Lecture 3 – Keynesian Economics by yaofenjin

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									     Lecture III Keynesian Model
   Keynes’ General Theory, by all accounts, is difficult to
    understand
   For this reason, Keynes’ ideas have come down to us
    filtered through the eyes of those that either were there
    when the ideas were being worked out or by later
    writers that have more or less guessed at what the
    “great master” had in mind
   In this way, Keynes is very much like Jesus Christ,
    whose words and meaning have come to us through the
    “apostles”; although in the case of Keynes, we do have
    his actual writings to fall back on
     What Keynes was proposing
   He was trying to work out a new way of looking at the
    economy that could explain the existence of widespread
    unemployment when so many people were willing to
    work for wages well below the market wage
   He referred to this phenomenon as “involuntary”
    unemployment
   The classical view was that this cannot occur; the wage
    rate will simply fall to the equilibrium wage and all
    markets, including the labor market, will be in
    equilibrium
   Thus general equilibrium at full employment is
    maintained
    The idea of “effective” demand
   Keynes begins with the notion that aggregate demand
    for the goods and services in the economy can be
    decomposed into two parts: a part that depends on the
    level of output and a second part that is exogenous
   Thus, D = D1(Y) + D2
   We can think of these two as D1(Y) = C and D2 = I,
    which is exogenous to Y
   Unlike classical theory, Keynes does not really look upon
    investment demand as depending strongly on the
    interest rate, although that will not be a major problem
    to his model
           Keynes on investment
   It is critical to his theory to understand how he felt about
    the decision to invest or not
   He viewed investment decisions by firms and
    entrepreneurs as dependent on their “animal spirits”,
    that is, once businesses are frightened off from the
    market, perhaps due to continued losses sustained by
    themselves and other investors, it may be next to
    impossible to convince them to return
   As a sidebar, much of the discussions we here today
    about what to do after the financial crisis, concerns the
    “credibility” of central banks actions; more on this later
                  IS-LM model
   John Hicks in Mr. Keynes and the “Classics” first
    introduced the IS-LM analysis
   Some of Keynes’ contemporaries argued that
    Keynes never used such models; however,
    writings of Keynes discovered after his death did
    find the he worked on such equations
   The IS curve is the locus of points in i-Y space at
    which the product market is in equilibrium while
    the LM curve does the same for the loanable
    funds market
                   The IS curve
   Keynes starts with the premise that expenditures E =
    output Y = C + I in a closed economy with no or limited
    government
   C depends primarily on Y, but let’s suppose some saving
    is generated through a rise in I, so C = c(i,Y) which
    implies that S = s(i,Y) where Si and SY > 0.
   Investment depends only on I and Ii < 0
   Equilibrium requires that S = I or I – S = 0; furthermore,
    for it to be maintained, the change in I – S must = 0, so
    d(I – S) = Ii di – (Si di + SY dY) = 0
    Solving for di/dY, we get di/dy = SY dY/(Ii di – SY dY)
    < 0; thus, the IS curve is down-sloping
                   The LM curve
   The demand for money depends on both Y and i, where
    people hold more money to finance transactions at
    higher levels of Y and economize on money holdings as i
    rises
   The supply of money is either fixed or rises with i say as
    financial institutions reduce excess reserves as the
    return on loans increases
   Again, we need Demand for money L to equal M, the
    money supply and along the LM curve, d(L – M) = 0
   So, Li di + LY dY – Mi di = 0 and solver for di/dY we get
    di/dY = LY/(Mi – Li) > 0
               Graph of IS and LM curves
                                       IS LM Curves
    0.45
                                      LM
     0.4
                                      IS
    0.35
     0.3
    0.25
r




     0.2
    0.15
     0.1
    0.05
      0
                     00


                           00


                                 00


                                       00


                                             00


                                                       00


                                                             00


                                                                   00


                                                                         00


                                                                               00


                                                                                     00
                0
           0


               50


                    10


                          15


                                20


                                      25


                                            30


                                                      35


                                                            40


                                                                  45


                                                                        50


                                                                              55


                                                                                    60
                                                  Y
           IS-LM in equation form
   E = A + cY – ai = Y, so (1 – c)Y = A – ai
   Real money demand M/P = mY – bi = Ms/P for monetary
    equilibrium
   Thus, i = [mY – Ms/P]/b; substituting into first equation we get
   (1 – c)Y = A – a[mY – Ms/P]/b
   Solving for Y we get [1 – c + (a/b)m] Y = A + (a/b)(Ms/P)/b and
   Y = A/[1 – (c – m(a/b))] + Ms/P[1/[m + (b/a)(1-c)]
   Keynes assumed both consumption and investment were relatively
    insensitive to i (that is, a is small) and demand for money was very
    sensitive to i when rates are close to 0 (that is, b is large)
   These two imply that changes in the money supply have very little
    influence on aggregate supply while the Keynesian multiplier is close
    to 1/(1-c)
    The Keynesian consol example
   A consol is a perpetuity bond that pays a fixed amount each period, say a
    year
   S = ∑1/(1+r)n, n = 1, ∞ = 1/(1+r) + 1/(1+r)2 + … + 1/(1+r)n + …
   (1+r)S = 1 + S => (1+r)S – S = rS = 1 and S = 1/r
   So I pay $20 for this console
   If the rate falls to 4%, I make $5, or 20% return for a 1% drop in interest
    rates; if r goes up to 6%, on the other hand, the price falls to $16.67 and I
    lose $3.33 or 16.67%
   What if the interest rate is near 0%? The rate can hardly fall, so the next
    move in interest rates must be upward; that is, I can only lose money (or
    stay the same) if I buy a consol now
   But I can earn the same return by simply hoarding my cash
   This Keynes referred to as the zero-bound or the liquidity trap
           The Keynesian Model in
          Undergraduate Economics
   Let Y = C + I = a + cY + I, a and I are exogenously determined
   Then at equilibrium Ye = [1/(1–c)](a + I), and 1/(1-c) = k, the
    Keynesian multiplier
   Now suppose Ye < Yp, potential, or full-employment, output
   Keynes argued that government should fill the expenditure gap,
    which he referred to as the recessionary gap.
   Now Y = a + cY + I + G, and we assume the government
    expenditures do not affect a, c, or I.
   Then solving for Ye gives Ye = k(a + I + G) which is greater than
    the previous equilibrium output
   So if kG = (Yp – Ye), so the recessionary gap is g = 1/k(Yp – Ye)
                              Example 1
      Y = C + I = 400 + .6Y + 1000 = 1400 + .6Y and
       solving for Y gives [1/(1-c)] (a +I0) = (1/.4)(1400)
       = 2.5*1400 = 3500, and k = 2.5
                              Keynesian Cross Diagram
     5000

     4500

     4000
                                    We see that AD = AS at the equilibrium AS of 3500
     3500

     3000
                                                                                          AD
AD




     2500                                                                                 45-degree

     2000

     1500

     1000

     500

       0
            0   500   1000   1500        2000          2500          3000          3500     4000      4500
                                                   AS
    Now if I declines to 900, AD will decline by
     k*d(AD) = - 250, so AD = 3250
    This is shown on the Keynesian cross diagram
     below
    To restore the equilibrium level of AD to the
     desired 3500 we need add G = 100 and we will
     be back to the original AD curve
                                  Keynesian Cross Diagram
         5000

         4500

         4000
                    When I = 1000, we see that AD = AS at the equilibrium AS of 3500
         3500

         3000                                                              AD
                                                                           45-degree
    AD




         2500
                                                                           I = 900
         2000

         1500
                                           Aggregate demand for I = 900; AD = AS at AS = 3250
         1000

         500

           0
                0   500    1000    1500    2000     2500    3000    3500     4000      4500
                                                  AS
     What about budget deficits?
   David Ricardo considered the case of debt financing of
    government expenditures and conjectured that, if the
    public perceived the increase in debt as a future tax
    liability, it might elect to save more, even and equal
    amount to the debt, as a way to pay the future liability
   Apparently, Ricardo rejected the idea of such foresight of
    the public, but the notion, called the Ricardian
    Equivalence Theorem, still bears his name
   But let’s suppose we decide to finance the expenditures
    with lump-sum tax today
   Then Y = a + c(Y – T) + I + G, T = G is a lump-sum tax
        Lump-sum tax multiplier
   Now our model is Y = a + c(Y – T) + I0 + G, where
    T=G
   Then solving for Ye we get Ye = [1/(1-c)](a – cT +
    I0 + G) = [1/(1-c)] (a + I0 + G – cG) = [1/(1-c)][a +
    I0 + (1-c)G] = [1/(1-c)] (a + I0) + G, since T = G
   Thus, the “balanced budget multiplier” is 1; if the
    government spends an amount just equal to Yp –
    Ye equilibrium is restored at full employment
            Income Tax financing
   Since taxes are collected from individuals and not the country
    as a whole (since passage of the 16th amendment in 1909), a
    more realistic model is
   Y = a + c(Y – tY) + I + G, tY = G
    Then Y(1 – c + tc) = Y(1 – c(1 – t)) = a + I + G, so Ye = 1/[1
    – c(1-t)] (a + I + G) and k* = 1/(1-c(1-t)) is smaller than before
   Thus the recessionary gap has increased to 1/k*( Yp – Ye)
   In our earlier example, suppose t = .2, then k* = 1/(1 - .6(1 -
    .2)) = 1/.52 or around 2
   It appears we now need to increase G to 250/2 = 125
                       Uh-oh!
   When we substitute the numbers back, they
    don’t work; Y = 2(a + I + G) = 2(400 + 900 +
    125) = 2850
   The reason is we collect too much in taxes;
    .2*2850 = 570, but we only need 125
   So let’s let the model tell us the optimal tax rate
    t*; t*Y = G, which we also need to solve for
   The second equation is (1-c(1-t*))Y = a+I+G;
    so (1-.6(1-t*))3500 = 400+900+G = 1300+G
               Optimal t* and G
   We get 3500 = (1/(.4+.6t*))(1300+G); but G = 3500t*
   So we solve for t* in the following equation 3500 =
    1/(.4+.6t*) (1300+3500t*)
   Dividing both sides by 3500, we get
    1=1/(.4+.6t*)(1300/3500+t*) so
   .4+.6t* = 1300/3500 +t* => .4t* = .4-13/35
   t* = 1-13/14 = 1/14
   G = t*(3500) = 3500/14 = 250!
   The same answer as we got with a lump-sum tax
   Thus, the balanced budget multiplier is again 1; is this
    just a coincidence? Let’s see.
            Solving using algebra
   Yp = a + c(Yp –t*Yp) + I + G; G = t*Yp
   So Yp = a + c(Yp –t*Yp) + I + t*Yp
   (1-c)Yp = a – ct*Yp + I + t*Yp = (a + I) + t*Yp(1-c)
   Thus, Yp = (a + I)/(1-c) + t*Yp = (a + I)/(1-c) + G
   That is, Y changes 1 for 1 with G; the multiplier on G financed
    using the optimal tax is still 1
   In general, however, a proportionate tax does reduce the
    multiplier to 1/(1 – c(1 – t))
What about an open economy?
   With trade the equation becomes Y = a + c(Y – T)
    + I + X – M, where X = exports and M = imports
   While exports are generally considered as
    determined externally to our economy, imports
    should grow with Y
   In fact, it is often the case that fast growing
    economies are great exporters; just think about
    China
   This issue will be covered later when we discuss
    the monetary approach to the balance of payments
            The general model

   Y = a + c(Y – t0 – t1Y) + I + G + X – M0 – mY
   Then Y – cY + ct1Y + mY = (1-c(1-t1)+m) = a
    +I+G+X
   In the literature, the right-hand side variables
    are called injections; savings, taxes and
    imports are referred to as leakages
   At equilibrium, injections must equal leakages
How does the degree of openness affect
 the slope and location of the IS curve?

   The more open an open is economy the less
    “bang for the buck”, that is the additional
    leakage from imports increases the slope so that
    a monetary change – a movement along the IS
    curve – will have less affect on Y and more on I
   The addition of export demand, say from greater
    world output, the further to the right the IS
    curve will lie
             IS-LM Exercises
   Exercise 1: Draw a set of IS-LM curves
   What is the effect of an increase in
    Government spending?
   What happens to equilibrium i and Y?
   Now, how can the Fed reduce crowding
    out?
   What now happens to equilibrium i and Y?
   What happens to the budget deficit?
   Exercise 2: Draw a set of IS-LM curves
   What is the effect of an increase in central
    bank credit to lending institutions?
   What happens to equilibrium i and Y?
   What happens to the budget deficit?
   What happens to equilibrium i and Y?
    The real wealth effects of deficits
   One issue with deficits financed by bond creation is the public
    perception of their increased bond holdings
   At one end is the Ricardian Equivalence, which believes that
    these holdings are viewed as both wealth and as a liability at
    its limit one for one
   At the other end of the spectrum is the belief that the public
    sees these bonds only as wealth and therefore will spend even
    more than the Keynesian model predicts (although this effect
    was never included in the model; we could show this as C = a
    + cY + gB, where B is the stock of government bonds held by
    the public)
   Since some of the expansion in the economy is financed by
    increased tax revenues, the amount needed to be financed
    through bonds is reduced and if a portion of the bonds held
    increases private spending through the wealth effect, the
    negative impact of the deficits can be reduced, making the
    Keynesian argument even stronger
 Arguments for and against the
wealth effect of government bonds
   To the extent that future generations may be impacted
    by the tax liability, the negative Ricardian effect is
    reduced
   Barro argues, however, that the fact that people
    bequeath wealth to their heirs indicates that they care
    about the higher tax liabilities they are leaving them
   But some don’t care; either they have no heirs or they
    figure the next generation will be so much better off that
    they can pay the taxes themselves
   Plus the government can borrow more cheaply than the
    private sector, so the burden is reduced
“Normal Case” with flexible wages and prices and no liquidity trap

                                     LMo   LM1                                 SL

  r                                              W/P
                                                       (W/P)o
                                                                 (W/P)f


                                                                          DL

                                IS
                                Y                                              L



                                45deg
 Y                                                Y




                     Yo    Yf   Y                        Lo     Lf             L

      With flexible wages and prices and the interest rate well above its lower bound
      the economy adjusts to full-employment equilibrium via monetary policy alone
    Flexible wage and prices; liquidity trap (inflexible r)

                                   LMo   LM1                               SL

r                                              W/P




                                                                           DL

                              IS
                                                                           L

                     Y

                              45deg
Y                                               Y




                     Y                                                     L

    Pushing out the LM curve does not lower the interest, which is already at
    its lower bound.
                               “Almost” in a liquidity trap

                                        LMo   LM1                                 SL

r                                                   W/P
                                                          (W/P)o
    Lower bound r                                                   (W/P)f


                                                                             DL

                                   IS
                                   Y                                              L



                                   45deg
Y                                                    Y




                    Yo   Y1 < Yf   Y                        Lo     L1 < Lf        L

    With flexible wages and prices and the interest rate close to its lower bound
    the economy adjusts to less than full-employment equilibrium via monetary policy alone
              The Pigou Effect
   Arthur Pigou, a contemporary and (kind of) a
    friend of Keynes, argued that the price declines
    will increase the real wealth of the public and
    thereby increase their expenditures
   Critiques are compelling: effect can be too slow;
    the fall in prices have negative effect on
    business optimism; increased bankruptcies
    reduce investment; postponement of
    consumption awaiting further price declines; etc.
           The Keynes-Pigou Debate
   Pigou may have won the intellectual debate, showing that the
    economy, given enough time and flexible wages and prices,
    would return to full employment on its own
   On the policy side, however, concerns about the speed of
    adjustment (“In the long run we’re all dead”) led most
    western economies to adopt Keynesian style fiscal policies
   Even today, this is the most often used model by most
    politicians and their staffs
   Central banks, on the other hand, have begun to use the
    alternative DSGE model for their analyses
   This incorporates more of the elements of rational
    expectations and take into account the Lucas Critique by
    allowing parameters of their models to adjust and by
    disaggregating the economy into several sectors
   Even these models, however, are limited as to the amount of
    disaggregation they employ
Open Economy & the Balance of Payments
    Let’s look at the BP line where BOP = 0
    As Y increases a country wants to import more
    As i increases, more capital flows inward
    Thus as Y increases i must also increase to
     maintain balance, so BP is positively sloped
    The slope depends on the interest elasticity of
     capital flows and the income elasticity of imports;
     the more the interest elasticity of capital flows,
     the smaller the adjustment in I needed to
     balance flows, so the flatter the BP curve; the
     greater the income elasticity of imports the
     greater the interest rate change needed to
     balance payments, so the steeper the BP line
Stimulative fiscal policy under a
     fixed exchange rate
                                                    LM          BP

                                      B

                                       C
                                  A

                                                          IS'

                                                     IS
                                                Y

Starting from an initial point of triple intersection of the IS, LM and BP curves.
If the LM curve is steeper than the BP curve, then a positive fiscal stimulus
increases the interest rate by more than enough to compensate for the
higher income and a BOP surplus results. The additional inflows of capital
may push down the interest rate. Under fixed exchange rates, capital inflows
increase the money supply and, assuming no sterilization of these flows,
pushes out the LM curve to a new triple intersection at point C.
             BP steeper than LM
                                                   BP          LM


                                     B

                                      C
                                 A

                                                         IS'

                                                    IS
                                               Y

If the LM curve is flatter than the BP curve, then a positive fiscal stimulus
increases the interest rate by less than enough to compensate for the
higher income and a BOP deficit results. The outflow of capital decreases
the money supply and and pulls inward the LM curve to a new triple
 intersection at point C.
    Keynesian model and the Phillips Curve

   Keynes worked in real values since inflation was
    not an issue in times of depression; if anything,
    prices fell
   But Keynesians had to address the issue of what
    happened as the economy approached full
    employment
   Let us look at the “stripped down” version of the
    aggregate supply-aggregate demand diagram
     Price




                                                                        AD'

                                                               Y = AS
                                                            AD
In the original version, the economy is in one of two states: full employment
or less than full employment. In the latter case, the economy faces no price
increases until it attains full employment, after which any shift in AD is met
with higher prices and no additional output
     Price




                                                               AD"


                                                        AD'
                                                AD                   AS


In the revised version, there is an intermediate range in which prices rise
with aggregate demand and supply. This range corresponds perfectly to the
Phillips Curve. As AS increases in response to the outward shift in demand,
prices rise as Y increases, ie unemployment decreases. This is the Phillips
Curve. So the publication of Phillips' article gave a story for Keynesians
to tell.
        The Phillips Controversy
   So the idea of a permanent and stable tradeoff
    relationship between inflation and
    unemployment provided additional armor
    against attacks from those that would worry
    about the hyper-inflationary danger of
    permanent deficits or monetary stimulus
   In fact, a thorough reading of Phillips himself
    shows that he did not intend for the empirical
    results to be inerpreted by policy makers as an
    excuse to inflate the economy so as to reduce
    unemployment
      Stagflation and the end of the
               Phillips Curve
   The events that occurred starting in 1970 demonstrated
    that the critics were correct after all; continued attempts
    to stimulate the economy in the face of real supply side
    shocks took its toll and inflation hit double digits with
    little effect on the unemployment rate
   This period became known as stagflation, and was only
    ended with the recession of 1981-83 caused by Paul
    Volcker
   During this recession unemployment hit 10% for the first
    time since the Great Depression
   Now we are once again experiencing such high rate of
    unemployment
The vertical long-run Phillips Curve

   The events in that began at the time of stagflation led
    most economists to abandon the conventional view and
    to adopt Friedman view that there is no long-run Phillips
    Curve
   Friedman viewed the relationship as a short-term fix that
    would eventually lead to expectations of inflation that
    would nullify the short-term benefits
   Later he adopted the rational expectations view that
    even the short run Phillips Curve tradeoff would
    disappear in favor of a vertical Phillips Curve at the
    permanent natural rate of unemployment

								
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