“unfunded liabilities” and uncertain fiscal financing · 1790 1800 1810 1820 1830 1840 1850...
TRANSCRIPT
![Page 1: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/1.jpg)
“Unfunded Liabilities” and UncertainFiscal Financing
Troy Davig*, Eric M. Leeper† & Todd B. Walker†
*Federal Reserve Bank of Kansas City† Indiana University
February 2010Banco de Espana Conference
![Page 2: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/2.jpg)
Introduction
I Profound uncertainty surrounds the funding of futurepromised transfers in the U.S.
![Page 3: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/3.jpg)
“Unfunded Liabilities”
Social Security
1962 1972 1982 1992 2002 2012 2022 2032 2042 2052 2062 2072 20820
5
10
15
20
25
30
35
Percentage
ofGDP
Source: CBO Long-Term Budget Outlook (June 2009)
![Page 4: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/4.jpg)
“Unfunded Liabilities”
Social Security
Medicare and Medicaid
1962 1972 1982 1992 2002 2012 2022 2032 2042 2052 2062 2072 20820
5
10
15
20
25
30
35
Percentage
ofGDP
Source: CBO Long-Term Budget Outlook (June 2009)
![Page 5: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/5.jpg)
“Unfunded Liabilities”
Social Security
Medicare and Medicaid
Other Federal Non-interest Spending
1962 1972 1982 1992 2002 2012 2022 2032 2042 2052 2062 2072 20820
5
10
15
20
25
30
35
Percentage
ofGDP
Source: CBO Long-Term Budget Outlook (June 2009)
![Page 6: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/6.jpg)
Introduction
I Profound uncertainty surrounds the funding of futurepromised transfers in the U.S.
I Unfunded liabilities is not an economically meaningfulterm—inconsistent with equilibrium
I The government will renege on promised transfers(i.e. “liabilities” do not exist)
I The government will fund the promised transfers(i.e. liabilities are not “unfunded”)
I CBO projects debt rising to over 700% of GDP
![Page 7: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/7.jpg)
Introduction
I Profound uncertainty surrounds the funding of futurepromised transfers in the U.S.
I Unfunded liabilities is not an economically meaningfulterm—inconsistent with equilibrium
I The government will renege on promised transfers(i.e. “liabilities” do not exist)
I The government will fund the promised transfers(i.e. liabilities are not “unfunded”)
I CBO projects debt rising to over 700% of GDP
![Page 8: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/8.jpg)
Rolling Spending Commitments into Debt
1790
1800
1810
1820
1830
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
2010
2020
2030
2040
2050
2060
2070
2080
0
100
200
300
400
500
600
700
800
Percentage
ofGDP
Alternative Fiscal Scenario
Extended-Baseline Scenario
� ��
��
�� � � � �
� � � �� � � �
�� � �
� �� �
� � � � � � � � � � � � � ��
� � � � � � � � � � � � � � � � � � � � � � � � � � � � �
�
�
��
� � � � ��
��
� � � � ��
�
��
� � � � �� �
� � � � � � � � � � � � � � � � � � � � � � � � � � � �
�
�
�
�
� �
��
�� � �
��
�
�
�
� � �
�� � � �
�
�
�
�
�
�
��
�
��
� �
�
�
��
�� �
��
��
� ��
� � � �� �
�� � � � � �
�
� ��
� � � ��
��
� � ��
�
�
�
��
�� � � � �
�
�
�
��
��
��
��
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�� � � � � � �
� � � � � � � � ��
��
��
��
��
��
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
1
Source: CBO Long-Term Budget Outlook (June 2009)
![Page 9: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/9.jpg)
Introduction
I Profound uncertainty surrounds the funding of futurepromised transfers in the U.S.
I Unfunded liabilities is not an economically meaningfulterm—inconsistent with equilibrium
I The government will renege on promised transfers(i.e. “liabilities” do not exist)
I The government will fund the promised transfers(i.e. liabilities are not “unfunded”)
I CBO projects debt rising to over 700% of GDP
⇒ future policy will change
...how and when?
![Page 10: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/10.jpg)
Introduction
I Profound uncertainty surrounds the funding of futurepromised transfers in the U.S.
I Unfunded liabilities is not an economically meaningfulterm—inconsistent with equilibrium
I The government will renege on promised transfers(i.e. “liabilities” do not exist)
I The government will fund the promised transfers(i.e. liabilities are not “unfunded”)
I CBO projects debt rising to over 700% of GDP
⇒ future policy will change...how and when?
![Page 11: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/11.jpg)
Introduction
I Nearly every advanced economyfaces this problem
![Page 12: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/12.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 13: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/13.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers
⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 14: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/14.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 15: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/15.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation
⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 16: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/16.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 17: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/17.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target
⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 18: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/18.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 19: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/19.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)
⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 20: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/20.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 21: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/21.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default
⇒ Are U.S. Treasuries risk-free assets?
![Page 22: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/22.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
4. Inflation financing (printing presses)⇒ Fiscal limithere also
5. Debt default⇒ Are U.S. Treasuries risk-free assets?
![Page 23: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/23.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
1. Reneging on transfers⇒ “Third Rail of Politics”
2. Distortionary taxation⇒ Fiscal limit
3. Sacrificing inflation target⇒ Volatile inflation
We model a combination of 1–3, emphasizinguncertainty about which policies adjust and whenpolicies adjust.
![Page 24: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/24.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
I Allow for switching among policy solutions
I Model fiscal limit as random variable = f (fiscalvariables)
I Focus on expectational effects in otherwise standardmacroeconomic DSGE model
![Page 25: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/25.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
I Allow for switching among policy solutions
I Model fiscal limit as random variable = f (fiscalvariables)
I Focus on expectational effects in otherwise standardmacroeconomic DSGE model
![Page 26: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/26.jpg)
What We Do
I Rational expectations framework to study alternativeways to resolve “unfunded liabilities” problem
I Allow for switching among policy solutions
I Model fiscal limit as random variable = f (fiscalvariables)
I Focus on expectational effects in otherwise standardmacroeconomic DSGE model
![Page 27: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/27.jpg)
Analytic Intuition: Simple ModelI Consider a flexible price, cashless, endowment
economy
I The consumption Euler equation reduces to theFisher equation
1Rt
= βEt
(Pt
Pt+1
)I Transfers grow at rate µ financed by lump-sum taxes
and debt
zt = (1− µ)z∗ + µzt−1 + εt, µ < 1/β
I Government’s Budget Constraint:Bt
Pt+ τt = zt +
Rt−1Bt−1
Pt
![Page 28: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/28.jpg)
Analytic Intuition: Simple ModelI Consider a flexible price, cashless, endowment
economy
I The consumption Euler equation reduces to theFisher equation
1Rt
= βEt
(Pt
Pt+1
)
I Transfers grow at rate µ financed by lump-sum taxesand debt
zt = (1− µ)z∗ + µzt−1 + εt, µ < 1/β
I Government’s Budget Constraint:Bt
Pt+ τt = zt +
Rt−1Bt−1
Pt
![Page 29: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/29.jpg)
Analytic Intuition: Simple ModelI Consider a flexible price, cashless, endowment
economy
I The consumption Euler equation reduces to theFisher equation
1Rt
= βEt
(Pt
Pt+1
)I Transfers grow at rate µ financed by lump-sum taxes
and debt
zt = (1− µ)z∗ + µzt−1 + εt, µ < 1/β
I Government’s Budget Constraint:Bt
Pt+ τt = zt +
Rt−1Bt−1
Pt
![Page 30: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/30.jpg)
Analytic Intuition: Simple ModelI Consider a flexible price, cashless, endowment
economy
I The consumption Euler equation reduces to theFisher equation
1Rt
= βEt
(Pt
Pt+1
)I Transfers grow at rate µ financed by lump-sum taxes
and debt
zt = (1− µ)z∗ + µzt−1 + εt, µ < 1/β
I Government’s Budget Constraint:Bt
Pt+ τt = zt +
Rt−1Bt−1
Pt
![Page 31: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/31.jpg)
Analytic Intuition: Policy Specification
At time T economy reaches fiscal limit
Regime 1t = 0, 1, . . . ,T − 1
Monetary Policy R−1t = R∗−1 + α
(Pt−1
Pt− 1
π∗
)Tax Policy τt = τ ∗ + γ
(Bt−1Pt−1− b∗
)
![Page 32: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/32.jpg)
Analytic Intuition: Policy Specification
At time T economy reaches fiscal limit
Regime 1t = 0, 1, . . . ,T − 1
Monetary Policy R−1t = R∗−1 + α
(Pt−1
Pt− 1
π∗
)Tax Policy τt = τ ∗ + γ
(Bt−1Pt−1− b∗
)
![Page 33: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/33.jpg)
Analytic Intuition: Policy Specification
At time T economy reaches fiscal limit
Regime 1 Regime 2t = 0, 1, . . . ,T − 1 t = T,T + 1, . . .
Monetary Policy R−1t = R∗−1 + α
(Pt−1
Pt− 1
π∗
)R−1
t = R∗−1
Tax Policy τt = τ ∗ + γ(
Bt−1Pt−1− b∗
)τt = τmax
![Page 34: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/34.jpg)
Analytic Intuition: Policy Specification
At time T economy reaches fiscal limit
Regime 1 Regime 2t = 0, 1, . . . ,T − 1 t = T,T + 1, . . .
Monetary Policy R−1t = R∗−1 + α
(Pt−1
Pt− 1
π∗
)R−1
t = R∗−1
Tax Policy τt = τ ∗ + γ(
Bt−1Pt−1− b∗
)τt = τmax
Fiscal limit may be economic (peak of Laffer curve) orpolitical (intolerance of taxation)
![Page 35: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/35.jpg)
Analytic Intuition: Polar Case 1
If Regime 1 were absorbing state (No Fiscal Limit)
α
βEt
(Pt
Pt+1− 1π∗
)=
Pt−1
Pt− 1π∗
(Regime 1)
Et−1
(Bt
Pt− b∗
)= Et−1(zt − z∗) + (β−1 − γ)
(Bt−1
Pt−1− b∗
)α/β > 1, β−1 − γ < 1⇒ Equilibrium πt = π∗
A Standard Monetary Equilibrium
![Page 36: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/36.jpg)
Analytic Intuition: Polar Case 1
If Regime 1 were absorbing state (No Fiscal Limit)
α
βEt
(Pt
Pt+1− 1π∗
)=
Pt−1
Pt− 1π∗
(Regime 1)
Et−1
(Bt
Pt− b∗
)= Et−1(zt − z∗) + (β−1 − γ)
(Bt−1
Pt−1− b∗
)α/β > 1, β−1 − γ < 1⇒ Equilibrium πt = π∗
A Standard Monetary Equilibrium
![Page 37: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/37.jpg)
Analytic Intuition: Polar Case 1
If Regime 1 were absorbing state (No Fiscal Limit)
α
βEt
(Pt
Pt+1− 1π∗
)=
Pt−1
Pt− 1π∗
(Regime 1)
Et−1
(Bt
Pt− b∗
)= Et−1(zt − z∗) + (β−1 − γ)
(Bt−1
Pt−1− b∗
)
α/β > 1, β−1 − γ < 1⇒ Equilibrium πt = π∗
A Standard Monetary Equilibrium
![Page 38: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/38.jpg)
Analytic Intuition: Polar Case 1
If Regime 1 were absorbing state (No Fiscal Limit)
α
βEt
(Pt
Pt+1− 1π∗
)=
Pt−1
Pt− 1π∗
(Regime 1)
Et−1
(Bt
Pt− b∗
)= Et−1(zt − z∗) + (β−1 − γ)
(Bt−1
Pt−1− b∗
)α/β > 1, β−1 − γ < 1⇒ Equilibrium πt = π∗
A Standard Monetary Equilibrium
![Page 39: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/39.jpg)
Analytic Intuition: Polar Case 2
If Regime 2 were absorbing state
Et
(Pt
Pt+1
)=
1βR∗
=1π∗
(Regime 2)
Bt
Pt=
(β
1− β
)τ ∗ − Et
∞∑j=1
βjzt+j
α = 0, γ = 0⇒ Actual Inflation
Pt =Rt−1Bt−1(
11−β
)τ ∗ − Et
∑∞j=0 β
jzt+j
A Standard Fiscal Equilibrium
![Page 40: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/40.jpg)
Analytic Intuition: Polar Case 2
If Regime 2 were absorbing state
Et
(Pt
Pt+1
)=
1βR∗
=1π∗
(Regime 2)
Bt
Pt=
(β
1− β
)τ ∗ − Et
∞∑j=1
βjzt+j
α = 0, γ = 0⇒ Actual Inflation
Pt =Rt−1Bt−1(
11−β
)τ ∗ − Et
∑∞j=0 β
jzt+j
A Standard Fiscal Equilibrium
![Page 41: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/41.jpg)
Analytic Intuition: Polar Case 2
If Regime 2 were absorbing state
Et
(Pt
Pt+1
)=
1βR∗
=1π∗
(Regime 2)
Bt
Pt=
(β
1− β
)τ ∗ − Et
∞∑j=1
βjzt+j
α = 0, γ = 0⇒ Actual Inflation
Pt =Rt−1Bt−1(
11−β
)τ ∗ − Et
∑∞j=0 β
jzt+j
A Standard Fiscal Equilibrium
![Page 42: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/42.jpg)
Analytic Intuition: Polar Case 2
If Regime 2 were absorbing state
Et
(Pt
Pt+1
)=
1βR∗
=1π∗
(Regime 2)
Bt
Pt=
(β
1− β
)τ ∗ − Et
∞∑j=1
βjzt+j
α = 0, γ = 0⇒ Actual Inflation
Pt =Rt−1Bt−1(
11−β
)τ ∗ − Et
∑∞j=0 β
jzt+j
A Standard Fiscal Equilibrium
![Page 43: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/43.jpg)
Fiscal Limit: Reneging
t = 0, 1, . . . ,T − 1 t = T,T + 1, . . .
Monetary Policy R−1t = R∗−1 + α
(Pt−1
Pt− 1
π∗
)same
Tax Policy τt = τ∗ + γ(
Bt−1Pt−1− b∗
)τt = τmax
Transfer Policy zt λtzt
Et−1[Bt/Pt] + τmax = Et−1λtzt + (β−1 − γ)(Bt−1/Pt−1)
πt = π∗
A Standard Monetary Equilibrium
![Page 44: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/44.jpg)
Fiscal Limit: No Reneging
t = 0, 1, . . . ,T − 1 t = T,T + 1, . . .
Monetary Policy R−1t = R∗−1 + α
(Pt−1
Pt− 1
π∗
)R−1
t = R∗−1
Tax Policy τt = τ∗ + γ(
Bt−1Pt−1− b∗
)τt = τmax
Transfer Policy zt same
Et
(Pt
Pt+1− 1π∗
)=α
β
(Pt−1
Pt− 1π∗
),
α
β> 1
Pt = f (zt; γ, µ, β, π∗)
A New Fiscal Equilibrium Before the Limit
![Page 45: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/45.jpg)
Analytic Intuition: Debt
0 5 10 15 20 25 30 35 40 45 500.44
0.46
0.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
Debt inRegime 2
Debt−GDP Target
Fiscal LimitT = 50
![Page 46: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/46.jpg)
Analytic Intuition: Debt
0 5 10 15 20 25 30 35 40 45 500.44
0.46
0.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
0.64
Debt inRegime 2
Debt−GDP Target
Fiscal LimitT = 50
Debt WhenFiscal Limit at T
![Page 47: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/47.jpg)
Analytic Intuition: Inflation
0 5 10 15 20 25 30 35 40 45 50
0.8
0.9
1
1.1
1.2
1.3
InflationTarget
Inflation inRegime 2
Fiscal LimitT = 50
![Page 48: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/48.jpg)
Analytic Intuition: Inflation
0 5 10 15 20 25 30 35 40 45 50
0.8
0.9
1
1.1
1.2
1.3
InflationTarget
Inflation inRegime 2
Inflation WhenFiscal Limitat T = 50
Fiscal LimitT = 50
![Page 49: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/49.jpg)
Analytic Intuition: Expected Inflation
0 5 10 15 20 25 30 35 40 45 50
0.8
0.9
1
1.1
1.2
1.3
InflationTarget
Inflation inRegime 2
Expected InflationWhen Fiscal Limit
at T = 50 Inflation WhenFiscal Limitat T = 50
Fiscal LimitT = 50
![Page 50: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/50.jpg)
Fiscal Limit: Implications
I Expectations of post-limit policies determine pre-limitequilibrium
I Inflation and debt not anchored on targets
I Expectations—and equilibrium—time varying asapproach limit
I Pre-limit equilibrium converges to post-limitequilibrium
![Page 51: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/51.jpg)
Promised Transfers in a DSGE Model
Other Federal Non-interest Spending
Medicare and Medicaid
Social Security
1962 1972 1982 1992 2002 2012 2022 2032 2042 2052 2062 2072 20820
5
10
15
20
25
30
35
Percentage
ofGDP
Revenues Model
![Page 52: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/52.jpg)
Full-Blown Model
I Standard DSGE model: capital accumulation, stickyprices, distorting taxation
I Government announces path of promised transfers
I Government debt and taxes grow until the economyhits fiscal limit
I Specify a set of policies that stabilize debt after fiscallimit
I Multiple layers of policy uncertainty
![Page 53: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/53.jpg)
Households and Firms
I Household utility depends on consumption, leisureand real balances
I Household’s budget constraint is
Ct + Kt +Bt
Pt+
Mt
Pt≤ (1− τt)
(Wt
PtNt + Rk
t Kt−1
)
+(1− δ)Kt−1 +Rt−1Bt−1
Pt+
Mt−1
Pt+ λtzt +
Dt
Pt
I Firms set prices as a markup over marginal costs(Rotemberg costly adjustment)
![Page 54: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/54.jpg)
Initial Period: Stationary Transfers
1
MP: Rt = R∗ + α(πt − π∗), α > 1/β
FP: τt = τ ∗ + γ(bt−1/Yt−1 − b∗), γ > r
Transfers: zt = (1− ρz)z∗ + ρzzt−1 + εt
![Page 55: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/55.jpg)
Non-Stationary Promised Transfers
1
MP: Rt = R∗ + α(πt − π∗), α > 1/β
FP: τt = τ ∗ + γ(bt−1/Yt−1 − b∗), γ > r
Transfers: zt = µzt−1 + εt, µ > 1
PZ
![Page 56: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/56.jpg)
Fiscal Limit
1
FP: τt = τmax
PL,t
PL,t =exp(η0+η1(τt−1−τ∗))
1+exp(η0+η1(τt−1−τ∗))
![Page 57: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/57.jpg)
Fiscal Limit: Regime 1 AM/AF/PT
1
MP: Rt = R∗ + α(πt − π∗), α > 1/β
FP: τt = τmax
Transfers: λtzt = λtµzt−1 + λtεt
q = 0.5
Regime 1
![Page 58: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/58.jpg)
Fiscal Limit: Regime 2 PM/AF/AT
1
MP: Rt = R∗
FP: τt = τmax
Transfers: zt = µzt−1 + εt 1− q = 0.5
Regime 2
Regime 1
![Page 59: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/59.jpg)
Fiscal Limit: Switch Between Regimes
1
MP: Rt =
{R∗ + α(πt − π∗), α > 1/βR∗
FP: τt = τmax
Transfers: zt =
{λtµzt−1 + λtεtµzt−1 + εt
Regime 2
1− p11
Regime 1
1− p22
![Page 60: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/60.jpg)
Counterfactual Experiments
I Layers of uncertainty call for a probabilisticdescription of outcomes
I Report equilibrium transition paths conditional onparticular realizations of policies
I decision rules based on true probability distributions
I agents always place probability on alternative futureregimes
I these are counterfactual exercises that induce policyregime surprises every period
![Page 61: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/61.jpg)
Pre-Limit as Transfers Grow
I Dominate forces are rising debt and taxes
I Rising tax rates discourage labor effort and reduceconsumption
I Inflection point in dynamics arises at limit, τmax
I Capital falls when τt < τmax, then rises when τt > τmax,in expectation of a future reduction in tax rates
![Page 62: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/62.jpg)
Pre-Limit as Transfers Grow
2010 2020 2030 2040 2050 2060−4
−2
0
Output (% deviation from 2009)
2010 2020 2030 2040 2050 2060−10
−5
0
Consumption (% deviation from 2009)
2010 2020 2030 2040 2050 2060−5
0
5
10Capital Stock (% deviation from 2009)
2010 2020 2030 2040 2050 2060−8−6−4−2
0
Labor (% deviation from 2009)
2010 2020 2030 2040 2050 20600.2
0.22
0.24
0.26
0.28Tax Rate
2010 2020 2030 2040 2050 20600.5
1
1.5Debt / Output
2010 2020 2030 2040 2050 20601
2
3Inflation (%)
2010 2020 2030 2040 2050 20603
4
5
6Nominal Interest Rate (%)
τmax
Conditional on not triggering fiscal limit
![Page 63: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/63.jpg)
Post-Limit Reneging (λt < 1)
I Monetary policy is active, but can’t stabilize inflation
I Agents believe can return to regime without reneging,but with passive monetary policy
2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 20600
0.5
1
1.5
2Inflation and Expectations (deviation from 2009 rate)
2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 20602
2.2
2.4
2.6
2.8
Ex−ante Real Rate (Rt − E
tπ
t+1)
Expectations
Inflation
![Page 64: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/64.jpg)
Post-Limit Reneging (λt < 1)
I Low real rates reduce savings
I Capital stock declines
2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 2060−10
−5
0Capital Stock (% deviation from 2009 level)
2010 2015 2020 2025 2030 2035 2040 2045 2050 2055 20602
2.2
2.4
2.6
2.8
Ex−ante Real Rate (Rt − E
t−π
t+1)
![Page 65: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/65.jpg)
Post-Limit Passive Monetary Policy
I Monetary policy is passive and λt = 1
I Agents still believe can move to reneging regime
2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 20600
1
2
3
Ex−ante Real Rate (Rt − E
tπ
t+1)
2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 20600
10
20
30Inflation
![Page 66: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/66.jpg)
Post-Limit Passive Monetary Policy
I Possibility of reneging in future increases savings andpostpones consumption
I Drives capital accumulation
2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 2060−10
0
10
20Capital Stock (% deviation from 2009 level)
2040 2042 2044 2046 2048 2050 2052 2054 2056 2058 20600
1
2
3
Ex−ante Real Rate (Rt − E
tπ
t+1)
![Page 67: “Unfunded Liabilities” and Uncertain Fiscal Financing · 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020](https://reader030.vdocuments.site/reader030/viewer/2022020318/5c2cdb4309d3f2c47f8d37c8/html5/thumbnails/67.jpg)
Conclusions
I Profound uncertainty surrounds the future financingof promised transfers
I Fiscal pressures will likely impair efforts to achieveany inflation objective
I Expected inflation will rise faster than inflation ifhouseholds believe the economy may hit the fiscallimit
I In the presence of a fiscal limit, effects of the limit kickin even during “normal” times
I Underscores that to understand an intrinsically “fiscalissue,” must integrate monetary policy