## 2.   Chile, Norway and Russia ñReserves and Ináation

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### I. Introduction and framing
- Observed episodes (China, Colombia, Chile, Norway, Russia) share large and accelerating foreign exchange reserve accumulation accompanied by exchange rate appreciation and rising domestic inflation.
- Paper frames the problem as a balance-of-payments "anti-crisis": a situation with an upper, not lower, sustainability limit on official foreign exchange reserves.
- Key policy question: what happens when the government (or markets) announce a maximum reserve level beyond which reserve accumulation will stop?
- Representative shock studied: government receives an additional tradables endowment equal to 1% of GDP (described as an additional tradables endowment equal to 1% of GDP).
- Monetary regimes analyzed: exchange rate targeting (ET), CPI inflation targeting (CPIT), and domestic (nontradables) inflation targeting (DIT).
- Main conceptual mechanism: announcement/constraint on reserves reduces allowable exchange rate depreciation, raising real money demand; if accommodated by nominal money issuance against foreign currency, this triggers a final burst of reserve accumulation (the anti-crisis).

### II. Model structure (overview)
- Small open economy with government, representative household, tradables and nontradables firms; real interest rates and international goods prices exogenous and constant (normalized to one); PPP for tradables; flexible nontradables prices.
- Households: CES aggregator for tradables cT and nontradables cN with elasticity of substitution  and tradables quasi-share ; cash-in-advance constraint on consumption; uncovered interest parity i_t = r + "t.
- Government: receives flow endowment d_t; chooses lump-sum transfers g_t and monetary policy rule consistent with one of the three regimes. May announce an upper limit on foreign exchange reserves x_t ≤ x.
- Key equilibrium conditions include market clearing, current account dynamics, and government budget/infinite-horizon constraint.
- Event chronology: initial steady state (balanced budget), at time 0 permanent increase in tradables endowment, targets initially unchanged, reserves would grow without bound absent upper limit x; constraint binds at endogenous time t =  and the economy transitions to final steady state.

### III. Calibration and solution
- Time unit: quarter for stock-flow ratios.
- Calibrated parameter values (selected, preserved exactly):
  - real international interest r = 3% p.a.
  - inverse velocity  = 1:55
  - tradables quasi-share  = 0:5
  - elasticity of substitution  = 0:5
  - initial labor supply h_ss = 1=3
  - labor income shares T = N = 0:4
  - CPI price level P_ss = 1
  - initial inflation rates = 0
  - initial central bank net foreign exchange reserves x_ss set equal to Chinaís average ratio of net foreign exchange reserves to annual output in 2006 = 22% (x_ss = 0:228 = 1:76)
  - government transfers g_ss set equal to interest earnings on reserves g_ss = 0:0132
  - permanent higher government tradables endowment d = 0:02 (equals 1% of overall output and 2% of tradables output)
  - upper limit on foreign exchange reserves x fixed at 24% of initial annual output (x = 1:92)
- Numerical implication: the higher endowment alone would take reserves to their upper limit within eight quarters; compound interest and increased money demand will shorten this time in practice.
- Solution method: nested shooting algorithm for CPIT and DIT; ET case involves simpler step paths.

### IV. Dynamics and quantitative findings from the policy experiment
- Common responses across regimes:
  - At time 0 households increase consumption immediately (positive wealth effect) and reduce labor supply; when inflation later declines households further increase consumption and labor increases slightly, so long-run consumption and labor are above initial steady state.
  - Relative price of tradables e falls initially and again during the anti-crisis; nontradables price rises; reallocation of employment to nontradables (Dutch disease).
  - Tradables output falls by about one third of the increase in the tradables endowment: 0.7% versus 2% of initial tradables output.
  - Initial current account surplus about 0.4% of GDP; during anti-crisis consumption rises sharply and final steady state current account is again balanced, with the gap between tradables consumption and output slightly over 2% of GDP (the size of the endowment increase plus interest on accumulated reserves).
  - Money demand increases on impact and again during the anti-crisis; by the cash-in-advance constraint this reflects higher consumption.
- Regime ranking in terms of speed and magnitude of reserve accumulation (fastest to slowest):
  - Exchange rate targeting (ET): strongest commitment to intervene and prevent appreciation; reserve gains fastest; anti-crisis happens earliest; upper limit reached after 5.5 quarters in the calibrated example (a full 1.5 quarters earlier than under DIT).
  - CPI inflation targeting (CPIT): intermediate commitment to intervene; larger reserve gains than DIT because preventing exchange rate appreciation to meet CPI target requires additional money growth and accumulation of reserves.
  - Domestic (nontradables) inflation targeting (DIT): weakest commitment to prevent exchange rate appreciation; appreciation can absorb some of the increase in real money demand, requiring much smaller additional money issuance and reserve gains; anti-crisis happens later.
- Specific calibrated quantitative points:
  - tradables endowment increase = 1% of initial GDP (d = 0:02 equals 1% of overall output and 2% of tradables output)
  - initial reserves as share of annual output for selected countries reported in discussion:
    - China gross/net reserves approximately 40%/25% of GDP
    - Russia corresponding figures 30%/20%
    - Norway reserves reached almost 100% of GDP
    - Chile and Colombia reserves around 15% of GDP
  - calibrated initial net reserves x_ss = 0:228 = 1:76
  - upper reserve limit x = 1:92 (24% of initial annual output)
  - g_ss = 0:0132
  - under ET the upper limit is reached after 5.5 quarters (versus 7.0 quarters under DIT in the calibrated comparison)
  - tradables output fall of 0.7% versus 2% endowment increase
  - initial current account surplus around 0.4% of GDP
  - final steady state reduction in seigniorage to GDP ratio by slightly more than one percentage point (to offset the 1 percentage point higher endowment and interest on larger reserves)
  - exchange rate depreciation halts at -2.7%; nominal interest rate reaches new steady state of 0.3% (just above zero lower bound)
- Important mechanism constraint:
  - The zero lower bound on nominal interest rates constrains how far exchange rate depreciation can fall, thereby imposing a non-arbitrary upper limit on foreign exchange reserves consistent with fiscal solvency.

### V. Policy implications and conclusions
- Anti-crises arise when reserve accumulation becomes unsustainable given fiscal dynamics and monetary regime constraints; an upper limit on reserves may be endogenous and binding.
- Monetary regime choice affects both the timing and intensity of anti-crises:
  - regimes that strongly commit to preventing exchange rate appreciation (ET, then CPIT) accelerate reserve accumulation and bring anti-crises forward;
  - regimes that allow appreciation (DIT) mitigate reserve accumulation and delay anti-crises.
- Fiscal stabilization via lower seigniorage is the mechanism that balances the government budget when reserve accumulation must stop; this adjustment is limited by the zero lower bound on nominal interest rates.
- Domestic inflation can rise sharply during the anti-crisis under CPI inflation targeting, consistent with observed episodes where domestic inflation increased alongside reserve accumulation and appreciation.
- The phenomenon remains relevant: the 2008/9 financial crisis altered government asset dynamics, but potential future commodity-price booms (e.g., renewed high energy prices) could trigger renewed explosive reserve dynamics among hydrocarbons exporters.

*Italic source: _wp09134 - 2.   Chile, Norway and Russia ñReserves and Ináation . . . . . . . . . . . .   17 (PDF chapter content provided).*

### References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   15

### _wp09134 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   15

### References
- References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   15

### Figures
- 1.   China and Colombia ñReserves and Ináation . . . . . . . . . . . . . . . . . . . .   16

*Source: _wp09134 - References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   15*

### 2.   Chile, Norway and Russia ñReserves and Ináation . . . . . . . . . . . . . . . .   17

### 2.   Chile, Norway and Russia ñReserves and Ináation

### I. Introduction and framing
- Observed episodes (China, Colombia, Chile, Norway, Russia) share large and accelerating foreign exchange reserve accumulation accompanied by exchange rate appreciation and rising domestic inflation.
- Paper frames the problem as a balance-of-payments "anti-crisis": a situation with an upper, not lower, sustainability limit on official foreign exchange reserves.
- Key policy question: what happens when the government (or markets) announce a maximum reserve level beyond which reserve accumulation will stop?
- Representative shock studied: government receives an additional tradables endowment equal to 1% of GDP (described as an additional tradables endowment equal to 1% of GDP).
- Monetary regimes analyzed: exchange rate targeting (ET), CPI inflation targeting (CPIT), and domestic (nontradables) inflation targeting (DIT).
- Main conceptual mechanism: announcement/constraint on reserves reduces allowable exchange rate depreciation, raising real money demand; if accommodated by nominal money issuance against foreign currency, this triggers a final burst of reserve accumulation (the anti-crisis).

### II. Model structure (overview)
- Small open economy with government, representative household, tradables and nontradables firms; real interest rates and international goods prices exogenous and constant (normalized to one); PPP for tradables; flexible nontradables prices.
- Households: CES aggregator for tradables cT and nontradables cN with elasticity of substitution  and tradables quasi-share ; cash-in-advance constraint on consumption; uncovered interest parity i_t = r + "t.
- Government: receives flow endowment d_t; chooses lump-sum transfers g_t and monetary policy rule consistent with one of the three regimes. May announce an upper limit on foreign exchange reserves x_t ≤ x.
- Key equilibrium conditions include market clearing, current account dynamics, and government budget/infinite-horizon constraint.
- Event chronology: initial steady state (balanced budget), at time 0 permanent increase in tradables endowment, targets initially unchanged, reserves would grow without bound absent upper limit x; constraint binds at endogenous time t =  and the economy transitions to final steady state.

### III. Calibration and solution
- Time unit: quarter for stock-flow ratios.
- Calibrated parameter values (selected, preserved exactly):
  - real international interest r = 3% p.a.
  - inverse velocity  = 1:55
  - tradables quasi-share  = 0:5
  - elasticity of substitution  = 0:5
  - initial labor supply h_ss = 1=3
  - labor income shares T = N = 0:4
  - CPI price level P_ss = 1
  - initial inflation rates = 0
  - initial central bank net foreign exchange reserves x_ss set equal to Chinaís average ratio of net foreign exchange reserves to annual output in 2006 = 22% (x_ss = 0:228 = 1:76)
  - government transfers g_ss set equal to interest earnings on reserves g_ss = 0:0132
  - permanent higher government tradables endowment d = 0:02 (equals 1% of overall output and 2% of tradables output)
  - upper limit on foreign exchange reserves x fixed at 24% of initial annual output (x = 1:92)
- Numerical implication: the higher endowment alone would take reserves to their upper limit within eight quarters; compound interest and increased money demand will shorten this time in practice.
- Solution method: nested shooting algorithm for CPIT and DIT; ET case involves simpler step paths.

### IV. Dynamics and quantitative findings from the policy experiment
- Common responses across regimes:
  - At time 0 households increase consumption immediately (positive wealth effect) and reduce labor supply; when inflation later declines households further increase consumption and labor increases slightly, so long-run consumption and labor are above initial steady state.
  - Relative price of tradables e falls initially and again during the anti-crisis; nontradables price rises; reallocation of employment to nontradables (Dutch disease).
  - Tradables output falls by about one third of the increase in the tradables endowment: 0.7% versus 2% of initial tradables output.
  - Initial current account surplus about 0.4% of GDP; during anti-crisis consumption rises sharply and final steady state current account is again balanced, with the gap between tradables consumption and output slightly over 2% of GDP (the size of the endowment increase plus interest on accumulated reserves).
  - Money demand increases on impact and again during the anti-crisis; by the cash-in-advance constraint this reflects higher consumption.
- Regime ranking in terms of speed and magnitude of reserve accumulation (fastest to slowest):
  - Exchange rate targeting (ET): strongest commitment to intervene and prevent appreciation; reserve gains fastest; anti-crisis happens earliest; upper limit reached after 5.5 quarters in the calibrated example (a full 1.5 quarters earlier than under DIT).
  - CPI inflation targeting (CPIT): intermediate commitment to intervene; larger reserve gains than DIT because preventing exchange rate appreciation to meet CPI target requires additional money growth and accumulation of reserves.
  - Domestic (nontradables) inflation targeting (DIT): weakest commitment to prevent exchange rate appreciation; appreciation can absorb some of the increase in real money demand, requiring much smaller additional money issuance and reserve gains; anti-crisis happens later.
- Specific calibrated quantitative points preserved exactly:
  - tradables endowment increase = 1% of initial GDP (d = 0:02 equals 1% of overall output and 2% of tradables output)
  - initial reserves as share of annual output for selected countries reported in discussion:
    - China gross/net reserves approximately 40%/25% of GDP
    - Russia corresponding figures 30%/20%
    - Norway reserves reached almost 100% of GDP
    - Chile and Colombia reserves around 15% of GDP
  - calibrated initial net reserves x_ss = 0:228 = 1:76
  - upper reserve limit x = 1:92 (24% of initial annual output)
  - g_ss = 0:0132
  - under ET the upper limit is reached after 5.5 quarters (versus 7.0 quarters under DIT in the calibrated comparison)
  - tradables output fall of 0.7% versus 2% endowment increase
  - initial current account surplus around 0.4% of GDP
  - final steady state reduction in seigniorage to GDP ratio by slightly more than one percentage point (to offset the 1 percentage point higher endowment and interest on larger reserves)
  - exchange rate depreciation halts at -2.7%; nominal interest rate reaches new steady state of 0.3% (just above zero lower bound)
- Important mechanism constraint:
  - The zero lower bound on nominal interest rates constrains how far exchange rate depreciation can fall, thereby imposing a non-arbitrary upper limit on foreign exchange reserves consistent with fiscal solvency.

### V. Policy implications and conclusions
- Anti-crises arise when reserve accumulation becomes unsustainable given fiscal dynamics and monetary regime constraints; an upper limit on reserves may be endogenous and binding.
- Monetary regime choice affects both the timing and intensity of anti-crises:
  - regimes that strongly commit to preventing exchange rate appreciation (ET, then CPIT) accelerate reserve accumulation and bring anti-crises forward;
  - regimes that allow appreciation (DIT) mitigate reserve accumulation and delay anti-crises.
- Fiscal stabilization via lower seigniorage is the mechanism that balances the government budget when reserve accumulation must stop; this adjustment is limited by the zero lower bound on nominal interest rates.
- Domestic inflation can rise sharply during the anti-crisis under CPI inflation targeting, consistent with observed episodes where domestic inflation increased alongside reserve accumulation and appreciation.
- The phenomenon remains relevant: the 2008/9 financial crisis altered government asset dynamics, but potential future commodity-price booms (e.g., renewed high energy prices) could trigger renewed explosive reserve dynamics among hydrocarbons exporters.

*Italic source: _wp09134 - 2.   Chile, Norway and Russia ñReserves and Ináation . . . . . . . . . . . . . . .   17 (PDF chapter content provided).*

### References

### _wp09134 - References

### References cited
- Calvo, G.A. (1987), ìBalance of Payments Crises in a Cash-in-Advance Economyî, Journal of Money, Credit and Banking, 19(1), 19-32.
- Calvo, G.A., Vegh, C.A. (1999), ìInáation Stabilization and BOP Crises in Developing Countriesî, Ch. 24 in: J.B. Taylor and M. Woodford, eds., Handbook of Macroeconomics, Volume 1C. Elsevier, Amsterdam, North Holland.
- International Energy Agency (2008), ìWorld Energy Outlook 2008î, Paris: OECD.
- Kamil, H. (2008), ìIs Central Bank Intervention E§ective Under Ináation Targeting Regimes? The Case of Colombiaî, IMF Working Paper WP/08/88.
- Krugman, P. (1979), ìA Model of Balance-of-Payments Crisesî, Journal of Money, Credit and Banking, 11(3), 311-325.
- Kuijs, L. (2005), ìInvestment and Saving in Chinaî, World Bank Policy Research Working Paper No. 3633.
- Kumhof, M., Li, S. and Yan, I. (2007), ìBalance of Payments Crises under Ináation Targetingî, Journal of International Economics, 72(1), 242-264.
- Mendoza, E. (2005), ìReal Exchange Rate Volatility and the Price of Nontradables in Sudden-Stop-Prone Economiesî, NBER Working Paper No. 11691.
- Reuters (2007), ìUpdate 1 - China to Stop Accumulating Foreign Reserves - Zhouî, available at http://www.reuters.com/bondsNews/idUSN2035119120070320.

### Figure 1 — China and Colombia: Reserves and Inflation (figures and series shown)
- China: Foreign Exchange Reserves ($ bn)
  - Vertical axis labels shown: 0, 200, 400, 600, 800, 1,000, 1,200, 1,400, 1,600
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: Gross FX Reserves; Net FX Reserves
- Colombia: Foreign Exchange Reserves ($ bn)
  - Vertical axis labels shown: 10, 12, 14, 16, 18, 20
  - Quarterly x-axis from 2002Q1 to 2007Q3
- China: Inflation (% p.a.)
  - Vertical axis labels shown: -6, -4, -2, 0, 2, 4, 6, 8
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: PPI Inflation; E Depreciation; CPI Inflation
- Colombia: Inflation (% p.a.)
  - Vertical axis labels shown: -25, -15, -5, 5, 15, 25, 35
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: PPI Inflation; E Depreciation; CPI Inflation
- Note: For China, both gross and net foreign exchange reserves are shown. The latter deduct from gross reserves the central bank bond liabilities issued for the purpose of sterilizing reserve accumulation. The model treats such bonds as perfect substitutes for international bonds.

### Figure 2 — Chile, Norway and Russia: Reserves, Inflation, Fiscal and External Balances (figures and series shown)
- Chile: Fiscal and External Balance (% of GDP)
  - Vertical axis labels: -4, -2, 0, 2, 4, 6, 8, 10, 12
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: Current Account/GDP; Government Balance/GDP
- Norway: Fiscal and External Balance (% of GDP)
  - Vertical axis labels: 0, 5, 10, 15, 20, 25
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: Current Account/GDP; Government Balance/GDP (annual data)
- Russia: Fiscal and External Balance (% of GDP)
  - Vertical axis labels: -6, -4, -2, 0, 2, 4, 6, 8, 10, 12, 14
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: Current Account/GDP; Government Balance/GDP
- Chile: Foreign Exchange Reserves ($ bn)
  - Vertical axis labels: 14, 18, 22, 26, 30
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Note: (including special foreign currency stabilization funds)
- Norway: Foreign Exchange Reserves ($ bn)
  - Vertical axis labels: 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Note: (including Petroleum Fund)
- Russia: Foreign Exchange Reserves ($ bn)
  - Vertical axis labels: 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: Gross FX Reserves; Net FX Reserves
- Chile: Inflation (% p.a.)
  - Vertical axis labels: -20, -15, -10, -5, 0, 5, 10, 15
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: PPI Inflation; E Depreciation; CPI Inflation
- Norway: Inflation (% p.a.)
  - Vertical axis labels: -20, -15, -10, -5, 0, 5, 10, 15
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: PPI Inflation; E Depreciation; CPI Inflation
- Russia: Inflation (% p.a.)
  - Vertical axis labels: -10, -5, 0, 5, 10, 15, 20, 25, 30
  - Quarterly x-axis from 2002Q1 to 2007Q3
  - Series: PPI Inflation; E Depreciation; CPI Inflation

### Figure 3 — Anti-Crisis model diagrams (panels (a)–(d) and variables shown)
- Figure 3. (a) Anti-Crisis — Overview
  - ET = --, CPIT = ―, DIT = ...
  - Variables/series depicted:
    - Nominal Interest Rate (i)
    - Relative Tradables Price (N P E e / =)
    - Nontradables Consumption (N c)
    - Tradables Consumption (T c)
    - Nontradables Output (N y)
    - Tradables Output (T y)
    - Aggregate Consumption (c)
    - Aggregate Labor (h)
- Figure 3. (b) Anti-Crisis — Labor Market
  - ET = --, CPIT = ―, DIT = ...
  - Variables/series depicted:
    - Nontradables Labor Demand (N h)
    - Real Wage in Nontradables (N N P W w /=)
    - Tradables Labor Demand (T h)
    - Real Wage in Tradables (E W w /=)
    - Aggregate Labor (h)
    - Real Wage in terms of CPI (P W w cpi /=)
    - Nominal Wage Level (W)
    - Nominal Wage Inflation (W π)
- Figure 3. (c) Anti-Crisis — Government Budget
  - ET = --, CPIT = ―, DIT = ...
  - Variables/series depicted:
    - Real Money Balances (m)
    - Foreign Exchange Reserves (x)
    - Current Account / GDP (ca/gdp)
    - Net Foreign Assets / GDP (f/gdp)
    - Endowment / GDP (d/gdp)
    - Seigniorage / GDP (m μ /gdp)
    - Inflation Tax / GDP (m ε /gdp)
    - Real Money Growth / GDP (• m/gdp)
- Figure 3. (d) Anti-Crisis — Price Levels and Inflation Rates
  - ET = --, CPIT = ―, DIT = ...
  - Variables/series depicted:
    - Nominal Money Stock (M)
    - Nominal Money Growth (μ)
    - Nominal Exchange Rate (E)
    - Nominal Depreciation (ε)
    - Nominal Nontradables Price Level (N P)
    - Nominal Nontradables Inflation (N π)
    - Nominal CPI Price Level (P)
    - Nominal CPI Inflation (π)

*Source: _wp09134 - References*

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