrap (MBB) and the stationary bootstrap (SB).
    - MBB captures persistence in time series data; SB prevents nonstationary issues from applying the bootstrap to time series data.
    - Simple and free of modeling assumptions but less amenable to sensitivity analysis.
    - Reflects extent of available data—with only 24 independent values of fiscal outcomes available—but accounts for non-Gaussian properties.

*Source: _wp07150 - _wp07150 (canonical URL: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07150.pdf).*

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

### _wp07150 - References..............................................................................................................

### I. INTRODUCTION
- Hong Kong SAR has amongst the most volatile fiscal revenues in the world, and faces significant spending pressures due to population aging.
- Revenue volatility creates risks to government service provision and complicates government planning because revenues frequently and unexpectedly fall short of expenditure needs even if revenues cover spending on average.
- Sudden falls in revenue may require governments to draw down accumulated savings or borrow, which can threaten sustainability given uncertainty about the duration of the revenue fall.
- The government has commenced, and plans further, public discussions on how to reform the healthcare financing systems, and on ways to broaden the revenue base.
- Methodology and policy scenarios studied:
  - Application of value at risk methodology to measure risks from extreme fiscal events and to provide numerical estimates of potential losses over various horizons and probability levels.
  - Sensitivity analysis of how measured risks change under alternate policies, specifically:
    - (i) the introduction of a broad-based goods and services tax; and
    - (ii) smoothing the return the government receives on its financial assets.
- Fiscal savings (fiscal reserves) have been integral given revenue volatility:
  - Fiscal reserves currently over 20 percent of GDP.
  - In the absence of policy change or reforms, reserves aimed at anticipating age-related fiscal pressures could be up to 30 percent of GDP by 2030.
  - Estimates of “prudential” reserves reflecting historical volatility could be around 30–50 percent of GDP.
- Broad conclusions:
  - Fiscal reserves will likely remain an important feature of future fiscal policy to anticipate age-related spending pressures and provide a buffer against fiscal shocks.
  - The optimal amount of self-insurance provided by accumulated fiscal savings is discussed (implicit market value and measurement).

### II. ANTICIPATED RISKS: AGE-RELATED FISCAL PRESSURES
- Demographic and fiscal projections:
  - Old-age dependency is expected to double by 2030.
- Expected fiscal impacts under current policies:
  - Most pressures likely to reflect health care spending because the government provides a relatively limited pension and the Mandatory Provident Fund (MPF) will be an increasing source of retirement income over time.
  - Pension-related transitional spending is unlikely to cumulatively amount to more than 5 percent of GDP by 2030–2035, when it stabilizes and begins declining as the MPF becomes a growing source of retirement income.
  - Without changes in healthcare financing or other fiscal policies, Leigh (2006) finds healthcare costs could result in cumulative deficits of almost 20 percent of GDP by 2030 and 50 percent of GDP by 2050.
- Policy options and limits:
  - If healthcare costs are mostly covered by individuals—possibly by raising the current contribution to the MPF by about 5 percentage points and earmarking it purely to finance the rise in healthcare due to aging—the fiscal impact could be limited.
  - A 2½ percentage point rise in the MPF contribution rate could account for only half of average age-related costs.
  - Private savings or voluntary insurance alone cannot fully mitigate risks because without universal catastrophic coverage the least healthy could remain uninsured, exposing the government to remaining fiscal risks.
- Institutional constraint:
  - Hong Kong SAR’s Basic Law directs the government to “... strive to achieve a fiscal balance, ... and keep the budget commensurate with the growth rate of its gross domestic product.”

### III. UNANTICIPATED RISKS: REVENUE VOLATILITY
- Measured volatility and historical ranges:
  - Since 1981, shares of Hong Kong SAR’s total and tax revenue in GDP have varied between 13½ percent and 20¾ percent (total revenue) and 8½ percent and 12¼ percent (tax revenue).
  - Measured by the coefficient of variation, the volatility of tax and total revenue (as shares of GDP) have each been around 11 percent of their average levels since 1981.
  - Even after controlling for tax policy changes, Hong Kong SAR has considerably more volatile revenue than other Asian countries, although volatility has fallen more recently.
- Drivers of volatility:
  - Revenue volatility principally reflects the importance of volatile non-tax revenue.
  - Non-tax revenue has accounted for over 90 percent of the variance of the SAR’s total revenue since FY1981/82.
  - The most volatile non-tax revenue items are investment income and the land premium, which make sustainable contributions to revenue.
  - Contribution to revenue volatility has varied over time; tax revenue contributed more to volatility during the period up to April, 1998 when fiscal reserves were treated as a time deposit with the Exchange Fund.
- Implications:
  - High reliance on non-tax revenue increases exposure to large swings in government receipts.
  - Policies that lower revenue volatility (for example, smoothing investment returns or introducing a broad-based consumption tax) would reduce fiscal risks and can help shore up the tax base as the aging population limits income tax revenue.

*Source: _wp07150 - References.*

### Box 1: Fiscal Policy in Volatile Environments

### Box 1: Fiscal Policy in Volatile Environments

### Overview
- Volatile economic and fiscal environments complicate fiscal policy; theory highlights an important role for the government’s net asset position when the fiscal environment is volatile.
- Two theoretical approaches are discussed:
  - Optimal fiscal policy with distortionary taxes, fluctuating spending pressures, and incomplete markets.
  - Government spending chosen to “insure” the private sector when revenue volatility is taken as given.

### Optimal Fiscal Policy
- Objective: minimize distortions over time in the face of economic and government spending shocks.
- Key theoretical results:
  - With complete markets and state-contingent bonds: minimize distortions by keeping tax rates relatively stable and allowing net assets to fluctuate (Chari, et. al., 1994).
  - With incomplete markets (government issues only risk-free bonds): under some conditions the government’s tax-setting problem can be recast as a permanent income problem (Aiyagari, et. al., 2002).
    - Government will choose taxes less volatile than exogenous spending and allow net assets to fluctuate.
    - If the government can accumulate assets up to its “natural” limit, it will do so and reduce taxes to zero, financing spending from the (fixed) return on assets.1
    - If asset income is sufficiently volatile, it may still be optimal to maintain low taxes (conjecture).
    - If assets cannot reach the “natural” limit, distortionary taxes remain positive and net assets fluctuate.
- Footnote summary reproduced from source:
  - Agents must be risk neutral to recast the tax problem as a permanent income one.
  - “Natural” asset limit: sufficient to finance government spending indefinitely.
  - “Natural” debt limit: debt can be repaid no matter how long exogenous spending remains high.
  - Under more general preferences, if government spending can enter an absorbing state, tax rates are likely to converge to a positive constant and the allocation reflects the complete markets case.

### Government Spending and Insurance when Revenue is Volatile
- In incomplete markets with volatile economy and revenue, government can act as an insurer by maintaining relatively smooth spending and transfers for the private sector.
- Mendoza and Oviedo (2005) calibrated to Mexican data (government cannot hold net assets and is constrained by the natural debt limit):
  - Governments with more volatile revenue cannot borrow as much as those with more stable revenue.
  - Government spending absorbs much of the volatility and is more volatile than in the complete markets equilibrium.
  - The constraint that governments cannot hold net assets can bind in the long run, suggesting holding net assets can be optimal.
  - A consumption tax should ease governmental borrowing constraints by stabilizing revenues.

### Value at Risk (VaR) Estimates of Fiscal Risks
- Purpose: provide a probability-based measure of a series of weak fiscal outcomes and therefore desired reserve holdings; technical details in Porter (2007).
- Data availability: FY1981/82–FY2004/05.
- Methods: Monte Carlo and bootstrap (moving block and stationary) simulation techniques are applied to Hong Kong SAR’s fiscal data.
  - Simulation count: 20,000 simulations for VaR estimates.
  - Bootstrap methods designed for time series applications: moving block and stationary.
  - Monte Carlo relies on an underlying economic model (subject to specification error) but is flexible for counterfactuals; bootstrap is less flexible but model-free.
- Measure: VaR based on cumulative fiscal balances over a number of years (sum of overall consolidated fiscal balances as a share of the final period GDP).
  - Rationale: persistence of deficits matters (example: five consecutive deficits FY2000/01–FY2004/05).
  - Reported results for accumulation periods T = 2–7 years (5–7 year period highlighted as reasonable).
- Key VaR findings:
  - Based on cumulative balances, bootstrap estimates suggest reserves within the range of 25–50 percent of GDP for consecutive balances over 5–7 years and confidence levels between 92.5 and 97.5 percent.
  - Monte Carlo estimates are larger, varying between 40 and 80 percent of GDP over the same range of parameters.
  - VaR increases with both the confidence level and the number of accumulated balances (T), and at an increasing rate.
  - The Monte Carlo method produces larger VaR because the large majority of cumulative balances are negative (density in Figure 2); Brownian motion model of risk factors may be too simple.
  - Bootstrap estimates reflect only historical volatility and do not depend on model choice.
  - Both estimates are affected by the limited historical fiscal data available.

### The Insurance Value of Fiscal Reserves
- Objective: place an implicit market value on the insurance provided by fiscal reserves to assess cost-effectiveness and optimal split between self- and market-based insurance.
- Approach: value insurance equivalently to a put option guaranteeing desired liquidity D given asset value V; European option pricing formula used as approximation (Lee, 2004; Merton, 1971).
- Assumptions and parameters used:
  - Asset insured: annual revenue (as a share of GDP).
  - Desired insurance (D) considered at 15, 20, and 23 percent of GDP (23 percent approximates current reserve holdings).
  - Revenue-to-GDP values used: minimum 13.5, average 16.5, FY2004/05 outcome 18.4, maximum 20.7 (FY1981/82–FY2004/05 sample).
  - Risk-free interest rate assumption: 3 percent.
- Key quantitative results:
  - Based on revenue and reserve holdings in FY2004/05, the average annual implicit market price of insurance would be around 0.17.
  - Implication: the cost of insurance equivalent to self-insurance provided by fiscal reserves of 23 percent of GDP would be around 3¾ percent of GDP annually.
  - Given the Exchange Fund’s historical average rate of return of 6.3 percent over 1994–2005, market insurance would likely not have been a cost-effective alternative to self-insurance at the levels held.
- Notes on sensitivity:
  - Implicit insurance prices fall rapidly as desired insurance falls and revenue increases.
  - The European option approximation may understate the cost of obtaining insurance even at “efficient” prices.
  - Borrowing is the likeliest market avenue for a buffer, but borrowing is not equivalent to insurance because its cost is not fixed ex ante and tends to be highest when needed most.

### Self-Insurance and Optimal Share of Self-Insured Coverage
- Concept: for a given desired insurance level, choose the share of self insurance where marginal benefit equals marginal cost.
  - Marginal cost: lower return from holding more liquid assets.
  - Marginal benefit: reduction in implicit per unit market cost from purchasing less market insurance.
- Findings:
  - Optimal share of self insurance decreases monotonically with the liquidity premium of a less liquid portfolio relative to reserves (Lee, 2004).
  - Given the Exchange Fund’s high historical return, the liquidity premium on these assets is likely low; high levels of self insurance can be optimal.
  - Calculations for desired insurance levels:
    - Around current levels (20 percent of GDP or slightly more than FY2004/05 revenue): less than complete self insurance is optimal for low liquidity premia.
    - 30 percent of GDP (1.6 times FY2004/05 revenue) and 50 percent of GDP (2.7 times FY2004/05 revenue): as revenue volatility increases, the optimal share self insured increases; for larger desired insurance levels, complete self-insurance quickly becomes optimal.
  - Availability and pricing of market insurance are uncertain; equivalence to European option pricing may understate market costs.

### Policy Choices That Can Limit Fiscal Risks (summary lead-in)
- Changes in policy or the structure of the economy will change fiscal risks and desired reserve holdings.
- The VaR-based desired reserve estimates are backward looking (based on historical volatility and policy) but desired reserves should be forward looking and reflect expected future volatility and policy settings.
- Preliminary assessment (introduced): two changes analyzed for sensitivity of desired reserves are:
  - Introduction of a goods and services tax (GST).
  - Move to fixed returns on fiscal reserves.
- Partial conclusion stated in source: moving to a fixed rate of return on reserves could significantly reduce fiscal risks and desired reserves (analysis continues beyond the provided excerpt).

*Source: Box 1, "Fiscal Policy in Volatile Environments", _wp07150 - Box 1: Fiscal Policy in Volatile Environments*

### introduction of a low-rate GST is likely to be more moderate. This is unsurprising given the

### _wp07150 - introduction of a low-rate GST is likely to be more moderate. This is unsurprising given the

### A. Introduction of a GST
- Purpose and channels:
  - A GST should limit the need for fiscal reserves by providing a more stable revenue base as the population ages and by limiting revenue volatility.
  - The consumption tax base could grow by 40 percent more than the salaries tax base as the aging population increasingly lives off previous savings, even assuming "moderate and declining real per capita consumption grow" and "moderate real wage growth."
  - Real per capita consumption growth is assumed to decline but average less than 1 percent per annum between 2005 and 2050, while real wages are assumed to grow at 1 percent during this period.
- Estimated volatility reduction from revenue-neutral substitution:
  - Replacing some historical indirect taxes with a revenue-neutral GST could reduce the variance of indirect taxes-to-GDP by 60–83 percent at rates of 3–5 percent.
  - The variance of total revenue-to-GDP could possibly fall by 6–8 percent.
  - Most of the variance reduction occurs at lower GST rates; the impact on overall revenue volatility is more muted than on indirect-tax variance.
- Tax base and yield assumptions (from National Accounts data):
  - Only household-related (including rent) spending are exempt, and there is a 25 percent leakage rate.
  - Such a tax base would imply that each percentage point in GST rate would yield around ½ percent of GDP revenue in FY2004/05, with a rate of 8–9 percent being able to completely replace historical indirect tax revenue.
- Fiscal risk and reserves:
  - Using the Monte Carlo VaR method, a GST introduced at rates of 3–5 percent, offsetting indirect tax revenue, could reduce fiscal risks by around 2–4 percentage points of GDP depending on the length of consecutive deficits considered.
  - The reduction in VaR is smaller than the direct impact on revenue variance because of interactions of risk factors with the GST base.
  - Although modest, this reduction in fiscal risks is a side-benefit of a policy that also offers longer-run stability and efficiency gains.

### B. Fixed Investment Returns
- Trade-offs of fixing investment returns:
  - Fixing investment returns should reduce revenue volatility but would also involve costs, including the removal of the possibility of very high investment income.
  - The party bearing return risk (probably the Exchange Fund) would implicitly charge for this risk-bearing by offering a lower rate of return.
- Estimated impact on VaR and reserves from fixing returns:
  - Assuming investment income equals income from fiscal reserves earning a fixed annual return equal to the historical average, moving to a fixed (or smoother) investment return could reduce reserves required to withstand a string of five deficits by around 7–10 percentage points of GDP.
  - Over a 7 year horizon, the reduction could be as much as 20 percentage points of GDP.
  - The reduction in required reserves increases significantly with the number of balances accumulated, but decreases with the confidence level.
  - Alternatives to a fixed return (e.g., moving average of historical returns) should reduce the fiscal VaR by some fraction of the fixed-returns estimate.
- Assumption used for fixed-return scenario:
  - Assumes fixed investment return of 6.4 percent.

### V. Conclusion
- Key message:
  - Significant reserves could continue to play an essential role in Hong Kong SAR’s fiscal policy as a buffer against fiscal risks.
  - The size of fiscal risks depends on policy choices, future volatility, and the extent of the government’s risk aversion.
  - Timely policy action, such as moving towards less volatile revenue sources, could significantly reduce the need for sizable reserves.

### Appendix: Methodological issues (VaR estimation)
- VaR techniques used and their properties:
  - Monte Carlo simulations:
    - Rely on model-based assumptions about behavior of fiscal variables and underlying risk factors.
    - Risk factors assumed to affect fiscal outcome include direct revenue and expenditure risks, interest rates, Hong Kong’s GDP and private consumption, CPI inflation, and equity and residential property prices in Hong Kong.
    - For this exercise: interest rates assumed to follow a mean-reverting process; other economic and financial risk factors follow geometric Brownian motion processes.
    - Captures correlation structure of risk factors; same as used in previous fiscal VaR applications (Barnhill and Kopits, 2003; Adrogué, 2005).
    - Main weakness: dependence on assumed model structure.
  - Bootstrapping:
    - Estimates VaR by resampling observed historical data.
    - Two bootstrap approaches used: the moving block bootstrap (MBB) and the stationary bootstrap (SB).
    - MBB captures persistence in time series data; SB prevents nonstationary issues from applying the bootstrap to time series data.
    - Simple and free of modeling assumptions but less amenable to sensitivity analysis.
    - Reflects extent of available data—with only 24 independent values of fiscal outcomes available—but accounts for non-Gaussian properties.

*Source: _wp07150 - introduction of a low-rate GST is likely to be more moderate. This is unsurprising given the; canonical URL: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07150.pdf*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07150.pdf_