EC6012 Lecture 7

                                             Stephen Kinsella


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Objectives today                     EC6012 Lecture 7

                                      Stephen Kinsella


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Notation

 Symbol    Meaning
    G      Pure government expenditures in nominal terms
   Y       National Income in Nomina...
Review

                       Households    Production   Government   Central Bank
       Money              +H          ...
Transactions Matrix
                                                                          Central Bank

              ...
Equation Systems

  Y    = G +C                                           (1)
 YD = Y − T + r−1 · Bh−1                    ...
Steady States                                      EC6012 Lecture 7

                                                    S...
PCEX                                                          EC6012 Lecture 7

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Expectation-Augmented Modeling                               EC6012 Lecture 7

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Puzzling Results from the Model                              EC6012 Lecture 7

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Real World Applications                                               EC6012 Lecture 7

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EC6012 Lecture 7
Debt/GDP
                                                     Stephen Kinsella


                        ...
Interest Cost                                 EC6012 Lecture 7

                                               Stephen Kin...
Other Oddities                                                 EC6012 Lecture 7

                                         ...
Next Time                                               EC6012 Lecture 7

                                                ...
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EC6012 Lecture 7

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EC6012 Lecture 7

  1. 1. EC6012 Lecture 7 Stephen Kinsella Notation Review Equation System EC6012 Lecture 7 Steady State Solutions Government Money with Portfolio Choice II Portfolio Choice with Expectations Puzzling Results from the model Real World Applications Stephen Kinsella January 24, 2008
  2. 2. Objectives today EC6012 Lecture 7 Stephen Kinsella Notation Review Notation Equation System Steady State Solutions Portfolio Choice with Expectations Puzzling Results from Review the model Real World Equation System Applications Steady State Solutions Portfolio Choice with Expectations Puzzling Results from the model Real World Applications
  3. 3. Notation Symbol Meaning G Pure government expenditures in nominal terms Y National Income in Nominal Terms C Consumption of goods supply by households, in nominal terms T Taxes θ Personal Income Tax Rate YD Disposable Income of Households α1 Propensity to consume out of regular (present) income α2 Propensity to consume out of past wealth ∆Hs Change in cash money supplied by the central bank ∆Hh Cash money held by households H, H−1 High Powered cash money today, and yesterday (−1 ) V Wealth of Households, in nominal terms Bh,cb Bills held by households, central banks.
  4. 4. Review Households Production Government Central Bank Money +H −H 0 Bills +Bh −B +Bcb 0 Balance (net worth) -V +V 0 0 0 0 0 Table: Balance Sheet for PC.
  5. 5. Transactions Matrix Central Bank Households Production Government Current Capital Consumption -C +C 0 Govt. Expenditures +G -G 0 Income = GDP +Y -Y 0 Interest Payments +r−1 · Bh−1 −r−1 · B−1 +r−1 · Bcb−1 0 Central Bank Profits +r−1 · Bcb−1 −r−1 · Bcb−1 0 Taxes -T +T 0 Change in Money −∆H +∆H 0 Change in Bills −∆Bh +∆B −∆Bcb 0 0 0 0 0 0 0 Table: Transactions matrix for PC.
  6. 6. Equation Systems Y = G +C (1) YD = Y − T + r−1 · Bh−1 (2) T = θ · (Y + r−1 · Bh−1 ) (3) V = V−1 + (YD − C ) (4) C = α1 · YD + α2 · V−1 , 0 < α1 < α2 < 1 (5) Hh YD = (1 − λ0 ) − λ1 · r + λ2 · (6) V V Bh YD = λ0 + λ 1 · r − λ 2 · (7) V V Hh = V − Bh (8) ∆Bs = Bs − Bs−1 = (G + r−1 · Bs−1 ) − (T + r−1 · Bcb−1 ) (9) ∆Hs = Hs − Hs−1 = ∆Bcb (10) Bcb = Bs − Bh (11) r = r (12)
  7. 7. Steady States EC6012 Lecture 7 Stephen Kinsella Notation Review α3 = α2 · (1 − α1 )/α2 (13) Equation System Steady State Solutions ∆V = α2 · (α3 − V−1 ) (14) Portfolio Choice V∗ with Expectations = α3 (15) Puzzling Results from YD ∗ the model Real World ∗ Bh · r Applications r∗ = (16) V∗
  8. 8. PCEX EC6012 Lecture 7 Stephen Kinsella Introducing expectations into PC is done through including Notation an expectation on disposable income, YD e . This changes Review the consumption function to Equation System Steady State Solutions C = α1 · YD e + α2 · V−1 . (17) Portfolio Choice with Expectations Puzzling Results from the model Real World Applications
  9. 9. Expectation-Augmented Modeling EC6012 Lecture 7 Stephen Kinsella Notation Bd YD e Review = λ 0 + λ 1 · r − λ2 · (18) Equation System Ve Ve Steady State Solutions Hd YD e Portfolio Choice with Expectations = (1 − λ0 ) − λ1 · r + λ2 · (19) Ve Ve Puzzling Results from the model Real World Hd = V e − Bd (20) Applications e e V = V−1 + (YD − C ) (21)
  10. 10. Puzzling Results from the Model EC6012 Lecture 7 Stephen Kinsella ∗ ↑ G ⇒↑ YD, ∂YD < 0 ∂G Notation ∗ ↑ r ⇒↑ YD, ∂YD > 0 ∂r Review Equation System ↑ λ0 ⇒ Govt. taking Bills ⇒↑ Y . So dropping liquidity Steady State Solutions preference implies increasing Y in PCEX. Portfolio Choice with Expectations ↑ α3 ⇒↑ Y (Paradox of Thrift?) Puzzling Results from the model Real World Applications
  11. 11. Real World Applications EC6012 Lecture 7 Stephen Kinsella Application 1 Notation Review PCEX implies that targeting debt to income ratios will have Equation System Steady State a positive effect on the fortunes of the country, if the Solutions government does the targeting in a credible way. In Portfolio Choice with Expectations particular, PCEX gives us a targeting rule of Puzzling Results from the model Real World V∗ Applications α3 = . (22) Y∗ 1+ θ · r · [(λ0 + λ1 · r ) · α3 − λ2 ] 1−θ
  12. 12. EC6012 Lecture 7 Debt/GDP Stephen Kinsella Notation Review Equation System Steady State Solutions Portfolio Choice with Expectations Puzzling Results from the model Real World Applications Figure: Debt/GDP Ratio in Ireland, 1990-2006
  13. 13. Interest Cost EC6012 Lecture 7 Stephen Kinsella Notation Review Equation System Steady State Solutions Portfolio Choice with Expectations Puzzling Results from the model Real World Applications Figure: Interest Cost Trend
  14. 14. Other Oddities EC6012 Lecture 7 Stephen Kinsella Application 2 Notation PCEX also implies that knowing α3 is important in Review Equation System forecasting behaviour. What does today’s news about the Steady State Solutions percentage of SSIA money actually spent imply about the Portfolio Choice with Expectations level of α3 in the Irish economy at present? Puzzling Results from the model According to yesterday’s Sunday Times, only three billion of Real World Applications the estimated ten billion to be paid out in the SSIAs has been spent, leaving seven billion sitting in banks. Why do you think this is?
  15. 15. Next Time EC6012 Lecture 7 Stephen Kinsella Presentations → Check Site. Notation Read Godley, Chapter 6 Review Equation System Read Expectations In Economics by Lachman (Link on Steady State Solutions Site, be in college) Portfolio Choice with Expectations The Open Economy! Puzzling Results from the model Real World Applications

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